diff --git a/parse/train/BkglSTNFDB/BkglSTNFDB.md b/parse/train/BkglSTNFDB/BkglSTNFDB.md
new file mode 100644
index 0000000000000000000000000000000000000000..4bb32d970971b2c34ca2f6c759dd6d3321d32bc3
--- /dev/null
+++ b/parse/train/BkglSTNFDB/BkglSTNFDB.md
@@ -0,0 +1,683 @@
+# Q-LEARNING WITH UCB EXPLORATION IS SAMPLE EFFICIENT FOR INFINITE-HORIZON MDP
+
+Kefan Dong\*, Yuanhao Wang∗   
+Institute for Interdisciplinary Information Sciences, Tsinghua University   
+{dkf16,yuanhao-16}@mails.tsinghua.edu.   
+Xiaoyu Chen   
+Key Laboratory of Machine Perception, MOE, School of EECS,   
+Peking University   
+cxy30@pku.edu.cn   
+Liwei Wang   
+Key Laboratory of Machine Perception, MOE, School of EECS   
+Center for Data Science, Peking University   
+wanglw@cis.pku.edu.cn
+
+# ABSTRACT
+
+A fundamental question in reinforcement learning is whether model-free algorithms are sample efficient. Recently, Jin et al. (2018) proposed a Q-learning algorithm with UCB exploration policy, and proved it has nearly optimal regret bound for finite-horizon episodic MDP. In this paper, we adapt Q-learning with UCB-exploration bonus to infinite-horizon MDP with discounted rewards without accessing a generative model. We show that the sample complexity of exploration of our algorithm is bounded by $\begin{array} { r } { \tilde { O } \big ( \frac { S A } { \epsilon ^ { 2 } ( 1 - \gamma ) ^ { 7 } } \big ) } \end{array}$ . This improves the previously best known result of $\begin{array} { r } { \tilde { O } \big ( \frac { S A } { \epsilon ^ { 4 } ( 1 - \gamma ) ^ { 8 } } \big ) } \end{array}$ in this setting achieved by delayed Q-learning (Strehl et al., 2006), and matches the lower bound in terms of $\epsilon$ as well as and up to logarithmic factors.
+
+# 1 INTRODUCTION
+
+The goal of reinforcement learning (RL) is to construct efficient algorithms that learn and plan in sequential decision making tasks when the underlying system dynamics are unknown. A typical model in RL is Markov Decision Process (MDP). At each time step, the environment is in a state $s$ . The agent takes an action $a$ , obtain a reward $r$ , and then the environment transits to another state. In reinforcement learning, the transition probability distribution is unknown. The algorithm needs to learn the transition dynamics of MDP, while aiming to maximize the cumulative reward. This poses the exploration-exploitation dilemma: whether to act to gain new information (explore) or to act consistently with past experience to maximize reward (exploit).
+
+Theoretical analyses of reinforcement learning fall into two broad categories: those assuming a simulator (a.k.a. generative model), and those without a simulator. In the first category, the algorithm is allowed to query the outcome of any state action pair from an oracle. The emphasis is on the number of calls needed to estimate the $Q$ value or to output a near-optimal policy. There has been extensive research in literature following this line of research, the majority of which focuses on discounted infinite horizon MDPs (Azar et al., 2011; Even-Dar & Mansour, 2003; Sidford et al., 2018b). The current results have achieved near-optimal time and sample complexities (Sidford et al., 2018b;a).
+
+Without a simulator, there is a dichotomy between finite-horizon and infinite-horizon settings. In finite-horizon settings, there are straightforward definitions for both regret and sample complexity; the latter is defined as the number of samples needed before the policy becomes near optimal. In this setting, extensive research in the past decade (Jin et al., 2018; Azar et al., 2017; Jaksch et al., 2010; Dann et al., 2017) has achieved great progress, and established nearly-tight bounds for both regret and sample complexity.
+
+The infinite-horizon setting is a very different matter. First of all, the performance measure cannot be a straightforward extension of the sample complexity defined above (See Strehl & Littman (2008) for detailed discussion). Instead, the measure of sample efficiency we adopt is the so-called sample complexity of exploration (Kakade et al., 2003), which is also a widely-accepted definition. This measure counts the number of times that the algorithm “makes mistakes” along the whole trajectory. See also (Strehl & Littman, 2008) for further discussions regarding this issue.
+
+Several model based algorithms have been proposed for infinite horizon MDP, for example Rmax (Brafman & Tennenholtz, 2003), MoRmax (Szita & Szepesvári, 2010) and UCRL- $\gamma$ (Lattimore & Hutter, 2012). It is noteworthy that there still exists a considerable gap between the state-of-the-art algorithm and the theoretical lower bound (Lattimore & Hutter, 2012) regarding $1 / ( 1 - \gamma )$ factor.
+
+Though model-based algorithms have been proved to be sample efficient in various MDP settings, most state-of-the-art RL algorithms are developed in the model-free paradigm (Schulman et al., 2015; Mnih et al., 2013; 2016). Model-free algorithms are more flexible and require less space, which have achieved remarkable performance on benchmarks such as Atari games and simulated robot control problems.
+
+For infinite horizon MDPs without access to simulator, the best model-free algorithm has a sample complexity of exploration $\begin{array} { r } { \tilde { \mathcal { O } } \big ( \frac { S A } { \epsilon ^ { 4 } ( 1 - \gamma ) ^ { 8 } } \big ) } \end{array}$ , achieved by delayed Q-learning (Strehl et al., 2006). The authors provide a novel strategy of argument when proving the upper bound for the sample complexity of exploration, namely identifying a sufficient condition for optimality, and then bound the number of times that this condition is violated.
+
+However, the results of Delayed Q-learning still leave a quadratic gap in $1 / \epsilon$ from the best-known lower bound. This is partly because the updates in Q-value are made in an over-conservative way. In fact, the loose sample complexity bound is a result of delayed Q-learning algorithm itself, as well as the mathematical artifact in their analysis. To illustrate this, we construct a hard instance showing that Delayed Q-learning incurs $\Omega ( 1 / \epsilon ^ { 3 } )$ sample complexity. This observation, as well as the success of the Q-learning with UCB algorithm (Jin et al., 2018) in proving a regret bound in finite-horizon settings, motivates us to incorporate a UCB-like exploration term into our algorithm.
+
+In this work, we propose a Q-learning algorithm with UCB exploration policy. We show the sample complexity of exploration bound of our algorithm is $\begin{array} { r } { \tilde { \mathcal { O } } \big ( \frac { S A } { \epsilon ^ { 2 } ( 1 - \gamma ) ^ { 7 } } \big ) } \end{array}$ . This strictly improves the previous best known result due to Delayed Q-learning. It also matches the lower bound in the dependence on $\epsilon$ , $S$ and $A$ up to logarithmic factors.
+
+We point out here that the infinite-horizon setting cannot be solved by reducing to finite-horizon setting. There are key technical differences between these two settings: the definition of sample complexity of exploration, time-invariant policies and the error propagation structure in Q-learning. In particular, the analysis techniques developed in (Jin et al., 2018) do not directly apply here. We refer the readers to Section 3.2 for detailed explanations and a concrete example.
+
+The rest of the paper is organized as follows. After introducing the notation used in the paper in Section 2, we describe our infinite Q-learning with UCB algorithm in Section 3. We then state our main theoretical results, which are in the form of PAC sample complexity bounds. In Section 4 we present some interesting properties beyond sample complexity bound. Finally, we conclude the paper in Section 5.
+
+# 2 PRELIMINARY
+
+We consider a Markov Decision Process defined by a five tuple $\langle S , \mathcal { A } , p , r , \gamma \rangle$ , where $s$ is the state space, $\mathcal { A }$ is the action space, $p ( s ^ { \prime } | s , a )$ is the transition function, $r : S \times \mathcal { A }  [ 0 , 1 ]$ is the deterministic reward function, and $0 \leq \gamma < 1$ is the discount factor for rewards. Let $S = | S |$ and $A = | { \mathcal { A } } |$ denote the number of states and the number of actions respectively.
+
+Starting from a state $s _ { 1 }$ , the agent interacts with the environment for infinite number of time steps. At each time step, the agent observes state $s _ { t } \in S$ , picks action $a _ { t } \in \mathcal A$ , and receives reward $r _ { t }$ ; the system then transits to next state $s _ { t + 1 }$ .
+
+Using the notations in Strehl et al. (2006), a policy $\pi _ { t }$ refers to the non-stationary control policy of the algorithm since step $t$ . We use $V ^ { \pi _ { t } } ( s )$ to denote the value function under policy $\pi _ { t }$ , which is defined as $\begin{array} { r } { V ^ { \pi _ { t } } ( s ) = \mathbb { E } \bigl [ \sum _ { i = 1 } ^ { \infty } \gamma ^ { i - 1 } r ( s _ { i } , \pi _ { t + i - 1 } ( s _ { i } ) ) | s _ { 1 } = s \bigr ] } \end{array}$ . We also use $V ^ { * } ( s ) = \operatorname* { s u p } _ { \pi } V ^ { \pi } ( s )$ to denote the value function of the optimal policy. Accordingly, we define $\begin{array} { r } { \mathbb { E } [ \sum _ { i = 2 } ^ { \infty } \gamma ^ { i - 1 } r ( s _ { i } , \pi _ { t + i - 1 } ( s _ { i } ) ) | s _ { 1 } = \stackrel { \cdot } { s } , a _ { 1 } = \stackrel { \cdot } { a } ] } \end{array}$ as the $\mathrm { Q }$ function under policy $Q ^ { \pi _ { t } } ( s , a ) = r ( s , a ) +$ $\pi _ { t }$ ; $Q ^ { * } ( s , a )$ is the Q function under optimal policy $\pi ^ { * }$ .
+
+We use the sample complexity of exploration defined in Kakade et al. (2003) to measure the learning efficiency of our algorithm. This sample complexity definition has been widely used in previous works Strehl et al. (2006); Lattimore & Hutter (2012); Strehl $\&$ Littman (2008).
+
+Definition 1. Sample complexity of Exploration of an algorithm $\mathcal { A L G }$ is defined as the number of time steps t such that the non-stationary policy $\pi _ { t }$ at time $t$ is not $\epsilon$ -optimal for current state $s _ { t }$ , i.e. $\dot { V } ^ { \pi _ { t } } \left( s _ { t } \right) \dot { < } V ^ { * } \left( s _ { t } \right) - \epsilon .$ .
+
+Roughly speaking, this measure counts the number of mistakes along the whole trajectory. We use the following definition of PAC-MDP Strehl et al. (2006).
+
+Definition 2. An algorithm $\mathcal { A L G }$ is said to be PAC-MDP (Probably Approximately Correct in Markov Decision Processes) $i f ,$ for any  and $\delta$ , the sample complexity of $\mathcal { A L G }$ is less than some polynomial in the relevant quantities $( S , A , 1 / \epsilon , 1 / \delta , 1 / ( 1 - \gamma ) )$ , with probability at least $1 - \delta$ .
+
+Finally, recall that Bellman equation is defined as the following:
+
+$$
+\left\{ \begin{array} { l l } { V ^ { \pi _ { t } } ( s ) = Q ^ { \pi _ { t } } \left( s , \pi _ { t } ( s ) \right) } \\ { Q ^ { \pi _ { t } } ( s , a ) : = \left( r _ { t } + \gamma \mathbb { P } V ^ { \pi _ { t + 1 } } \right) ( s , a ) , } \end{array} \right. \quad \left\{ \begin{array} { l l } { V ^ { * } ( s ) = Q ^ { * } \left( s , \pi ^ { * } ( s ) \right) } \\ { Q ^ { * } ( s , a ) : = \left( r _ { t } + \gamma \mathbb { P } V ^ { * } \right) ( s , a ) , } \end{array} \right.
+$$
+
+which is frequently used in our analysis. Here we denote $\left[ \mathbb { P } V ^ { \pi _ { t } } \right] ( s , a ) : = \mathbb { E } _ { s ^ { \prime } \sim p ( \cdot \vert s , a ) } V ^ { \pi _ { t + 1 } } ( s ^ { \prime } ) .$
+
+# 3 MAIN RESULTS
+
+In this section, we present the UCB Q-learning algorithm and the sample complexity bound.
+
+# 3.1 ALGORITHM
+
+# Algorithm 1 Infinite Q-learning with UCB
+
+Parameters: , γ, δ Initializ $\begin{array} { r l } & { \textnormal { \texttt { e } } Q ( s , a ) , \hat { Q } ( s , a ) \gets \frac { 1 } { 1 - \gamma } , N ( s , a ) \gets 0 , \epsilon _ { 1 } \gets \frac { \epsilon } { 2 4 R M \ln \frac { 1 } { 1 - \gamma } } , H \gets \frac { \ln 1 / ( ( 1 - \gamma ) \epsilon _ { 1 } ) } { \ln 1 / \gamma } . } \\ & { \cdot ( k ) = \ln ( S A ( k + 1 ) ( k + 2 ) / \delta ) , \alpha _ { k } = \frac { H + 1 } { H + k } . } \end{array}$ Define for $t = 1 , 2 , \dots \mathbf { d o }$   
+5: Take action $a _ { t } \gets \arg \operatorname* { m a x } _ { a ^ { \prime } } \hat { Q } ( s _ { t } , a ^ { \prime } )$ Receive reward rt and transit to st+1 $\begin{array} { r l r } & { N ( s _ { t } , a _ { t } ) \gets N ( s _ { t } , a _ { t } ) + 1 } & \\ & { N ( s _ { t } , a _ { t } ) \gets N ( s _ { t } , a _ { t } ) + 1 } & \\ & { k \gets N ( s _ { t } , a _ { t } ) , b _ { k } \gets \frac { c _ { 2 } } { 1 - \gamma } \sqrt { \frac { H ( k ) } { k } } } & \\ & { \hat { V } ( s _ { t + 1 } ) \gets \operatorname* { m a x } _ { a \in A } \hat { Q } ( s _ { t + 1 } , a ) } & \\ & { Q ( s _ { t } , a _ { t } ) \gets ( 1 - \alpha _ { k } ) Q ( s _ { t } , a _ { t } ) + \alpha _ { k } \left[ r ( s _ { t } , a _ { t } ) + b _ { k } + \gamma \hat { V } ( s _ { t + 1 } ) \right] } \\ & { \hat { Q } ( s _ { t } , a _ { t } ) \gets \operatorname* { m i n } ( \hat { Q } ( s _ { t } , a _ { t } ) , Q ( s _ { t } , a _ { t } ) ) } & \end{array}$ t and can be set to $4 { \sqrt { 2 } }$   
+10: end for
+
+Here $c _ { 2 } = 4 \sqrt { 2 }$ is a constant. $\begin{array} { r } { R = \lceil \ln \frac { 3 } { \epsilon ( 1 - \gamma ) } / ( 1 - \gamma ) \rceil } \end{array}$ , while the choice of $M$ can be found in Section. 3.3. ${ \cal { \left( M = 0 \left( \ln 1 / ( 1 - \gamma ) \epsilon \right) \right) } }$ ). The learning rate is defined as $\alpha _ { k } = ( H + 1 ) / ( H + k )$ . $H$ is chosen as $\frac { \ln { 1 } / ( ( 1 - \gamma ) \epsilon _ { 1 } ) } { \ln { 1 } / \gamma }$ , which satisfies $H \leq \frac { \ln 1 / ( ( 1 - \gamma ) \epsilon _ { 1 } ) } { 1 - \gamma }$ .
+
+Our UCB Q-learning algorithm (Algorithm 1) maintains an optimistic estimation of action value function $Q ( s , a )$ and its historical minimum value $\hat { Q } ( s , a )$ . $N _ { t } ( s , a )$ denotes the number of times that $( s , a )$ is experienced before time step $t$ ; $\tau ( s , a , k )$ denotes the time step $t$ at which $( s _ { t } , a _ { t } ) = ( s , a )$ for the $k$ -th time; if this state-action pair is not visited that many times, $\tau ( s , a , k ) = \infty$ . $Q _ { t } ( s , a )$ and $\hat { Q } _ { t } ( s , a )$ denotes the $Q$ and $\hat { Q }$ value of $( s , a )$ that the algorithm maintains when arriving at $s _ { t }$ respectively.
+
+# 3.2 SAMPLE COMPLEXITY OF EXPLORATION
+
+Our main result is the following sample complexity of exploration bound.
+
+Theorem 1. For any $\epsilon > 0$ , $\delta > 0 , 1 / 2 < \gamma < 1$ , with probability $1 - \delta$ , the sample complexity of exploration (i.e., the number of time steps t such that $\pi _ { t }$ is not $\epsilon$ -optimal at $s _ { t . }$ ) of Algorithm 1 is at most
+
+$$
+\tilde { \mathcal { O } } \left( \frac { S A \ln { 1 / \delta } } { \epsilon ^ { 2 } \left( 1 - \gamma \right) ^ { 7 } } \right) ,
+$$
+
+where $\tilde { \mathcal { O } }$ suppresses logarithmic factors of $1 / \epsilon , 1 / ( 1 - \gamma )$ and $S A$ .
+
+We first point out the obstacles for proving the theorem and reasons why the techniques in Jin et al.   
+(2018) do not directly apply here. We then give a high level description of the ideas of our approach.
+
+One important issue is caused by the difference in the definition of sample complexity for finite and infinite horizon MDP. In finite horizon settings, sample complexity (and regret) is determined in the first $T$ timesteps, and only measures the performance at the initial state $s _ { 1 }$ (i.e. $( V ^ { * } - V ^ { \pi } ) ( s _ { 1 } ) )$ . However, in the infinite horizon setting, the agent may enter under-explored regions at any time period, and sample complexity of exploration characterizes the performance at all states the agent enters.
+
+The following example clearly illustrates the key difference between infinite-horizon and finitehorizon. Consider an MDP with a starting state $s _ { 1 }$ where the probability of leaving $s _ { 1 }$ is $o ( T ^ { - 1 } )$ . In this case, with high probability, it would take more than $T$ timesteps to leave $s _ { 1 }$ . Hence, guarantees about the learning in the first $T$ timesteps or about the performance at $s _ { 1 }$ imply almost nothing about the number of mistakes the algorithm would make in the rest of the MDP (i.e. the sample complexity of exploration of the algorithm). As a result, the analysis for finite horizon MDPs cannot be directly applied to infinite horizon setting.
+
+This calls for techniques for counting mistakes along the entire trajectory, such as those employed by Strehl et al. (2006). In particular, we need to establish convenient sufficient conditions for being $\epsilon$ -optimal at timestep $t$ and state $s _ { t }$ , i.e. $V ^ { \ast } ( s _ { t } ) - V ^ { \pi _ { t } } ( s _ { t } ) \leq \epsilon$ . Then, bounding the number of violations of such conditions gives a bound on sample complexity.
+
+Another technical reason why the proof in Jin et al. (2018) cannot be directly applied to our problem is the following: In finite horizon settings, Jin et al. (2018) decomposed the learning error at episode $k$ and time $h$ as errors from a set of consecutive episodes before $k$ at time $h + 1$ using a clever design of learning rate. However, in the infinite horizon setting, this property does not hold. Suppose at time $t$ the agent is at state $s _ { t }$ and takes action $a _ { t }$ . Then the learning error at $t$ only depends on those previous time steps such that the agent encountered the same state as $s _ { t }$ and took the same action as $a _ { t }$ . Thus the learning error at time $t$ cannot be decomposed as errors from a set of consecutive time steps before $t$ , but errors from a set of non-consecutive time steps without any structure. Therefore, we have to control the sum of learning errors over an unstructured set of time steps. This makes the analysis more challenging.
+
+Now we give a brief road map of the proof of Theorem 1. Our first goal is to establish a sufficient condition so that $\pi _ { t }$ learned at step $t$ is $\epsilon$ -optimal for state $s _ { t }$ . As an intermediate step we show that a sufficient condition for $V ^ { * } ( s _ { t } ) - V ^ { \pi _ { t } } ( s _ { t } ) \leq \epsilon$ is that $V ^ { \ast } ( s _ { t ^ { \prime } } ) - Q ^ { \ast } ( s _ { t ^ { \prime } } , a _ { t ^ { \prime } } )$ is small for a few time steps $t ^ { \prime }$ within an interval $[ t , t + R ]$ for a carefully chosen $R$ (Condition 1). Then we show the desired sufficient condition (Condition 2) implies Condition 1. We then bound the total number of bad time steps on which $V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } )$ is large for the whole MDP; this implies a bound on the number of violations of Condition 2. This in turn relies on a key technical lemma (Lemma 2).
+
+The remaining part of this section is organized as follows. We establish the sufficient condition for $\epsilon$ -optimality in Section 3.3. The key lemma is presented in Section 3.4. Finally we prove Theorem 1 in Section 3.5.
+
+# 3.3 SUFFICIENT CONDITION FOR $\epsilon$ -OPTIMALITY
+
+In this section, we establish a sufficient condition (Condition 2) for $\epsilon$ -optimality at time step $t$ .
+
+For a fixed $s _ { t }$ , let TRAJ $( R )$ be the set of length- $R$ trajectories starting from $s _ { t }$ . Our goal is to give a sufficient condition so that $\pi _ { t }$ , the policy learned at step $t$ , is $\epsilon$ -optimal. For any $\epsilon _ { 2 } > 0$ , define $\begin{array} { r } { R : = \lceil \ln \frac { 1 } { \epsilon _ { 2 } ( 1 - \gamma ) } / ( 1 - \gamma ) \rceil } \end{array}$ . Denote $V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } )$ by $\Delta _ { t }$ . We have
+
+$$
+\begin{array} { r l } & { \quad V ^ { * } ( s _ { t } ) - V ^ { \pi } ( s _ { t } ) } \\ & { = V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) + Q ^ { * } ( s _ { t } , a _ { t } ) - V ^ { \pi } ( s _ { t } ) } \\ & { = V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) + \gamma \mathbb { P } ( V ^ { * } - V ^ { \pi } ) ( s _ { t } , \pi _ { t } ( s _ { t } ) ) } \\ & { = V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) + \gamma \sum _ { s + 1 } ^ { \infty } p ( s _ { t + 1 } | s _ { t } , \pi _ { t } ( s _ { t } ) ) \cdot [ V ^ { * } ( s _ { t + 1 } ) - Q ^ { * } ( s _ { t + 1 } , a _ { t + 1 } ) ] + } \\ & { \quad \Big . \Big . \Big . \Big . \Big . \Big . } \\ & { \quad \quad \Big .  \gamma _ { s + 1 , s ^ { * } + 2 } \mathrm { ~ } p ( s _ { t + 2 } | s _ { t + 1 } , \pi _ { t + 1 } ( s _ { t + 1 } ) ) \cdot p ( s _ { t + 1 } | s _ { t } , \pi _ { t } ( s _ { t } ) ) \big [ V ^ { * } ( s _ { t + 2 } ) - Q ^ { * } ( s _ { t + 2 } , a _ { t + 2 } ) \Big ] } \\ & { \quad \quad \cdot \dots } \\ & { \le \epsilon _ { 2 } + \displaystyle \sum _ { s ^ { \prime } = s ^ { \prime } } p ( t r a _ { t } ) \cdot [ \frac { n - 1 } { \lambda _ { 2 } } \gamma ^ { 2 } \Delta _ { t + 2 } ] , } \\ & { \quad \quad \pi _ { s \lambda ^ { ( 2 ) } ( L ) } ^ { R , a } } \end{array}
+$$
+
+where the last inequality holds because $\frac { \gamma ^ { R } } { 1 - \gamma } \leq \epsilon _ { 2 }$ , which follows from the definition of $R$
+
+For any fixed trajectory of length $R$ starting from $s _ { t }$ , consider the sequence $\left( \Delta _ { t ^ { \prime } } \right) _ { t \leq t ^ { \prime } < t + R }$ . Let $X _ { t } ^ { ( i ) }$ be the $i$ -th largest item of $\left( \Delta _ { t ^ { \prime } } \right) _ { t \leq t ^ { \prime } < t + R }$ . Rearranging Eq. (1), we obtain
+
+$$
+V ^ { \ast } ( s _ { t } ) - V ^ { \pi _ { t } } ( s _ { t } ) \leq \epsilon _ { 2 } + E _ { t r a j } \left[ \sum _ { i = 1 } ^ { R } \gamma ^ { i - 1 } X _ { t } ^ { ( i ) } \right] .
+$$
+
+We first prove that Condition 1 implies $\epsilon$ -optimality at time step $t$ when $\epsilon _ { 2 } = \epsilon / 3$
+
+Condition 1. Let $\begin{array} { r } { \xi _ { i } : = \frac { 1 } { 2 ^ { i + 2 } } \epsilon _ { 2 } \left( \ln \frac { 1 } { 1 - \gamma } \right) ^ { - 1 } } \end{array}$ . For all $0 \leq i \leq \lfloor \log _ { 2 } R \rfloor$
+
+$$
+E [ X _ { t } ^ { ( 2 ^ { i } ) } ] \leq \xi _ { i } .
+$$
+
+Claim 1. If Condition $^ { l }$ is satisfied at time step $t$ , the policy $\pi _ { t }$ is $\epsilon$ -optimal at state $s _ { t }$ , i.e. $V ^ { \ast } ( s _ { t } ) -$   
+$V ^ { \pi _ { t } } ( s _ { t } ) \leq \epsilon$ .
+
+Proof. Note that $E [ X _ { t } ^ { ( 2 ^ { \lfloor \log _ { 2 } i \rfloor } ) } ]$ t. Eq. (3) implies that for $X _ { t } ^ { ( i ) }$ is monotonically decreasing with respect to $1 / 2 < \gamma < 1$ , $i$ . Therefore, $E [ X _ { t } ^ { ( i ) } ] \ \leq$
+
+$$
+\begin{array} { r l } & { E \left[ \displaystyle \sum _ { i = 1 } ^ { R } \gamma ^ { i - 1 } X _ { t } ^ { ( i ) } \right] = \displaystyle \sum _ { i = 1 } ^ { R } \gamma ^ { i - 1 } E [ X _ { t } ^ { ( i ) } ] \leq \displaystyle \sum _ { i = 1 } ^ { R } \gamma ^ { i - 1 } E [ X _ { t } ^ { ( 2 ^ { \lfloor \log _ { 2 } i \rfloor } ) } ] } \\ & { \leq \displaystyle \sum _ { i = 1 } ^ { R } \gamma ^ { i - 1 } 2 ^ { - \lfloor \log _ { 2 } i \rfloor - 2 } \epsilon _ { 2 } \left( \ln \frac { 1 } { 1 - \gamma } \right) ^ { - 1 } \leq \displaystyle \sum _ { i = 1 } ^ { R } \frac { \gamma ^ { i - 1 } } { i } \epsilon _ { 2 } \left( \ln \frac { 1 } { 1 - \gamma } \right) ^ { - 1 } \leq 2 \epsilon _ { 2 } , } \end{array}
+$$
+
+where the last inequality follows from the fact that $\begin{array} { r } { \sum _ { i = 1 } ^ { \infty } \frac { \gamma ^ { i - 1 } } { i } = \frac { 1 } { \gamma } \ln \frac { 1 } { 1 - \gamma } } \end{array}$ and $\gamma > 1 / 2$
+
+Combining with Eq. 2, we have, $\begin{array} { r } { V ^ { \ast } ( s _ { t } ) - V ^ { \pi _ { t } } ( s _ { t } ) \leq \epsilon _ { 2 } + E \left[ \sum _ { i = 1 } ^ { R } \gamma ^ { i - 1 } X _ { t } ^ { ( i ) } \right] \leq 3 \epsilon _ { 2 } = \epsilon . } \end{array}$
+
+Next we show that given $i , t$ , Condition 2 implies Eq. (3).
+
+Condition 2. Define $L = \lfloor \log _ { 2 } R \rfloor$ . Let $\begin{array} { r } { M = \operatorname* { m a x } \left\{ \lceil 2 \log _ { 2 } \frac { 1 } { \xi _ { L } ( 1 - \gamma ) } \rceil , 1 0 \right\} } \end{array}$ , and $\begin{array} { r } { \eta _ { j } = \frac { \xi _ { i } } { M } \cdot 2 ^ { j - 1 } } \end{array}$ .   
+For all $\begin{array} { r } { \because j \le M , \eta _ { j } \operatorname* { P r } [ X _ { t } ^ { ( 2 ^ { i } ) } > \eta _ { j - 1 } ] \le \frac { \xi _ { i } } { M } , } \end{array}$ .
+
+Claim 2. Given i, t, Eq. (3) holds if Condition 2 is satisfied.
+
+Proof. The reason behind the choice of $M$ is to ensure that $\eta _ { M } > 1 / ( 1 - \gamma )$ 1. It follows that, assuming Condition 2 holds, for $1 \leq j \leq M$ ,
+
+$$
+E \left[ { X _ { t } ^ { ( 2 ^ { i } ) } } \right] = \int _ { 0 } ^ { 1 / ( 1 - \gamma ) } \operatorname* { P r } \left[ { X _ { t } ^ { ( 2 ^ { i } ) } } > x \right] d x \le \eta _ { 1 } + \sum _ { j = 2 } ^ { M } \eta _ { j } \operatorname* { P r } [ { X _ { t } ^ { ( 2 ^ { i } ) } } > \eta _ { j - 1 } ] \le \xi _ { i } .
+$$
+
+Therefore, if a time step $t$ is not $\epsilon _ { 2 }$ -optimal, there exists $0 \leq i < \lfloor \log _ { 2 } R \rfloor$ and $2 \leq j \leq M$ such that
+
+$$
+\eta _ { j } \mathrm { P r } [ X _ { t } ^ { ( 2 ^ { i } ) } > \eta _ { j - 1 } ] > \frac { \xi _ { i } } { M } .
+$$
+
+Now, the sample complexity can be bounded by the number of $( t , i , j )$ pairs that Eq. (4) is violated. Following the approach of Strehl et al. (2006), for a fixed $( i , j )$ -pair, instead of directly counting the number of time steps $t$ such that $\begin{array} { r } { \operatorname* { P r } [ X _ { t } ^ { ( 2 ^ { i } ) } > \eta _ { j - 1 } ] > \frac { \xi _ { i } } { M \eta _ { j } } } \end{array}$ , we count the number of time steps that $X _ { t } ^ { ( 2 ^ { i } ) } > \eta _ { j - 1 }$ . Lemma 1 provides an upper bound of the number of such $t$ .
+
+# 3.4 KEY LEMMAS
+
+In this section, we present two key lemmas. Lemma 1 bounds the number of sub-optimal actions, which in turn, bounds the sample complexity of our algorithm. Lemma 2 bounds the weighted sum of learning error, i.e. $( \hat { Q } _ { t } - Q ^ { * } ) ( s , a )$ , with the sum and maximum of weights. Then, we show that Lemma 1 follows from Lemma 2.
+
+Lemma 1. For fixed $t$ and $\eta > 0$ , let ${ B } _ { \eta } ^ { ( t ) }$ be the event that $\begin{array} { r } { V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > \frac { \eta } { 1 - \gamma } } \end{array}$ in step t. If $\eta > 2 \epsilon _ { 1 }$ , then with probability at least $1 - \delta / 2$ ,
+
+$$
+\sum _ { t = 1 } ^ { t = \infty } I \left[ B _ { \eta } ^ { ( t ) } \right] \leq \frac { S A \ln S A \ln 1 / \delta } { \eta ^ { 2 } ( 1 - \gamma ) ^ { 3 } } \cdot p o l y l o g \left( \frac { 1 } { \epsilon _ { 1 } } , \frac { 1 } { 1 - \gamma } \right) ,
+$$
+
+where $I [ \cdot ]$ is the indicator function.
+
+Before presenting Lemma 2, we define a class of sequence that occurs in the proof.
+
+Definition 3. A sequence $( w _ { t } ) _ { t \geq 1 }$ is said to be a $( C , w )$ -sequence for $C , w > 0$ , $i f 0 \le w _ { t } \le w$ for all $t \geq 1$ , and $\begin{array} { r } { \sum _ { t \geq 1 } w _ { t } \leq C } \end{array}$ .
+
+Lemma 2. For every $( C , w )$ -sequence $( w _ { t } ) _ { t \geq 1 }$ , with probability $1 - \delta / 2$ , the following holds:
+
+$$
+\sum _ { t \ge 1 } w _ { t } ( \hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) \le \frac { C \epsilon _ { 1 } } { 1 - \gamma } + \mathcal { O } \left( \frac { \sqrt { w S A C \ell ( C ) } } { ( 1 - \gamma ) ^ { 2 . 5 } } + \frac { w S A \ln C } { ( 1 - \gamma ) ^ { 3 } } \ln \frac { 1 } { ( 1 - \gamma ) \epsilon _ { 1 } } \right) .
+$$
+
+$\begin{array} { r } { \ell ( C ) = \iota ( C ) \ln { \frac { 1 } { ( 1 - \gamma ) \epsilon _ { 1 } } } } \end{array}$
+
+Proof of Lemma 2 is quite technical, and is therefore deferred to supplementary materials.
+
+Now, we briefly explain how to prove Lemma 1 with Lemma 2. (Full proof can be found in supplementary materials.) Note that since $\hat { Q } _ { t } \geq Q ^ { * }$ and $a _ { t } = \arg \operatorname* { m a x } _ { a } \hat { Q } _ { t } ( s _ { t } , a )$ ,
+
+$$
+V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) \leq \hat { Q } _ { t } ( s _ { t } , a _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) .
+$$
+
+We now consider a set $J = \{ t : \ V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > \eta ( 1 - \gamma ) ^ { - 1 } \}$ , and consider the $( | J | , 1 )$ - weight sequence defined by $w _ { t } ~ = ~ I \left[ t \in J \right]$ . We can now apply Lemma 2 to weighted sum $\begin{array} { r } { \sum _ { t \geq 1 } \dot { w } _ { t } \left[ \bar { V } ^ { \ast } ( s _ { t } ) - Q ^ { \ast } ( s _ { t } , \dot { a } _ { t } ) \right] , } \end{array}$ . On the one hand, this quantity is obviously at least $| J | \bar { \eta ( 1 - \gamma ) } ^ { - 1 }$ . On the other hand, by lemma 2, it is upper bounded by the weighted sum of $( \hat { Q } - Q ^ { * } ) ( s _ { t } , a _ { t } )$ . Thus we get
+
+$$
+| J | \eta ( 1 - \gamma ) ^ { - 1 } \leq \frac { C \epsilon _ { 1 } } { 1 - \gamma } + \mathcal { O } \left( \frac { \sqrt { S A | J | \ell ( | J | ) } } { ( 1 - \gamma ) ^ { 2 . 5 } } + \frac { w S A \ln | J | } { ( 1 - \gamma ) ^ { 3 } } \ln \frac { 1 } { ( 1 - \gamma ) \epsilon _ { 1 } } \right) .
+$$
+
+Now focus on the dependence on $| J |$ . The left-hand-side has linear dependence on $| J |$ , whereas the left-hand-side has a $\tilde { \mathcal { O } } \left( \sqrt { | J | } \right)$ dependence. This allows us to solve out an upper bound on $| J |$ with quadratic dependence on $1 / \eta$ .
+
+# 3.5 PROOF FOR THEOREM 1
+
+We prove the theorem by stitching Lemma 1 and Condition 2.
+
+Proof. (Proof for Theorem 1)
+
+By lemma 1, for any $2 \leq j \leq M , \sum _ { t = 1 } ^ { \infty } I \left[ V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > \eta _ { j - 1 } \right] \leq C$ , where $C = \frac { S A \ln S A \ln 1 / \delta } { \eta _ { j - 1 } ^ { 2 } ( 1 - \gamma ) ^ { 5 } } \cdot \tilde { P } .$
+
+Here $\tilde { P }$ is a shorthand for polylog $\begin{array} { r } { \left( \frac { 1 } { \epsilon _ { 1 } } , \frac { 1 } { 1 - \gamma } \right) } \end{array}$
+
+Let $A _ { t } = I [ X _ { t } ^ { ( 2 ^ { i } ) } \geq \eta _ { j - 1 } ]$ be a Bernoulli random variable, and $\{ \mathcal { F } _ { t } \} _ { t \ge 1 }$ be the filtration generated by random variables $\bar { \{ ( s _ { \tau } , a _ { \tau } ) : 1 \leq \tau \leq t \} }$ . Since $A _ { t }$ is $\mathcal { F } _ { t + R }$ −measurable, for any $0 \leq k < R$ , $\{ \dot { A } _ { k + t R } - E [ A _ { k + t R } \ | \ \mathcal { F } _ { k + t R } ] \} _ { t \geq 0 }$ is a martingale difference sequence. For now, consider a fixed $0 \leq k < R$ . By Azuma-Hoeffiding inequality, after $\begin{array} { r } { T = \mathcal { O } \left( \frac { C } { 2 ^ { i } } \cdot \frac { M \eta _ { j } } { \xi _ { i } } \ln ( R M L ) \right) } \end{array}$ · M ηjξ ln(RM L) time steps (if it happens that many times) with
+
+$$
+\operatorname* { P r } \left[ X _ { k + t R } ^ { ( 2 ^ { i } ) } \geq \eta _ { j - 1 } \right] = \mathbb { E } [ A _ { k + t R } ] > \frac { \xi _ { i } } { M \eta _ { j } } ,
+$$
+
+we have $\textstyle \sum _ { t } A _ { k + t R } \geq C / 2 ^ { i }$ with probability at least $1 - \delta / ( 2 M R L )$ .
+
+On the other hand, if $A _ { k + t R }$ happens, within $[ k + t R , k + t R + R - 1 ]$ , there must be at least $2 ^ { i }$ time steps at which $V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > ^ { \mathsf { ^ { * } } } \eta _ { j - 1 }$ . The latter event happens at most $C$ times, and the $[ k + t R , k + t R + R - 1 ]$ are disjoint. Tppens at most erefore, times f $\textstyle \sum _ { t = 0 } ^ { \infty } A _ { k + t R } \leq C / 2 ^ { i }$ . This suggests that a union bound on $T$ $i$ $j$ $0 \leq k < R$ , we can show that with probability $1 - \delta / ( 2 M L )$ , there are at most $R T$ time steps where $\mathrm { P r } \left[ X _ { t } ^ { ( 2 ^ { i } ) } \geq \eta _ { j - 1 } \right] > \xi _ { i } / ( M \eta _ { j } )$ . Thus, the number of sub-optimal steps is bounded by,
+
+$$
+\begin{array} { r l r } {  { \sum _ { t = 1 } ^ { \ell - 1 } I [ V ^ { * } ( s _ { t } ) - V ^ { \pi _ { t } } ( s _ { t } ) > \epsilon ] } } \\ & { \leq \sum _ { t = 1 } ^ { \infty } \sum _ { i = 0 } ^ { L } \sum _ { j = 2 } ^ { M } I [ \eta _ { j } \operatorname* { P r } [ X _ { t } ^ { ( 2 ^ { i } ) } > \eta _ { j - 1 } ] > \frac { \xi _ { i } } { M } ] = \sum _ { i = 0 } ^ { L } \sum _ { j = 2 } ^ { M } \sum _ { t = 1 } ^ { \infty } I [ \operatorname* { P r } [ X _ { t } ^ { ( 2 ^ { i } ) } > \eta _ { j - 1 } ] > \frac { \xi _ { i } } { \eta _ { j } M } ] } \\ & { \leq \sum _ { i = 0 } ^ { L } \sum _ { j = 2 } ^ { M } \frac { S A M R \ln 1 / \delta \ln S A } { \eta _ { j } \xi _ { i } \cdot 2 ^ { i } ( 1 - \gamma ) ^ { 5 } } \tilde { P } \leq \sum _ { i = 0 } ^ { L } \frac { S A \cdot 2 ^ { i + 4 } \ln S A \ln 1 / \delta } { \epsilon _ { 2 } ^ { 2 } ( 1 - \gamma ) ^ { 6 } } \tilde { P } \mathrm { ( B y ~ d e f i n i t i o n ~ o f } \xi _ { i } \mathrm { ~ a n d } \eta _ { j } ) } \\ & { \leq \frac { S A R \ln S A \ln 1 / \delta } { \epsilon _ { 2 } ^ { 2 } ( 1 - \gamma ) ^ { 6 } } \tilde { P } \leq \frac { S A \ln S A \ln 1 / \delta } { \epsilon _ { 2 } ^ { 2 } ( 1 - \gamma ) ^ { 7 } } \tilde { P } . } & { \mathrm { ( B y ~ d e f i n i t i o n ~ o f } \hbar ) } \end{array}
+$$
+
+It should be stressed that throughout the lines, $\tilde { P }$ is a shorthand for an asymptotic expression, instead of an exact value. Our final choice of 2 and 1 are 2 = 3 , and 1 = 24RM ln . It is not hard 1−γ to see that $\ln 1 / \epsilon _ { 1 } = \mathrm { p o l y } ( \ln \textstyle \frac { 1 } { \epsilon } , \ln \frac { 1 } { 1 - \gamma } )$ . This immediately implies that with probability $1 - \delta$ , the number of time steps such that $\left( V ^ { * } - \dot { V } ^ { \pi } \right) \left( s _ { t } \right) > \epsilon$ is
+
+$$
+\tilde { \mathcal { O } } \left( \frac { S A \ln 1 / \delta } { \epsilon ^ { 2 } ( 1 - \gamma ) ^ { 7 } } \right) ,
+$$
+
+where hidden factors are $\begin{array} { r } { \operatorname { p o l y } ( \ln { \frac { 1 } { \epsilon } } , \ln { \frac { 1 } { 1 - \gamma } } , \ln S A ) } \end{array}$ .
+
+# 4 DISCUSSION
+
+In this section, we discuss the implication of our results, and present some interesting properties of our algorithm beyond its sample complexity bound.
+
+# 4.1 COMPARISON WITH PREVIOUS RESULTS
+
+Lower bound To the best of our knowledge, the current best lower bound for worst-case sample complexity is  SA2(1−γ)3 ln 1/δ due to Lattimore & Hutter (2012). The gap between our results and this lower bound lies only in the dependence on $1 / ( 1 - \gamma )$ and logarithmic terms of $\mathrm { { } } ^ { \mathrm { { 3 } } A , 1 / ( 1 - \gamma ) }$ and $1 / \epsilon$ .
+
+Model-free algorithms Previously, the best sample complexity bound for a model-free algorithm is $\begin{array} { r } { \tilde { \mathcal O } \left( \frac { S A } { \epsilon ^ { 4 } ( 1 - \gamma ) ^ { 8 } } \right) } \end{array}$ (suppressing all logarithmic terms), achieved by Delayed Q-learning Strehl et al. (2006). Our results improve this upper bound by a factor of $\frac { 1 } { \epsilon ^ { 2 } ( 1 - \gamma ) }$ , and closes the quadratic gap in $1 / \epsilon$ between Delayed Q-learning’s result and the lower bound. In fact, the following theorem shows that UCB Q-learning can indeed outperform Delayed Q-learning.
+
+Theorem 2. There exists a family of MDPs with constant $S$ and $A$ , in which with probability $1 - \delta$ , Delayed $Q$ -learning incurs sample complexity of exploration of $\Omega \left( \frac { \epsilon ^ { - 3 } } { \ln ( 1 / \delta ) } \right)$ , assuming that $\ln ( 1 / \delta ) < \epsilon ^ { - 2 }$ .
+
+The construction of this hard MDP family is given in the supplementary material.
+
+Model-based algorithms For model-based algorithms, better sample complexity results in infinite horizon settings have been claimed Szita & Szepesvári (2010). To the best of our knowledge, the best published result without further restrictions on MDPs is $\begin{array} { r } { \tilde { \mathcal O } \left( \frac { S A } { \epsilon ^ { 2 } ( 1 - \gamma ) ^ { 6 } } \right) } \end{array}$ claimed by Szita & Szepesvári (2010), which is $( 1 - \gamma )$ smaller than our upper bound. From the space complexity point of view, our algorithm is much more memory-efficient. Our algorithm stores $O ( S A )$ values, whereas the algorithm in Szita & Szepesvári (2010) needs $\Omega ( S ^ { 2 } A )$ memory to store the transition model.
+
+# 4.2 EXTENSION TO OTHER SETTINGS
+
+Due to length limits, detailed discussion in this section is deferred to supplementary materials.
+
+Finite horizon MDP The sample complexity of exploration bounds of UCB Q-learning implies $\tilde { \mathcal { O } } \left( \epsilon ^ { - 2 } \right)$ PAC sample complexity and a $\bar { \mathcal { O } } \left( T ^ { 1 / 2 } \right)$ regret bound in finite horizon MDPs. That is, our algorithm implies a PAC algorithm for finite horizon MDPs. We are not aware of reductions of the opposite direction (from finite horizon sample complexity to infinite horizon sample complexity of exploration).
+
+Regret The reason why our results can imply an $\tilde { \mathcal { O } } ( { \sqrt { T } } )$ regret is that, after choosing $\epsilon _ { 1 }$ , it follows from the argument of Theorem 1 that with probability $1 - \delta$ , for all $\epsilon _ { 2 } > \tilde { \mathcal { O } } ( \epsilon _ { 1 } / ( 1 - \gamma ) )$ , the number of $\epsilon _ { 2 }$ -suboptimal steps is bounded by
+
+$$
+\mathcal { O } \left( \frac { S A \ln S A \ln 1 / \delta } { \epsilon _ { 2 } ^ { 2 } ( 1 - \gamma ) ^ { 7 } } \mathrm { p o l y l o g } \left( \frac { 1 } { \epsilon _ { 1 } } , \frac { 1 } { 1 - \gamma } \right) \right) .
+$$
+
+In contrast, Delayed Q-learning Strehl et al. (2006) can only give an upper bound on $\epsilon _ { 1 }$ -suboptimal steps after setting parameter $\epsilon _ { 1 }$ .
+
+# 5 CONCLUSION
+
+Infinite-horizon MDP with discounted reward is a setting that is arguably more difficult than other popular settings, such as finite-horizon MDP. Previously, the best samby model-free reinforcement learning algorithms in this setting is $\tilde { \cal O } \big ( { \textstyle \frac { S A } { \epsilon ^ { 4 } ( 1 - \gamma _ { _ { - } } ) ^ { 8 } } } \big )$ y bound achieved, due to Delayed Q-learning Strehl et al. (2006). In this paper, we propose a variant of Q-learning that incorporates upper confidence bound, and show that it has a sample complexity of $\begin{array} { r } { \tilde { \mathcal { O } } \big ( \frac { S A } { \epsilon ^ { 2 } ( 1 - \gamma ) ^ { 7 } } \big ) } \end{array}$ . This matches the best lower bound except in dependence on $1 / ( 1 - \gamma )$ and logarithmic factors.
+
+# 6 ACKNOWLEDGEMENTS
+
+The authors thank Chi Jin and Chongjie Zhang for helpful discussions. This work is supported by National Basic Research Program of China (973 Program) (grant no. 2015CB352502), NSFC (61573026), BJNSF (L172037) and Beijing Acedemy of Artificial Intelligence.
+
+# REFERENCES
+
+Mohammad Gheshlaghi Azar, Remi Munos, Mohammad Ghavamzadeh, and Hilbert Kappen. Speedy q-learning. In Advances in neural information processing systems, 2011.
+
+Mohammad Gheshlaghi Azar, Ian Osband, and Rémi Munos. Minimax regret bounds for reinforcement learning. arXiv preprint arXiv:1703.05449, 2017.
+
+Ronen I. Brafman and Moshe Tennenholtz. R-max - a general polynomial time algorithm for near-optimal reinforcement learning. J. Mach. Learn. Res., 3:213–231, March 2003. ISSN 1532-4435. doi: 10.1162/153244303765208377. URL https://doi.org/10.1162/ 153244303765208377.
+
+Christoph Dann, Tor Lattimore, and Emma Brunskill. Unifying pac and regret: Uniform pac bounds for episodic reinforcement learning. In Advances in Neural Information Processing Systems, pp. 5713–5723, 2017.
+
+Eyal Even-Dar and Yishay Mansour. Learning rates for q-learning. Journal of Machine Learning Research, 5(Dec):1–25, 2003.
+
+Thomas Jaksch, Ronald Ortner, and Peter Auer. Near-optimal regret bounds for reinforcement learning. Journal of Machine Learning Research, 11(Apr):1563–1600, 2010.
+
+Chi Jin, Zeyuan Allen-Zhu, Sebastien Bubeck, and Michael I Jordan. Is q-learning provably efficient? In Advances in Neural Information Processing Systems, pp. 4864–4874, 2018.
+
+Sham Machandranath Kakade et al. On the sample complexity of reinforcement learning. PhD thesis, University of London London, England, 2003.
+
+Tor Lattimore and Marcus Hutter. Pac bounds for discounted mdps. In International Conference on Algorithmic Learning Theory, pp. 320–334. Springer, 2012.
+
+Volodymyr Mnih, Koray Kavukcuoglu, David Silver, Alex Graves, Ioannis Antonoglou, Daan Wierstra, and Martin Riedmiller. Playing atari with deep reinforcement learning. arXiv preprint arXiv:1312.5602, 2013.
+
+Volodymyr Mnih, Adria Puigdomenech Badia, Mehdi Mirza, Alex Graves, Timothy Lillicrap, Tim Harley, David Silver, and Koray Kavukcuoglu. Asynchronous methods for deep reinforcement learning. In International conference on machine learning, pp. 1928–1937, 2016.
+
+John Schulman, Sergey Levine, Pieter Abbeel, Michael Jordan, and Philipp Moritz. Trust region policy optimization. In International Conference on Machine Learning, pp. 1889–1897, 2015.
+
+Aaron Sidford, Mengdi Wang, Xian Wu, Lin Yang, and Yinyu Ye. Near-optimal time and sample complexities for solving markov decision processes with a generative model. In Advances in Neural Information Processing Systems, pp. 5186–5196, 2018a.
+
+Aaron Sidford, Mengdi Wang, Xian Wu, and Yinyu Ye. Variance reduced value iteration and faster algorithms for solving markov decision processes. In Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 770–787. Society for Industrial and Applied Mathematics, 2018b.
+
+Alexander L Strehl and Michael L Littman. An analysis of model-based interval estimation for markov decision processes. Journal of Computer and System Sciences, 74(8):1309–1331, 2008.
+
+Alexander L Strehl, Lihong Li, Eric Wiewiora, John Langford, and Michael L Littman. Pac modelfree reinforcement learning. In Proceedings of the 23rd international conference on Machine learning, pp. 881–888. ACM, 2006.
+
+István Szita and Csaba Szepesvári. Model-based reinforcement learning with nearly tight exploration complexity bounds. In Proceedings of the 27th International Conference on Machine Learning (ICML-10), pp. 1031–1038, 2010.
+
+# A PROOF OF LEMMA 1
+
+Lemma 1. For fixed t and $\eta > 0$ , let $B _ { \eta } ^ { ( t ) }$ be the event that $\begin{array} { r } { V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > \frac { \eta } { 1 - \gamma } } \end{array}$ in step t. If $\eta > 2 \epsilon _ { 1 }$ , then with probability at least $1 - \delta / 2$ ,
+
+$$
+\sum _ { t = 1 } ^ { t = \infty } I \left[ B _ { \eta } ^ { ( t ) } \right] \leq \frac { S A \ln S A \ln 1 / \delta } { \eta ^ { 2 } ( 1 - \gamma ) ^ { 3 } } \cdot p o l y l o g \left( \frac { 1 } { \epsilon _ { 1 } } , \frac { 1 } { 1 - \gamma } \right) ,
+$$
+
+where $I [ \cdot ]$ is the indicator function.
+
+Proof. When $\eta > 1$ the lemma holds trivially. Now consider the case that $\eta \leq 1$ .
+
+Let $\begin{array} { r } { I = \{ t \colon V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > \frac { \eta } { 1 - \gamma } \} } \end{array}$ . By lemma 2, with probability $1 - \delta$
+
+$$
+\begin{array} { r l } & { \frac { \eta | I | } { 1 - \gamma } \leq \displaystyle \sum _ { t \in I } \left( V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) \right) \leq \displaystyle \sum _ { t \in I } \left[ \left( \hat { Q } _ { t } - Q ^ { * } \right) ( s _ { t } , a _ { t } ) \right] } \\ & { \qquad \leq \displaystyle \frac { | I | \epsilon _ { 1 } } { 1 - \gamma } + \mathcal { O } \left( \frac { 1 } { ( 1 - \gamma ) ^ { 5 / 2 } } \sqrt { S A | I | \ell | ( I | ) } + \frac { S A } { ( 1 - \gamma ) ^ { 3 } } \ln | I | \ln \frac { 1 } { \epsilon _ { 1 } ( 1 - \gamma ) } \right) } \\ & { \qquad \leq \displaystyle \frac { | I | \epsilon _ { 1 } } { 1 - \gamma } + \mathcal { O } \left( \ln \frac { 1 } { \epsilon _ { 1 } ( 1 - \gamma ) } \cdot \left( \frac { \sqrt { S A | I | \ln \frac { S A | I | } { \delta } } } { ( 1 - \gamma ) ^ { 5 / 2 } } + \frac { S A \ln | I | } { ( 1 - \gamma ) ^ { 3 } } \right) \right) } \\ & { \qquad \leq \displaystyle \frac { | I | \epsilon _ { 1 } } { 1 - \gamma } + \mathcal { O } \left( \sqrt { \ln \frac { 1 } { \delta } } \ln \frac { 1 } { \epsilon _ { 1 } ( 1 - \gamma ) } \cdot \left( \frac { \sqrt { S A | I | \ln S A | I | } } { ( 1 - \gamma ) ^ { 5 / 2 } } + \frac { S A \ln | I | } { ( 1 - \gamma ) ^ { 3 } } \right) \right) } \end{array}
+$$
+
+Suppose that $\begin{array} { r } { | I | = \frac { S A k ^ { 2 } } { \eta ^ { 2 } ( 1 - \gamma ) ^ { 3 } } \ln S A } \end{array}$ , for some $k > 1$ . Then it follows that for some constant $C _ { 1 }$ ,
+
+$$
+\begin{array} { r l } & { \frac { \eta | I | } { 1 - \gamma } = \cfrac { k ^ { 2 } S A \ln S A } { ( 1 - \gamma ) ^ { 4 } \eta } \leq 2 \cfrac { ( \eta - \epsilon _ { 1 } ) | I | } { 1 - \gamma } } \\ & { \qquad \leq C _ { 1 } \sqrt { \ln \frac { 1 } { \delta } } \ln \cfrac { 1 } { \epsilon _ { 1 } ( 1 - \gamma ) } \left( \cfrac { \sqrt { S A | I | \ln \left( S A | I | \right) } } { ( 1 - \gamma ) ^ { 5 / 2 } } + \cfrac { S A \ln | I | } { ( 1 - \gamma ) ^ { 3 } } \right) } \\ & { \qquad \leq C _ { 1 } \sqrt { \ln \frac { 1 } { \delta } } \ln \cfrac { 1 } { \epsilon _ { 1 } ( 1 - \gamma ) } \left( \cfrac { S A k } { \eta ( 1 - \gamma ) ^ { 4 } } \sqrt { \ln S A \cdot ( \ln S A + \ln | I | ) } + \cfrac { S A \ln | I | } { ( 1 - \gamma ) ^ { 3 } } \right) . } \end{array}
+$$
+
+Therefore
+
+$$
+\begin{array} { r l } & { k ^ { 2 } \ln ( S A ) \le C _ { 1 } \sqrt { \ln \displaystyle \frac { 1 } { \delta } } \ln \frac { 1 } { \epsilon _ { 1 } ( 1 - \gamma ) } \left( k \left( \ln S A + \ln | I | \right) + \eta ( 1 - \gamma ) \ln | I | \right) } \\ & { \qquad \le k C _ { 1 } \sqrt { \ln \displaystyle \frac { 1 } { \delta } } \ln \frac { 1 } { \epsilon _ { 1 } ( 1 - \gamma ) } \cdot \left( \ln S A + 2 \ln | I | \right) } \\ & { \qquad \le k C _ { 1 } \sqrt { \ln \displaystyle \frac { 1 } { \delta } } \ln \frac { 1 } { \epsilon _ { 1 } ( 1 - \gamma ) } \cdot \left( 3 \ln S A + 4 \ln k + 6 \ln \frac { 1 } { \eta ( 1 - \gamma ) } \right) } \\ & { \qquad \le 6 k C _ { 1 } \sqrt { \ln \displaystyle \frac { 1 } { \delta } } \ln ^ { 2 } \frac { 1 } { \epsilon _ { 1 } ( 1 - \gamma ) } \left( \ln S A + \ln \epsilon k \right) . } \end{array}
+$$
+
+Let $\begin{array} { r } { C ^ { \prime } = \operatorname* { m a x } \lbrace 2 , 6 C _ { 1 } \sqrt { \ln \frac { 1 } { \delta } } \ln ^ { 2 } \frac { 1 } { \epsilon _ { 1 } ( 1 - \gamma ) } \rbrace } \end{array}$ . Then
+
+$$
+k \leq C ^ { \prime } ( 2 + \ln k ) .
+$$
+
+If $k \geq 1 0 C ^ { \prime } \ln C ^ { \prime }$ , then
+
+$$
+\begin{array} { c } { k - C ^ { \prime } \left( 2 + \ln k \right) \geq 8 C ^ { \prime } \ln C ^ { \prime } - ( 2 + \ln 1 0 ) C ^ { \prime } } \\ { \geq 4 C ^ { \prime } \left( 2 \ln C ^ { \prime } - 4 \right) \geq 0 , } \end{array}
+$$
+
+which means violation of (9). Therefore, since $C ^ { \prime } \geq 2$
+
+$$
+k \leq 1 0 C ^ { \prime } \ln C ^ { \prime } \leq 3 6 0 C _ { 1 } ^ { 2 } \operatorname* { m a x } \{ \ln ^ { 4 } { \frac { 1 } { \epsilon _ { 1 } ( 1 - \gamma ) } } , 2 0 \ln 2 \} .
+$$
+
+It immediately follows that
+
+$$
+\begin{array} { r l r } {  { \vert I \vert = \frac { S A k ^ { 2 } } { \eta ^ { 2 } ( 1 - \gamma ) ^ { 3 } } \ln S A } } \\ & { \leq \frac { S A \ln S A } { \eta ^ { 2 } ( 1 - \gamma ) ^ { 5 } } \cdot \ln \frac { 1 } { \delta } \cdot \mathcal { O } ( \ln ^ { 8 } \frac { 1 } { \epsilon _ { 1 } ( 1 - \gamma ) } ) . } \end{array}
+$$
+
+# B PROOF OF LEMMA 2
+
+Lemma 2. For every $( C , w )$ -sequence $( w _ { t } ) _ { t \geq 1 }$ , with probability $1 - \delta / 2$ , the following holds:
+
+$$
+\sum _ { t \ge 1 } w _ { t } ( \hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) \le \frac { C \epsilon _ { 1 } } { 1 - \gamma } + \mathcal { O } \left( \frac { \sqrt { w S A C \ell ( C ) } } { ( 1 - \gamma ) ^ { 2 . 5 } } + \frac { w S A \ln C } { ( 1 - \gamma ) ^ { 3 } } \ln \frac { 1 } { ( 1 - \gamma ) \epsilon _ { 1 } } \right) .
+$$
+
+where $\begin{array} { r } { \ell ( C ) = \iota ( C ) \ln { \frac { 1 } { ( 1 - \gamma ) \epsilon _ { 1 } } } } \end{array}$ is a log-factor.
+
+Fact 1. (1) The following statement holds throughout the algorithm,
+
+$$
+\hat { Q } _ { p + 1 } ( s , a ) \leq Q _ { p + 1 } ( s , a ) .
+$$
+
+(2) For any $p$ , there exists $p ^ { \prime } \leq p$ such that
+
+$$
+{ \hat { Q } } _ { p + 1 } ( s , a ) \geq Q _ { p ^ { \prime } + 1 } ( s , a ) .
+$$
+
+Proof. Both properties are results of the update rule at line 11 of Algorithm 1.
+
+Before proving lemma 2, we will prove two auxiliary lemmas.
+
+Lemma 3. The following properties hold for $\alpha _ { t } ^ { i }$ :
+
+1. $\begin{array} { r } { \sqrt { \frac { 1 } { t } } \leq \sum _ { i = 1 } ^ { t } \alpha _ { t } ^ { i } \sqrt { \frac { 1 } { i } } \leq 2 \sqrt { \frac { 1 } { t } } } \end{array}$ for every $t \geq 1 , c > 0$ .
+
+2. $\begin{array} { r } { \operatorname* { m a x } _ { i \in [ t ] } \alpha _ { t } ^ { i } \leq \frac { 2 H } { t } } \end{array}$ and $\begin{array} { r } { \sum _ { i = 1 } ^ { t } ( \alpha _ { t } ^ { i } ) ^ { 2 } \le \frac { 2 H } { t } } \end{array}$ for every $t \geq 1$
+
+3. $\textstyle \sum _ { t = i } ^ { \infty } \alpha _ { t } ^ { i } = 1 + 1 / H$ , for every $i \geq 1$
+
+Proof. Recall that
+
+$$
+\alpha _ { t } = \frac { H + 1 } { H + t } , \quad \alpha _ { t } ^ { 0 } = \prod _ { j = 1 } ^ { t } ( 1 - \alpha _ { j } ) , \quad \alpha _ { t } ^ { i } = \alpha _ { i } \prod _ { j = i + 1 } ^ { t } ( 1 - \alpha _ { j } ) .
+$$
+
+Properties 1-3 are proven by Jin et al. (2018). Now we prove the last property.
+
+On the one hand,
+
+$$
+\sum _ { i = 1 } ^ { t } \alpha _ { t } ^ { i } \sqrt { \frac { \iota ( i ) } { i } } \leq \sum _ { i = 1 } ^ { t } \alpha _ { t } ^ { i } \sqrt { \frac { \iota ( t ) } { i } } \leq 2 \sqrt { \frac { \iota ( t ) } { t } } ,
+$$
+
+where the last inequality follows from property 1.
+
+The left-hand side is proven by induction on $t$ . For the base case, when $t = 1 , \alpha _ { t } ^ { t } = 1$ . For $t \geq 2$ , we have $\alpha _ { t } ^ { i } = ( 1 - \alpha _ { t } ) \dot { \alpha _ { t - 1 } ^ { i } }$ for $1 \leq i \leq t - 1$ . It follows that
+
+$$
+\sum _ { i = 1 } ^ { t } \alpha _ { t } ^ { i } \sqrt { \frac { \iota ( i ) } { i } } = \alpha _ { t } \sqrt { \frac { \iota ( t ) } { t } } + ( 1 - \alpha _ { t } ) \sum _ { i = 1 } ^ { t - 1 } \alpha _ { t - 1 } ^ { i } \sqrt { \frac { \iota ( i ) } { i } } \geq \alpha _ { t } \sqrt { \frac { \iota ( t ) } { t } } + ( 1 - \alpha _ { t } ) \sqrt { \frac { \iota ( t - 1 ) } { t - 1 } } .
+$$
+
+Since function $f ( t ) = \iota ( t ) / t$ is monotonically decreasing for $t \geq 1 , c \geq 1$ , we have
+
+$$
+\alpha _ { t } \sqrt { \frac { \iota ( t ) } { t } } + ( 1 - \alpha _ { t } ) \sqrt { \frac { \iota ( t - 1 ) } { t - 1 } } \geq \alpha _ { t } \sqrt { \frac { \iota ( t ) } { t } } + ( 1 - \alpha _ { t } ) \sqrt { \frac { \iota ( t ) } { t } } \geq \sqrt { \frac { \iota ( t ) } { t } } .
+$$
+
+Lemma 4. With probability at least $1 - \delta / 2$ , for all $p \geq 0$ and $( s , a )$ -pair,
+
+$$
+\begin{array} { r l } & { 0 \le ( Q _ { p } - Q ^ { * } ) ( s , a ) \le \displaystyle \frac { \alpha _ { t } ^ { 0 } } { 1 - \gamma } + \displaystyle \sum _ { i = 1 } ^ { t } \gamma \alpha _ { t } ^ { i } ( { \hat { V } } _ { t _ { i } } - V ^ { * } ) ( s _ { t _ { i } + 1 } ) + \beta _ { t } , } \\ & { 0 \le ( { \hat { Q } } _ { p } - Q ^ { * } ) ( s , a ) , } \end{array}
+$$
+
+where $t = N _ { p } ( s , a ) , t _ { i } = \tau ( s , a , i )$ and $\beta _ { t } = c _ { 3 } \sqrt { H \iota ( t ) / ( ( 1 - \gamma ) ^ { 2 } t ) }$ .
+
+Proof. Recall that
+
+$$
+\alpha _ { t } ^ { 0 } = \prod _ { j = 1 } ^ { t } ( 1 - \alpha _ { j } ) , \quad \alpha _ { t } ^ { i } = \alpha _ { i } \prod _ { j = i + 1 } ^ { t } ( 1 - \alpha _ { j } ) .
+$$
+
+From the update rule, it can be seen that our algorithm maintains the following $Q ( s , a )$ :
+
+$$
+Q _ { p } ( s , a ) = \alpha _ { t } ^ { 0 } \frac { 1 } { 1 - \gamma } + \sum _ { i = 1 } ^ { t } \alpha _ { t } ^ { i } \left[ r ( s , a ) + b _ { i } + \gamma \hat { V } _ { t _ { i } } ( s _ { t _ { i } + 1 } ) \right] .
+$$
+
+Bellman optimality equation gives:
+
+$$
+Q ^ { * } ( s , a ) = r ( s , a ) + \gamma \mathbb { P } V ^ { * } ( s , a ) = \alpha _ { t } ^ { 0 } Q ^ { * } ( s , a ) + \sum _ { i = 1 } ^ { t } \alpha _ { t } ^ { i } \left[ r ( s , a ) + \gamma \mathbb { P } V ^ { * } ( s , a ) \right] .
+$$
+
+Subtracting the two equations gives
+
+$$
+Q _ { p } - Q ^ { * } ) ( s , a ) = \alpha _ { t } ^ { 0 } ( \frac { 1 } { 1 - \gamma } - Q ^ { * } ( s , a ) ) + \sum _ { i = 1 } ^ { t } \alpha _ { t } ^ { i } \left[ b _ { i } + \gamma \left( V _ { t _ { i } } - V ^ { * } \right) \left( s _ { t _ { i } + 1 } \right) + \gamma \left( V ^ { * } \left( s _ { t _ { i } + 1 } \right) - \mathbb { P } V ^ { * } \right) \right] ,
+$$
+
+The identity above holds for arbitrary $p , s$ and $a$ . Now fix $s \in S$ , $a \in A$ and $p \in \mathbb N$ . Let $t = N _ { p } ( s , a )$ , $t _ { i } = \tau ( s , a , i )$ . The $t = 0$ case is trivial; we assume $t \geq 1$ below. Now consider an arbitrary fixed $k$ . Define
+
+$$
+\Delta _ { i } = \left( \alpha _ { k } ^ { i } \cdot I [ t _ { i } < \infty ] \cdot \left( \mathbb { P } V ^ { * } - \mathbb { \hat { P } } _ { t _ { i } } V ^ { * } \right) ( s , a ) \right)
+$$
+
+Let $F _ { i }$ be the $\sigma$ -Field generated by random variables $( s _ { 1 } , a _ { 1 } , . . . , s _ { t _ { i } } , a _ { t _ { i } } )$ . It can be seen that $\mathbb { E } \left[ \Delta _ { i } | F _ { i } \right] = 0$ , while $\Delta _ { i }$ is measurable in $F _ { i + 1 }$ . Also, since $\textstyle 0 \leq V ^ { \ast } ( s , { \bar { a } } ) \leq { \frac { 1 } { 1 - \gamma } }$ , $\begin{array} { r } { | \Delta _ { i } | \le \frac { 2 } { 1 - \gamma } } \end{array}$ . Therefore, $\Delta _ { i }$ is a martingale difference sequence; by the Azuma-Hoeffding inequality,
+
+$$
+\mathrm { P r } \left[ \left| \sum _ { i = 1 } ^ { k } \Delta _ { i } \right| > \eta \right] \leq 2 \exp \left\{ - \frac { \eta ^ { 2 } } { 8 \left( 1 - \gamma \right) ^ { - 2 } \sum _ { i = 1 } ^ { k } ( \alpha _ { k } ^ { i } ) ^ { 2 } } \right\} .
+$$
+
+By choosing $\eta$ , we can show that with probability $1 - \delta / \left[ S A ( k + 1 ) ( k + 2 ) \right]$ ,
+
+$$
+\left| \sum _ { i = 1 } ^ { k } \Delta _ { i } \right| \leq \frac { 2 \sqrt { 2 } } { 1 - \gamma } \cdot \sqrt { \sum _ { i = 1 } ^ { k } ( \alpha _ { k } ^ { i } ) ^ { 2 } \cdot \ln \frac { 2 ( k + 1 ) ( k + 2 ) S A } { \delta } } \leq \frac { c _ { 2 } } { 1 - \gamma } \sqrt { \frac { H \iota ( k ) } { k } } .
+$$
+
+Here $c _ { 2 } = 4 \sqrt { 2 }$ , $\begin{array} { r } { \iota ( k ) = \ln { \frac { ( k + 1 ) ( k + 2 ) S A } { \delta } } } \end{array}$ . By a union bound for all $k$ , this holds for arbitrary $k > 0$ arbitrary $s \in S , a \in A$ simultaneously with probability
+
+$$
+1 - \sum _ { s ^ { \prime } \in S , a ^ { \prime } \in A } \sum _ { k = 1 } ^ { \infty } \frac { \delta } { 2 S A ( k + 1 ) ( k + 2 ) } = 1 - \frac { \delta } { 2 } .
+$$
+
+Therefore, we conclude that (16) holds for the random variable $t = N _ { p } ( s , a )$ and for all $p$ , with probability $1 - \delta / 2$ as well.
+
+Proof of the right hand side of (13): We also know that $\begin{array} { r } { ( b _ { k } = \frac { c _ { 2 } } { 1 - \gamma } \sqrt { \frac { H \iota ( k ) } { k } } ) } \end{array}$
+
+$$
+\frac { c _ { 2 } } { 1 - \gamma } \sqrt { \frac { H \iota ( k ) } { k } } \leq \sum _ { i = 1 } ^ { k } \alpha _ { k } ^ { i } b _ { i } \leq \frac { 2 c _ { 2 } } { 1 - \gamma } \sqrt { \frac { H \iota ( k ) } { k } } .
+$$
+
+It is implied by (16) that
+
+$$
+\begin{array} { r l } & { ( Q _ { p } - Q ^ { * } ) ( s , a ) \leq \displaystyle \frac { \alpha _ { t } ^ { 0 } } { 1 - \gamma } + \gamma \left| \displaystyle \sum _ { i = 1 } ^ { t } \Delta _ { i } \right| + \displaystyle \sum _ { i = 1 } ^ { t } \alpha _ { t } ^ { i } \left[ \gamma ( \hat { V } _ { t _ { i } } - V ^ { * } ) ( x _ { t _ { i } + 1 } ) + b _ { i } \right] } \\ & { \qquad \leq \displaystyle \frac { \alpha _ { t } ^ { 0 } } { 1 - \gamma } + \displaystyle \frac { 3 c _ { 2 } } { 1 - \gamma } \sqrt { \frac { H \iota ( t ) } { t } } + \displaystyle \sum _ { i = 1 } ^ { t } \gamma \alpha _ { t } ^ { i } ( \hat { V } ^ { t _ { i } } - V ^ { * } ) ( x _ { t _ { i } + 1 } ) } \end{array}
+$$
+
+$$
+\leq \frac { \alpha _ { t } ^ { 0 } } { 1 - \gamma } + \sum _ { i = 1 } ^ { t } \gamma \alpha _ { t } ^ { i } ( { \hat { V } } ^ { t _ { i } } - V ^ { * } ) ( x _ { t _ { i } + 1 } ) + \beta _ { t } .
+$$
+
+Note that $\beta _ { t } = c _ { 3 } ( 1 - \gamma ) ^ { - 1 } \sqrt { H \iota ( t ) / t }$ ; $c _ { 3 } = 3 c _ { 2 } = 1 2 { \sqrt { 2 } } .$ .
+
+Proof of the left hand side of (13): Now, we assume that event that (16) holds. We assert that $Q _ { p } \geq Q ^ { * }$ for all $( s , a )$ and $p \leq p ^ { \prime }$ . This assertion is obviously true when $p ^ { \prime } = 0$ . Then
+
+$$
+\begin{array} { c l } { ( Q _ { p } - Q ^ { * } ) ( s , a ) \geq - \gamma \displaystyle \left| \displaystyle \sum _ { i = 1 } ^ { t } \Delta _ { i } \right| + \displaystyle \sum _ { i = 1 } ^ { t } \alpha _ { t } ^ { i } \left[ \gamma ( \hat { V } _ { t _ { i } } - V ^ { * } ) ( x _ { t _ { i } + 1 } ) + b _ { i } \right] } \\ { \geq \displaystyle \sum _ { i = 1 } ^ { t } \alpha _ { t } ^ { i } b _ { i } - \gamma \displaystyle \left| \displaystyle \sum _ { i = 1 } ^ { t } \Delta _ { i } \right| \geq 0 . } \end{array}
+$$
+
+Therefore the assertion holds for $p ^ { \prime } + 1$ as well. By induction, it holds for all $p$ .
+
+We now see that (13) holds for probability $1 - \delta / 2$ for all $p , s , a$ . Since $\hat { Q } _ { p } ( s , a )$ is always greater than $Q _ { p ^ { \prime } } ( s , a )$ for some $p ^ { \prime } \leq p$ , we know that $\hat { Q } _ { p } ( s , a ) \geq Q _ { p ^ { \prime } } ( s , a ) \geq Q ^ { * } ( s , a )$ , thus proving (14).
+
+We now give a proof for lemma 2. Recall the definition for a $( C , w )$ -sequence. A sequence $( w _ { t } ) _ { t \geq 1 }$ is said to be a $( C , w )$ -sequence for $C , w > 0$ , if $0 \leq w _ { t } \leq w$ for all $t \geq 1$ , and $\textstyle \sum _ { t \geq 1 } w _ { t } \leq C$ .
+
+Proof. Let $n _ { t } = N _ { t } ( s _ { t } , a _ { t } )$ for simplicity; we have
+
+$$
+\begin{array} { r l } {  { \sum _ { t \geq 1 } w _ { t } ( \hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) } } \\ & { \leq \sum _ { t \geq 1 } w _ { t } ( Q _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) } \\ & { \leq \sum _ { t \geq 1 } w _ { t } [ \cfrac { \alpha _ { n _ { t } } ^ { 0 } } { 1 - \gamma } + \beta _ { n _ { t } } + \gamma \sum _ { i = 1 } ^ { n _ { t } } \alpha _ { n _ { t } } ^ { i } ( \hat { V } _ { \tau ( s _ { t } , a _ { t } , i ) } - V ^ { * } ) ( s _ { \tau ( s _ { t } , a _ { t } , i ) + 1 } ) ] } \end{array}
+$$
+
+The last inequality is due to lemma 4. Note that $\alpha _ { n _ { t } } ^ { 0 } = \mathbb { I } [ n _ { t } = 0 ]$ , the first term in the summation can be bounded by,
+
+$$
+\sum _ { t \geq 1 } w _ { t } \frac { \alpha _ { n _ { t } } ^ { 0 } } { 1 - \gamma } \leq \frac { S A w } { 1 - \gamma } .
+$$
+
+For the second term, define $u ( s , a ) = \operatorname* { s u p } _ { t } N _ { t } ( s , a )$ .2 It follows that,
+
+$$
+\begin{array} { l } { \displaystyle \sum _ { t \geq 1 } w _ { t } \beta _ { n _ { t } } = \sum _ { s , o } ^ { u ( s , o ) } w _ { \tau ( s , a , i ) } \beta _ { i } } \\ { \displaystyle \qquad \leq \sum _ { s , a } ( 1 - \gamma ) ^ { - 1 } c _ { 3 } \sum _ { i = 1 } ^ { C _ { s , a } / w } \sqrt { \frac { H \iota ( i ) } { i } } w } \\ { \displaystyle \qquad \leq 2 \sum _ { s , a } ( 1 - \gamma ) ^ { - 1 } c _ { 3 } \sqrt { \iota ( C ) H C _ { s , a } w } } \\ { \displaystyle \qquad \leq 2 c _ { 3 } ( 1 - \gamma ) ^ { - 1 } \sqrt { w S A H C \iota ( C ) } . } \end{array}
+$$
+
+Where $\begin{array} { r } { C _ { s , a } = \sum _ { t \geq 1 , ( s _ { t } , a _ { t } ) = ( s , a ) } w _ { t } } \end{array}$ . Inequality (19) follows from rearrangement inequality, since $\iota ( x ) / x$ is monotonically decreasing. Inequality (21) follows from Jensen’s inequality.
+
+For the third term of the summation, we have
+
+$$
+\begin{array} { c } { { \displaystyle \sum _ { t \ge 1 } w _ { t } \sum _ { i = 1 } ^ { n _ { t } } \alpha _ { n _ { t } } ^ { i } \left( \hat { V } _ { \tau ( s _ { t } , a _ { t } , i ) } - V ^ { * } \right) \left( s _ { \tau ( s _ { t } , a _ { t } , i ) + 1 } \right) } } \\ { { \displaystyle \le \sum _ { t ^ { \prime } \ge 1 } \left( \hat { V } _ { t ^ { \prime } } - V ^ { * } \right) \left( s _ { t ^ { \prime } + 1 } \right) \left( \sum _ { t = t ^ { \prime } + 1 } ^ { \infty } \alpha _ { n _ { t } } ^ { n _ { t ^ { \prime } } } w _ { t } \right) . } } \end{array}
+$$
+
+Define
+
+$$
+w _ { t ^ { \prime } + 1 } ^ { \prime } = \left( \sum _ { \stackrel { t = t ^ { \prime } + 1 } { ( s _ { t } , a _ { t } ) = ( s _ { t } ^ { \prime } , a _ { t } ^ { \prime } ) } } ^ { \infty } \alpha _ { n _ { t } } ^ { n _ { t ^ { \prime } } } w _ { t } \right) .
+$$
+
+We claim that $w _ { t + 1 } ^ { \prime }$ is a $\textstyle ( C , ( 1 + { \frac { 1 } { H } } ) w )$ -sequence. We now prove this claim. By lemma 3, for any $t ^ { \prime } \geq 0$ ,
+
+$$
+w _ { t ^ { \prime } + 1 } ^ { \prime } \leq w \sum _ { j = n _ { t ^ { \prime } } } ^ { \infty } \alpha _ { j } ^ { n _ { t ^ { \prime } } } = ( 1 + 1 / H ) w .
+$$
+
+By $\textstyle \sum _ { j = 0 } ^ { i } \alpha _ { i } ^ { j } = 1$ , we have $\begin{array} { r } { \sum _ { t ^ { \prime } \geq 1 } w _ { t ^ { \prime } + 1 } ^ { \prime } \leq \sum _ { t \geq 1 } w _ { t } \leq C . } \end{array}$ . This proves the assertion. It follows from (22) that
+
+$$
+\begin{array} { r l } & { \quad \underset { t \geq 1 } { \sum \sigma } u _ { t + 1 } ^ { \prime } \left( \hat { V } _ { t } - V ^ { * } \right) \left( s _ { t + 1 } \right) } \\ & { = \underset { t \geq 1 } { \sum \sigma } u _ { t + 1 } ^ { \prime } \left( \hat { V } _ { t + 1 } - V ^ { * } \right) \left( s _ { t + 1 } \right) + \underset { t \geq 1 } { \sum \sigma } u _ { t + 1 } ^ { \prime } \left( \hat { V } _ { t } - \hat { V } _ { t + 1 } \right) \left( s _ { t + 1 } \right) } \\ & { \quad \leq \underset { t \geq 1 } { \sum \sigma } u _ { t + 1 } ^ { \prime } \left( \hat { V } _ { t + 1 } - V ^ { * } \right) \left( s _ { t + 1 } \right) + \underset { t \geq 1 } { \sum \sigma } u _ { t + 1 } ^ { \prime } \left( 2 \alpha _ { n _ { t } + 1 } \frac { 1 } { 1 - \gamma } \right) } \\ & { \quad \leq \underset { t \geq 1 } { \sum \sigma } w _ { t + 1 } ^ { \prime } \left( \hat { V } _ { t + 1 } - V ^ { * } \right) \left( s _ { t + 1 } \right) + \mathcal { O } \left( \frac { w S A H } { 1 - \gamma } \ln { C } \right) } \\ & { \quad \leq \underset { t \geq 1 } { \sum \sigma } w _ { t + 1 } ^ { \prime } \left( \hat { Q } _ { t + 1 } - Q ^ { * } \right) \left( s _ { t + 1 } , a _ { t + 1 } \right) + \mathcal { O } \left( \frac { w S A H } { 1 - \gamma } \ln { C } \right) } \end{array}
+$$
+
+Inequality (25) comes from the update rule of our algorithm. Inequality (26) comes from the fact that $\dot { \alpha } _ { t } = ( H + 1 ) / ( H + t ) \overset { \cdot } { \leq } H / t$ and Jensen’s Inequality. More specifically, let $C _ { s , a } ^ { \prime } =$ $\scriptstyle \sum _ { t \geq 1 , ( s _ { t } , a _ { t } = s , a } w _ { t + 1 } ^ { \prime }$ , $w ^ { \prime } = w ( 1 + 1 / H )$ . Then
+
+$$
+\sum _ { t \geq 1 } w _ { t + 1 } ^ { \prime } \alpha _ { n _ { t } + 1 } \leq \sum _ { s , a } \sum _ { n = 1 } ^ { C _ { s , a } ^ { \prime } / w ^ { \prime } } w ^ { \prime } \frac { H } { n } \leq \sum _ { s , a } H w ^ { \prime } \ln ( C _ { s , a } ^ { \prime } / w ) \leq 2 S A H w \ln C .
+$$
+
+Putting (18), (21) and (27) together, we have,
+
+$$
+\begin{array} { r l } & { \displaystyle \sum _ { t \geq 1 } w _ { t } ( \hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) } \\ & { \leq 2 c _ { 3 } \frac { \sqrt { w S A H C \iota ( C ) } } { 1 - \gamma } + \mathcal { O } \left( \frac { w S A H } { 1 - \gamma } \ln C \right) + \gamma \displaystyle \sum _ { t \geq 1 } w _ { t + 1 } ^ { \prime } \left( \hat { Q } _ { t + 1 } - Q ^ { * } \right) ( s _ { t + 1 } , a _ { t + 1 } ) . } \end{array}
+$$
+
+Observe that the third term is another weighted sum with the same form as (17). Therefore, we can unroll this term repetitively with changing weight sequences.Suppose that our original weight sequence is also denoted by $\{ \bar { w _ { t } ^ { ( 0 ) } } \} _ { t \ge 1 }$ , while $\{ w _ { t } ^ { ( k ) } \} _ { t \ge 1 }$ denotes the weight sequence after unrolling for $k$ times. Let $w ^ { ( k ) }$ be $w \cdot \left( 1 + 1 / H \right) ^ { k }$ . Then we can see that $\{ w _ { t } ^ { ( k ) } \} _ { t \ge 1 }$ is a $( C , w ^ { ( k ) } )$ -sequence. Suppose that we unroll for $H$ times. Then
+
+$$
+\begin{array} { r l } & { \displaystyle \sum _ { t \geq 1 } w _ { t } ( \hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) } \\ & { \leq 2 c _ { 3 } \frac { \sqrt { w ^ { ( H ) } S A H C \iota ( C ) } } { ( 1 - \gamma ) ^ { 2 } } + \mathcal { O } \left( \frac { w ^ { ( H ) } S A H } { ( 1 - \gamma ) ^ { 2 } } \ln C \right) + \gamma ^ { H } \displaystyle \sum _ { t \geq 1 } w _ { t } ^ { ( H ) } \left( \hat { Q } _ { t } - Q ^ { * } \right) ( s _ { t } , a _ { t } ) } \\ & { \leq 2 c _ { 3 } \frac { \sqrt { w ^ { ( H ) } S A H C \iota ( C ) } } { ( 1 - \gamma ) ^ { 2 } } + \mathcal { O } \left( \frac { w ^ { ( H ) } S A H } { ( 1 - \gamma ) ^ { 2 } } \ln C \right) + \gamma ^ { H } \frac { C } { 1 - \gamma } . } \end{array}
+$$
+
+We set $\begin{array} { r } { H = \frac { \ln 1 / ( ( 1 - \gamma ) \epsilon _ { 1 } ) } { \ln 1 / \gamma } \leq \frac { \ln 1 / ( ( 1 - \gamma ) \epsilon _ { 1 } ) } { 1 - \gamma } , } \end{array}$ . It follows that $w ^ { ( H ) } = ( 1 + 1 / H ) ^ { H } w ^ { ( 0 ) } \leq e w ^ { ( 0 ) }$ , and that γH C1−γ $\gamma ^ { H } \frac { C } { 1 - \gamma } \leq C \epsilon _ { 1 }$ . Also, let $\ell ( C ) = \iota ( C ) \ln ( ( 1 - \gamma ) ^ { - 1 } \epsilon _ { 1 } ^ { - 1 } )$ . Therefore,
+
+$$
+\sum _ { t \geq 1 } w _ { t } ( \hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) \leq \frac { C \epsilon _ { 1 } } { 1 - \gamma } + \mathcal { O } \left( \frac { \sqrt { w S A C \ell ( C ) } } { ( 1 - \gamma ) ^ { 2 . 5 } } + \frac { w S A } { ( 1 - \gamma ) ^ { 3 } } \ln C \ln \frac { 1 } { ( 1 - \gamma ) \epsilon _ { 1 } } \right) .
+$$
+
+# C EXTENSION TO OTHER SETTINGS
+
+First we define a mapping from a finite horizon MDP to an infinite horizon MDP so that our algorithm can be applied. For an arbitrary finite horizon MDP $\mathcal { M } = ( S , A , H , r _ { h } ( s _ { \perp } a ) , p _ { h } ( s ^ { \prime } \mid s , a ) )$ where $H$ is the length of episode, the corresponding infinite horizon MDP $\mathcal { M } = ( S , A , \gamma , \bar { r } ( \bar { s } , \bar { a } ) , \bar { p } ( \bar { s } ^ { \prime } \mid \bar { s } , \bar { a } ) )$ is defined as,
+
+$\begin{array} { l } { { \bullet \ { \bar { S } } = S \times H , { \bar { A } } = A ; } } \\ { { \bullet \ \gamma = ( 1 - 1 / H ) ; } } \end{array}$ • for a state $s$ at step $h$ , let $\bar { s } _ { s , h }$ be the corresponding state. For any action $a$ and next state $s ^ { \prime }$ , define $\bar { r } ( \bar { s } _ { s , h } , a ) = \gamma ^ { H - h + 1 } r _ { h } ( s , a )$ and $\bar { p } ( \bar { s } _ { s ^ { \prime } , h + 1 } \mid \bar { s } _ { s , h } , a ) = p _ { h } ( s ^ { \prime } \mid s , h )$ . And for $h = H$ , set $\bar { r } ( \bar { s } _ { s , h } , a ) = 0$ and $\bar { p } ( \bar { s } _ { s ^ { \prime } , 1 } \mid \bar { s } _ { s , h } , a ) = I [ s ^ { \prime } = s _ { 1 } ]$ for a fixed starting state $s _ { 1 }$ .
+
+Let $\bar { V } _ { t }$ be the value function in $\bar { \mathcal { M } }$ at time $t$ and $V _ { h } ^ { k }$ the value function in $\mathcal { M }$ at episode $k$ , step $h$ . It follows that $\begin{array} { r } { \bar { V } ^ { \ast } ( \bar { s } _ { s _ { 1 } , 1 } ) = \frac { \gamma ^ { H } } { 1 - \gamma ^ { H } } V _ { 1 } ^ { \ast } ( s _ { 1 } ) } \end{array}$ . And the policy mapping is defined as $\pi _ { h } ( s ) = \bar { \pi } ( \bar { s } _ { s , h } )$ for policy $\bar { \pi }$ in $\bar { \mathcal { M } }$ . Value functions in MDP $\mathcal { M }$ and $\bar { \mathcal { M } }$ are closely related in a sense that, any $\epsilon$ -optimal policy $\bar { \pi }$ of $\bar { \mathcal { M } }$ corresponding to an $( \epsilon / \gamma ^ { H } )$ -optimal policy $\pi$ in $\mathcal { M }$ (see section C.1 for proof). Note that here $\gamma ^ { H } = ( 1 - \dot { 1 } / H ) ^ { \tilde { H } } = \mathcal { O } ( \dot { 1 } )$ is a constant.
+
+For any visited a $\epsilon > 0$ g our algorithm on  times, and at most $\bar { M }$ for of $\tilde { \mathcal O } \big ( \frac { 3 S A H ^ { 9 } } { \epsilon ^ { 2 } } \big )$ tt me steps, the starting state -optimal. If we select the p $s _ { 1 }$ iscy $\tilde { \mathcal O } \big ( { \textstyle { \frac { 3 S A H ^ { 8 } } { \epsilon ^ { 2 } } } } \big )$ $1 / 3$ $\epsilon$ uniformly randomly from the policy $\pi ^ { t H + 1 }$ for $0 \leq t < T / H$ , with probability at least $2 / 3$ we can get an $\epsilon$ -optimal policy. Therefore the PAC sample complexity is $\tilde { \mathcal { O } } \left( \epsilon ^ { - 2 } \right)$ after hiding $S , A , H$ terms.
+
+On the other hand, we want to show that for any $K$ episodes,
+
+$$
+\mathrm { R e g r e t } ( T ) = \sum _ { k = 1 } ^ { T / H } \left[ V ^ { * } ( s _ { 1 } ) - V _ { 1 } ^ { k } ( s _ { 1 } ) \right] \propto T ^ { 1 / 2 } .
+$$
+
+The reason why our algorithm can have a better reduction from regret to PAC is that, after choosing $\epsilon _ { 1 }$ , it follows from the argument of theorem 1 that for all $\epsilon _ { 2 } > \tilde { \mathcal { O } } ( \epsilon _ { 1 } / ( 1 - \gamma ) )$ , the number of $\epsilon _ { 2 }$ -suboptimal steps is bounded by
+
+$$
+\mathcal { O } \left( \frac { S A \ln S A \ln 1 / \delta } { \epsilon _ { 2 } ^ { 2 } ( 1 - \gamma ) ^ { 7 } } \mathrm { p o l y l o g } \left( \frac { 1 } { \epsilon _ { 1 } } , \frac { 1 } { 1 - \gamma } \right) \right)
+$$
+
+with probability $1 - \delta$ . In contrast, delayed Q-learning can only give an upper bound on $\epsilon _ { 1 }$ -suboptimal steps after setting parameter $\epsilon _ { 1 }$ .
+
+Formally, let $X _ { k } = V ^ { \ast } ( s _ { 1 } ) - V _ { 1 } ^ { k } ( s _ { 1 } )$ be the regret of $k$ -th episode. For any $T$ , set $\epsilon = \sqrt { S A / T }$ and $\epsilon _ { 2 } = \tilde { \mathcal { O } } ( \epsilon _ { 1 } / ( 1 - \gamma ) )$ . Let $\begin{array} { r } { M = \lceil \log _ { 2 } \frac { 1 } { \epsilon _ { 2 } ( 1 - \gamma ) } \rceil } \end{array}$ . It follows that,
+
+$$
+\begin{array} { r l r } {  { \operatorname { R e g r e t } ( T ) \le T \epsilon _ { 2 } + \sum _ { i = 1 } ^ { M } ( | k : \{ X _ { k } \ge \epsilon _ { 2 } \cdot 2 ^ { i - 1 } \} | ) \epsilon _ { 2 } \cdot 2 ^ { i } } } \\ & { } & \\ & { } & { \le \tilde { \mathcal { O } } ( T \epsilon _ { 2 } + \sum _ { i = 1 } ^ { M } \frac { S A \ln 1 / \delta } { \epsilon _ { 2 } \cdot 2 ^ { i - 2 } } ) } \\ & { } & { \le \tilde { \mathcal { O } } ( \sqrt { S A T } \ln 1 / \delta ) } \end{array}
+$$
+
+with probability $1 - \delta$ . Note that the $\tilde { \mathcal { O } }$ notation hides the poly $( 1 / ( 1 - \gamma ) , \log { 1 / \epsilon _ { 1 } } )$ which is, by our reduction, poly $( H , \log T , \log S , \log A )$ .
+
+# C.1 CONNECTION BETWEEN VALUE FUNCTIONS
+
+Recall that our MDP mapping from $\begin{array} { r c l } { \mathcal { M } } & { = } & { ( S , A , H , r _ { h } ( s , a ) , p _ { h } ( s ^ { \prime } \mathrm { ~  ~ \chi ~ } | \mathrm { ~  ~ \chi ~ } s , a ) ) } \end{array}$ to $\begin{array} { r l } { \bar { \mathcal { M } } } & { { } = } \end{array}$ $( \bar { S } , \bar { A } , \gamma , \bar { r } ( \bar { s } , \bar { a } ) , \bar { p } ( \bar { s } ^ { \prime } \mid \bar { s } , \bar { a } ) )$ is defined as,
+
+• $\bar { S } = S \times H , \bar { A } = A$ ;   
+• $\gamma = ( 1 - 1 / H )$ ;   
+• for a state $s$ at step $h$ , let $\bar { s } _ { s , h }$ be the corresponding state. For any action $a$ and next state $s ^ { \prime }$ , define $\bar { r } ( \bar { s } _ { s , h } , a ) = \gamma ^ { H - h + 1 } r _ { h } ( s , a )$ and $\bar { p } ( \bar { s } _ { s ^ { \prime } , h + 1 } \mid \bar { s } _ { s , h } , a ) = p _ { h } ( s , h )$ . And for $h = H$ , set $\bar { r } ( \bar { s } _ { s , h } , a ) = 0$ and $\bar { p } ( \bar { s } _ { s ^ { \prime } , 1 } \mid \bar { s } _ { s , h } , a ) = I [ s ^ { \prime } = s _ { 1 } ]$ for a fixed starting state $s _ { 1 }$ .
+
+For a trajectory $\left\{ { \left( { \bar { s } } _ { s _ { 1 } , 1 } , { \bar { a } } _ { 1 } \right) } , { \left( { \bar { s } } _ { s _ { 2 } , 2 } , { \bar { a } } _ { 2 } \right) } , \cdot \cdot \cdot \right\}$ in $\bar { \mathcal { M } }$ , let $\{ ( s _ { 1 } , a _ { 1 } ) , ( s _ { 2 } , a _ { 2 } ) , \cdot \cdot \cdot \}$ be the corresponding trajectory in $\mathcal { M }$ . Note that $\mathcal { M }$ has a unique fixed starting state $s _ { 1 }$ , which means that $s _ { t H + 1 } = s _ { 1 }$ for all $t \geq 0$ . Denote the corresponding policy of $\bar { \pi } ^ { t }$ as $\pi ^ { t }$ (may be non-stationary), then we have
+
+$$
+\begin{array} { r l } & { \bar { \gamma } ^ { \pi ^ { t } } ( \bar { s } _ { s _ { 1 } , 1 } ) = \mathbb { E } \left[ \bar { r } ( \bar { s } _ { s _ { 1 } , 1 } , \bar { a } _ { 1 } ) + \gamma \bar { r } ( \bar { s } _ { s _ { 2 } , 2 } , \bar { a } _ { 2 } ) + \cdot \cdot \cdot + \gamma ^ { H - 1 } \bar { r } ( \bar { s } _ { s _ { H - 1 } , H - 1 } , \bar { a } _ { H - 1 } ) + \gamma ^ { H } \bar { V } ^ { \pi _ { t + H - 1 } } ( \bar { s } _ { s _ { H + 1 } , 1 } ) \right] } \\ & { \phantom { \frac { 1 } { 1 } } = \gamma ^ { H } \mathbb { E } \left[ r _ { 1 } ( s _ { 1 } , a _ { 1 } ) + r _ { 2 } ( s _ { 2 } , a _ { 2 } ) + \cdot \cdot \cdot + r _ { H - 1 } ( s _ { H - 1 } , a _ { H - 1 } ) + \bar { V } ^ { \pi _ { t + H } } ( \bar { s } _ { s _ { H + 1 } , 1 } ) \right] } \\ & { \phantom { \frac { 1 } { 1 } } = \gamma ^ { H } V ^ { \pi ^ { t } } ( s _ { 1 } ) + \gamma ^ { H } \bar { V } ^ { \pi + H } ( \bar { s } _ { s _ { 1 } , 1 } ) . } \end{array}
+$$
+
+Then for a stationary policy $\bar { \pi }$ , we can conclude $\begin{array} { r } { \bar { V } ^ { \bar { \pi } } ( \bar { s } _ { s _ { 1 } , 1 } ) = \frac { \gamma ^ { H } } { 1 - \gamma ^ { H } } V ^ { \pi } ( s _ { 1 } ) } \end{array}$ . Since the optimal policy $\bar { \pi } ^ { * }$ is stationary, we have $\begin{array} { r } { \bar { V } ^ { \ast } ( \bar { s } _ { s _ { 1 } , 1 } ) = \frac { \gamma ^ { H } } { 1 - \gamma ^ { H } } V ^ { \ast } ( s _ { 1 } ) } \end{array}$ .
+
+By definition, $\bar { \pi }$ is $\epsilon$ -optimal at time step $t$ means that
+
+$$
+\begin{array} { r } { \bar { V } ^ { \bar { \pi } ^ { t } } ( \bar { s } _ { s _ { 1 } , 1 } ) \geq \bar { V } ^ { * } ( \bar { s } _ { s _ { 1 } , 1 } ) - \epsilon . } \end{array}
+$$
+
+It follows that
+
+$$
+\gamma ^ { H } V ^ { \pi ^ { t } } ( s _ { 1 } ) + \gamma ^ { H } \bar { V } ^ { \pi _ { t + H } } ( \bar { s } _ { s _ { 1 } , 1 } ) = \bar { V } ^ { \bar { \pi } } ( \bar { s } _ { s _ { 1 } , 1 } ) \geq \bar { V } ^ { * } ( \bar { s } _ { s _ { 1 } , 1 } ) - \epsilon ,
+$$
+
+hence
+
+$$
+^ { H } V ^ { \pi ^ { \varepsilon } } ( s _ { 1 } ) \geq ( 1 - \gamma ^ { H } ) \bar { V } ^ { * } ( \bar { s } _ { s _ { 1 } , 1 } ) + \gamma ^ { H } ( \bar { V } ^ { * } ( \bar { s } _ { s _ { 1 } , 1 } ) - \bar { V } ^ { \pi _ { t + H } } ( \bar { s } _ { s _ { 1 } , 1 } ) ) - \epsilon \geq ( 1 - \gamma ^ { H } ) \bar { V } ^ { * } ( \bar { s } _ { s _ { 1 } , 1 } ) - \epsilon .
+$$
+
+Therefore we have
+
+$$
+{ V ^ { \pi } } ^ { t } ( s _ { 1 } ) \ge \frac { 1 - \gamma ^ { H } } { \gamma ^ { H } } \bar { V } ^ { * } ( \bar { s } _ { s 1 , 1 } ) - \epsilon / \gamma ^ { H } = V ^ { * } ( s _ { 1 } ) - \epsilon / \gamma ^ { H } ,
+$$
+
+which means that $\pi ^ { t }$ is an $( \epsilon / \gamma ^ { H } )$ -optimal policy.
+
+# D A HARD INSTANCE FOR DELAYED Q-LEARNING
+
+In this section, we prove Theorem 2 regarding the performance of Delayed Q-learning.
+
+Theorem 2. There exists a family of MDPs with constant $S$ and $A$ , in which with probability $1 - \delta$ , Delayed $Q$ -learning incurs sample complexity of exploration of $\Omega \left( \frac { \epsilon ^ { - 3 } } { \ln ( 1 / \delta ) } \right)$ , assuming that $\ln ( 1 / \delta ) < \epsilon ^ { - 2 }$ .
+
+![](images/d5ea7466679255528080a8e623d46ab5efe02c60983c67939e2c04d8974b3167.jpg)  
+Figure 1: The MDP family. Actions are denoted by arrows. Actions with red color have reward 1, and reward 0 otherwise.
+
+Proof. For each $0 < \epsilon < \frac { 1 } { 1 0 }$ , consider the following MDP (see also Fig. 1): state space is ${ \boldsymbol { s } } =$ $\{ a , b , c \}$ while action set is $\overset { \vartriangle } { \mathcal { A } } = \{ \ v { x } , \ v { y } \}$ ; transition probabilities are $P ( b | a , y ) = 1 - 1 0 \epsilon$ , $P ( c | a , y ) =$ 10, $P ( b | a , x ) = 1$ , $P ( a | b , \cdot ) = P ( a | c , \cdot ) = 1$ . Rewards are all 1, except $R ( c , \cdot ) = 0$ .
+
+Assume that Delayed Q-learning is called for this MDP starting from state $a$ , with discount $\begin{array} { r } { \gamma > \frac { 1 } { 2 } } \end{array}$ and precision set as $\epsilon$ . Denote the $Q$ value maintained by the algorithm by $\hat { Q }$ . Without loss of generality, assume that the initial tie-breaking favors action $y$ when comparing $\hat { Q } ( a , x )$ and $\hat { Q } ( a , y )$ . In that case, unless $\hat { Q } ( a , y )$ is updated, the agent will always choose $y$ in state $a$ . Since $Q ( a , x ) - Q ( a , y ) = 1 0 \epsilon \gamma > \epsilon$ for any policy, choosing $y$ at state $a$ implies that the timestep is not $\epsilon$ -optimal. In other words, sample complexity for exploration is at least the number of times the agent visits $a$ before the first update of $\hat { Q } ( a , y )$ .
+
+In the Delayed Q-learning algorithm, $\hat { Q } ( \cdot , \cdot )$ are initialized to $1 / ( 1 - \gamma )$ . Therefore, $\hat { Q } ( a , y )$ could only be updated if max $\hat { Q } ( c , \cdot )$ is updated (and becomes smaller than $1 / ( 1 - \gamma ) )$ . According to the algorithm, this can only happen if $c$ is visited $\begin{array} { r } { m = \Omega \left( \frac { 1 } { \epsilon ^ { 2 } } \right) } \end{array}$ times.
+
+However, each time the agent visits $a$ , there is less than $1 0 \epsilon$ probability of transiting to $c$ . Let $t _ { 0 } = m / ( 1 0 \epsilon C )$ , where $\begin{array} { r } { C ^ { ' } = 3 \ln \frac { 1 } { \delta } + 1 } \end{array}$ . $\delta$ is chosen such that $C \leq m$ . In the first $2 t _ { 0 }$ timesteps, $a$ will be visited $t _ { 0 }$ times. By Chernoff’s bound, with probability $1 - \delta$ , state $c$ will be visited less than $m$ times. In that case, $\hat { Q } ( a , y )$ will not be updated in the first $2 t _ { 0 }$ timesteps. Therefore, with probability $1 - \delta$ , sample complexity of exploration is at least
+
+$$
+t _ { 0 } = \Omega \left( { \frac { 1 } { \epsilon ^ { 3 } \left( \ln { 1 / \delta } \right) } } \right) .
+$$
+
+When $\ln ( 1 / \delta ) < \epsilon ^ { - 2 }$ , it can be seen that $\begin{array} { r } { C = 3 \ln \frac { 1 } { \delta } + 1 < \frac { 4 } { \epsilon ^ { 2 } } < m } \end{array}$
\ No newline at end of file
diff --git a/parse/train/BkglSTNFDB/BkglSTNFDB_content_list.json b/parse/train/BkglSTNFDB/BkglSTNFDB_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..47248d499e0138decfd6a6face1b216abc5e7766
--- /dev/null
+++ b/parse/train/BkglSTNFDB/BkglSTNFDB_content_list.json
@@ -0,0 +1,3148 @@
+[
+    {
+        "type": "text",
+        "text": "Q-LEARNING WITH UCB EXPLORATION IS SAMPLE EFFICIENT FOR INFINITE-HORIZON MDP ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            98,
+            823,
+            146
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Kefan Dong\\*, Yuanhao Wang∗   \nInstitute for Interdisciplinary Information Sciences, Tsinghua University   \n{dkf16,yuanhao-16}@mails.tsinghua.edu.   \nXiaoyu Chen   \nKey Laboratory of Machine Perception, MOE, School of EECS,   \nPeking University   \ncxy30@pku.edu.cn   \nLiwei Wang   \nKey Laboratory of Machine Perception, MOE, School of EECS   \nCenter for Data Science, Peking University   \nwanglw@cis.pku.edu.cn ",
+        "bbox": [
+            183,
+            169,
+            555,
+            226
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            184,
+            247,
+            604,
+            303
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            183,
+            324,
+            601,
+            380
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            416,
+            544,
+            431
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "A fundamental question in reinforcement learning is whether model-free algorithms are sample efficient. Recently, Jin et al. (2018) proposed a Q-learning algorithm with UCB exploration policy, and proved it has nearly optimal regret bound for finite-horizon episodic MDP. In this paper, we adapt Q-learning with UCB-exploration bonus to infinite-horizon MDP with discounted rewards without accessing a generative model. We show that the sample complexity of exploration of our algorithm is bounded by $\\begin{array} { r } { \\tilde { O } \\big ( \\frac { S A } { \\epsilon ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\big ) } \\end{array}$ . This improves the previously best known result of $\\begin{array} { r } { \\tilde { O } \\big ( \\frac { S A } { \\epsilon ^ { 4 } ( 1 - \\gamma ) ^ { 8 } } \\big ) } \\end{array}$ in this setting achieved by delayed Q-learning (Strehl et al., 2006), and matches the lower bound in terms of $\\epsilon$ as well as and up to logarithmic factors. ",
+        "bbox": [
+            233,
+            450,
+            766,
+            599
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            632,
+            336,
+            647
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "The goal of reinforcement learning (RL) is to construct efficient algorithms that learn and plan in sequential decision making tasks when the underlying system dynamics are unknown. A typical model in RL is Markov Decision Process (MDP). At each time step, the environment is in a state $s$ . The agent takes an action $a$ , obtain a reward $r$ , and then the environment transits to another state. In reinforcement learning, the transition probability distribution is unknown. The algorithm needs to learn the transition dynamics of MDP, while aiming to maximize the cumulative reward. This poses the exploration-exploitation dilemma: whether to act to gain new information (explore) or to act consistently with past experience to maximize reward (exploit). ",
+        "bbox": [
+            173,
+            665,
+            825,
+            777
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Theoretical analyses of reinforcement learning fall into two broad categories: those assuming a simulator (a.k.a. generative model), and those without a simulator. In the first category, the algorithm is allowed to query the outcome of any state action pair from an oracle. The emphasis is on the number of calls needed to estimate the $Q$ value or to output a near-optimal policy. There has been extensive research in literature following this line of research, the majority of which focuses on discounted infinite horizon MDPs (Azar et al., 2011; Even-Dar & Mansour, 2003; Sidford et al., 2018b). The current results have achieved near-optimal time and sample complexities (Sidford et al., 2018b;a). ",
+        "bbox": [
+            174,
+            784,
+            825,
+            895
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Without a simulator, there is a dichotomy between finite-horizon and infinite-horizon settings. In finite-horizon settings, there are straightforward definitions for both regret and sample complexity; the latter is defined as the number of samples needed before the policy becomes near optimal. In this setting, extensive research in the past decade (Jin et al., 2018; Azar et al., 2017; Jaksch et al., 2010; Dann et al., 2017) has achieved great progress, and established nearly-tight bounds for both regret and sample complexity. ",
+        "bbox": [
+            174,
+            103,
+            825,
+            188
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The infinite-horizon setting is a very different matter. First of all, the performance measure cannot be a straightforward extension of the sample complexity defined above (See Strehl & Littman (2008) for detailed discussion). Instead, the measure of sample efficiency we adopt is the so-called sample complexity of exploration (Kakade et al., 2003), which is also a widely-accepted definition. This measure counts the number of times that the algorithm “makes mistakes” along the whole trajectory. See also (Strehl & Littman, 2008) for further discussions regarding this issue. ",
+        "bbox": [
+            174,
+            194,
+            825,
+            279
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Several model based algorithms have been proposed for infinite horizon MDP, for example Rmax (Brafman & Tennenholtz, 2003), MoRmax (Szita & Szepesvári, 2010) and UCRL- $\\gamma$ (Lattimore & Hutter, 2012). It is noteworthy that there still exists a considerable gap between the state-of-the-art algorithm and the theoretical lower bound (Lattimore & Hutter, 2012) regarding $1 / ( 1 - \\gamma )$ factor. ",
+        "bbox": [
+            174,
+            285,
+            825,
+            340
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Though model-based algorithms have been proved to be sample efficient in various MDP settings, most state-of-the-art RL algorithms are developed in the model-free paradigm (Schulman et al., 2015; Mnih et al., 2013; 2016). Model-free algorithms are more flexible and require less space, which have achieved remarkable performance on benchmarks such as Atari games and simulated robot control problems. ",
+        "bbox": [
+            174,
+            347,
+            825,
+            417
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "For infinite horizon MDPs without access to simulator, the best model-free algorithm has a sample complexity of exploration $\\begin{array} { r } { \\tilde { \\mathcal { O } } \\big ( \\frac { S A } { \\epsilon ^ { 4 } ( 1 - \\gamma ) ^ { 8 } } \\big ) } \\end{array}$ , achieved by delayed Q-learning (Strehl et al., 2006). The authors provide a novel strategy of argument when proving the upper bound for the sample complexity of exploration, namely identifying a sufficient condition for optimality, and then bound the number of times that this condition is violated. ",
+        "bbox": [
+            174,
+            424,
+            825,
+            498
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "However, the results of Delayed Q-learning still leave a quadratic gap in $1 / \\epsilon$ from the best-known lower bound. This is partly because the updates in Q-value are made in an over-conservative way. In fact, the loose sample complexity bound is a result of delayed Q-learning algorithm itself, as well as the mathematical artifact in their analysis. To illustrate this, we construct a hard instance showing that Delayed Q-learning incurs $\\Omega ( 1 / \\epsilon ^ { 3 } )$ sample complexity. This observation, as well as the success of the Q-learning with UCB algorithm (Jin et al., 2018) in proving a regret bound in finite-horizon settings, motivates us to incorporate a UCB-like exploration term into our algorithm. ",
+        "bbox": [
+            174,
+            505,
+            825,
+            603
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this work, we propose a Q-learning algorithm with UCB exploration policy. We show the sample complexity of exploration bound of our algorithm is $\\begin{array} { r } { \\tilde { \\mathcal { O } } \\big ( \\frac { S A } { \\epsilon ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\big ) } \\end{array}$ . This strictly improves the previous best known result due to Delayed Q-learning. It also matches the lower bound in the dependence on $\\epsilon$ , $S$ and $A$ up to logarithmic factors. ",
+        "bbox": [
+            174,
+            609,
+            825,
+            670
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We point out here that the infinite-horizon setting cannot be solved by reducing to finite-horizon setting. There are key technical differences between these two settings: the definition of sample complexity of exploration, time-invariant policies and the error propagation structure in Q-learning. In particular, the analysis techniques developed in (Jin et al., 2018) do not directly apply here. We refer the readers to Section 3.2 for detailed explanations and a concrete example. ",
+        "bbox": [
+            174,
+            676,
+            825,
+            747
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The rest of the paper is organized as follows. After introducing the notation used in the paper in Section 2, we describe our infinite Q-learning with UCB algorithm in Section 3. We then state our main theoretical results, which are in the form of PAC sample complexity bounds. In Section 4 we present some interesting properties beyond sample complexity bound. Finally, we conclude the paper in Section 5. ",
+        "bbox": [
+            174,
+            753,
+            825,
+            823
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 PRELIMINARY ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            856,
+            323,
+            872
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We consider a Markov Decision Process defined by a five tuple $\\langle S , \\mathcal { A } , p , r , \\gamma \\rangle$ , where $s$ is the state space, $\\mathcal { A }$ is the action space, $p ( s ^ { \\prime } | s , a )$ is the transition function, $r : S \\times \\mathcal { A }  [ 0 , 1 ]$ is the deterministic reward function, and $0 \\leq \\gamma < 1$ is the discount factor for rewards. Let $S = | S |$ and $A = | { \\mathcal { A } } |$ denote the number of states and the number of actions respectively. ",
+        "bbox": [
+            173,
+            895,
+            823,
+            924
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            171,
+            103,
+            823,
+            132
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Starting from a state $s _ { 1 }$ , the agent interacts with the environment for infinite number of time steps. At each time step, the agent observes state $s _ { t } \\in S$ , picks action $a _ { t } \\in \\mathcal A$ , and receives reward $r _ { t }$ ; the system then transits to next state $s _ { t + 1 }$ . ",
+        "bbox": [
+            174,
+            138,
+            823,
+            181
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Using the notations in Strehl et al. (2006), a policy $\\pi _ { t }$ refers to the non-stationary control policy of the algorithm since step $t$ . We use $V ^ { \\pi _ { t } } ( s )$ to denote the value function under policy $\\pi _ { t }$ , which is defined as $\\begin{array} { r } { V ^ { \\pi _ { t } } ( s ) = \\mathbb { E } \\bigl [ \\sum _ { i = 1 } ^ { \\infty } \\gamma ^ { i - 1 } r ( s _ { i } , \\pi _ { t + i - 1 } ( s _ { i } ) ) | s _ { 1 } = s \\bigr ] } \\end{array}$ . We also use $V ^ { * } ( s ) = \\operatorname* { s u p } _ { \\pi } V ^ { \\pi } ( s )$ to denote the value function of the optimal policy. Accordingly, we define $\\begin{array} { r } { \\mathbb { E } [ \\sum _ { i = 2 } ^ { \\infty } \\gamma ^ { i - 1 } r ( s _ { i } , \\pi _ { t + i - 1 } ( s _ { i } ) ) | s _ { 1 } = \\stackrel { \\cdot } { s } , a _ { 1 } = \\stackrel { \\cdot } { a } ] } \\end{array}$ as the $\\mathrm { Q }$ function under policy $Q ^ { \\pi _ { t } } ( s , a ) = r ( s , a ) +$ $\\pi _ { t }$ ; $Q ^ { * } ( s , a )$ is the Q function under optimal policy $\\pi ^ { * }$ . ",
+        "bbox": [
+            173,
+            186,
+            825,
+            272
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We use the sample complexity of exploration defined in Kakade et al. (2003) to measure the learning efficiency of our algorithm. This sample complexity definition has been widely used in previous works Strehl et al. (2006); Lattimore & Hutter (2012); Strehl $\\&$ Littman (2008). ",
+        "bbox": [
+            176,
+            279,
+            821,
+            320
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Definition 1. Sample complexity of Exploration of an algorithm $\\mathcal { A L G }$ is defined as the number of time steps t such that the non-stationary policy $\\pi _ { t }$ at time $t$ is not $\\epsilon$ -optimal for current state $s _ { t }$ , i.e. $\\dot { V } ^ { \\pi _ { t } } \\left( s _ { t } \\right) \\dot { < } V ^ { * } \\left( s _ { t } \\right) - \\epsilon .$ . ",
+        "bbox": [
+            173,
+            323,
+            826,
+            366
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Roughly speaking, this measure counts the number of mistakes along the whole trajectory. We use the following definition of PAC-MDP Strehl et al. (2006). ",
+        "bbox": [
+            174,
+            375,
+            823,
+            404
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Definition 2. An algorithm $\\mathcal { A L G }$ is said to be PAC-MDP (Probably Approximately Correct in Markov Decision Processes) $i f ,$ for any \u000f and $\\delta$ , the sample complexity of $\\mathcal { A L G }$ is less than some polynomial in the relevant quantities $( S , A , 1 / \\epsilon , 1 / \\delta , 1 / ( 1 - \\gamma ) )$ , with probability at least $1 - \\delta$ . ",
+        "bbox": [
+            173,
+            405,
+            825,
+            449
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Finally, recall that Bellman equation is defined as the following: ",
+        "bbox": [
+            174,
+            457,
+            593,
+            472
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/59cd62d5ec6d571803efed659b258dfba8d0141783a9422cc7a1cf15db20a44e.jpg",
+        "text": "$$\n\\left\\{ \\begin{array} { l l } { V ^ { \\pi _ { t } } ( s ) = Q ^ { \\pi _ { t } } \\left( s , \\pi _ { t } ( s ) \\right) } \\\\ { Q ^ { \\pi _ { t } } ( s , a ) : = \\left( r _ { t } + \\gamma \\mathbb { P } V ^ { \\pi _ { t + 1 } } \\right) ( s , a ) , } \\end{array} \\right. \\quad \\left\\{ \\begin{array} { l l } { V ^ { * } ( s ) = Q ^ { * } \\left( s , \\pi ^ { * } ( s ) \\right) } \\\\ { Q ^ { * } ( s , a ) : = \\left( r _ { t } + \\gamma \\mathbb { P } V ^ { * } \\right) ( s , a ) , } \\end{array} \\right.\n$$",
+        "text_format": "latex",
+        "bbox": [
+            232,
+            473,
+            754,
+            508
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "which is frequently used in our analysis. Here we denote $\\left[ \\mathbb { P } V ^ { \\pi _ { t } } \\right] ( s , a ) : = \\mathbb { E } _ { s ^ { \\prime } \\sim p ( \\cdot \\vert s , a ) } V ^ { \\pi _ { t + 1 } } ( s ^ { \\prime } ) .$ ",
+        "bbox": [
+            168,
+            508,
+            805,
+            525
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 MAIN RESULTS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            542,
+            336,
+            559
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section, we present the UCB Q-learning algorithm and the sample complexity bound. ",
+        "bbox": [
+            166,
+            573,
+            776,
+            589
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1 ALGORITHM ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            603,
+            303,
+            618
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 1 Infinite Q-learning with UCB ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            633,
+            455,
+            648
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Parameters: \u000f, γ, δ Initializ $\\begin{array} { r l } & { \\textnormal { \\texttt { e } } Q ( s , a ) , \\hat { Q } ( s , a ) \\gets \\frac { 1 } { 1 - \\gamma } , N ( s , a ) \\gets 0 , \\epsilon _ { 1 } \\gets \\frac { \\epsilon } { 2 4 R M \\ln \\frac { 1 } { 1 - \\gamma } } , H \\gets \\frac { \\ln 1 / ( ( 1 - \\gamma ) \\epsilon _ { 1 } ) } { \\ln 1 / \\gamma } . } \\\\ & { \\cdot ( k ) = \\ln ( S A ( k + 1 ) ( k + 2 ) / \\delta ) , \\alpha _ { k } = \\frac { H + 1 } { H + k } . } \\end{array}$ Define for $t = 1 , 2 , \\dots \\mathbf { d o }$   \n5: Take action $a _ { t } \\gets \\arg \\operatorname* { m a x } _ { a ^ { \\prime } } \\hat { Q } ( s _ { t } , a ^ { \\prime } )$ Receive reward rt and transit to st+1 $\\begin{array} { r l r } & { N ( s _ { t } , a _ { t } ) \\gets N ( s _ { t } , a _ { t } ) + 1 } & \\\\ & { N ( s _ { t } , a _ { t } ) \\gets N ( s _ { t } , a _ { t } ) + 1 } & \\\\ & { k \\gets N ( s _ { t } , a _ { t } ) , b _ { k } \\gets \\frac { c _ { 2 } } { 1 - \\gamma } \\sqrt { \\frac { H ( k ) } { k } } } & \\\\ & { \\hat { V } ( s _ { t + 1 } ) \\gets \\operatorname* { m a x } _ { a \\in A } \\hat { Q } ( s _ { t + 1 } , a ) } & \\\\ & { Q ( s _ { t } , a _ { t } ) \\gets ( 1 - \\alpha _ { k } ) Q ( s _ { t } , a _ { t } ) + \\alpha _ { k } \\left[ r ( s _ { t } , a _ { t } ) + b _ { k } + \\gamma \\hat { V } ( s _ { t + 1 } ) \\right] } \\\\ & { \\hat { Q } ( s _ { t } , a _ { t } ) \\gets \\operatorname* { m i n } ( \\hat { Q } ( s _ { t } , a _ { t } ) , Q ( s _ { t } , a _ { t } ) ) } & \\end{array}$ t and can be set to $4 { \\sqrt { 2 } }$   \n10: end for ",
+        "bbox": [
+            179,
+            651,
+            823,
+            859
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Here $c _ { 2 } = 4 \\sqrt { 2 }$ is a constant. $\\begin{array} { r } { R = \\lceil \\ln \\frac { 3 } { \\epsilon ( 1 - \\gamma ) } / ( 1 - \\gamma ) \\rceil } \\end{array}$ , while the choice of $M$ can be found in Section. 3.3. ${ \\cal { \\left( M = 0 \\left( \\ln 1 / ( 1 - \\gamma ) \\epsilon \\right) \\right) } }$ ). The learning rate is defined as $\\alpha _ { k } = ( H + 1 ) / ( H + k )$ . $H$ is chosen as $\\frac { \\ln { 1 } / ( ( 1 - \\gamma ) \\epsilon _ { 1 } ) } { \\ln { 1 } / \\gamma }$ , which satisfies $H \\leq \\frac { \\ln 1 / ( ( 1 - \\gamma ) \\epsilon _ { 1 } ) } { 1 - \\gamma }$ . ",
+        "bbox": [
+            174,
+            872,
+            825,
+            928
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Our UCB Q-learning algorithm (Algorithm 1) maintains an optimistic estimation of action value function $Q ( s , a )$ and its historical minimum value $\\hat { Q } ( s , a )$ . $N _ { t } ( s , a )$ denotes the number of times that $( s , a )$ is experienced before time step $t$ ; $\\tau ( s , a , k )$ denotes the time step $t$ at which $( s _ { t } , a _ { t } ) = ( s , a )$ for the $k$ -th time; if this state-action pair is not visited that many times, $\\tau ( s , a , k ) = \\infty$ . $Q _ { t } ( s , a )$ and $\\hat { Q } _ { t } ( s , a )$ denotes the $Q$ and $\\hat { Q }$ value of $( s , a )$ that the algorithm maintains when arriving at $s _ { t }$ respectively. ",
+        "bbox": [
+            173,
+            103,
+            825,
+            193
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2 SAMPLE COMPLEXITY OF EXPLORATION ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            213,
+            500,
+            228
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Our main result is the following sample complexity of exploration bound. ",
+        "bbox": [
+            174,
+            241,
+            656,
+            256
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Theorem 1. For any $\\epsilon > 0$ , $\\delta > 0 , 1 / 2 < \\gamma < 1$ , with probability $1 - \\delta$ , the sample complexity of exploration (i.e., the number of time steps t such that $\\pi _ { t }$ is not $\\epsilon$ -optimal at $s _ { t . }$ ) of Algorithm 1 is at most ",
+        "bbox": [
+            174,
+            261,
+            828,
+            304
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/cc2b5aa0f63178566f02139857adabb797f2f963feb35907fc51fd7501fb1693.jpg",
+        "text": "$$\n\\tilde { \\mathcal { O } } \\left( \\frac { S A \\ln { 1 / \\delta } } { \\epsilon ^ { 2 } \\left( 1 - \\gamma \\right) ^ { 7 } } \\right) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            433,
+            305,
+            563,
+            348
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $\\tilde { \\mathcal { O } }$ suppresses logarithmic factors of $1 / \\epsilon , 1 / ( 1 - \\gamma )$ and $S A$ . ",
+        "bbox": [
+            173,
+            357,
+            612,
+            375
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We first point out the obstacles for proving the theorem and reasons why the techniques in Jin et al.   \n(2018) do not directly apply here. We then give a high level description of the ideas of our approach. ",
+        "bbox": [
+            173,
+            387,
+            825,
+            416
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "One important issue is caused by the difference in the definition of sample complexity for finite and infinite horizon MDP. In finite horizon settings, sample complexity (and regret) is determined in the first $T$ timesteps, and only measures the performance at the initial state $s _ { 1 }$ (i.e. $( V ^ { * } - V ^ { \\pi } ) ( s _ { 1 } ) )$ . However, in the infinite horizon setting, the agent may enter under-explored regions at any time period, and sample complexity of exploration characterizes the performance at all states the agent enters. ",
+        "bbox": [
+            173,
+            421,
+            826,
+            506
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The following example clearly illustrates the key difference between infinite-horizon and finitehorizon. Consider an MDP with a starting state $s _ { 1 }$ where the probability of leaving $s _ { 1 }$ is $o ( T ^ { - 1 } )$ . In this case, with high probability, it would take more than $T$ timesteps to leave $s _ { 1 }$ . Hence, guarantees about the learning in the first $T$ timesteps or about the performance at $s _ { 1 }$ imply almost nothing about the number of mistakes the algorithm would make in the rest of the MDP (i.e. the sample complexity of exploration of the algorithm). As a result, the analysis for finite horizon MDPs cannot be directly applied to infinite horizon setting. ",
+        "bbox": [
+            174,
+            512,
+            825,
+            611
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "This calls for techniques for counting mistakes along the entire trajectory, such as those employed by Strehl et al. (2006). In particular, we need to establish convenient sufficient conditions for being $\\epsilon$ -optimal at timestep $t$ and state $s _ { t }$ , i.e. $V ^ { \\ast } ( s _ { t } ) - V ^ { \\pi _ { t } } ( s _ { t } ) \\leq \\epsilon$ . Then, bounding the number of violations of such conditions gives a bound on sample complexity. ",
+        "bbox": [
+            173,
+            617,
+            825,
+            674
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Another technical reason why the proof in Jin et al. (2018) cannot be directly applied to our problem is the following: In finite horizon settings, Jin et al. (2018) decomposed the learning error at episode $k$ and time $h$ as errors from a set of consecutive episodes before $k$ at time $h + 1$ using a clever design of learning rate. However, in the infinite horizon setting, this property does not hold. Suppose at time $t$ the agent is at state $s _ { t }$ and takes action $a _ { t }$ . Then the learning error at $t$ only depends on those previous time steps such that the agent encountered the same state as $s _ { t }$ and took the same action as $a _ { t }$ . Thus the learning error at time $t$ cannot be decomposed as errors from a set of consecutive time steps before $t$ , but errors from a set of non-consecutive time steps without any structure. Therefore, we have to control the sum of learning errors over an unstructured set of time steps. This makes the analysis more challenging. ",
+        "bbox": [
+            173,
+            680,
+            825,
+            820
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Now we give a brief road map of the proof of Theorem 1. Our first goal is to establish a sufficient condition so that $\\pi _ { t }$ learned at step $t$ is $\\epsilon$ -optimal for state $s _ { t }$ . As an intermediate step we show that a sufficient condition for $V ^ { * } ( s _ { t } ) - V ^ { \\pi _ { t } } ( s _ { t } ) \\leq \\epsilon$ is that $V ^ { \\ast } ( s _ { t ^ { \\prime } } ) - Q ^ { \\ast } ( s _ { t ^ { \\prime } } , a _ { t ^ { \\prime } } )$ is small for a few time steps $t ^ { \\prime }$ within an interval $[ t , t + R ]$ for a carefully chosen $R$ (Condition 1). Then we show the desired sufficient condition (Condition 2) implies Condition 1. We then bound the total number of bad time steps on which $V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } )$ is large for the whole MDP; this implies a bound on the number of violations of Condition 2. This in turn relies on a key technical lemma (Lemma 2). ",
+        "bbox": [
+            173,
+            825,
+            825,
+            924
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The remaining part of this section is organized as follows. We establish the sufficient condition for $\\epsilon$ -optimality in Section 3.3. The key lemma is presented in Section 3.4. Finally we prove Theorem 1 in Section 3.5. ",
+        "bbox": [
+            173,
+            103,
+            825,
+            146
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3 SUFFICIENT CONDITION FOR $\\epsilon$ -OPTIMALITY ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            162,
+            519,
+            178
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In this section, we establish a sufficient condition (Condition 2) for $\\epsilon$ -optimality at time step $t$ . ",
+        "bbox": [
+            173,
+            188,
+            789,
+            205
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For a fixed $s _ { t }$ , let TRAJ $( R )$ be the set of length- $R$ trajectories starting from $s _ { t }$ . Our goal is to give a sufficient condition so that $\\pi _ { t }$ , the policy learned at step $t$ , is $\\epsilon$ -optimal. For any $\\epsilon _ { 2 } > 0$ , define $\\begin{array} { r } { R : = \\lceil \\ln \\frac { 1 } { \\epsilon _ { 2 } ( 1 - \\gamma ) } / ( 1 - \\gamma ) \\rceil } \\end{array}$ . Denote $V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } )$ by $\\Delta _ { t }$ . We have ",
+        "bbox": [
+            174,
+            210,
+            826,
+            256
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/0a9ed2938f048cb014418095c8bf22495e13c88841960e9512dce70e6eff25c2.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\quad V ^ { * } ( s _ { t } ) - V ^ { \\pi } ( s _ { t } ) } \\\\ & { = V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) + Q ^ { * } ( s _ { t } , a _ { t } ) - V ^ { \\pi } ( s _ { t } ) } \\\\ & { = V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) + \\gamma \\mathbb { P } ( V ^ { * } - V ^ { \\pi } ) ( s _ { t } , \\pi _ { t } ( s _ { t } ) ) } \\\\ & { = V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) + \\gamma \\sum _ { s + 1 } ^ { \\infty } p ( s _ { t + 1 } | s _ { t } , \\pi _ { t } ( s _ { t } ) ) \\cdot [ V ^ { * } ( s _ { t + 1 } ) - Q ^ { * } ( s _ { t + 1 } , a _ { t + 1 } ) ] + } \\\\ & { \\quad \\Big . \\Big . \\Big . \\Big . \\Big . \\Big . } \\\\ & { \\quad \\quad \\Big .  \\gamma _ { s + 1 , s ^ { * } + 2 } \\mathrm { ~ } p ( s _ { t + 2 } | s _ { t + 1 } , \\pi _ { t + 1 } ( s _ { t + 1 } ) ) \\cdot p ( s _ { t + 1 } | s _ { t } , \\pi _ { t } ( s _ { t } ) ) \\big [ V ^ { * } ( s _ { t + 2 } ) - Q ^ { * } ( s _ { t + 2 } , a _ { t + 2 } ) \\Big ] } \\\\ & { \\quad \\quad \\cdot \\dots } \\\\ & { \\le \\epsilon _ { 2 } + \\displaystyle \\sum _ { s ^ { \\prime } = s ^ { \\prime } } p ( t r a _ { t } ) \\cdot [ \\frac { n - 1 } { \\lambda _ { 2 } } \\gamma ^ { 2 } \\Delta _ { t + 2 } ] , } \\\\ & { \\quad \\quad \\pi _ { s \\lambda ^ { ( 2 ) } ( L ) } ^ { R , a } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            202,
+            263,
+            792,
+            469
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where the last inequality holds because $\\frac { \\gamma ^ { R } } { 1 - \\gamma } \\leq \\epsilon _ { 2 }$ , which follows from the definition of $R$ ",
+        "bbox": [
+            173,
+            474,
+            763,
+            497
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For any fixed trajectory of length $R$ starting from $s _ { t }$ , consider the sequence $\\left( \\Delta _ { t ^ { \\prime } } \\right) _ { t \\leq t ^ { \\prime } < t + R }$ . Let $X _ { t } ^ { ( i ) }$ be the $i$ -th largest item of $\\left( \\Delta _ { t ^ { \\prime } } \\right) _ { t \\leq t ^ { \\prime } < t + R }$ . Rearranging Eq. (1), we obtain ",
+        "bbox": [
+            173,
+            506,
+            821,
+            540
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/353a318648b4e83bfc1d70cd63fedbd78d74dcde5d09d9484e43d06da944118d.jpg",
+        "text": "$$\nV ^ { \\ast } ( s _ { t } ) - V ^ { \\pi _ { t } } ( s _ { t } ) \\leq \\epsilon _ { 2 } + E _ { t r a j } \\left[ \\sum _ { i = 1 } ^ { R } \\gamma ^ { i - 1 } X _ { t } ^ { ( i ) } \\right] .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            331,
+            547,
+            666,
+            592
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We first prove that Condition 1 implies $\\epsilon$ -optimality at time step $t$ when $\\epsilon _ { 2 } = \\epsilon / 3$ ",
+        "bbox": [
+            173,
+            604,
+            705,
+            621
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Condition 1. Let $\\begin{array} { r } { \\xi _ { i } : = \\frac { 1 } { 2 ^ { i + 2 } } \\epsilon _ { 2 } \\left( \\ln \\frac { 1 } { 1 - \\gamma } \\right) ^ { - 1 } } \\end{array}$ . For all $0 \\leq i \\leq \\lfloor \\log _ { 2 } R \\rfloor$ ",
+        "bbox": [
+            173,
+            626,
+            638,
+            652
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/4c5556442dd84c67ed2f8017702e406cf2d4d5acde09b8b3242d907ec73dda13.jpg",
+        "text": "$$\nE [ X _ { t } ^ { ( 2 ^ { i } ) } ] \\leq \\xi _ { i } .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            447,
+            659,
+            549,
+            681
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Claim 1. If Condition $^ { l }$ is satisfied at time step $t$ , the policy $\\pi _ { t }$ is $\\epsilon$ -optimal at state $s _ { t }$ , i.e. $V ^ { \\ast } ( s _ { t } ) -$   \n$V ^ { \\pi _ { t } } ( s _ { t } ) \\leq \\epsilon$ . ",
+        "bbox": [
+            173,
+            688,
+            825,
+            718
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Proof. Note that $E [ X _ { t } ^ { ( 2 ^ { \\lfloor \\log _ { 2 } i \\rfloor } ) } ]$ t. Eq. (3) implies that for $X _ { t } ^ { ( i ) }$ is monotonically decreasing with respect to $1 / 2 < \\gamma < 1$ , $i$ . Therefore, $E [ X _ { t } ^ { ( i ) } ] \\ \\leq$ ",
+        "bbox": [
+            176,
+            733,
+            825,
+            773
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/62ba3bea0f084d11903c964028d906643070d34916bde88924637c5e08ea73d6.jpg",
+        "text": "$$\n\\begin{array} { r l } & { E \\left[ \\displaystyle \\sum _ { i = 1 } ^ { R } \\gamma ^ { i - 1 } X _ { t } ^ { ( i ) } \\right] = \\displaystyle \\sum _ { i = 1 } ^ { R } \\gamma ^ { i - 1 } E [ X _ { t } ^ { ( i ) } ] \\leq \\displaystyle \\sum _ { i = 1 } ^ { R } \\gamma ^ { i - 1 } E [ X _ { t } ^ { ( 2 ^ { \\lfloor \\log _ { 2 } i \\rfloor } ) } ] } \\\\ & { \\leq \\displaystyle \\sum _ { i = 1 } ^ { R } \\gamma ^ { i - 1 } 2 ^ { - \\lfloor \\log _ { 2 } i \\rfloor - 2 } \\epsilon _ { 2 } \\left( \\ln \\frac { 1 } { 1 - \\gamma } \\right) ^ { - 1 } \\leq \\displaystyle \\sum _ { i = 1 } ^ { R } \\frac { \\gamma ^ { i - 1 } } { i } \\epsilon _ { 2 } \\left( \\ln \\frac { 1 } { 1 - \\gamma } \\right) ^ { - 1 } \\leq 2 \\epsilon _ { 2 } , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            235,
+            779,
+            761,
+            867
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where the last inequality follows from the fact that $\\begin{array} { r } { \\sum _ { i = 1 } ^ { \\infty } \\frac { \\gamma ^ { i - 1 } } { i } = \\frac { 1 } { \\gamma } \\ln \\frac { 1 } { 1 - \\gamma } } \\end{array}$ and $\\gamma > 1 / 2$ ",
+        "bbox": [
+            169,
+            873,
+            754,
+            896
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Combining with Eq. 2, we have, $\\begin{array} { r } { V ^ { \\ast } ( s _ { t } ) - V ^ { \\pi _ { t } } ( s _ { t } ) \\leq \\epsilon _ { 2 } + E \\left[ \\sum _ { i = 1 } ^ { R } \\gamma ^ { i - 1 } X _ { t } ^ { ( i ) } \\right] \\leq 3 \\epsilon _ { 2 } = \\epsilon . } \\end{array}$ ",
+        "bbox": [
+            166,
+            901,
+            777,
+            928
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Next we show that given $i , t$ , Condition 2 implies Eq. (3). ",
+        "bbox": [
+            173,
+            102,
+            552,
+            119
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Condition 2. Define $L = \\lfloor \\log _ { 2 } R \\rfloor$ . Let $\\begin{array} { r } { M = \\operatorname* { m a x } \\left\\{ \\lceil 2 \\log _ { 2 } \\frac { 1 } { \\xi _ { L } ( 1 - \\gamma ) } \\rceil , 1 0 \\right\\} } \\end{array}$ , and $\\begin{array} { r } { \\eta _ { j } = \\frac { \\xi _ { i } } { M } \\cdot 2 ^ { j - 1 } } \\end{array}$ .   \nFor all $\\begin{array} { r } { \\because j \\le M , \\eta _ { j } \\operatorname* { P r } [ X _ { t } ^ { ( 2 ^ { i } ) } > \\eta _ { j - 1 } ] \\le \\frac { \\xi _ { i } } { M } , } \\end{array}$ . ",
+        "bbox": [
+            173,
+            122,
+            826,
+            169
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Claim 2. Given i, t, Eq. (3) holds if Condition 2 is satisfied. ",
+        "bbox": [
+            173,
+            171,
+            571,
+            186
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Proof. The reason behind the choice of $M$ is to ensure that $\\eta _ { M } > 1 / ( 1 - \\gamma )$ 1. It follows that, assuming Condition 2 holds, for $1 \\leq j \\leq M$ , ",
+        "bbox": [
+            169,
+            203,
+            826,
+            234
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/b1e98198c486d877466252bbfdd5d0afb8e4019bc37fc19f80c274168b0bb6a3.jpg",
+        "text": "$$\nE \\left[ { X _ { t } ^ { ( 2 ^ { i } ) } } \\right] = \\int _ { 0 } ^ { 1 / ( 1 - \\gamma ) } \\operatorname* { P r } \\left[ { X _ { t } ^ { ( 2 ^ { i } ) } } > x \\right] d x \\le \\eta _ { 1 } + \\sum _ { j = 2 } ^ { M } \\eta _ { j } \\operatorname* { P r } [ { X _ { t } ^ { ( 2 ^ { i } ) } } > \\eta _ { j - 1 } ] \\le \\xi _ { i } .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            227,
+            241,
+            769,
+            286
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Therefore, if a time step $t$ is not $\\epsilon _ { 2 }$ -optimal, there exists $0 \\leq i < \\lfloor \\log _ { 2 } R \\rfloor$ and $2 \\leq j \\leq M$ such that ",
+        "bbox": [
+            171,
+            327,
+            825,
+            343
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/7d918d021bc39256ac2de308ee455c6a54396bc36335cd0f685f840f0c5005d1.jpg",
+        "text": "$$\n\\eta _ { j } \\mathrm { P r } [ X _ { t } ^ { ( 2 ^ { i } ) } > \\eta _ { j - 1 } ] > \\frac { \\xi _ { i } } { M } .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            405,
+            349,
+            593,
+            381
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Now, the sample complexity can be bounded by the number of $( t , i , j )$ pairs that Eq. (4) is violated. Following the approach of Strehl et al. (2006), for a fixed $( i , j )$ -pair, instead of directly counting the number of time steps $t$ such that $\\begin{array} { r } { \\operatorname* { P r } [ X _ { t } ^ { ( 2 ^ { i } ) } > \\eta _ { j - 1 } ] > \\frac { \\xi _ { i } } { M \\eta _ { j } } } \\end{array}$ , we count the number of time steps that $X _ { t } ^ { ( 2 ^ { i } ) } > \\eta _ { j - 1 }$ . Lemma 1 provides an upper bound of the number of such $t$ . ",
+        "bbox": [
+            173,
+            387,
+            826,
+            460
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3.4 KEY LEMMAS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            477,
+            313,
+            491
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In this section, we present two key lemmas. Lemma 1 bounds the number of sub-optimal actions, which in turn, bounds the sample complexity of our algorithm. Lemma 2 bounds the weighted sum of learning error, i.e. $( \\hat { Q } _ { t } - Q ^ { * } ) ( s , a )$ , with the sum and maximum of weights. Then, we show that Lemma 1 follows from Lemma 2. ",
+        "bbox": [
+            173,
+            502,
+            826,
+            561
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Lemma 1. For fixed $t$ and $\\eta > 0$ , let ${ B } _ { \\eta } ^ { ( t ) }$ be the event that $\\begin{array} { r } { V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > \\frac { \\eta } { 1 - \\gamma } } \\end{array}$ in step t. If $\\eta > 2 \\epsilon _ { 1 }$ , then with probability at least $1 - \\delta / 2$ , ",
+        "bbox": [
+            171,
+            563,
+            825,
+            598
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/8e6137e01a7beea297bf95283d863b21a785d17463e6944e2efedb515bf7d808.jpg",
+        "text": "$$\n\\sum _ { t = 1 } ^ { t = \\infty } I \\left[ B _ { \\eta } ^ { ( t ) } \\right] \\leq \\frac { S A \\ln S A \\ln 1 / \\delta } { \\eta ^ { 2 } ( 1 - \\gamma ) ^ { 3 } } \\cdot p o l y l o g \\left( \\frac { 1 } { \\epsilon _ { 1 } } , \\frac { 1 } { 1 - \\gamma } \\right) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            303,
+            604,
+            691,
+            648
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $I [ \\cdot ]$ is the indicator function. ",
+        "bbox": [
+            174,
+            655,
+            405,
+            671
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Before presenting Lemma 2, we define a class of sequence that occurs in the proof. ",
+        "bbox": [
+            173,
+            683,
+            718,
+            698
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Definition 3. A sequence $( w _ { t } ) _ { t \\geq 1 }$ is said to be a $( C , w )$ -sequence for $C , w > 0$ , $i f 0 \\le w _ { t } \\le w$ for all $t \\geq 1$ , and $\\begin{array} { r } { \\sum _ { t \\geq 1 } w _ { t } \\leq C } \\end{array}$ . ",
+        "bbox": [
+            171,
+            702,
+            823,
+            733
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Lemma 2. For every $( C , w )$ -sequence $( w _ { t } ) _ { t \\geq 1 }$ , with probability $1 - \\delta / 2$ , the following holds: ",
+        "bbox": [
+            171,
+            737,
+            792,
+            755
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/576704e0ba7bc113c9eb1c2218a2bd6ace18a8d09188a27f397409e00cdaad49.jpg",
+        "text": "$$\n\\sum _ { t \\ge 1 } w _ { t } ( \\hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) \\le \\frac { C \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\frac { \\sqrt { w S A C \\ell ( C ) } } { ( 1 - \\gamma ) ^ { 2 . 5 } } + \\frac { w S A \\ln C } { ( 1 - \\gamma ) ^ { 3 } } \\ln \\frac { 1 } { ( 1 - \\gamma ) \\epsilon _ { 1 } } \\right) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            207,
+            779,
+            789,
+            821
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "$\\begin{array} { r } { \\ell ( C ) = \\iota ( C ) \\ln { \\frac { 1 } { ( 1 - \\gamma ) \\epsilon _ { 1 } } } } \\end{array}$ ",
+        "bbox": [
+            174,
+            838,
+            472,
+            859
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Proof of Lemma 2 is quite technical, and is therefore deferred to supplementary materials. ",
+        "bbox": [
+            169,
+            869,
+            764,
+            886
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Now, we briefly explain how to prove Lemma 1 with Lemma 2. (Full proof can be found in supplementary materials.) Note that since $\\hat { Q } _ { t } \\geq Q ^ { * }$ and $a _ { t } = \\arg \\operatorname* { m a x } _ { a } \\hat { Q } _ { t } ( s _ { t } , a )$ , ",
+        "bbox": [
+            173,
+            103,
+            825,
+            135
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "img_path": "images/e36c4bae9f64d8b170464eae13de7df006383d23275ffcf8d31e0711f7c4678a.jpg",
+        "text": "$$\nV ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) \\leq \\hat { Q } _ { t } ( s _ { t } , a _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            338,
+            137,
+            653,
+            156
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We now consider a set $J = \\{ t : \\ V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > \\eta ( 1 - \\gamma ) ^ { - 1 } \\}$ , and consider the $( | J | , 1 )$ - weight sequence defined by $w _ { t } ~ = ~ I \\left[ t \\in J \\right]$ . We can now apply Lemma 2 to weighted sum $\\begin{array} { r } { \\sum _ { t \\geq 1 } \\dot { w } _ { t } \\left[ \\bar { V } ^ { \\ast } ( s _ { t } ) - Q ^ { \\ast } ( s _ { t } , \\dot { a } _ { t } ) \\right] , } \\end{array}$ . On the one hand, this quantity is obviously at least $| J | \\bar { \\eta ( 1 - \\gamma ) } ^ { - 1 }$ . On the other hand, by lemma 2, it is upper bounded by the weighted sum of $( \\hat { Q } - Q ^ { * } ) ( s _ { t } , a _ { t } )$ . Thus we get ",
+        "bbox": [
+            173,
+            157,
+            826,
+            233
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "img_path": "images/dc3a723cc9eab16cf16971abf7bbf69938ee49002e529fdd61110b29bb930e71.jpg",
+        "text": "$$\n| J | \\eta ( 1 - \\gamma ) ^ { - 1 } \\leq \\frac { C \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\frac { \\sqrt { S A | J | \\ell ( | J | ) } } { ( 1 - \\gamma ) ^ { 2 . 5 } } + \\frac { w S A \\ln | J | } { ( 1 - \\gamma ) ^ { 3 } } \\ln \\frac { 1 } { ( 1 - \\gamma ) \\epsilon _ { 1 } } \\right) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            238,
+            234,
+            758,
+            276
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Now focus on the dependence on $| J |$ . The left-hand-side has linear dependence on $| J |$ , whereas the left-hand-side has a $\\tilde { \\mathcal { O } } \\left( \\sqrt { | J | } \\right)$ dependence. This allows us to solve out an upper bound on $| J |$ with quadratic dependence on $1 / \\eta$ . ",
+        "bbox": [
+            173,
+            279,
+            825,
+            332
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "3.5 PROOF FOR THEOREM 1 ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            347,
+            382,
+            361
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We prove the theorem by stitching Lemma 1 and Condition 2. ",
+        "bbox": [
+            173,
+            372,
+            578,
+            388
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Proof. (Proof for Theorem 1) ",
+        "bbox": [
+            174,
+            402,
+            372,
+            417
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "By lemma 1, for any $2 \\leq j \\leq M , \\sum _ { t = 1 } ^ { \\infty } I \\left[ V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > \\eta _ { j - 1 } \\right] \\leq C$ , where $C = \\frac { S A \\ln S A \\ln 1 / \\delta } { \\eta _ { j - 1 } ^ { 2 } ( 1 - \\gamma ) ^ { 5 } } \\cdot \\tilde { P } .$ ",
+        "bbox": [
+            174,
+            422,
+            733,
+            478
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Here $\\tilde { P }$ is a shorthand for polylog $\\begin{array} { r } { \\left( \\frac { 1 } { \\epsilon _ { 1 } } , \\frac { 1 } { 1 - \\gamma } \\right) } \\end{array}$ ",
+        "bbox": [
+            173,
+            481,
+            475,
+            506
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Let $A _ { t } = I [ X _ { t } ^ { ( 2 ^ { i } ) } \\geq \\eta _ { j - 1 } ]$ be a Bernoulli random variable, and $\\{ \\mathcal { F } _ { t } \\} _ { t \\ge 1 }$ be the filtration generated by random variables $\\bar { \\{ ( s _ { \\tau } , a _ { \\tau } ) : 1 \\leq \\tau \\leq t \\} }$ . Since $A _ { t }$ is $\\mathcal { F } _ { t + R }$ −measurable, for any $0 \\leq k < R$ , $\\{ \\dot { A } _ { k + t R } - E [ A _ { k + t R } \\ | \\ \\mathcal { F } _ { k + t R } ] \\} _ { t \\geq 0 }$ is a martingale difference sequence. For now, consider a fixed $0 \\leq k < R$ . By Azuma-Hoeffiding inequality, after $\\begin{array} { r } { T = \\mathcal { O } \\left( \\frac { C } { 2 ^ { i } } \\cdot \\frac { M \\eta _ { j } } { \\xi _ { i } } \\ln ( R M L ) \\right) } \\end{array}$ · M ηjξ ln(RM L)\u0011 time steps (if it happens that many times) with ",
+        "bbox": [
+            171,
+            512,
+            826,
+            597
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "img_path": "images/b83b246b4683938705ff27511cfa875c502578f40906ac3c2c49408d5a5881f3.jpg",
+        "text": "$$\n\\operatorname* { P r } \\left[ X _ { k + t R } ^ { ( 2 ^ { i } ) } \\geq \\eta _ { j - 1 } \\right] = \\mathbb { E } [ A _ { k + t R } ] > \\frac { \\xi _ { i } } { M \\eta _ { j } } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            354,
+            598,
+            642,
+            632
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "we have $\\textstyle \\sum _ { t } A _ { k + t R } \\geq C / 2 ^ { i }$ with probability at least $1 - \\delta / ( 2 M R L )$ . ",
+        "bbox": [
+            174,
+            633,
+            632,
+            651
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "On the other hand, if $A _ { k + t R }$ happens, within $[ k + t R , k + t R + R - 1 ]$ , there must be at least $2 ^ { i }$ time steps at which $V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > ^ { \\mathsf { ^ { * } } } \\eta _ { j - 1 }$ . The latter event happens at most $C$ times, and the $[ k + t R , k + t R + R - 1 ]$ are disjoint. Tppens at most erefore, times f $\\textstyle \\sum _ { t = 0 } ^ { \\infty } A _ { k + t R } \\leq C / 2 ^ { i }$ . This suggests that a union bound on $T$ $i$ $j$ $0 \\leq k < R$ , we can show that with probability $1 - \\delta / ( 2 M L )$ , there are at most $R T$ time steps where $\\mathrm { P r } \\left[ X _ { t } ^ { ( 2 ^ { i } ) } \\geq \\eta _ { j - 1 } \\right] > \\xi _ { i } / ( M \\eta _ { j } )$ . Thus, the number of sub-optimal steps is bounded by, ",
+        "bbox": [
+            173,
+            655,
+            826,
+            752
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "img_path": "images/19060e0af63eb5746ff2fa8e81a511f198a258681b5fb178d09da3690eab476b.jpg",
+        "text": "$$\n\\begin{array} { r l r } {  { \\sum _ { t = 1 } ^ { \\ell - 1 } I [ V ^ { * } ( s _ { t } ) - V ^ { \\pi _ { t } } ( s _ { t } ) > \\epsilon ] } } \\\\ & { \\leq \\sum _ { t = 1 } ^ { \\infty } \\sum _ { i = 0 } ^ { L } \\sum _ { j = 2 } ^ { M } I [ \\eta _ { j } \\operatorname* { P r } [ X _ { t } ^ { ( 2 ^ { i } ) } > \\eta _ { j - 1 } ] > \\frac { \\xi _ { i } } { M } ] = \\sum _ { i = 0 } ^ { L } \\sum _ { j = 2 } ^ { M } \\sum _ { t = 1 } ^ { \\infty } I [ \\operatorname* { P r } [ X _ { t } ^ { ( 2 ^ { i } ) } > \\eta _ { j - 1 } ] > \\frac { \\xi _ { i } } { \\eta _ { j } M } ] } \\\\ & { \\leq \\sum _ { i = 0 } ^ { L } \\sum _ { j = 2 } ^ { M } \\frac { S A M R \\ln 1 / \\delta \\ln S A } { \\eta _ { j } \\xi _ { i } \\cdot 2 ^ { i } ( 1 - \\gamma ) ^ { 5 } } \\tilde { P } \\leq \\sum _ { i = 0 } ^ { L } \\frac { S A \\cdot 2 ^ { i + 4 } \\ln S A \\ln 1 / \\delta } { \\epsilon _ { 2 } ^ { 2 } ( 1 - \\gamma ) ^ { 6 } } \\tilde { P } \\mathrm { ( B y ~ d e f i n i t i o n ~ o f } \\xi _ { i } \\mathrm { ~ a n d } \\eta _ { j } ) } \\\\ & { \\leq \\frac { S A R \\ln S A \\ln 1 / \\delta } { \\epsilon _ { 2 } ^ { 2 } ( 1 - \\gamma ) ^ { 6 } } \\tilde { P } \\leq \\frac { S A \\ln S A \\ln 1 / \\delta } { \\epsilon _ { 2 } ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\tilde { P } . } & { \\mathrm { ( B y ~ d e f i n i t i o n ~ o f } \\hbar ) } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            184,
+            762,
+            836,
+            926
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "It should be stressed that throughout the lines, $\\tilde { P }$ is a shorthand for an asymptotic expression, instead of an exact value. Our final choice of \u000f2 and \u000f1 are \u000f2 = \u000f3 , and \u000f1 = \u000f24RM ln . It is not hard 1−γ to see that $\\ln 1 / \\epsilon _ { 1 } = \\mathrm { p o l y } ( \\ln \\textstyle \\frac { 1 } { \\epsilon } , \\ln \\frac { 1 } { 1 - \\gamma } )$ . This immediately implies that with probability $1 - \\delta$ , the number of time steps such that $\\left( V ^ { * } - \\dot { V } ^ { \\pi } \\right) \\left( s _ { t } \\right) > \\epsilon$ is ",
+        "bbox": [
+            173,
+            102,
+            825,
+            171
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "equation",
+        "img_path": "images/112b2a0ff239fa280515807bb22278ab6c902bb4dd2bada09b6a5e780e0dcd78.jpg",
+        "text": "$$\n\\tilde { \\mathcal { O } } \\left( \\frac { S A \\ln 1 / \\delta } { \\epsilon ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\right) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            434,
+            176,
+            560,
+            212
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "where hidden factors are $\\begin{array} { r } { \\operatorname { p o l y } ( \\ln { \\frac { 1 } { \\epsilon } } , \\ln { \\frac { 1 } { 1 - \\gamma } } , \\ln S A ) } \\end{array}$ . ",
+        "bbox": [
+            173,
+            218,
+            511,
+            237
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4 DISCUSSION ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            253,
+            312,
+            271
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this section, we discuss the implication of our results, and present some interesting properties of our algorithm beyond its sample complexity bound. ",
+        "bbox": [
+            174,
+            286,
+            825,
+            315
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.1 COMPARISON WITH PREVIOUS RESULTS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            332,
+            490,
+            345
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Lower bound To the best of our knowledge, the current best lower bound for worst-case sample complexity is \u0010 SA\u000f2(1−γ)3 ln 1/δ\u0011 due to Lattimore & Hutter (2012). The gap between our results and this lower bound lies only in the dependence on $1 / ( 1 - \\gamma )$ and logarithmic terms of $\\mathrm { { } } ^ { \\mathrm { { 3 } } A , 1 / ( 1 - \\gamma ) }$ and $1 / \\epsilon$ . ",
+        "bbox": [
+            173,
+            357,
+            826,
+            424
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Model-free algorithms Previously, the best sample complexity bound for a model-free algorithm is $\\begin{array} { r } { \\tilde { \\mathcal O } \\left( \\frac { S A } { \\epsilon ^ { 4 } ( 1 - \\gamma ) ^ { 8 } } \\right) } \\end{array}$ (suppressing all logarithmic terms), achieved by Delayed Q-learning Strehl et al. (2006). Our results improve this upper bound by a factor of $\\frac { 1 } { \\epsilon ^ { 2 } ( 1 - \\gamma ) }$ , and closes the quadratic gap in $1 / \\epsilon$ between Delayed Q-learning’s result and the lower bound. In fact, the following theorem shows that UCB Q-learning can indeed outperform Delayed Q-learning. ",
+        "bbox": [
+            173,
+            429,
+            826,
+            515
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Theorem 2. There exists a family of MDPs with constant $S$ and $A$ , in which with probability $1 - \\delta$ , Delayed $Q$ -learning incurs sample complexity of exploration of $\\Omega \\left( \\frac { \\epsilon ^ { - 3 } } { \\ln ( 1 / \\delta ) } \\right)$ , assuming that $\\ln ( 1 / \\delta ) < \\epsilon ^ { - 2 }$ . ",
+        "bbox": [
+            173,
+            518,
+            825,
+            571
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The construction of this hard MDP family is given in the supplementary material. ",
+        "bbox": [
+            173,
+            582,
+            705,
+            598
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Model-based algorithms For model-based algorithms, better sample complexity results in infinite horizon settings have been claimed Szita & Szepesvári (2010). To the best of our knowledge, the best published result without further restrictions on MDPs is $\\begin{array} { r } { \\tilde { \\mathcal O } \\left( \\frac { S A } { \\epsilon ^ { 2 } ( 1 - \\gamma ) ^ { 6 } } \\right) } \\end{array}$ claimed by Szita & Szepesvári (2010), which is $( 1 - \\gamma )$ smaller than our upper bound. From the space complexity point of view, our algorithm is much more memory-efficient. Our algorithm stores $O ( S A )$ values, whereas the algorithm in Szita & Szepesvári (2010) needs $\\Omega ( S ^ { 2 } A )$ memory to store the transition model. ",
+        "bbox": [
+            173,
+            603,
+            826,
+            699
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.2 EXTENSION TO OTHER SETTINGS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            715,
+            442,
+            729
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Due to length limits, detailed discussion in this section is deferred to supplementary materials. ",
+        "bbox": [
+            173,
+            739,
+            790,
+            756
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Finite horizon MDP The sample complexity of exploration bounds of UCB Q-learning implies $\\tilde { \\mathcal { O } } \\left( \\epsilon ^ { - 2 } \\right)$ PAC sample complexity and a $\\bar { \\mathcal { O } } \\left( T ^ { 1 / 2 } \\right)$ regret bound in finite horizon MDPs. That is, our algorithm implies a PAC algorithm for finite horizon MDPs. We are not aware of reductions of the opposite direction (from finite horizon sample complexity to infinite horizon sample complexity of exploration). ",
+        "bbox": [
+            173,
+            761,
+            825,
+            834
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Regret The reason why our results can imply an $\\tilde { \\mathcal { O } } ( { \\sqrt { T } } )$ regret is that, after choosing $\\epsilon _ { 1 }$ , it follows from the argument of Theorem 1 that with probability $1 - \\delta$ , for all $\\epsilon _ { 2 } > \\tilde { \\mathcal { O } } ( \\epsilon _ { 1 } / ( 1 - \\gamma ) )$ , the number of $\\epsilon _ { 2 }$ -suboptimal steps is bounded by ",
+        "bbox": [
+            174,
+            840,
+            825,
+            887
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "equation",
+        "img_path": "images/4312c45d17cd6e06d125f0e95014a5792379fa26cd13205bd4de52e4ac033fac.jpg",
+        "text": "$$\n\\mathcal { O } \\left( \\frac { S A \\ln S A \\ln 1 / \\delta } { \\epsilon _ { 2 } ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\mathrm { p o l y l o g } \\left( \\frac { 1 } { \\epsilon _ { 1 } } , \\frac { 1 } { 1 - \\gamma } \\right) \\right) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            344,
+            893,
+            651,
+            929
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In contrast, Delayed Q-learning Strehl et al. (2006) can only give an upper bound on $\\epsilon _ { 1 }$ -suboptimal steps after setting parameter $\\epsilon _ { 1 }$ . ",
+        "bbox": [
+            173,
+            103,
+            823,
+            132
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            151,
+            318,
+            167
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Infinite-horizon MDP with discounted reward is a setting that is arguably more difficult than other popular settings, such as finite-horizon MDP. Previously, the best samby model-free reinforcement learning algorithms in this setting is $\\tilde { \\cal O } \\big ( { \\textstyle \\frac { S A } { \\epsilon ^ { 4 } ( 1 - \\gamma _ { _ { - } } ) ^ { 8 } } } \\big )$ y bound achieved, due to Delayed Q-learning Strehl et al. (2006). In this paper, we propose a variant of Q-learning that incorporates upper confidence bound, and show that it has a sample complexity of $\\begin{array} { r } { \\tilde { \\mathcal { O } } \\big ( \\frac { S A } { \\epsilon ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\big ) } \\end{array}$ . This matches the best lower bound except in dependence on $1 / ( 1 - \\gamma )$ and logarithmic factors. ",
+        "bbox": [
+            174,
+            183,
+            825,
+            277
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "6 ACKNOWLEDGEMENTS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            297,
+            395,
+            313
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "The authors thank Chi Jin and Chongjie Zhang for helpful discussions. This work is supported by National Basic Research Program of China (973 Program) (grant no. 2015CB352502), NSFC (61573026), BJNSF (L172037) and Beijing Acedemy of Artificial Intelligence. ",
+        "bbox": [
+            174,
+            328,
+            823,
+            371
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "REFERENCES ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            391,
+            287,
+            406
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Mohammad Gheshlaghi Azar, Remi Munos, Mohammad Ghavamzadeh, and Hilbert Kappen. Speedy q-learning. In Advances in neural information processing systems, 2011. ",
+        "bbox": [
+            174,
+            415,
+            823,
+            443
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Mohammad Gheshlaghi Azar, Ian Osband, and Rémi Munos. Minimax regret bounds for reinforcement learning. arXiv preprint arXiv:1703.05449, 2017. ",
+        "bbox": [
+            173,
+            452,
+            823,
+            481
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Ronen I. Brafman and Moshe Tennenholtz. R-max - a general polynomial time algorithm for near-optimal reinforcement learning. J. Mach. Learn. Res., 3:213–231, March 2003. ISSN 1532-4435. doi: 10.1162/153244303765208377. URL https://doi.org/10.1162/ 153244303765208377. ",
+        "bbox": [
+            174,
+            488,
+            826,
+            545
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Christoph Dann, Tor Lattimore, and Emma Brunskill. Unifying pac and regret: Uniform pac bounds for episodic reinforcement learning. In Advances in Neural Information Processing Systems, pp. 5713–5723, 2017. ",
+        "bbox": [
+            173,
+            554,
+            823,
+            597
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Eyal Even-Dar and Yishay Mansour. Learning rates for q-learning. Journal of Machine Learning Research, 5(Dec):1–25, 2003. ",
+        "bbox": [
+            173,
+            604,
+            823,
+            633
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Thomas Jaksch, Ronald Ortner, and Peter Auer. Near-optimal regret bounds for reinforcement learning. Journal of Machine Learning Research, 11(Apr):1563–1600, 2010. ",
+        "bbox": [
+            173,
+            642,
+            823,
+            672
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Chi Jin, Zeyuan Allen-Zhu, Sebastien Bubeck, and Michael I Jordan. Is q-learning provably efficient? In Advances in Neural Information Processing Systems, pp. 4864–4874, 2018. ",
+        "bbox": [
+            173,
+            680,
+            823,
+            710
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Sham Machandranath Kakade et al. On the sample complexity of reinforcement learning. PhD thesis, University of London London, England, 2003. ",
+        "bbox": [
+            173,
+            718,
+            825,
+            747
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Tor Lattimore and Marcus Hutter. Pac bounds for discounted mdps. In International Conference on Algorithmic Learning Theory, pp. 320–334. Springer, 2012. ",
+        "bbox": [
+            171,
+            755,
+            823,
+            785
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Volodymyr Mnih, Koray Kavukcuoglu, David Silver, Alex Graves, Ioannis Antonoglou, Daan Wierstra, and Martin Riedmiller. Playing atari with deep reinforcement learning. arXiv preprint arXiv:1312.5602, 2013. ",
+        "bbox": [
+            176,
+            791,
+            825,
+            835
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Volodymyr Mnih, Adria Puigdomenech Badia, Mehdi Mirza, Alex Graves, Timothy Lillicrap, Tim Harley, David Silver, and Koray Kavukcuoglu. Asynchronous methods for deep reinforcement learning. In International conference on machine learning, pp. 1928–1937, 2016. ",
+        "bbox": [
+            173,
+            843,
+            823,
+            887
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "John Schulman, Sergey Levine, Pieter Abbeel, Michael Jordan, and Philipp Moritz. Trust region policy optimization. In International Conference on Machine Learning, pp. 1889–1897, 2015. ",
+        "bbox": [
+            173,
+            895,
+            820,
+            924
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Aaron Sidford, Mengdi Wang, Xian Wu, Lin Yang, and Yinyu Ye. Near-optimal time and sample complexities for solving markov decision processes with a generative model. In Advances in Neural Information Processing Systems, pp. 5186–5196, 2018a. ",
+        "bbox": [
+            176,
+            103,
+            823,
+            146
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Aaron Sidford, Mengdi Wang, Xian Wu, and Yinyu Ye. Variance reduced value iteration and faster algorithms for solving markov decision processes. In Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 770–787. Society for Industrial and Applied Mathematics, 2018b. ",
+        "bbox": [
+            174,
+            155,
+            825,
+            212
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Alexander L Strehl and Michael L Littman. An analysis of model-based interval estimation for markov decision processes. Journal of Computer and System Sciences, 74(8):1309–1331, 2008. ",
+        "bbox": [
+            171,
+            219,
+            821,
+            250
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Alexander L Strehl, Lihong Li, Eric Wiewiora, John Langford, and Michael L Littman. Pac modelfree reinforcement learning. In Proceedings of the 23rd international conference on Machine learning, pp. 881–888. ACM, 2006. ",
+        "bbox": [
+            174,
+            257,
+            826,
+            301
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "István Szita and Csaba Szepesvári. Model-based reinforcement learning with nearly tight exploration complexity bounds. In Proceedings of the 27th International Conference on Machine Learning (ICML-10), pp. 1031–1038, 2010. ",
+        "bbox": [
+            174,
+            309,
+            825,
+            353
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "A PROOF OF LEMMA 1 ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            378,
+            379,
+            395
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Lemma 1. For fixed t and $\\eta > 0$ , let $B _ { \\eta } ^ { ( t ) }$ be the event that $\\begin{array} { r } { V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > \\frac { \\eta } { 1 - \\gamma } } \\end{array}$ in step t. If $\\eta > 2 \\epsilon _ { 1 }$ , then with probability at least $1 - \\delta / 2$ , ",
+        "bbox": [
+            171,
+            407,
+            825,
+            443
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "equation",
+        "img_path": "images/0b9f09a826319782774c08f51f81a7e3a19a570518937c623163e273091ef961.jpg",
+        "text": "$$\n\\sum _ { t = 1 } ^ { t = \\infty } I \\left[ B _ { \\eta } ^ { ( t ) } \\right] \\leq \\frac { S A \\ln S A \\ln 1 / \\delta } { \\eta ^ { 2 } ( 1 - \\gamma ) ^ { 3 } } \\cdot p o l y l o g \\left( \\frac { 1 } { \\epsilon _ { 1 } } , \\frac { 1 } { 1 - \\gamma } \\right) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            303,
+            449,
+            691,
+            492
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "where $I [ \\cdot ]$ is the indicator function. ",
+        "bbox": [
+            174,
+            498,
+            405,
+            513
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Proof. When $\\eta > 1$ the lemma holds trivially. Now consider the case that $\\eta \\leq 1$ . ",
+        "bbox": [
+            173,
+            527,
+            704,
+            545
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Let $\\begin{array} { r } { I = \\{ t \\colon V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > \\frac { \\eta } { 1 - \\gamma } \\} } \\end{array}$ . By lemma 2, with probability $1 - \\delta$ ",
+        "bbox": [
+            173,
+            549,
+            702,
+            568
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "equation",
+        "img_path": "images/c3600e24303e29ac9ff643f0f4892a82d147d38d65c5111e6d8ac103703617e6.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\frac { \\eta | I | } { 1 - \\gamma } \\leq \\displaystyle \\sum _ { t \\in I } \\left( V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) \\right) \\leq \\displaystyle \\sum _ { t \\in I } \\left[ \\left( \\hat { Q } _ { t } - Q ^ { * } \\right) ( s _ { t } , a _ { t } ) \\right] } \\\\ & { \\qquad \\leq \\displaystyle \\frac { | I | \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\frac { 1 } { ( 1 - \\gamma ) ^ { 5 / 2 } } \\sqrt { S A | I | \\ell | ( I | ) } + \\frac { S A } { ( 1 - \\gamma ) ^ { 3 } } \\ln | I | \\ln \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\right) } \\\\ & { \\qquad \\leq \\displaystyle \\frac { | I | \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\ln \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\cdot \\left( \\frac { \\sqrt { S A | I | \\ln \\frac { S A | I | } { \\delta } } } { ( 1 - \\gamma ) ^ { 5 / 2 } } + \\frac { S A \\ln | I | } { ( 1 - \\gamma ) ^ { 3 } } \\right) \\right) } \\\\ & { \\qquad \\leq \\displaystyle \\frac { | I | \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\sqrt { \\ln \\frac { 1 } { \\delta } } \\ln \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\cdot \\left( \\frac { \\sqrt { S A | I | \\ln S A | I | } } { ( 1 - \\gamma ) ^ { 5 / 2 } } + \\frac { S A \\ln | I | } { ( 1 - \\gamma ) ^ { 3 } } \\right) \\right) } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            225,
+            577,
+            771,
+            747
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Suppose that $\\begin{array} { r } { | I | = \\frac { S A k ^ { 2 } } { \\eta ^ { 2 } ( 1 - \\gamma ) ^ { 3 } } \\ln S A } \\end{array}$ , for some $k > 1$ . Then it follows that for some constant $C _ { 1 }$ , ",
+        "bbox": [
+            173,
+            779,
+            795,
+            800
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "equation",
+        "img_path": "images/c06bd9e11a4120e53c0b8d2cd822906d72211ae50589d30086bcbaef0151ca3a.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\frac { \\eta | I | } { 1 - \\gamma } = \\cfrac { k ^ { 2 } S A \\ln S A } { ( 1 - \\gamma ) ^ { 4 } \\eta } \\leq 2 \\cfrac { ( \\eta - \\epsilon _ { 1 } ) | I | } { 1 - \\gamma } } \\\\ & { \\qquad \\leq C _ { 1 } \\sqrt { \\ln \\frac { 1 } { \\delta } } \\ln \\cfrac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\left( \\cfrac { \\sqrt { S A | I | \\ln \\left( S A | I | \\right) } } { ( 1 - \\gamma ) ^ { 5 / 2 } } + \\cfrac { S A \\ln | I | } { ( 1 - \\gamma ) ^ { 3 } } \\right) } \\\\ & { \\qquad \\leq C _ { 1 } \\sqrt { \\ln \\frac { 1 } { \\delta } } \\ln \\cfrac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\left( \\cfrac { S A k } { \\eta ( 1 - \\gamma ) ^ { 4 } } \\sqrt { \\ln S A \\cdot ( \\ln S A + \\ln | I | ) } + \\cfrac { S A \\ln | I | } { ( 1 - \\gamma ) ^ { 3 } } \\right) . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            209,
+            806,
+            789,
+            925
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Therefore ",
+        "bbox": [
+            173,
+            103,
+            240,
+            118
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "equation",
+        "img_path": "images/bae465b19e019059a91e97016934af5f7bf0c47e9357a7ca6741dfa6dd715015.jpg",
+        "text": "$$\n\\begin{array} { r l } & { k ^ { 2 } \\ln ( S A ) \\le C _ { 1 } \\sqrt { \\ln \\displaystyle \\frac { 1 } { \\delta } } \\ln \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\left( k \\left( \\ln S A + \\ln | I | \\right) + \\eta ( 1 - \\gamma ) \\ln | I | \\right) } \\\\ & { \\qquad \\le k C _ { 1 } \\sqrt { \\ln \\displaystyle \\frac { 1 } { \\delta } } \\ln \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\cdot \\left( \\ln S A + 2 \\ln | I | \\right) } \\\\ & { \\qquad \\le k C _ { 1 } \\sqrt { \\ln \\displaystyle \\frac { 1 } { \\delta } } \\ln \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\cdot \\left( 3 \\ln S A + 4 \\ln k + 6 \\ln \\frac { 1 } { \\eta ( 1 - \\gamma ) } \\right) } \\\\ & { \\qquad \\le 6 k C _ { 1 } \\sqrt { \\ln \\displaystyle \\frac { 1 } { \\delta } } \\ln ^ { 2 } \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\left( \\ln S A + \\ln \\epsilon k \\right) . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            245,
+            122,
+            753,
+            273
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Let $\\begin{array} { r } { C ^ { \\prime } = \\operatorname* { m a x } \\lbrace 2 , 6 C _ { 1 } \\sqrt { \\ln \\frac { 1 } { \\delta } } \\ln ^ { 2 } \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\rbrace } \\end{array}$ . Then ",
+        "bbox": [
+            171,
+            280,
+            495,
+            304
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "equation",
+        "img_path": "images/6648dce62ed22bd5032b6259b54c85d35efee676cf37255340a1199f339eda3d.jpg",
+        "text": "$$\nk \\leq C ^ { \\prime } ( 2 + \\ln k ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            437,
+            310,
+            560,
+            330
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "If $k \\geq 1 0 C ^ { \\prime } \\ln C ^ { \\prime }$ , then ",
+        "bbox": [
+            173,
+            335,
+            328,
+            351
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "equation",
+        "img_path": "images/4ae996b10596e3c7079276b4b960d96f44d70fb21ef5f209a0ea7326b6d16c83.jpg",
+        "text": "$$\n\\begin{array} { c } { k - C ^ { \\prime } \\left( 2 + \\ln k \\right) \\geq 8 C ^ { \\prime } \\ln C ^ { \\prime } - ( 2 + \\ln 1 0 ) C ^ { \\prime } } \\\\ { \\geq 4 C ^ { \\prime } \\left( 2 \\ln C ^ { \\prime } - 4 \\right) \\geq 0 , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            341,
+            356,
+            655,
+            397
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "which means violation of (9). Therefore, since $C ^ { \\prime } \\geq 2$ ",
+        "bbox": [
+            173,
+            401,
+            532,
+            416
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "equation",
+        "img_path": "images/3659eb39bbdbcc0c60a416911c59460e57107ec3dbd0e6f62d3b7b93a525422e.jpg",
+        "text": "$$\nk \\leq 1 0 C ^ { \\prime } \\ln C ^ { \\prime } \\leq 3 6 0 C _ { 1 } ^ { 2 } \\operatorname* { m a x } \\{ \\ln ^ { 4 } { \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } } , 2 0 \\ln 2 \\} .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            315,
+            421,
+            681,
+            455
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "It immediately follows that ",
+        "bbox": [
+            173,
+            462,
+            354,
+            476
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "equation",
+        "img_path": "images/ad528682451c2a80d59b5c6f1508b5b7b9f26c92e6092f8aeb71c929441cec39.jpg",
+        "text": "$$\n\\begin{array} { r l r } {  { \\vert I \\vert = \\frac { S A k ^ { 2 } } { \\eta ^ { 2 } ( 1 - \\gamma ) ^ { 3 } } \\ln S A } } \\\\ & { \\leq \\frac { S A \\ln S A } { \\eta ^ { 2 } ( 1 - \\gamma ) ^ { 5 } } \\cdot \\ln \\frac { 1 } { \\delta } \\cdot \\mathcal { O } ( \\ln ^ { 8 } \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } ) . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            343,
+            482,
+            655,
+            555
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "B PROOF OF LEMMA 2 ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            602,
+            380,
+            618
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Lemma 2. For every $( C , w )$ -sequence $( w _ { t } ) _ { t \\geq 1 }$ , with probability $1 - \\delta / 2$ , the following holds: ",
+        "bbox": [
+            168,
+            632,
+            790,
+            650
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "equation",
+        "img_path": "images/ff487b4def18b98c770f155f72c7d52760fabc4d6097e5e050552ffa5fb8baab.jpg",
+        "text": "$$\n\\sum _ { t \\ge 1 } w _ { t } ( \\hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) \\le \\frac { C \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\frac { \\sqrt { w S A C \\ell ( C ) } } { ( 1 - \\gamma ) ^ { 2 . 5 } } + \\frac { w S A \\ln C } { ( 1 - \\gamma ) ^ { 3 } } \\ln \\frac { 1 } { ( 1 - \\gamma ) \\epsilon _ { 1 } } \\right) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            209,
+            674,
+            787,
+            717
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "where $\\begin{array} { r } { \\ell ( C ) = \\iota ( C ) \\ln { \\frac { 1 } { ( 1 - \\gamma ) \\epsilon _ { 1 } } } } \\end{array}$ is a log-factor. ",
+        "bbox": [
+            174,
+            732,
+            472,
+            752
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Fact 1. (1) The following statement holds throughout the algorithm, ",
+        "bbox": [
+            173,
+            755,
+            622,
+            770
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "equation",
+        "img_path": "images/33f263fc3dd14df50727d4ef76ef6c4ffe1d222ffa11393ce94b14974de75afd.jpg",
+        "text": "$$\n\\hat { Q } _ { p + 1 } ( s , a ) \\leq Q _ { p + 1 } ( s , a ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            410,
+            776,
+            586,
+            797
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "(2) For any $p$ , there exists $p ^ { \\prime } \\leq p$ such that ",
+        "bbox": [
+            173,
+            803,
+            452,
+            818
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "equation",
+        "img_path": "images/6fac3e0bba44afb720a787e2593dcafd19d5e03a7a0d6878331dbb6aecc146fa.jpg",
+        "text": "$$\n{ \\hat { Q } } _ { p + 1 } ( s , a ) \\geq Q _ { p ^ { \\prime } + 1 } ( s , a ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            408,
+            824,
+            588,
+            844
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Proof. Both properties are results of the update rule at line 11 of Algorithm 1. ",
+        "bbox": [
+            173,
+            858,
+            686,
+            875
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Before proving lemma 2, we will prove two auxiliary lemmas. ",
+        "bbox": [
+            171,
+            890,
+            583,
+            906
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Lemma 3. The following properties hold for $\\alpha _ { t } ^ { i }$ : ",
+        "bbox": [
+            174,
+            909,
+            498,
+            924
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "1. $\\begin{array} { r } { \\sqrt { \\frac { 1 } { t } } \\leq \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\sqrt { \\frac { 1 } { i } } \\leq 2 \\sqrt { \\frac { 1 } { t } } } \\end{array}$ for every $t \\geq 1 , c > 0$ . ",
+        "bbox": [
+            210,
+            99,
+            576,
+            127
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "2. $\\begin{array} { r } { \\operatorname* { m a x } _ { i \\in [ t ] } \\alpha _ { t } ^ { i } \\leq \\frac { 2 H } { t } } \\end{array}$ and $\\begin{array} { r } { \\sum _ { i = 1 } ^ { t } ( \\alpha _ { t } ^ { i } ) ^ { 2 } \\le \\frac { 2 H } { t } } \\end{array}$ for every $t \\geq 1$ ",
+        "bbox": [
+            210,
+            133,
+            611,
+            155
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "3. $\\textstyle \\sum _ { t = i } ^ { \\infty } \\alpha _ { t } ^ { i } = 1 + 1 / H$ , for every $i \\geq 1$ ",
+        "bbox": [
+            210,
+            161,
+            480,
+            179
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Proof. Recall that ",
+        "bbox": [
+            173,
+            227,
+            295,
+            242
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "equation",
+        "img_path": "images/242c5979af7b492fba1d80135236539576c26cc515f271d589d39be0ce0b496a.jpg",
+        "text": "$$\n\\alpha _ { t } = \\frac { H + 1 } { H + t } , \\quad \\alpha _ { t } ^ { 0 } = \\prod _ { j = 1 } ^ { t } ( 1 - \\alpha _ { j } ) , \\quad \\alpha _ { t } ^ { i } = \\alpha _ { i } \\prod _ { j = i + 1 } ^ { t } ( 1 - \\alpha _ { j } ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            292,
+            246,
+            705,
+            290
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Properties 1-3 are proven by Jin et al. (2018). Now we prove the last property. ",
+        "bbox": [
+            173,
+            294,
+            686,
+            309
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "On the one hand, ",
+        "bbox": [
+            173,
+            315,
+            287,
+            330
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "equation",
+        "img_path": "images/07ae804a6b110033f8bf12b32de163cad5567ec4167d97952b977363794b7bc4.jpg",
+        "text": "$$\n\\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\sqrt { \\frac { \\iota ( i ) } { i } } \\leq \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\sqrt { \\frac { \\iota ( t ) } { i } } \\leq 2 \\sqrt { \\frac { \\iota ( t ) } { t } } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            357,
+            327,
+            637,
+            369
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "where the last inequality follows from property 1. ",
+        "bbox": [
+            173,
+            371,
+            500,
+            386
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "The left-hand side is proven by induction on $t$ . For the base case, when $t = 1 , \\alpha _ { t } ^ { t } = 1$ . For $t \\geq 2$ , we have $\\alpha _ { t } ^ { i } = ( 1 - \\alpha _ { t } ) \\dot { \\alpha _ { t - 1 } ^ { i } }$ for $1 \\leq i \\leq t - 1$ . It follows that ",
+        "bbox": [
+            173,
+            391,
+            825,
+            420
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "equation",
+        "img_path": "images/ab4e05f21481995ad7b6907c39b07eca8dcf1b1707af7599ec0fb0ba9984a116.jpg",
+        "text": "$$\n\\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\sqrt { \\frac { \\iota ( i ) } { i } } = \\alpha _ { t } \\sqrt { \\frac { \\iota ( t ) } { t } } + ( 1 - \\alpha _ { t } ) \\sum _ { i = 1 } ^ { t - 1 } \\alpha _ { t - 1 } ^ { i } \\sqrt { \\frac { \\iota ( i ) } { i } } \\geq \\alpha _ { t } \\sqrt { \\frac { \\iota ( t ) } { t } } + ( 1 - \\alpha _ { t } ) \\sqrt { \\frac { \\iota ( t - 1 ) } { t - 1 } } .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            199,
+            425,
+            795,
+            469
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Since function $f ( t ) = \\iota ( t ) / t$ is monotonically decreasing for $t \\geq 1 , c \\geq 1$ , we have ",
+        "bbox": [
+            173,
+            473,
+            720,
+            489
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "equation",
+        "img_path": "images/7a7308ee3372dff7c4a6c3cae36090077c647b119d15a408f894359ff305977f.jpg",
+        "text": "$$\n\\alpha _ { t } \\sqrt { \\frac { \\iota ( t ) } { t } } + ( 1 - \\alpha _ { t } ) \\sqrt { \\frac { \\iota ( t - 1 ) } { t - 1 } } \\geq \\alpha _ { t } \\sqrt { \\frac { \\iota ( t ) } { t } } + ( 1 - \\alpha _ { t } ) \\sqrt { \\frac { \\iota ( t ) } { t } } \\geq \\sqrt { \\frac { \\iota ( t ) } { t } } .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            253,
+            492,
+            743,
+            529
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Lemma 4. With probability at least $1 - \\delta / 2$ , for all $p \\geq 0$ and $( s , a )$ -pair, ",
+        "bbox": [
+            171,
+            553,
+            661,
+            570
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "equation",
+        "img_path": "images/bf1a7588fbf4d42939d18d2d26129510541081c72f7d186c33706ba60d0c68e1.jpg",
+        "text": "$$\n\\begin{array} { r l } & { 0 \\le ( Q _ { p } - Q ^ { * } ) ( s , a ) \\le \\displaystyle \\frac { \\alpha _ { t } ^ { 0 } } { 1 - \\gamma } + \\displaystyle \\sum _ { i = 1 } ^ { t } \\gamma \\alpha _ { t } ^ { i } ( { \\hat { V } } _ { t _ { i } } - V ^ { * } ) ( s _ { t _ { i } + 1 } ) + \\beta _ { t } , } \\\\ & { 0 \\le ( { \\hat { Q } } _ { p } - Q ^ { * } ) ( s , a ) , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            277,
+            574,
+            717,
+            638
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "where $t = N _ { p } ( s , a ) , t _ { i } = \\tau ( s , a , i )$ and $\\beta _ { t } = c _ { 3 } \\sqrt { H \\iota ( t ) / ( ( 1 - \\gamma ) ^ { 2 } t ) }$ . ",
+        "bbox": [
+            174,
+            643,
+            630,
+            661
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Proof. Recall that ",
+        "bbox": [
+            173,
+            674,
+            295,
+            689
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "equation",
+        "img_path": "images/88278a9f30fd7a368323e468f5e3ad316e4a238d906d20218881efa56614124b.jpg",
+        "text": "$$\n\\alpha _ { t } ^ { 0 } = \\prod _ { j = 1 } ^ { t } ( 1 - \\alpha _ { j } ) , \\quad \\alpha _ { t } ^ { i } = \\alpha _ { i } \\prod _ { j = i + 1 } ^ { t } ( 1 - \\alpha _ { j } ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            346,
+            686,
+            650,
+            731
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "From the update rule, it can be seen that our algorithm maintains the following $Q ( s , a )$ : ",
+        "bbox": [
+            171,
+            733,
+            746,
+            748
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "equation",
+        "img_path": "images/1b23fc9ed7edc8e4d294bbfadc8232c0e3a3f7ae514e3b0f9f7eb6f05a9180e4.jpg",
+        "text": "$$\nQ _ { p } ( s , a ) = \\alpha _ { t } ^ { 0 } \\frac { 1 } { 1 - \\gamma } + \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\left[ r ( s , a ) + b _ { i } + \\gamma \\hat { V } _ { t _ { i } } ( s _ { t _ { i } + 1 } ) \\right] .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            297,
+            752,
+            700,
+            795
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Bellman optimality equation gives: ",
+        "bbox": [
+            173,
+            799,
+            405,
+            814
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "equation",
+        "img_path": "images/7f3af02c43fff8510d8c8a82457783c482e400b5602396a1f237a333d06d0211.jpg",
+        "text": "$$\nQ ^ { * } ( s , a ) = r ( s , a ) + \\gamma \\mathbb { P } V ^ { * } ( s , a ) = \\alpha _ { t } ^ { 0 } Q ^ { * } ( s , a ) + \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\left[ r ( s , a ) + \\gamma \\mathbb { P } V ^ { * } ( s , a ) \\right] .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            228,
+            818,
+            767,
+            861
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Subtracting the two equations gives ",
+        "bbox": [
+            174,
+            864,
+            408,
+            880
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "equation",
+        "img_path": "images/4daae5a78519cf382ebb3c39463504ef4bdc6c481b0042a0fad9b5891adc01b0.jpg",
+        "text": "$$\nQ _ { p } - Q ^ { * } ) ( s , a ) = \\alpha _ { t } ^ { 0 } ( \\frac { 1 } { 1 - \\gamma } - Q ^ { * } ( s , a ) ) + \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\left[ b _ { i } + \\gamma \\left( V _ { t _ { i } } - V ^ { * } \\right) \\left( s _ { t _ { i } + 1 } \\right) + \\gamma \\left( V ^ { * } \\left( s _ { t _ { i } + 1 } \\right) - \\mathbb { P } V ^ { * } \\right) \\right] ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            181,
+            883,
+            839,
+            926
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "The identity above holds for arbitrary $p , s$ and $a$ . Now fix $s \\in S$ , $a \\in A$ and $p \\in \\mathbb N$ . Let $t = N _ { p } ( s , a )$ , $t _ { i } = \\tau ( s , a , i )$ . The $t = 0$ case is trivial; we assume $t \\geq 1$ below. Now consider an arbitrary fixed $k$ . Define ",
+        "bbox": [
+            173,
+            103,
+            826,
+            145
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "equation",
+        "img_path": "images/7ed6137165be41b2ad3ac59dec10e06c5f86c9778d1953d9a7904ac5097d5be4.jpg",
+        "text": "$$\n\\Delta _ { i } = \\left( \\alpha _ { k } ^ { i } \\cdot I [ t _ { i } < \\infty ] \\cdot \\left( \\mathbb { P } V ^ { * } - \\mathbb { \\hat { P } } _ { t _ { i } } V ^ { * } \\right) ( s , a ) \\right)\n$$",
+        "text_format": "latex",
+        "bbox": [
+            336,
+            145,
+            660,
+            172
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Let $F _ { i }$ be the $\\sigma$ -Field generated by random variables $( s _ { 1 } , a _ { 1 } , . . . , s _ { t _ { i } } , a _ { t _ { i } } )$ . It can be seen that $\\mathbb { E } \\left[ \\Delta _ { i } | F _ { i } \\right] = 0$ , while $\\Delta _ { i }$ is measurable in $F _ { i + 1 }$ . Also, since $\\textstyle 0 \\leq V ^ { \\ast } ( s , { \\bar { a } } ) \\leq { \\frac { 1 } { 1 - \\gamma } }$ , $\\begin{array} { r } { | \\Delta _ { i } | \\le \\frac { 2 } { 1 - \\gamma } } \\end{array}$ . Therefore, $\\Delta _ { i }$ is a martingale difference sequence; by the Azuma-Hoeffding inequality, ",
+        "bbox": [
+            173,
+            174,
+            828,
+            219
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "equation",
+        "img_path": "images/e1fd0592f2fbfb43a68fa1b2348697afc8a3b51894eb01a3c12dfc2769dfd098.jpg",
+        "text": "$$\n\\mathrm { P r } \\left[ \\left| \\sum _ { i = 1 } ^ { k } \\Delta _ { i } \\right| > \\eta \\right] \\leq 2 \\exp \\left\\{ - \\frac { \\eta ^ { 2 } } { 8 \\left( 1 - \\gamma \\right) ^ { - 2 } \\sum _ { i = 1 } ^ { k } ( \\alpha _ { k } ^ { i } ) ^ { 2 } } \\right\\} .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            299,
+            220,
+            699,
+            265
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "By choosing $\\eta$ , we can show that with probability $1 - \\delta / \\left[ S A ( k + 1 ) ( k + 2 ) \\right]$ , ",
+        "bbox": [
+            173,
+            266,
+            687,
+            282
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "equation",
+        "img_path": "images/4635fc976e34fd23da44f8967bc69d839d0dafaecc85d492653e8f8184e7782e.jpg",
+        "text": "$$\n\\left| \\sum _ { i = 1 } ^ { k } \\Delta _ { i } \\right| \\leq \\frac { 2 \\sqrt { 2 } } { 1 - \\gamma } \\cdot \\sqrt { \\sum _ { i = 1 } ^ { k } ( \\alpha _ { k } ^ { i } ) ^ { 2 } \\cdot \\ln \\frac { 2 ( k + 1 ) ( k + 2 ) S A } { \\delta } } \\leq \\frac { c _ { 2 } } { 1 - \\gamma } \\sqrt { \\frac { H \\iota ( k ) } { k } } .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            241,
+            304,
+            753,
+            352
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Here $c _ { 2 } = 4 \\sqrt { 2 }$ , $\\begin{array} { r } { \\iota ( k ) = \\ln { \\frac { ( k + 1 ) ( k + 2 ) S A } { \\delta } } } \\end{array}$ . By a union bound for all $k$ , this holds for arbitrary $k > 0$ arbitrary $s \\in S , a \\in A$ simultaneously with probability ",
+        "bbox": [
+            176,
+            354,
+            826,
+            386
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "equation",
+        "img_path": "images/d36f303c3c54ca211346b95b702c878d2e496acc0473679ca8912f1c49bc42a5.jpg",
+        "text": "$$\n1 - \\sum _ { s ^ { \\prime } \\in S , a ^ { \\prime } \\in A } \\sum _ { k = 1 } ^ { \\infty } \\frac { \\delta } { 2 S A ( k + 1 ) ( k + 2 ) } = 1 - \\frac { \\delta } { 2 } .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            334,
+            387,
+            660,
+            430
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Therefore, we conclude that (16) holds for the random variable $t = N _ { p } ( s , a )$ and for all $p$ , with probability $1 - \\delta / 2$ as well. ",
+        "bbox": [
+            173,
+            433,
+            823,
+            462
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Proof of the right hand side of (13): We also know that $\\begin{array} { r } { ( b _ { k } = \\frac { c _ { 2 } } { 1 - \\gamma } \\sqrt { \\frac { H \\iota ( k ) } { k } } ) } \\end{array}$ ",
+        "bbox": [
+            173,
+            470,
+            683,
+            493
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "equation",
+        "img_path": "images/881fb37a93a36ca33279a8cb7352a55121d9d63aa62473943680b180547b1336.jpg",
+        "text": "$$\n\\frac { c _ { 2 } } { 1 - \\gamma } \\sqrt { \\frac { H \\iota ( k ) } { k } } \\leq \\sum _ { i = 1 } ^ { k } \\alpha _ { k } ^ { i } b _ { i } \\leq \\frac { 2 c _ { 2 } } { 1 - \\gamma } \\sqrt { \\frac { H \\iota ( k ) } { k } } .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            339,
+            496,
+            655,
+            539
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "It is implied by (16) that ",
+        "bbox": [
+            173,
+            540,
+            336,
+            555
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "equation",
+        "img_path": "images/d2bbc005947d28dd95e009c07818fe62e6d9b1e5309a47331c5537b6fbe06992.jpg",
+        "text": "$$\n\\begin{array} { r l } & { ( Q _ { p } - Q ^ { * } ) ( s , a ) \\leq \\displaystyle \\frac { \\alpha _ { t } ^ { 0 } } { 1 - \\gamma } + \\gamma \\left| \\displaystyle \\sum _ { i = 1 } ^ { t } \\Delta _ { i } \\right| + \\displaystyle \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\left[ \\gamma ( \\hat { V } _ { t _ { i } } - V ^ { * } ) ( x _ { t _ { i } + 1 } ) + b _ { i } \\right] } \\\\ & { \\qquad \\leq \\displaystyle \\frac { \\alpha _ { t } ^ { 0 } } { 1 - \\gamma } + \\displaystyle \\frac { 3 c _ { 2 } } { 1 - \\gamma } \\sqrt { \\frac { H \\iota ( t ) } { t } } + \\displaystyle \\sum _ { i = 1 } ^ { t } \\gamma \\alpha _ { t } ^ { i } ( \\hat { V } ^ { t _ { i } } - V ^ { * } ) ( x _ { t _ { i } + 1 } ) } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            243,
+            558,
+            754,
+            643
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "equation",
+        "img_path": "images/53eab3d1f26c37eff9f588636d51ccb07f492de053eae442ba9c0192a7489963.jpg",
+        "text": "$$\n\\leq \\frac { \\alpha _ { t } ^ { 0 } } { 1 - \\gamma } + \\sum _ { i = 1 } ^ { t } \\gamma \\alpha _ { t } ^ { i } ( { \\hat { V } } ^ { t _ { i } } - V ^ { * } ) ( x _ { t _ { i } + 1 } ) + \\beta _ { t } .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            356,
+            660,
+            658,
+            702
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Note that $\\beta _ { t } = c _ { 3 } ( 1 - \\gamma ) ^ { - 1 } \\sqrt { H \\iota ( t ) / t }$ ; $c _ { 3 } = 3 c _ { 2 } = 1 2 { \\sqrt { 2 } } .$ . ",
+        "bbox": [
+            171,
+            704,
+            560,
+            723
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Proof of the left hand side of (13): Now, we assume that event that (16) holds. We assert that $Q _ { p } \\geq Q ^ { * }$ for all $( s , a )$ and $p \\leq p ^ { \\prime }$ . This assertion is obviously true when $p ^ { \\prime } = 0$ . Then ",
+        "bbox": [
+            173,
+            727,
+            825,
+            757
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "equation",
+        "img_path": "images/70ff20e4e31a1bb0299ebb34008753b3eaca5c5e3da766015eda50bc514d5a51.jpg",
+        "text": "$$\n\\begin{array} { c l } { ( Q _ { p } - Q ^ { * } ) ( s , a ) \\geq - \\gamma \\displaystyle \\left| \\displaystyle \\sum _ { i = 1 } ^ { t } \\Delta _ { i } \\right| + \\displaystyle \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\left[ \\gamma ( \\hat { V } _ { t _ { i } } - V ^ { * } ) ( x _ { t _ { i } + 1 } ) + b _ { i } \\right] } \\\\ { \\geq \\displaystyle \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } b _ { i } - \\gamma \\displaystyle \\left| \\displaystyle \\sum _ { i = 1 } ^ { t } \\Delta _ { i } \\right| \\geq 0 . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            266,
+            758,
+            730,
+            847
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Therefore the assertion holds for $p ^ { \\prime } + 1$ as well. By induction, it holds for all $p$ . ",
+        "bbox": [
+            173,
+            847,
+            694,
+            863
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "We now see that (13) holds for probability $1 - \\delta / 2$ for all $p , s , a$ . Since $\\hat { Q } _ { p } ( s , a )$ is always greater than $Q _ { p ^ { \\prime } } ( s , a )$ for some $p ^ { \\prime } \\leq p$ , we know that $\\hat { Q } _ { p } ( s , a ) \\geq Q _ { p ^ { \\prime } } ( s , a ) \\geq Q ^ { * } ( s , a )$ , thus proving (14). ",
+        "bbox": [
+            173,
+            869,
+            825,
+            905
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "We now give a proof for lemma 2. Recall the definition for a $( C , w )$ -sequence. A sequence $( w _ { t } ) _ { t \\geq 1 }$ is said to be a $( C , w )$ -sequence for $C , w > 0$ , if $0 \\leq w _ { t } \\leq w$ for all $t \\geq 1$ , and $\\textstyle \\sum _ { t \\geq 1 } w _ { t } \\leq C$ . ",
+        "bbox": [
+            169,
+            102,
+            825,
+            135
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Proof. Let $n _ { t } = N _ { t } ( s _ { t } , a _ { t } )$ for simplicity; we have ",
+        "bbox": [
+            173,
+            148,
+            511,
+            165
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "equation",
+        "img_path": "images/56de998ef0518be48301779db9712c42690034bbbfeba7d7ae47e786453e29e7.jpg",
+        "text": "$$\n\\begin{array} { r l } {  { \\sum _ { t \\geq 1 } w _ { t } ( \\hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) } } \\\\ & { \\leq \\sum _ { t \\geq 1 } w _ { t } ( Q _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) } \\\\ & { \\leq \\sum _ { t \\geq 1 } w _ { t } [ \\cfrac { \\alpha _ { n _ { t } } ^ { 0 } } { 1 - \\gamma } + \\beta _ { n _ { t } } + \\gamma \\sum _ { i = 1 } ^ { n _ { t } } \\alpha _ { n _ { t } } ^ { i } ( \\hat { V } _ { \\tau ( s _ { t } , a _ { t } , i ) } - V ^ { * } ) ( s _ { \\tau ( s _ { t } , a _ { t } , i ) + 1 } ) ] } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            258,
+            169,
+            736,
+            285
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "The last inequality is due to lemma 4. Note that $\\alpha _ { n _ { t } } ^ { 0 } = \\mathbb { I } [ n _ { t } = 0 ]$ , the first term in the summation can be bounded by, ",
+        "bbox": [
+            173,
+            290,
+            825,
+            320
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "equation",
+        "img_path": "images/fb8a30f2f69b0a0ef551b8c5d16a0c30b4272df4f37761a5fa9bb9799022d5bd.jpg",
+        "text": "$$\n\\sum _ { t \\geq 1 } w _ { t } \\frac { \\alpha _ { n _ { t } } ^ { 0 } } { 1 - \\gamma } \\leq \\frac { S A w } { 1 - \\gamma } .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            418,
+            323,
+            578,
+            366
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "For the second term, define $u ( s , a ) = \\operatorname* { s u p } _ { t } N _ { t } ( s , a )$ .2 It follows that, ",
+        "bbox": [
+            173,
+            377,
+            624,
+            395
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "equation",
+        "img_path": "images/bce9df1dbdecfd18cd0fbd700e55e9d74ea6aeee786233ea436d7b29badc95fc.jpg",
+        "text": "$$\n\\begin{array} { l } { \\displaystyle \\sum _ { t \\geq 1 } w _ { t } \\beta _ { n _ { t } } = \\sum _ { s , o } ^ { u ( s , o ) } w _ { \\tau ( s , a , i ) } \\beta _ { i } } \\\\ { \\displaystyle \\qquad \\leq \\sum _ { s , a } ( 1 - \\gamma ) ^ { - 1 } c _ { 3 } \\sum _ { i = 1 } ^ { C _ { s , a } / w } \\sqrt { \\frac { H \\iota ( i ) } { i } } w } \\\\ { \\displaystyle \\qquad \\leq 2 \\sum _ { s , a } ( 1 - \\gamma ) ^ { - 1 } c _ { 3 } \\sqrt { \\iota ( C ) H C _ { s , a } w } } \\\\ { \\displaystyle \\qquad \\leq 2 c _ { 3 } ( 1 - \\gamma ) ^ { - 1 } \\sqrt { w S A H C \\iota ( C ) } . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            338,
+            400,
+            656,
+            553
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Where $\\begin{array} { r } { C _ { s , a } = \\sum _ { t \\geq 1 , ( s _ { t } , a _ { t } ) = ( s , a ) } w _ { t } } \\end{array}$ . Inequality (19) follows from rearrangement inequality, since $\\iota ( x ) / x$ is monotonically decreasing. Inequality (21) follows from Jensen’s inequality. ",
+        "bbox": [
+            173,
+            555,
+            826,
+            588
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "For the third term of the summation, we have ",
+        "bbox": [
+            173,
+            593,
+            472,
+            608
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "equation",
+        "img_path": "images/a3e0c01b442b6f3c208a66bd1e6c84604cad0908954b7748b2f4faaaf3ab9889.jpg",
+        "text": "$$\n\\begin{array} { c } { { \\displaystyle \\sum _ { t \\ge 1 } w _ { t } \\sum _ { i = 1 } ^ { n _ { t } } \\alpha _ { n _ { t } } ^ { i } \\left( \\hat { V } _ { \\tau ( s _ { t } , a _ { t } , i ) } - V ^ { * } \\right) \\left( s _ { \\tau ( s _ { t } , a _ { t } , i ) + 1 } \\right) } } \\\\ { { \\displaystyle \\le \\sum _ { t ^ { \\prime } \\ge 1 } \\left( \\hat { V } _ { t ^ { \\prime } } - V ^ { * } \\right) \\left( s _ { t ^ { \\prime } + 1 } \\right) \\left( \\sum _ { t = t ^ { \\prime } + 1 } ^ { \\infty } \\alpha _ { n _ { t } } ^ { n _ { t ^ { \\prime } } } w _ { t } \\right) . } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            323,
+            612,
+            676,
+            723
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Define ",
+        "bbox": [
+            173,
+            746,
+            220,
+            760
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "equation",
+        "img_path": "images/90d6cf339da0fc0bd898216b68464ffc95f01fd8012796a3a8c23865fc73b784.jpg",
+        "text": "$$\nw _ { t ^ { \\prime } + 1 } ^ { \\prime } = \\left( \\sum _ { \\stackrel { t = t ^ { \\prime } + 1 } { ( s _ { t } , a _ { t } ) = ( s _ { t } ^ { \\prime } , a _ { t } ^ { \\prime } ) } } ^ { \\infty } \\alpha _ { n _ { t } } ^ { n _ { t ^ { \\prime } } } w _ { t } \\right) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            380,
+            755,
+            616,
+            821
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "We claim that $w _ { t + 1 } ^ { \\prime }$ is a $\\textstyle ( C , ( 1 + { \\frac { 1 } { H } } ) w )$ -sequence. We now prove this claim. By lemma 3, for any $t ^ { \\prime } \\geq 0$ , ",
+        "bbox": [
+            173,
+            832,
+            823,
+            861
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "equation",
+        "img_path": "images/4253341d3793835fab3da24d7c177c2e36a4c25bd994300d52241f505a8a3adc.jpg",
+        "text": "$$\nw _ { t ^ { \\prime } + 1 } ^ { \\prime } \\leq w \\sum _ { j = n _ { t ^ { \\prime } } } ^ { \\infty } \\alpha _ { j } ^ { n _ { t ^ { \\prime } } } = ( 1 + 1 / H ) w .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            370,
+            858,
+            625,
+            901
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "By $\\textstyle \\sum _ { j = 0 } ^ { i } \\alpha _ { i } ^ { j } = 1$ , we have $\\begin{array} { r } { \\sum _ { t ^ { \\prime } \\geq 1 } w _ { t ^ { \\prime } + 1 } ^ { \\prime } \\leq \\sum _ { t \\geq 1 } w _ { t } \\leq C . } \\end{array}$ . This proves the assertion. It follows from (22) that ",
+        "bbox": [
+            169,
+            102,
+            825,
+            133
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "equation",
+        "img_path": "images/a1c63f8ce8866bfa935cc54ba0fa4060644052edbd98620aad79e7ef97f0f148.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\quad \\underset { t \\geq 1 } { \\sum \\sigma } u _ { t + 1 } ^ { \\prime } \\left( \\hat { V } _ { t } - V ^ { * } \\right) \\left( s _ { t + 1 } \\right) } \\\\ & { = \\underset { t \\geq 1 } { \\sum \\sigma } u _ { t + 1 } ^ { \\prime } \\left( \\hat { V } _ { t + 1 } - V ^ { * } \\right) \\left( s _ { t + 1 } \\right) + \\underset { t \\geq 1 } { \\sum \\sigma } u _ { t + 1 } ^ { \\prime } \\left( \\hat { V } _ { t } - \\hat { V } _ { t + 1 } \\right) \\left( s _ { t + 1 } \\right) } \\\\ & { \\quad \\leq \\underset { t \\geq 1 } { \\sum \\sigma } u _ { t + 1 } ^ { \\prime } \\left( \\hat { V } _ { t + 1 } - V ^ { * } \\right) \\left( s _ { t + 1 } \\right) + \\underset { t \\geq 1 } { \\sum \\sigma } u _ { t + 1 } ^ { \\prime } \\left( 2 \\alpha _ { n _ { t } + 1 } \\frac { 1 } { 1 - \\gamma } \\right) } \\\\ & { \\quad \\leq \\underset { t \\geq 1 } { \\sum \\sigma } w _ { t + 1 } ^ { \\prime } \\left( \\hat { V } _ { t + 1 } - V ^ { * } \\right) \\left( s _ { t + 1 } \\right) + \\mathcal { O } \\left( \\frac { w S A H } { 1 - \\gamma } \\ln { C } \\right) } \\\\ & { \\quad \\leq \\underset { t \\geq 1 } { \\sum \\sigma } w _ { t + 1 } ^ { \\prime } \\left( \\hat { Q } _ { t + 1 } - Q ^ { * } \\right) \\left( s _ { t + 1 } , a _ { t + 1 } \\right) + \\mathcal { O } \\left( \\frac { w S A H } { 1 - \\gamma } \\ln { C } \\right) } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            276,
+            138,
+            715,
+            337
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Inequality (25) comes from the update rule of our algorithm. Inequality (26) comes from the fact that $\\dot { \\alpha } _ { t } = ( H + 1 ) / ( H + t ) \\overset { \\cdot } { \\leq } H / t$ and Jensen’s Inequality. More specifically, let $C _ { s , a } ^ { \\prime } =$ $\\scriptstyle \\sum _ { t \\geq 1 , ( s _ { t } , a _ { t } = s , a } w _ { t + 1 } ^ { \\prime }$ , $w ^ { \\prime } = w ( 1 + 1 / H )$ . Then ",
+        "bbox": [
+            176,
+            340,
+            821,
+            387
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "equation",
+        "img_path": "images/9834ce9a1e7dc58cf0a708f75e6b5b858bcdc589ad24752ed45e1722a959c115.jpg",
+        "text": "$$\n\\sum _ { t \\geq 1 } w _ { t + 1 } ^ { \\prime } \\alpha _ { n _ { t } + 1 } \\leq \\sum _ { s , a } \\sum _ { n = 1 } ^ { C _ { s , a } ^ { \\prime } / w ^ { \\prime } } w ^ { \\prime } \\frac { H } { n } \\leq \\sum _ { s , a } H w ^ { \\prime } \\ln ( C _ { s , a } ^ { \\prime } / w ) \\leq 2 S A H w \\ln C .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            241,
+            392,
+            754,
+            443
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Putting (18), (21) and (27) together, we have, ",
+        "bbox": [
+            173,
+            454,
+            472,
+            469
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "equation",
+        "img_path": "images/fca33e0caf6dada43c874ac741c299779e61219671c7f66b39e75e1f2d6533ae.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\displaystyle \\sum _ { t \\geq 1 } w _ { t } ( \\hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) } \\\\ & { \\leq 2 c _ { 3 } \\frac { \\sqrt { w S A H C \\iota ( C ) } } { 1 - \\gamma } + \\mathcal { O } \\left( \\frac { w S A H } { 1 - \\gamma } \\ln C \\right) + \\gamma \\displaystyle \\sum _ { t \\geq 1 } w _ { t + 1 } ^ { \\prime } \\left( \\hat { Q } _ { t + 1 } - Q ^ { * } \\right) ( s _ { t + 1 } , a _ { t + 1 } ) . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            191,
+            491,
+            779,
+            571
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Observe that the third term is another weighted sum with the same form as (17). Therefore, we can unroll this term repetitively with changing weight sequences.Suppose that our original weight sequence is also denoted by $\\{ \\bar { w _ { t } ^ { ( 0 ) } } \\} _ { t \\ge 1 }$ , while $\\{ w _ { t } ^ { ( k ) } \\} _ { t \\ge 1 }$ denotes the weight sequence after unrolling for $k$ times. Let $w ^ { ( k ) }$ be $w \\cdot \\left( 1 + 1 / H \\right) ^ { k }$ . Then we can see that $\\{ w _ { t } ^ { ( k ) } \\} _ { t \\ge 1 }$ is a $( C , w ^ { ( k ) } )$ -sequence. Suppose that we unroll for $H$ times. Then ",
+        "bbox": [
+            173,
+            575,
+            828,
+            654
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "equation",
+        "img_path": "images/4b3ee4cb41b96d3c4f223bc4146fc59bb343a3cac7f567861e3ed3154212ede1.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\displaystyle \\sum _ { t \\geq 1 } w _ { t } ( \\hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) } \\\\ & { \\leq 2 c _ { 3 } \\frac { \\sqrt { w ^ { ( H ) } S A H C \\iota ( C ) } } { ( 1 - \\gamma ) ^ { 2 } } + \\mathcal { O } \\left( \\frac { w ^ { ( H ) } S A H } { ( 1 - \\gamma ) ^ { 2 } } \\ln C \\right) + \\gamma ^ { H } \\displaystyle \\sum _ { t \\geq 1 } w _ { t } ^ { ( H ) } \\left( \\hat { Q } _ { t } - Q ^ { * } \\right) ( s _ { t } , a _ { t } ) } \\\\ & { \\leq 2 c _ { 3 } \\frac { \\sqrt { w ^ { ( H ) } S A H C \\iota ( C ) } } { ( 1 - \\gamma ) ^ { 2 } } + \\mathcal { O } \\left( \\frac { w ^ { ( H ) } S A H } { ( 1 - \\gamma ) ^ { 2 } } \\ln C \\right) + \\gamma ^ { H } \\frac { C } { 1 - \\gamma } . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            204,
+            659,
+            795,
+            779
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "We set $\\begin{array} { r } { H = \\frac { \\ln 1 / ( ( 1 - \\gamma ) \\epsilon _ { 1 } ) } { \\ln 1 / \\gamma } \\leq \\frac { \\ln 1 / ( ( 1 - \\gamma ) \\epsilon _ { 1 } ) } { 1 - \\gamma } , } \\end{array}$ . It follows that $w ^ { ( H ) } = ( 1 + 1 / H ) ^ { H } w ^ { ( 0 ) } \\leq e w ^ { ( 0 ) }$ , and that γH C1−γ $\\gamma ^ { H } \\frac { C } { 1 - \\gamma } \\leq C \\epsilon _ { 1 }$ . Also, let $\\ell ( C ) = \\iota ( C ) \\ln ( ( 1 - \\gamma ) ^ { - 1 } \\epsilon _ { 1 } ^ { - 1 } )$ . Therefore, ",
+        "bbox": [
+            173,
+            799,
+            826,
+            839
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "equation",
+        "img_path": "images/11b4d3a7f4cf29588edd0397db246aa8a18f798a841609b619f1a546acf17d46.jpg",
+        "text": "$$\n\\sum _ { t \\geq 1 } w _ { t } ( \\hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) \\leq \\frac { C \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\frac { \\sqrt { w S A C \\ell ( C ) } } { ( 1 - \\gamma ) ^ { 2 . 5 } } + \\frac { w S A } { ( 1 - \\gamma ) ^ { 3 } } \\ln C \\ln \\frac { 1 } { ( 1 - \\gamma ) \\epsilon _ { 1 } } \\right) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            184,
+            861,
+            787,
+            904
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "C EXTENSION TO OTHER SETTINGS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            102,
+            482,
+            118
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "First we define a mapping from a finite horizon MDP to an infinite horizon MDP so that our algorithm can be applied. For an arbitrary finite horizon MDP $\\mathcal { M } = ( S , A , H , r _ { h } ( s _ { \\perp } a ) , p _ { h } ( s ^ { \\prime } \\mid s , a ) )$ where $H$ is the length of episode, the corresponding infinite horizon MDP $\\mathcal { M } = ( S , A , \\gamma , \\bar { r } ( \\bar { s } , \\bar { a } ) , \\bar { p } ( \\bar { s } ^ { \\prime } \\mid \\bar { s } , \\bar { a } ) )$ is defined as, ",
+        "bbox": [
+            174,
+            132,
+            826,
+            189
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "$\\begin{array} { l } { { \\bullet \\ { \\bar { S } } = S \\times H , { \\bar { A } } = A ; } } \\\\ { { \\bullet \\ \\gamma = ( 1 - 1 / H ) ; } } \\end{array}$ • for a state $s$ at step $h$ , let $\\bar { s } _ { s , h }$ be the corresponding state. For any action $a$ and next state $s ^ { \\prime }$ , define $\\bar { r } ( \\bar { s } _ { s , h } , a ) = \\gamma ^ { H - h + 1 } r _ { h } ( s , a )$ and $\\bar { p } ( \\bar { s } _ { s ^ { \\prime } , h + 1 } \\mid \\bar { s } _ { s , h } , a ) = p _ { h } ( s ^ { \\prime } \\mid s , h )$ . And for $h = H$ , set $\\bar { r } ( \\bar { s } _ { s , h } , a ) = 0$ and $\\bar { p } ( \\bar { s } _ { s ^ { \\prime } , 1 } \\mid \\bar { s } _ { s , h } , a ) = I [ s ^ { \\prime } = s _ { 1 } ]$ for a fixed starting state $s _ { 1 }$ . ",
+        "bbox": [
+            214,
+            198,
+            825,
+            285
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Let $\\bar { V } _ { t }$ be the value function in $\\bar { \\mathcal { M } }$ at time $t$ and $V _ { h } ^ { k }$ the value function in $\\mathcal { M }$ at episode $k$ , step $h$ . It follows that $\\begin{array} { r } { \\bar { V } ^ { \\ast } ( \\bar { s } _ { s _ { 1 } , 1 } ) = \\frac { \\gamma ^ { H } } { 1 - \\gamma ^ { H } } V _ { 1 } ^ { \\ast } ( s _ { 1 } ) } \\end{array}$ . And the policy mapping is defined as $\\pi _ { h } ( s ) = \\bar { \\pi } ( \\bar { s } _ { s , h } )$ for policy $\\bar { \\pi }$ in $\\bar { \\mathcal { M } }$ . Value functions in MDP $\\mathcal { M }$ and $\\bar { \\mathcal { M } }$ are closely related in a sense that, any $\\epsilon$ -optimal policy $\\bar { \\pi }$ of $\\bar { \\mathcal { M } }$ corresponding to an $( \\epsilon / \\gamma ^ { H } )$ -optimal policy $\\pi$ in $\\mathcal { M }$ (see section C.1 for proof). Note that here $\\gamma ^ { H } = ( 1 - \\dot { 1 } / H ) ^ { \\tilde { H } } = \\mathcal { O } ( \\dot { 1 } )$ is a constant. ",
+        "bbox": [
+            173,
+            294,
+            826,
+            375
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "For any visited a $\\epsilon > 0$ g our algorithm on  times, and at most $\\bar { M }$ for of $\\tilde { \\mathcal O } \\big ( \\frac { 3 S A H ^ { 9 } } { \\epsilon ^ { 2 } } \\big )$ tt me steps, the starting state -optimal. If we select the p $s _ { 1 }$ iscy $\\tilde { \\mathcal O } \\big ( { \\textstyle { \\frac { 3 S A H ^ { 8 } } { \\epsilon ^ { 2 } } } } \\big )$ $1 / 3$ $\\epsilon$ uniformly randomly from the policy $\\pi ^ { t H + 1 }$ for $0 \\leq t < T / H$ , with probability at least $2 / 3$ we can get an $\\epsilon$ -optimal policy. Therefore the PAC sample complexity is $\\tilde { \\mathcal { O } } \\left( \\epsilon ^ { - 2 } \\right)$ after hiding $S , A , H$ terms. ",
+        "bbox": [
+            173,
+            381,
+            826,
+            450
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "On the other hand, we want to show that for any $K$ episodes, ",
+        "bbox": [
+            173,
+            455,
+            573,
+            470
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "equation",
+        "img_path": "images/dfeb0feb59d694c97b8d3ad8daa0ee95cb21f9b5f8a16f568ba86cb50b2a11bd.jpg",
+        "text": "$$\n\\mathrm { R e g r e t } ( T ) = \\sum _ { k = 1 } ^ { T / H } \\left[ V ^ { * } ( s _ { 1 } ) - V _ { 1 } ^ { k } ( s _ { 1 } ) \\right] \\propto T ^ { 1 / 2 } .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            341,
+            476,
+            655,
+            522
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "The reason why our algorithm can have a better reduction from regret to PAC is that, after choosing $\\epsilon _ { 1 }$ , it follows from the argument of theorem 1 that for all $\\epsilon _ { 2 } > \\tilde { \\mathcal { O } } ( \\epsilon _ { 1 } / ( 1 - \\gamma ) )$ , the number of $\\epsilon _ { 2 }$ -suboptimal steps is bounded by ",
+        "bbox": [
+            173,
+            534,
+            826,
+            578
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "equation",
+        "img_path": "images/fc17daba551915b444155b637b9972b89541ce4691b2e2c14706d565e8c89847.jpg",
+        "text": "$$\n\\mathcal { O } \\left( \\frac { S A \\ln S A \\ln 1 / \\delta } { \\epsilon _ { 2 } ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\mathrm { p o l y l o g } \\left( \\frac { 1 } { \\epsilon _ { 1 } } , \\frac { 1 } { 1 - \\gamma } \\right) \\right)\n$$",
+        "text_format": "latex",
+        "bbox": [
+            348,
+            583,
+            648,
+            618
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "with probability $1 - \\delta$ . In contrast, delayed Q-learning can only give an upper bound on $\\epsilon _ { 1 }$ -suboptimal steps after setting parameter $\\epsilon _ { 1 }$ . ",
+        "bbox": [
+            174,
+            623,
+            825,
+            652
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Formally, let $X _ { k } = V ^ { \\ast } ( s _ { 1 } ) - V _ { 1 } ^ { k } ( s _ { 1 } )$ be the regret of $k$ -th episode. For any $T$ , set $\\epsilon = \\sqrt { S A / T }$ and $\\epsilon _ { 2 } = \\tilde { \\mathcal { O } } ( \\epsilon _ { 1 } / ( 1 - \\gamma ) )$ . Let $\\begin{array} { r } { M = \\lceil \\log _ { 2 } \\frac { 1 } { \\epsilon _ { 2 } ( 1 - \\gamma ) } \\rceil } \\end{array}$ . It follows that, ",
+        "bbox": [
+            171,
+            659,
+            825,
+            695
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "equation",
+        "img_path": "images/1d7fa9ef3cc29e1e3ac2d0a868dec889d151fa6dfb8e0d2bbd8979285d9e7f25.jpg",
+        "text": "$$\n\\begin{array} { r l r } {  { \\operatorname { R e g r e t } ( T ) \\le T \\epsilon _ { 2 } + \\sum _ { i = 1 } ^ { M } ( | k : \\{ X _ { k } \\ge \\epsilon _ { 2 } \\cdot 2 ^ { i - 1 } \\} | ) \\epsilon _ { 2 } \\cdot 2 ^ { i } } } \\\\ & { } & \\\\ & { } & { \\le \\tilde { \\mathcal { O } } ( T \\epsilon _ { 2 } + \\sum _ { i = 1 } ^ { M } \\frac { S A \\ln 1 / \\delta } { \\epsilon _ { 2 } \\cdot 2 ^ { i - 2 } } ) } \\\\ & { } & { \\le \\tilde { \\mathcal { O } } ( \\sqrt { S A T } \\ln 1 / \\delta ) } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            312,
+            702,
+            686,
+            818
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "with probability $1 - \\delta$ . Note that the $\\tilde { \\mathcal { O } }$ notation hides the poly $( 1 / ( 1 - \\gamma ) , \\log { 1 / \\epsilon _ { 1 } } )$ which is, by our reduction, poly $( H , \\log T , \\log S , \\log A )$ . ",
+        "bbox": [
+            173,
+            823,
+            823,
+            854
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "C.1 CONNECTION BETWEEN VALUE FUNCTIONS ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            869,
+            521,
+            883
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Recall that our MDP mapping from $\\begin{array} { r c l } { \\mathcal { M } } & { = } & { ( S , A , H , r _ { h } ( s , a ) , p _ { h } ( s ^ { \\prime } \\mathrm { ~  ~ \\chi ~ } | \\mathrm { ~  ~ \\chi ~ } s , a ) ) } \\end{array}$ to $\\begin{array} { r l } { \\bar { \\mathcal { M } } } & { { } = } \\end{array}$ $( \\bar { S } , \\bar { A } , \\gamma , \\bar { r } ( \\bar { s } , \\bar { a } ) , \\bar { p } ( \\bar { s } ^ { \\prime } \\mid \\bar { s } , \\bar { a } ) )$ is defined as, ",
+        "bbox": [
+            173,
+            893,
+            825,
+            924
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "• $\\bar { S } = S \\times H , \\bar { A } = A$ ;   \n• $\\gamma = ( 1 - 1 / H )$ ;   \n• for a state $s$ at step $h$ , let $\\bar { s } _ { s , h }$ be the corresponding state. For any action $a$ and next state $s ^ { \\prime }$ , define $\\bar { r } ( \\bar { s } _ { s , h } , a ) = \\gamma ^ { H - h + 1 } r _ { h } ( s , a )$ and $\\bar { p } ( \\bar { s } _ { s ^ { \\prime } , h + 1 } \\mid \\bar { s } _ { s , h } , a ) = p _ { h } ( s , h )$ . And for $h = H$ , set $\\bar { r } ( \\bar { s } _ { s , h } , a ) = 0$ and $\\bar { p } ( \\bar { s } _ { s ^ { \\prime } , 1 } \\mid \\bar { s } _ { s , h } , a ) = I [ s ^ { \\prime } = s _ { 1 } ]$ for a fixed starting state $s _ { 1 }$ . ",
+        "bbox": [
+            214,
+            102,
+            830,
+            186
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "For a trajectory $\\left\\{ { \\left( { \\bar { s } } _ { s _ { 1 } , 1 } , { \\bar { a } } _ { 1 } \\right) } , { \\left( { \\bar { s } } _ { s _ { 2 } , 2 } , { \\bar { a } } _ { 2 } \\right) } , \\cdot \\cdot \\cdot \\right\\}$ in $\\bar { \\mathcal { M } }$ , let $\\{ ( s _ { 1 } , a _ { 1 } ) , ( s _ { 2 } , a _ { 2 } ) , \\cdot \\cdot \\cdot \\}$ be the corresponding trajectory in $\\mathcal { M }$ . Note that $\\mathcal { M }$ has a unique fixed starting state $s _ { 1 }$ , which means that $s _ { t H + 1 } = s _ { 1 }$ for all $t \\geq 0$ . Denote the corresponding policy of $\\bar { \\pi } ^ { t }$ as $\\pi ^ { t }$ (may be non-stationary), then we have ",
+        "bbox": [
+            176,
+            195,
+            828,
+            239
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "equation",
+        "img_path": "images/52704ae56896c370e8ec3e398577b25911ebb487e2237bb93613270924e4d24c.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\bar { \\gamma } ^ { \\pi ^ { t } } ( \\bar { s } _ { s _ { 1 } , 1 } ) = \\mathbb { E } \\left[ \\bar { r } ( \\bar { s } _ { s _ { 1 } , 1 } , \\bar { a } _ { 1 } ) + \\gamma \\bar { r } ( \\bar { s } _ { s _ { 2 } , 2 } , \\bar { a } _ { 2 } ) + \\cdot \\cdot \\cdot + \\gamma ^ { H - 1 } \\bar { r } ( \\bar { s } _ { s _ { H - 1 } , H - 1 } , \\bar { a } _ { H - 1 } ) + \\gamma ^ { H } \\bar { V } ^ { \\pi _ { t + H - 1 } } ( \\bar { s } _ { s _ { H + 1 } , 1 } ) \\right] } \\\\ & { \\phantom { \\frac { 1 } { 1 } } = \\gamma ^ { H } \\mathbb { E } \\left[ r _ { 1 } ( s _ { 1 } , a _ { 1 } ) + r _ { 2 } ( s _ { 2 } , a _ { 2 } ) + \\cdot \\cdot \\cdot + r _ { H - 1 } ( s _ { H - 1 } , a _ { H - 1 } ) + \\bar { V } ^ { \\pi _ { t + H } } ( \\bar { s } _ { s _ { H + 1 } , 1 } ) \\right] } \\\\ & { \\phantom { \\frac { 1 } { 1 } } = \\gamma ^ { H } V ^ { \\pi ^ { t } } ( s _ { 1 } ) + \\gamma ^ { H } \\bar { V } ^ { \\pi + H } ( \\bar { s } _ { s _ { 1 } , 1 } ) . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            181,
+            244,
+            839,
+            309
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "Then for a stationary policy $\\bar { \\pi }$ , we can conclude $\\begin{array} { r } { \\bar { V } ^ { \\bar { \\pi } } ( \\bar { s } _ { s _ { 1 } , 1 } ) = \\frac { \\gamma ^ { H } } { 1 - \\gamma ^ { H } } V ^ { \\pi } ( s _ { 1 } ) } \\end{array}$ . Since the optimal policy $\\bar { \\pi } ^ { * }$ is stationary, we have $\\begin{array} { r } { \\bar { V } ^ { \\ast } ( \\bar { s } _ { s _ { 1 } , 1 } ) = \\frac { \\gamma ^ { H } } { 1 - \\gamma ^ { H } } V ^ { \\ast } ( s _ { 1 } ) } \\end{array}$ . ",
+        "bbox": [
+            174,
+            314,
+            825,
+            358
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "By definition, $\\bar { \\pi }$ is $\\epsilon$ -optimal at time step $t$ means that ",
+        "bbox": [
+            173,
+            362,
+            526,
+            377
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "equation",
+        "img_path": "images/f086319de63ecc59068ffa365e9e62e72d387018083ec5144b0aa425136c465f.jpg",
+        "text": "$$\n\\begin{array} { r } { \\bar { V } ^ { \\bar { \\pi } ^ { t } } ( \\bar { s } _ { s _ { 1 } , 1 } ) \\geq \\bar { V } ^ { * } ( \\bar { s } _ { s _ { 1 } , 1 } ) - \\epsilon . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            401,
+            382,
+            594,
+            404
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "It follows that ",
+        "bbox": [
+            173,
+            409,
+            267,
+            422
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "equation",
+        "img_path": "images/5cce7a222551bc6274bbc52ffdb272aeca3dced98abbbc8f80d2fab7858deadf.jpg",
+        "text": "$$\n\\gamma ^ { H } V ^ { \\pi ^ { t } } ( s _ { 1 } ) + \\gamma ^ { H } \\bar { V } ^ { \\pi _ { t + H } } ( \\bar { s } _ { s _ { 1 } , 1 } ) = \\bar { V } ^ { \\bar { \\pi } } ( \\bar { s } _ { s _ { 1 } , 1 } ) \\geq \\bar { V } ^ { * } ( \\bar { s } _ { s _ { 1 } , 1 } ) - \\epsilon ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            289,
+            424,
+            705,
+            445
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "hence ",
+        "bbox": [
+            173,
+            450,
+            215,
+            464
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "equation",
+        "img_path": "images/a3a5a1e7d68659f678d45d1177dbe36c95439ce8dceba0366c8e7ffef18cce5d.jpg",
+        "text": "$$\n^ { H } V ^ { \\pi ^ { \\varepsilon } } ( s _ { 1 } ) \\geq ( 1 - \\gamma ^ { H } ) \\bar { V } ^ { * } ( \\bar { s } _ { s _ { 1 } , 1 } ) + \\gamma ^ { H } ( \\bar { V } ^ { * } ( \\bar { s } _ { s _ { 1 } , 1 } ) - \\bar { V } ^ { \\pi _ { t + H } } ( \\bar { s } _ { s _ { 1 } , 1 } ) ) - \\epsilon \\geq ( 1 - \\gamma ^ { H } ) \\bar { V } ^ { * } ( \\bar { s } _ { s _ { 1 } , 1 } ) - \\epsilon .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            181,
+            468,
+            823,
+            488
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "Therefore we have ",
+        "bbox": [
+            174,
+            492,
+            299,
+            507
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "equation",
+        "img_path": "images/1f1b44222a0c1087458d2ccf43ee9da0e84754c0602268ed6cbc91b7c6c5c549.jpg",
+        "text": "$$\n{ V ^ { \\pi } } ^ { t } ( s _ { 1 } ) \\ge \\frac { 1 - \\gamma ^ { H } } { \\gamma ^ { H } } \\bar { V } ^ { * } ( \\bar { s } _ { s 1 , 1 } ) - \\epsilon / \\gamma ^ { H } = V ^ { * } ( s _ { 1 } ) - \\epsilon / \\gamma ^ { H } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            305,
+            510,
+            691,
+            544
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "which means that $\\pi ^ { t }$ is an $( \\epsilon / \\gamma ^ { H } )$ -optimal policy. ",
+        "bbox": [
+            173,
+            549,
+            500,
+            566
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "D A HARD INSTANCE FOR DELAYED Q-LEARNING ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            583,
+            607,
+            602
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "In this section, we prove Theorem 2 regarding the performance of Delayed Q-learning. ",
+        "bbox": [
+            176,
+            616,
+            745,
+            632
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "Theorem 2. There exists a family of MDPs with constant $S$ and $A$ , in which with probability $1 - \\delta$ , Delayed $Q$ -learning incurs sample complexity of exploration of $\\Omega \\left( \\frac { \\epsilon ^ { - 3 } } { \\ln ( 1 / \\delta ) } \\right)$ , assuming that $\\ln ( 1 / \\delta ) < \\epsilon ^ { - 2 }$ . ",
+        "bbox": [
+            173,
+            633,
+            826,
+            688
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "image",
+        "img_path": "images/d5ea7466679255528080a8e623d46ab5efe02c60983c67939e2c04d8974b3167.jpg",
+        "image_caption": [
+            "Figure 1: The MDP family. Actions are denoted by arrows. Actions with red color have reward 1, and reward 0 otherwise. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            397,
+            705,
+            599,
+            829
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "Proof. For each $0 < \\epsilon < \\frac { 1 } { 1 0 }$ , consider the following MDP (see also Fig. 1): state space is ${ \\boldsymbol { s } } =$ $\\{ a , b , c \\}$ while action set is $\\overset { \\vartriangle } { \\mathcal { A } } = \\{ \\ v { x } , \\ v { y } \\}$ ; transition probabilities are $P ( b | a , y ) = 1 - 1 0 \\epsilon$ , $P ( c | a , y ) =$ 10\u000f, $P ( b | a , x ) = 1$ , $P ( a | b , \\cdot ) = P ( a | c , \\cdot ) = 1$ . Rewards are all 1, except $R ( c , \\cdot ) = 0$ . ",
+        "bbox": [
+            174,
+            881,
+            825,
+            925
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "Assume that Delayed Q-learning is called for this MDP starting from state $a$ , with discount $\\begin{array} { r } { \\gamma > \\frac { 1 } { 2 } } \\end{array}$ and precision set as $\\epsilon$ . Denote the $Q$ value maintained by the algorithm by $\\hat { Q }$ . Without loss of generality, assume that the initial tie-breaking favors action $y$ when comparing $\\hat { Q } ( a , x )$ and $\\hat { Q } ( a , y )$ . In that case, unless $\\hat { Q } ( a , y )$ is updated, the agent will always choose $y$ in state $a$ . Since $Q ( a , x ) - Q ( a , y ) = 1 0 \\epsilon \\gamma > \\epsilon$ for any policy, choosing $y$ at state $a$ implies that the timestep is not $\\epsilon$ -optimal. In other words, sample complexity for exploration is at least the number of times the agent visits $a$ before the first update of $\\hat { Q } ( a , y )$ . ",
+        "bbox": [
+            173,
+            102,
+            825,
+            213
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "In the Delayed Q-learning algorithm, $\\hat { Q } ( \\cdot , \\cdot )$ are initialized to $1 / ( 1 - \\gamma )$ . Therefore, $\\hat { Q } ( a , y )$ could only be updated if max $\\hat { Q } ( c , \\cdot )$ is updated (and becomes smaller than $1 / ( 1 - \\gamma ) )$ . According to the algorithm, this can only happen if $c$ is visited $\\begin{array} { r } { m = \\Omega \\left( \\frac { 1 } { \\epsilon ^ { 2 } } \\right) } \\end{array}$ times. ",
+        "bbox": [
+            174,
+            219,
+            826,
+            268
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "However, each time the agent visits $a$ , there is less than $1 0 \\epsilon$ probability of transiting to $c$ . Let $t _ { 0 } = m / ( 1 0 \\epsilon C )$ , where $\\begin{array} { r } { C ^ { ' } = 3 \\ln \\frac { 1 } { \\delta } + 1 } \\end{array}$ . $\\delta$ is chosen such that $C \\leq m$ . In the first $2 t _ { 0 }$ timesteps, $a$ will be visited $t _ { 0 }$ times. By Chernoff’s bound, with probability $1 - \\delta$ , state $c$ will be visited less than $m$ times. In that case, $\\hat { Q } ( a , y )$ will not be updated in the first $2 t _ { 0 }$ timesteps. Therefore, with probability $1 - \\delta$ , sample complexity of exploration is at least ",
+        "bbox": [
+            173,
+            273,
+            825,
+            345
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "equation",
+        "img_path": "images/446057ad76737ed78dbeb6c14c391ec04ae8a21d0dea27c95bf135aaaf7cc43f.jpg",
+        "text": "$$\nt _ { 0 } = \\Omega \\left( { \\frac { 1 } { \\epsilon ^ { 3 } \\left( \\ln { 1 / \\delta } \\right) } } \\right) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            419,
+            352,
+            578,
+            387
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "When $\\ln ( 1 / \\delta ) < \\epsilon ^ { - 2 }$ , it can be seen that $\\begin{array} { r } { C = 3 \\ln \\frac { 1 } { \\delta } + 1 < \\frac { 4 } { \\epsilon ^ { 2 } } < m } \\end{array}$ ",
+        "bbox": [
+            173,
+            393,
+            620,
+            411
+        ],
+        "page_idx": 17
+    }
+]
\ No newline at end of file
diff --git a/parse/train/BkglSTNFDB/BkglSTNFDB_middle.json b/parse/train/BkglSTNFDB/BkglSTNFDB_middle.json
new file mode 100644
index 0000000000000000000000000000000000000000..1112d3bc82a64774b1a91fc9feb603b851a7f818
--- /dev/null
+++ b/parse/train/BkglSTNFDB/BkglSTNFDB_middle.json
@@ -0,0 +1,60344 @@
+{
+    "pdf_info": [
+        {
+            "preproc_blocks": [
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        78,
+                        504,
+                        116
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                78,
+                                505,
+                                97
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        78,
+                                        505,
+                                        97
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Q-LEARNING WITH UCB EXPLORATION IS SAMPLE",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                99,
+                                411,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        99,
+                                        411,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "EFFICIENT FOR INFINITE-HORIZON MDP",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        112,
+                        134,
+                        340,
+                        179
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                112,
+                                134,
+                                243,
+                                147
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        112,
+                                        134,
+                                        243,
+                                        147
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Kefan Dong*, Yuanhao Wang∗",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                111,
+                                145,
+                                320,
+                                159
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        145,
+                                        320,
+                                        159
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Institute for Interdisciplinary Information Sciences,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                111,
+                                156,
+                                196,
+                                169
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        156,
+                                        196,
+                                        169
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Tsinghua University",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                113,
+                                168,
+                                341,
+                                181
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        168,
+                                        341,
+                                        181
+                                    ],
+                                    "score": 1.0,
+                                    "content": "{dkf16,yuanhao-16}@mails.tsinghua.edu.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        }
+                    ],
+                    "index": 3.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        113,
+                        196,
+                        370,
+                        240
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                112,
+                                196,
+                                171,
+                                208
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        112,
+                                        196,
+                                        171,
+                                        208
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Xiaoyu Chen",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                111,
+                                206,
+                                371,
+                                219
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        206,
+                                        371,
+                                        219
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Key Laboratory of Machine Perception, MOE, School of EECS,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                111,
+                                217,
+                                187,
+                                231
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        217,
+                                        187,
+                                        231
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Peking University",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                112,
+                                229,
+                                210,
+                                241
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        112,
+                                        229,
+                                        210,
+                                        241
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cxy30@pku.edu.cn",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 7.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        112,
+                        257,
+                        368,
+                        301
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                111,
+                                255,
+                                167,
+                                271
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        255,
+                                        167,
+                                        271
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Liwei Wang",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                112,
+                                268,
+                                368,
+                                280
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        112,
+                                        268,
+                                        368,
+                                        280
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Key Laboratory of Machine Perception, MOE, School of EECS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                111,
+                                277,
+                                287,
+                                291
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        277,
+                                        287,
+                                        291
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Center for Data Science, Peking University",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                111,
+                                290,
+                                241,
+                                302
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        290,
+                                        241,
+                                        302
+                                    ],
+                                    "score": 1.0,
+                                    "content": "wanglw@cis.pku.edu.cn",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 11.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        278,
+                        330,
+                        333,
+                        342
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                276,
+                                329,
+                                336,
+                                344
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        276,
+                                        329,
+                                        336,
+                                        344
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ABSTRACT",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        143,
+                        357,
+                        469,
+                        475
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                141,
+                                357,
+                                470,
+                                370
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        357,
+                                        470,
+                                        370
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A fundamental question in reinforcement learning is whether model-free algo-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                367,
+                                469,
+                                381
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        367,
+                                        469,
+                                        381
+                                    ],
+                                    "score": 1.0,
+                                    "content": "rithms are sample efficient. Recently, Jin et al. (2018) proposed a Q-learning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                379,
+                                469,
+                                392
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        379,
+                                        469,
+                                        392
+                                    ],
+                                    "score": 1.0,
+                                    "content": "algorithm with UCB exploration policy, and proved it has nearly optimal regret",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                390,
+                                469,
+                                403
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        390,
+                                        469,
+                                        403
+                                    ],
+                                    "score": 1.0,
+                                    "content": "bound for finite-horizon episodic MDP. In this paper, we adapt Q-learning with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                401,
+                                469,
+                                413
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        401,
+                                        469,
+                                        413
+                                    ],
+                                    "score": 1.0,
+                                    "content": "UCB-exploration bonus to infinite-horizon MDP with discounted rewards without",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                412,
+                                469,
+                                426
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        412,
+                                        469,
+                                        426
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accessing a generative model. We show that the sample complexity of exploration",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                139,
+                                422,
+                                471,
+                                443
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        139,
+                                        422,
+                                        272,
+                                        443
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of our algorithm is bounded by",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        273,
+                                        423,
+                                        323,
+                                        439
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { r } { \\tilde { O } \\big ( \\frac { S A } { \\epsilon ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\big ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        324,
+                                        422,
+                                        471,
+                                        443
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". This improves the previously best",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                136,
+                                432,
+                                474,
+                                460
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        136,
+                                        432,
+                                        206,
+                                        460
+                                    ],
+                                    "score": 1.0,
+                                    "content": "known result of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        207,
+                                        438,
+                                        257,
+                                        454
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { r } { \\tilde { O } \\big ( \\frac { S A } { \\epsilon ^ { 4 } ( 1 - \\gamma ) ^ { 8 } } \\big ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        257,
+                                        432,
+                                        474,
+                                        460
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in this setting achieved by delayed Q-learning (Strehl",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                452,
+                                469,
+                                466
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        452,
+                                        362,
+                                        466
+                                    ],
+                                    "score": 1.0,
+                                    "content": "et al., 2006), and matches the lower bound in terms of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        362,
+                                        455,
+                                        367,
+                                        463
+                                    ],
+                                    "score": 0.73,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        368,
+                                        452,
+                                        410,
+                                        466
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as well as",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        419,
+                                        452,
+                                        436,
+                                        466
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        446,
+                                        452,
+                                        469,
+                                        466
+                                    ],
+                                    "score": 1.0,
+                                    "content": "up to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                464,
+                                222,
+                                476
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        464,
+                                        222,
+                                        476
+                                    ],
+                                    "score": 1.0,
+                                    "content": "logarithmic factors.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 19.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        501,
+                        206,
+                        513
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                499,
+                                208,
+                                516
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        499,
+                                        208,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1 INTRODUCTION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        527,
+                        505,
+                        616
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                528,
+                                505,
+                                540
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        528,
+                                        505,
+                                        540
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The goal of reinforcement learning (RL) is to construct efficient algorithms that learn and plan in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                539,
+                                505,
+                                551
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        539,
+                                        505,
+                                        551
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sequential decision making tasks when the underlying system dynamics are unknown. A typical",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                550,
+                                506,
+                                562
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        550,
+                                        506,
+                                        562
+                                    ],
+                                    "score": 1.0,
+                                    "content": "model in RL is Markov Decision Process (MDP). At each time step, the environment is in a state",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                561,
+                                506,
+                                573
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        563,
+                                        113,
+                                        570
+                                    ],
+                                    "score": 0.52,
+                                    "content": "s",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        113,
+                                        561,
+                                        221,
+                                        573
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". The agent takes an action",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        221,
+                                        563,
+                                        227,
+                                        570
+                                    ],
+                                    "score": 0.7,
+                                    "content": "a",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        227,
+                                        561,
+                                        295,
+                                        573
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", obtain a reward",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        295,
+                                        563,
+                                        301,
+                                        571
+                                    ],
+                                    "score": 0.75,
+                                    "content": "r",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        302,
+                                        561,
+                                        506,
+                                        573
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and then the environment transits to another state.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                572,
+                                506,
+                                584
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        572,
+                                        506,
+                                        584
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In reinforcement learning, the transition probability distribution is unknown. The algorithm needs",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                583,
+                                506,
+                                595
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        583,
+                                        506,
+                                        595
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to learn the transition dynamics of MDP, while aiming to maximize the cumulative reward. This",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                594,
+                                506,
+                                606
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        594,
+                                        506,
+                                        606
+                                    ],
+                                    "score": 1.0,
+                                    "content": "poses the exploration-exploitation dilemma: whether to act to gain new information (explore) or to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                605,
+                                375,
+                                617
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        605,
+                                        375,
+                                        617
+                                    ],
+                                    "score": 1.0,
+                                    "content": "act consistently with past experience to maximize reward (exploit).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 29.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        621,
+                        505,
+                        709
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                620,
+                                506,
+                                635
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        620,
+                                        506,
+                                        635
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Theoretical analyses of reinforcement learning fall into two broad categories: those assuming a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                632,
+                                505,
+                                645
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        632,
+                                        505,
+                                        645
+                                    ],
+                                    "score": 1.0,
+                                    "content": "simulator (a.k.a. generative model), and those without a simulator. In the first category, the algorithm",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                644,
+                                505,
+                                656
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        644,
+                                        505,
+                                        656
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is allowed to query the outcome of any state action pair from an oracle. The emphasis is on the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                654,
+                                505,
+                                667
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        654,
+                                        265,
+                                        667
+                                    ],
+                                    "score": 1.0,
+                                    "content": "number of calls needed to estimate the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        265,
+                                        655,
+                                        275,
+                                        666
+                                    ],
+                                    "score": 0.82,
+                                    "content": "Q",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        275,
+                                        654,
+                                        505,
+                                        667
+                                    ],
+                                    "score": 1.0,
+                                    "content": "value or to output a near-optimal policy. There has been",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                665,
+                                505,
+                                678
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        665,
+                                        505,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "extensive research in literature following this line of research, the majority of which focuses on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                675,
+                                507,
+                                689
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        675,
+                                        507,
+                                        689
+                                    ],
+                                    "score": 1.0,
+                                    "content": "discounted infinite horizon MDPs (Azar et al., 2011; Even-Dar & Mansour, 2003; Sidford et al.,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                686,
+                                507,
+                                700
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        686,
+                                        507,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2018b). The current results have achieved near-optimal time and sample complexities (Sidford et al.,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                697,
+                                147,
+                                711
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        697,
+                                        147,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2018b;a).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        }
+                    ],
+                    "index": 37.5
+                }
+            ],
+            "page_idx": 0,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        119,
+                        722,
+                        262,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                118,
+                                719,
+                                263,
+                                734
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        118,
+                                        719,
+                                        263,
+                                        734
+                                    ],
+                                    "score": 1.0,
+                                    "content": "∗These two authors contributed equally.",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        294,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                294,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        294,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        751,
+                        308,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                302,
+                                751,
+                                309,
+                                762
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        302,
+                                        751,
+                                        309,
+                                        762
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        78,
+                        504,
+                        116
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                78,
+                                505,
+                                97
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        78,
+                                        505,
+                                        97
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Q-LEARNING WITH UCB EXPLORATION IS SAMPLE",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                99,
+                                411,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        99,
+                                        411,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "EFFICIENT FOR INFINITE-HORIZON MDP",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5
+                },
+                {
+                    "type": "list",
+                    "bbox": [
+                        112,
+                        134,
+                        340,
+                        179
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                112,
+                                134,
+                                243,
+                                147
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        112,
+                                        134,
+                                        243,
+                                        147
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Kefan Dong*, Yuanhao Wang∗",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                111,
+                                145,
+                                320,
+                                159
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        145,
+                                        320,
+                                        159
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Institute for Interdisciplinary Information Sciences,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                111,
+                                156,
+                                196,
+                                169
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        156,
+                                        196,
+                                        169
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Tsinghua University",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                113,
+                                168,
+                                341,
+                                181
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        168,
+                                        341,
+                                        181
+                                    ],
+                                    "score": 1.0,
+                                    "content": "{dkf16,yuanhao-16}@mails.tsinghua.edu.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                112,
+                                196,
+                                171,
+                                208
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        112,
+                                        196,
+                                        171,
+                                        208
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Xiaoyu Chen",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                111,
+                                206,
+                                371,
+                                219
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        206,
+                                        371,
+                                        219
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Key Laboratory of Machine Perception, MOE, School of EECS,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                111,
+                                217,
+                                187,
+                                231
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        217,
+                                        187,
+                                        231
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Peking University",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                112,
+                                229,
+                                210,
+                                241
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        112,
+                                        229,
+                                        210,
+                                        241
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cxy30@pku.edu.cn",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                111,
+                                255,
+                                167,
+                                271
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        255,
+                                        167,
+                                        271
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Liwei Wang",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                112,
+                                268,
+                                368,
+                                280
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        112,
+                                        268,
+                                        368,
+                                        280
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Key Laboratory of Machine Perception, MOE, School of EECS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                111,
+                                277,
+                                287,
+                                291
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        277,
+                                        287,
+                                        291
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Center for Data Science, Peking University",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                111,
+                                290,
+                                241,
+                                302
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        290,
+                                        241,
+                                        302
+                                    ],
+                                    "score": 1.0,
+                                    "content": "wanglw@cis.pku.edu.cn",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13,
+                            "is_list_start_line": true
+                        }
+                    ],
+                    "index": 3.5,
+                    "bbox_fs": [
+                        111,
+                        134,
+                        341,
+                        181
+                    ]
+                },
+                {
+                    "type": "list",
+                    "bbox": [
+                        113,
+                        196,
+                        370,
+                        240
+                    ],
+                    "lines": [],
+                    "index": 7.5,
+                    "bbox_fs": [
+                        111,
+                        196,
+                        371,
+                        241
+                    ],
+                    "lines_deleted": true
+                },
+                {
+                    "type": "list",
+                    "bbox": [
+                        112,
+                        257,
+                        368,
+                        301
+                    ],
+                    "lines": [],
+                    "index": 11.5,
+                    "bbox_fs": [
+                        111,
+                        255,
+                        368,
+                        302
+                    ],
+                    "lines_deleted": true
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        278,
+                        330,
+                        333,
+                        342
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                276,
+                                329,
+                                336,
+                                344
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        276,
+                                        329,
+                                        336,
+                                        344
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ABSTRACT",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        143,
+                        357,
+                        469,
+                        475
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                141,
+                                357,
+                                470,
+                                370
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        357,
+                                        470,
+                                        370
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A fundamental question in reinforcement learning is whether model-free algo-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                367,
+                                469,
+                                381
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        367,
+                                        469,
+                                        381
+                                    ],
+                                    "score": 1.0,
+                                    "content": "rithms are sample efficient. Recently, Jin et al. (2018) proposed a Q-learning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                379,
+                                469,
+                                392
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        379,
+                                        469,
+                                        392
+                                    ],
+                                    "score": 1.0,
+                                    "content": "algorithm with UCB exploration policy, and proved it has nearly optimal regret",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                390,
+                                469,
+                                403
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        390,
+                                        469,
+                                        403
+                                    ],
+                                    "score": 1.0,
+                                    "content": "bound for finite-horizon episodic MDP. In this paper, we adapt Q-learning with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                401,
+                                469,
+                                413
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        401,
+                                        469,
+                                        413
+                                    ],
+                                    "score": 1.0,
+                                    "content": "UCB-exploration bonus to infinite-horizon MDP with discounted rewards without",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                412,
+                                469,
+                                426
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        412,
+                                        469,
+                                        426
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accessing a generative model. We show that the sample complexity of exploration",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                139,
+                                422,
+                                471,
+                                443
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        139,
+                                        422,
+                                        272,
+                                        443
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of our algorithm is bounded by",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        273,
+                                        423,
+                                        323,
+                                        439
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { r } { \\tilde { O } \\big ( \\frac { S A } { \\epsilon ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\big ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        324,
+                                        422,
+                                        471,
+                                        443
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". This improves the previously best",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                136,
+                                432,
+                                474,
+                                460
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        136,
+                                        432,
+                                        206,
+                                        460
+                                    ],
+                                    "score": 1.0,
+                                    "content": "known result of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        207,
+                                        438,
+                                        257,
+                                        454
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { r } { \\tilde { O } \\big ( \\frac { S A } { \\epsilon ^ { 4 } ( 1 - \\gamma ) ^ { 8 } } \\big ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        257,
+                                        432,
+                                        474,
+                                        460
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in this setting achieved by delayed Q-learning (Strehl",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                452,
+                                469,
+                                466
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        452,
+                                        362,
+                                        466
+                                    ],
+                                    "score": 1.0,
+                                    "content": "et al., 2006), and matches the lower bound in terms of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        362,
+                                        455,
+                                        367,
+                                        463
+                                    ],
+                                    "score": 0.73,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        368,
+                                        452,
+                                        410,
+                                        466
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as well as",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        419,
+                                        452,
+                                        436,
+                                        466
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        446,
+                                        452,
+                                        469,
+                                        466
+                                    ],
+                                    "score": 1.0,
+                                    "content": "up to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                464,
+                                222,
+                                476
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        464,
+                                        222,
+                                        476
+                                    ],
+                                    "score": 1.0,
+                                    "content": "logarithmic factors.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 19.5,
+                    "bbox_fs": [
+                        136,
+                        357,
+                        474,
+                        476
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        501,
+                        206,
+                        513
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                499,
+                                208,
+                                516
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        499,
+                                        208,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1 INTRODUCTION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        527,
+                        505,
+                        616
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                528,
+                                505,
+                                540
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        528,
+                                        505,
+                                        540
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The goal of reinforcement learning (RL) is to construct efficient algorithms that learn and plan in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                539,
+                                505,
+                                551
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        539,
+                                        505,
+                                        551
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sequential decision making tasks when the underlying system dynamics are unknown. A typical",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                550,
+                                506,
+                                562
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        550,
+                                        506,
+                                        562
+                                    ],
+                                    "score": 1.0,
+                                    "content": "model in RL is Markov Decision Process (MDP). At each time step, the environment is in a state",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                561,
+                                506,
+                                573
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        563,
+                                        113,
+                                        570
+                                    ],
+                                    "score": 0.52,
+                                    "content": "s",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        113,
+                                        561,
+                                        221,
+                                        573
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". The agent takes an action",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        221,
+                                        563,
+                                        227,
+                                        570
+                                    ],
+                                    "score": 0.7,
+                                    "content": "a",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        227,
+                                        561,
+                                        295,
+                                        573
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", obtain a reward",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        295,
+                                        563,
+                                        301,
+                                        571
+                                    ],
+                                    "score": 0.75,
+                                    "content": "r",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        302,
+                                        561,
+                                        506,
+                                        573
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and then the environment transits to another state.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                572,
+                                506,
+                                584
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        572,
+                                        506,
+                                        584
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In reinforcement learning, the transition probability distribution is unknown. The algorithm needs",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                583,
+                                506,
+                                595
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        583,
+                                        506,
+                                        595
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to learn the transition dynamics of MDP, while aiming to maximize the cumulative reward. This",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                594,
+                                506,
+                                606
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        594,
+                                        506,
+                                        606
+                                    ],
+                                    "score": 1.0,
+                                    "content": "poses the exploration-exploitation dilemma: whether to act to gain new information (explore) or to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                605,
+                                375,
+                                617
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        605,
+                                        375,
+                                        617
+                                    ],
+                                    "score": 1.0,
+                                    "content": "act consistently with past experience to maximize reward (exploit).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 29.5,
+                    "bbox_fs": [
+                        105,
+                        528,
+                        506,
+                        617
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        621,
+                        505,
+                        709
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                620,
+                                506,
+                                635
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        620,
+                                        506,
+                                        635
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Theoretical analyses of reinforcement learning fall into two broad categories: those assuming a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                632,
+                                505,
+                                645
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        632,
+                                        505,
+                                        645
+                                    ],
+                                    "score": 1.0,
+                                    "content": "simulator (a.k.a. generative model), and those without a simulator. In the first category, the algorithm",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                644,
+                                505,
+                                656
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        644,
+                                        505,
+                                        656
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is allowed to query the outcome of any state action pair from an oracle. The emphasis is on the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                654,
+                                505,
+                                667
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        654,
+                                        265,
+                                        667
+                                    ],
+                                    "score": 1.0,
+                                    "content": "number of calls needed to estimate the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        265,
+                                        655,
+                                        275,
+                                        666
+                                    ],
+                                    "score": 0.82,
+                                    "content": "Q",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        275,
+                                        654,
+                                        505,
+                                        667
+                                    ],
+                                    "score": 1.0,
+                                    "content": "value or to output a near-optimal policy. There has been",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                665,
+                                505,
+                                678
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        665,
+                                        505,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "extensive research in literature following this line of research, the majority of which focuses on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                675,
+                                507,
+                                689
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        675,
+                                        507,
+                                        689
+                                    ],
+                                    "score": 1.0,
+                                    "content": "discounted infinite horizon MDPs (Azar et al., 2011; Even-Dar & Mansour, 2003; Sidford et al.,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                686,
+                                507,
+                                700
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        686,
+                                        507,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2018b). The current results have achieved near-optimal time and sample complexities (Sidford et al.,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                697,
+                                147,
+                                711
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        697,
+                                        147,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2018b;a).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        }
+                    ],
+                    "index": 37.5,
+                    "bbox_fs": [
+                        105,
+                        620,
+                        507,
+                        711
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        82,
+                        505,
+                        149
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                82,
+                                505,
+                                94
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        82,
+                                        505,
+                                        94
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Without a simulator, there is a dichotomy between finite-horizon and infinite-horizon settings. In",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                92,
+                                506,
+                                107
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        92,
+                                        506,
+                                        107
+                                    ],
+                                    "score": 1.0,
+                                    "content": "finite-horizon settings, there are straightforward definitions for both regret and sample complexity;",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                105,
+                                505,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        105,
+                                        505,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the latter is defined as the number of samples needed before the policy becomes near optimal. In this",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                115,
+                                506,
+                                127
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        115,
+                                        506,
+                                        127
+                                    ],
+                                    "score": 1.0,
+                                    "content": "setting, extensive research in the past decade (Jin et al., 2018; Azar et al., 2017; Jaksch et al., 2010;",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                126,
+                                505,
+                                139
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        126,
+                                        505,
+                                        139
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Dann et al., 2017) has achieved great progress, and established nearly-tight bounds for both regret",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                137,
+                                203,
+                                150
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        137,
+                                        203,
+                                        150
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and sample complexity.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        }
+                    ],
+                    "index": 2.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        154,
+                        505,
+                        221
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                154,
+                                505,
+                                167
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        154,
+                                        505,
+                                        167
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The infinite-horizon setting is a very different matter. First of all, the performance measure cannot be",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                165,
+                                506,
+                                177
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        165,
+                                        506,
+                                        177
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a straightforward extension of the sample complexity defined above (See Strehl & Littman (2008)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                175,
+                                505,
+                                189
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        175,
+                                        505,
+                                        189
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for detailed discussion). Instead, the measure of sample efficiency we adopt is the so-called sample",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                187,
+                                505,
+                                200
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        187,
+                                        505,
+                                        200
+                                    ],
+                                    "score": 1.0,
+                                    "content": "complexity of exploration (Kakade et al., 2003), which is also a widely-accepted definition. This",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                196,
+                                507,
+                                212
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        196,
+                                        507,
+                                        212
+                                    ],
+                                    "score": 1.0,
+                                    "content": "measure counts the number of times that the algorithm “makes mistakes” along the whole trajectory.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                208,
+                                418,
+                                222
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        208,
+                                        418,
+                                        222
+                                    ],
+                                    "score": 1.0,
+                                    "content": "See also (Strehl & Littman, 2008) for further discussions regarding this issue.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 8.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        226,
+                        505,
+                        270
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                226,
+                                507,
+                                239
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        226,
+                                        507,
+                                        239
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Several model based algorithms have been proposed for infinite horizon MDP, for example R-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                237,
+                                505,
+                                249
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        237,
+                                        452,
+                                        249
+                                    ],
+                                    "score": 1.0,
+                                    "content": "max (Brafman & Tennenholtz, 2003), MoRmax (Szita & Szepesvári, 2010) and UCRL-",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        452,
+                                        239,
+                                        460,
+                                        249
+                                    ],
+                                    "score": 0.8,
+                                    "content": "\\gamma",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        460,
+                                        237,
+                                        505,
+                                        249
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(Lattimore",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                248,
+                                505,
+                                260
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        248,
+                                        505,
+                                        260
+                                    ],
+                                    "score": 1.0,
+                                    "content": "& Hutter, 2012). It is noteworthy that there still exists a considerable gap between the state-of-the-art",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                258,
+                                499,
+                                272
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        258,
+                                        428,
+                                        272
+                                    ],
+                                    "score": 1.0,
+                                    "content": "algorithm and the theoretical lower bound (Lattimore & Hutter, 2012) regarding",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        428,
+                                        259,
+                                        470,
+                                        271
+                                    ],
+                                    "score": 0.92,
+                                    "content": "1 / ( 1 - \\gamma )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        470,
+                                        258,
+                                        499,
+                                        272
+                                    ],
+                                    "score": 1.0,
+                                    "content": "factor.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 13.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        275,
+                        505,
+                        331
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                275,
+                                507,
+                                289
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        275,
+                                        507,
+                                        289
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Though model-based algorithms have been proved to be sample efficient in various MDP settings,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                287,
+                                506,
+                                299
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        287,
+                                        506,
+                                        299
+                                    ],
+                                    "score": 1.0,
+                                    "content": "most state-of-the-art RL algorithms are developed in the model-free paradigm (Schulman et al., 2015;",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                297,
+                                506,
+                                311
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        297,
+                                        506,
+                                        311
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Mnih et al., 2013; 2016). Model-free algorithms are more flexible and require less space, which have",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                308,
+                                506,
+                                322
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        308,
+                                        506,
+                                        322
+                                    ],
+                                    "score": 1.0,
+                                    "content": "achieved remarkable performance on benchmarks such as Atari games and simulated robot control",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                319,
+                                150,
+                                332
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        319,
+                                        150,
+                                        332
+                                    ],
+                                    "score": 1.0,
+                                    "content": "problems.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        336,
+                        505,
+                        395
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                336,
+                                505,
+                                349
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        336,
+                                        505,
+                                        349
+                                    ],
+                                    "score": 1.0,
+                                    "content": "For infinite horizon MDPs without access to simulator, the best model-free algorithm has a sample",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                103,
+                                347,
+                                507,
+                                366
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        103,
+                                        347,
+                                        215,
+                                        366
+                                    ],
+                                    "score": 1.0,
+                                    "content": "complexity of exploration",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        215,
+                                        348,
+                                        266,
+                                        364
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { r } { \\tilde { \\mathcal { O } } \\big ( \\frac { S A } { \\epsilon ^ { 4 } ( 1 - \\gamma ) ^ { 8 } } \\big ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        266,
+                                        347,
+                                        507,
+                                        366
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", achieved by delayed Q-learning (Strehl et al., 2006). The",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                362,
+                                505,
+                                375
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        362,
+                                        505,
+                                        375
+                                    ],
+                                    "score": 1.0,
+                                    "content": "authors provide a novel strategy of argument when proving the upper bound for the sample complexity",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                373,
+                                506,
+                                385
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        373,
+                                        506,
+                                        385
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of exploration, namely identifying a sufficient condition for optimality, and then bound the number of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                384,
+                                251,
+                                396
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        384,
+                                        251,
+                                        396
+                                    ],
+                                    "score": 1.0,
+                                    "content": "times that this condition is violated.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 23
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        400,
+                        505,
+                        478
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                400,
+                                505,
+                                414
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        400,
+                                        401,
+                                        414
+                                    ],
+                                    "score": 1.0,
+                                    "content": "However, the results of Delayed Q-learning still leave a quadratic gap in",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        402,
+                                        401,
+                                        417,
+                                        413
+                                    ],
+                                    "score": 0.86,
+                                    "content": "1 / \\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        417,
+                                        400,
+                                        505,
+                                        414
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from the best-known",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                411,
+                                505,
+                                424
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        411,
+                                        505,
+                                        424
+                                    ],
+                                    "score": 1.0,
+                                    "content": "lower bound. This is partly because the updates in Q-value are made in an over-conservative way. In",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                423,
+                                505,
+                                434
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        423,
+                                        505,
+                                        434
+                                    ],
+                                    "score": 1.0,
+                                    "content": "fact, the loose sample complexity bound is a result of delayed Q-learning algorithm itself, as well as",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                433,
+                                505,
+                                446
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        433,
+                                        505,
+                                        446
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the mathematical artifact in their analysis. To illustrate this, we construct a hard instance showing",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                444,
+                                505,
+                                457
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        444,
+                                        231,
+                                        457
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that Delayed Q-learning incurs",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        231,
+                                        444,
+                                        266,
+                                        457
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\Omega ( 1 / \\epsilon ^ { 3 } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        266,
+                                        444,
+                                        505,
+                                        457
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sample complexity. This observation, as well as the success",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                455,
+                                505,
+                                468
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        455,
+                                        505,
+                                        468
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of the Q-learning with UCB algorithm (Jin et al., 2018) in proving a regret bound in finite-horizon",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                466,
+                                446,
+                                479
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        466,
+                                        446,
+                                        479
+                                    ],
+                                    "score": 1.0,
+                                    "content": "settings, motivates us to incorporate a UCB-like exploration term into our algorithm.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 29
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        483,
+                        505,
+                        531
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                483,
+                                505,
+                                496
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        483,
+                                        505,
+                                        496
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In this work, we propose a Q-learning algorithm with UCB exploration policy. We show the sample",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                495,
+                                507,
+                                510
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        495,
+                                        312,
+                                        510
+                                    ],
+                                    "score": 1.0,
+                                    "content": "complexity of exploration bound of our algorithm is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        312,
+                                        495,
+                                        363,
+                                        510
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { r } { \\tilde { \\mathcal { O } } \\big ( \\frac { S A } { \\epsilon ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\big ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        363,
+                                        495,
+                                        507,
+                                        510
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". This strictly improves the previous",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                508,
+                                505,
+                                521
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        508,
+                                        505,
+                                        521
+                                    ],
+                                    "score": 1.0,
+                                    "content": "best known result due to Delayed Q-learning. It also matches the lower bound in the dependence on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                519,
+                                255,
+                                533
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        522,
+                                        112,
+                                        529
+                                    ],
+                                    "score": 0.41,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        112,
+                                        519,
+                                        115,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        116,
+                                        520,
+                                        123,
+                                        530
+                                    ],
+                                    "score": 0.72,
+                                    "content": "S",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        124,
+                                        519,
+                                        141,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        142,
+                                        520,
+                                        150,
+                                        529
+                                    ],
+                                    "score": 0.68,
+                                    "content": "A",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        151,
+                                        519,
+                                        255,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": "up to logarithmic factors.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 34.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        536,
+                        505,
+                        592
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                536,
+                                505,
+                                550
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        536,
+                                        505,
+                                        550
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We point out here that the infinite-horizon setting cannot be solved by reducing to finite-horizon",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                547,
+                                504,
+                                560
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        547,
+                                        504,
+                                        560
+                                    ],
+                                    "score": 1.0,
+                                    "content": "setting. There are key technical differences between these two settings: the definition of sample",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                558,
+                                506,
+                                572
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        558,
+                                        506,
+                                        572
+                                    ],
+                                    "score": 1.0,
+                                    "content": "complexity of exploration, time-invariant policies and the error propagation structure in Q-learning.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                569,
+                                505,
+                                582
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        569,
+                                        505,
+                                        582
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In particular, the analysis techniques developed in (Jin et al., 2018) do not directly apply here. We",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                579,
+                                430,
+                                594
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        579,
+                                        430,
+                                        594
+                                    ],
+                                    "score": 1.0,
+                                    "content": "refer the readers to Section 3.2 for detailed explanations and a concrete example.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        }
+                    ],
+                    "index": 39
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        597,
+                        505,
+                        652
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                596,
+                                505,
+                                610
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        596,
+                                        505,
+                                        610
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The rest of the paper is organized as follows. After introducing the notation used in the paper in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                608,
+                                505,
+                                620
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        608,
+                                        505,
+                                        620
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Section 2, we describe our infinite Q-learning with UCB algorithm in Section 3. We then state our",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                619,
+                                505,
+                                631
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        619,
+                                        505,
+                                        631
+                                    ],
+                                    "score": 1.0,
+                                    "content": "main theoretical results, which are in the form of PAC sample complexity bounds. In Section 4 we",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                630,
+                                505,
+                                644
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        630,
+                                        505,
+                                        644
+                                    ],
+                                    "score": 1.0,
+                                    "content": "present some interesting properties beyond sample complexity bound. Finally, we conclude the paper",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                642,
+                                159,
+                                653
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        642,
+                                        159,
+                                        653
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in Section 5.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        }
+                    ],
+                    "index": 44
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        678,
+                        198,
+                        691
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                677,
+                                200,
+                                693
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        677,
+                                        200,
+                                        693
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2 PRELIMINARY",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        }
+                    ],
+                    "index": 47
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        709,
+                        504,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                709,
+                                506,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        709,
+                                        364,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We consider a Markov Decision Process defined by a five tuple",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        364,
+                                        710,
+                                        419,
+                                        721
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\langle S , \\mathcal { A } , p , r , \\gamma \\rangle",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        420,
+                                        709,
+                                        450,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        451,
+                                        710,
+                                        459,
+                                        720
+                                    ],
+                                    "score": 0.81,
+                                    "content": "s",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        459,
+                                        709,
+                                        506,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the state",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                720,
+                                505,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        720,
+                                        133,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "space,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        133,
+                                        721,
+                                        142,
+                                        730
+                                    ],
+                                    "score": 0.8,
+                                    "content": "\\mathcal { A }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        142,
+                                        720,
+                                        217,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the action space,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        218,
+                                        720,
+                                        255,
+                                        732
+                                    ],
+                                    "score": 0.94,
+                                    "content": "p ( s ^ { \\prime } | s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        256,
+                                        720,
+                                        355,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the transition function,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        356,
+                                        721,
+                                        428,
+                                        732
+                                    ],
+                                    "score": 0.9,
+                                    "content": "r : S \\times \\mathcal { A }  [ 0 , 1 ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        428,
+                                        720,
+                                        505,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the deterministic",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        }
+                    ],
+                    "index": 48.5
+                }
+            ],
+            "page_idx": 1,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        108,
+                        27,
+                        293,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                294,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        294,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        751,
+                        309,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                301,
+                                750,
+                                310,
+                                763
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        301,
+                                        750,
+                                        310,
+                                        763
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        82,
+                        505,
+                        149
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                82,
+                                505,
+                                94
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        82,
+                                        505,
+                                        94
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Without a simulator, there is a dichotomy between finite-horizon and infinite-horizon settings. In",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                92,
+                                506,
+                                107
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        92,
+                                        506,
+                                        107
+                                    ],
+                                    "score": 1.0,
+                                    "content": "finite-horizon settings, there are straightforward definitions for both regret and sample complexity;",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                105,
+                                505,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        105,
+                                        505,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the latter is defined as the number of samples needed before the policy becomes near optimal. In this",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                115,
+                                506,
+                                127
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        115,
+                                        506,
+                                        127
+                                    ],
+                                    "score": 1.0,
+                                    "content": "setting, extensive research in the past decade (Jin et al., 2018; Azar et al., 2017; Jaksch et al., 2010;",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                126,
+                                505,
+                                139
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        126,
+                                        505,
+                                        139
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Dann et al., 2017) has achieved great progress, and established nearly-tight bounds for both regret",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                137,
+                                203,
+                                150
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        137,
+                                        203,
+                                        150
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and sample complexity.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        }
+                    ],
+                    "index": 2.5,
+                    "bbox_fs": [
+                        105,
+                        82,
+                        506,
+                        150
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        154,
+                        505,
+                        221
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                154,
+                                505,
+                                167
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        154,
+                                        505,
+                                        167
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The infinite-horizon setting is a very different matter. First of all, the performance measure cannot be",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                165,
+                                506,
+                                177
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        165,
+                                        506,
+                                        177
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a straightforward extension of the sample complexity defined above (See Strehl & Littman (2008)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                175,
+                                505,
+                                189
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        175,
+                                        505,
+                                        189
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for detailed discussion). Instead, the measure of sample efficiency we adopt is the so-called sample",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                187,
+                                505,
+                                200
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        187,
+                                        505,
+                                        200
+                                    ],
+                                    "score": 1.0,
+                                    "content": "complexity of exploration (Kakade et al., 2003), which is also a widely-accepted definition. This",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                196,
+                                507,
+                                212
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        196,
+                                        507,
+                                        212
+                                    ],
+                                    "score": 1.0,
+                                    "content": "measure counts the number of times that the algorithm “makes mistakes” along the whole trajectory.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                208,
+                                418,
+                                222
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        208,
+                                        418,
+                                        222
+                                    ],
+                                    "score": 1.0,
+                                    "content": "See also (Strehl & Littman, 2008) for further discussions regarding this issue.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 8.5,
+                    "bbox_fs": [
+                        104,
+                        154,
+                        507,
+                        222
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        226,
+                        505,
+                        270
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                226,
+                                507,
+                                239
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        226,
+                                        507,
+                                        239
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Several model based algorithms have been proposed for infinite horizon MDP, for example R-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                237,
+                                505,
+                                249
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        237,
+                                        452,
+                                        249
+                                    ],
+                                    "score": 1.0,
+                                    "content": "max (Brafman & Tennenholtz, 2003), MoRmax (Szita & Szepesvári, 2010) and UCRL-",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        452,
+                                        239,
+                                        460,
+                                        249
+                                    ],
+                                    "score": 0.8,
+                                    "content": "\\gamma",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        460,
+                                        237,
+                                        505,
+                                        249
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(Lattimore",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                248,
+                                505,
+                                260
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        248,
+                                        505,
+                                        260
+                                    ],
+                                    "score": 1.0,
+                                    "content": "& Hutter, 2012). It is noteworthy that there still exists a considerable gap between the state-of-the-art",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                258,
+                                499,
+                                272
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        258,
+                                        428,
+                                        272
+                                    ],
+                                    "score": 1.0,
+                                    "content": "algorithm and the theoretical lower bound (Lattimore & Hutter, 2012) regarding",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        428,
+                                        259,
+                                        470,
+                                        271
+                                    ],
+                                    "score": 0.92,
+                                    "content": "1 / ( 1 - \\gamma )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        470,
+                                        258,
+                                        499,
+                                        272
+                                    ],
+                                    "score": 1.0,
+                                    "content": "factor.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 13.5,
+                    "bbox_fs": [
+                        105,
+                        226,
+                        507,
+                        272
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        275,
+                        505,
+                        331
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                275,
+                                507,
+                                289
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        275,
+                                        507,
+                                        289
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Though model-based algorithms have been proved to be sample efficient in various MDP settings,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                287,
+                                506,
+                                299
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        287,
+                                        506,
+                                        299
+                                    ],
+                                    "score": 1.0,
+                                    "content": "most state-of-the-art RL algorithms are developed in the model-free paradigm (Schulman et al., 2015;",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                297,
+                                506,
+                                311
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        297,
+                                        506,
+                                        311
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Mnih et al., 2013; 2016). Model-free algorithms are more flexible and require less space, which have",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                308,
+                                506,
+                                322
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        308,
+                                        506,
+                                        322
+                                    ],
+                                    "score": 1.0,
+                                    "content": "achieved remarkable performance on benchmarks such as Atari games and simulated robot control",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                319,
+                                150,
+                                332
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        319,
+                                        150,
+                                        332
+                                    ],
+                                    "score": 1.0,
+                                    "content": "problems.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 18,
+                    "bbox_fs": [
+                        104,
+                        275,
+                        507,
+                        332
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        336,
+                        505,
+                        395
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                336,
+                                505,
+                                349
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        336,
+                                        505,
+                                        349
+                                    ],
+                                    "score": 1.0,
+                                    "content": "For infinite horizon MDPs without access to simulator, the best model-free algorithm has a sample",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                103,
+                                347,
+                                507,
+                                366
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        103,
+                                        347,
+                                        215,
+                                        366
+                                    ],
+                                    "score": 1.0,
+                                    "content": "complexity of exploration",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        215,
+                                        348,
+                                        266,
+                                        364
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { r } { \\tilde { \\mathcal { O } } \\big ( \\frac { S A } { \\epsilon ^ { 4 } ( 1 - \\gamma ) ^ { 8 } } \\big ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        266,
+                                        347,
+                                        507,
+                                        366
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", achieved by delayed Q-learning (Strehl et al., 2006). The",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                362,
+                                505,
+                                375
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        362,
+                                        505,
+                                        375
+                                    ],
+                                    "score": 1.0,
+                                    "content": "authors provide a novel strategy of argument when proving the upper bound for the sample complexity",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                373,
+                                506,
+                                385
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        373,
+                                        506,
+                                        385
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of exploration, namely identifying a sufficient condition for optimality, and then bound the number of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                384,
+                                251,
+                                396
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        384,
+                                        251,
+                                        396
+                                    ],
+                                    "score": 1.0,
+                                    "content": "times that this condition is violated.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 23,
+                    "bbox_fs": [
+                        103,
+                        336,
+                        507,
+                        396
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        400,
+                        505,
+                        478
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                400,
+                                505,
+                                414
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        400,
+                                        401,
+                                        414
+                                    ],
+                                    "score": 1.0,
+                                    "content": "However, the results of Delayed Q-learning still leave a quadratic gap in",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        402,
+                                        401,
+                                        417,
+                                        413
+                                    ],
+                                    "score": 0.86,
+                                    "content": "1 / \\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        417,
+                                        400,
+                                        505,
+                                        414
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from the best-known",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                411,
+                                505,
+                                424
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        411,
+                                        505,
+                                        424
+                                    ],
+                                    "score": 1.0,
+                                    "content": "lower bound. This is partly because the updates in Q-value are made in an over-conservative way. In",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                423,
+                                505,
+                                434
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        423,
+                                        505,
+                                        434
+                                    ],
+                                    "score": 1.0,
+                                    "content": "fact, the loose sample complexity bound is a result of delayed Q-learning algorithm itself, as well as",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                433,
+                                505,
+                                446
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        433,
+                                        505,
+                                        446
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the mathematical artifact in their analysis. To illustrate this, we construct a hard instance showing",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                444,
+                                505,
+                                457
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        444,
+                                        231,
+                                        457
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that Delayed Q-learning incurs",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        231,
+                                        444,
+                                        266,
+                                        457
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\Omega ( 1 / \\epsilon ^ { 3 } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        266,
+                                        444,
+                                        505,
+                                        457
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sample complexity. This observation, as well as the success",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                455,
+                                505,
+                                468
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        455,
+                                        505,
+                                        468
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of the Q-learning with UCB algorithm (Jin et al., 2018) in proving a regret bound in finite-horizon",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                466,
+                                446,
+                                479
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        466,
+                                        446,
+                                        479
+                                    ],
+                                    "score": 1.0,
+                                    "content": "settings, motivates us to incorporate a UCB-like exploration term into our algorithm.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 29,
+                    "bbox_fs": [
+                        105,
+                        400,
+                        505,
+                        479
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        483,
+                        505,
+                        531
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                483,
+                                505,
+                                496
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        483,
+                                        505,
+                                        496
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In this work, we propose a Q-learning algorithm with UCB exploration policy. We show the sample",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                495,
+                                507,
+                                510
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        495,
+                                        312,
+                                        510
+                                    ],
+                                    "score": 1.0,
+                                    "content": "complexity of exploration bound of our algorithm is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        312,
+                                        495,
+                                        363,
+                                        510
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { r } { \\tilde { \\mathcal { O } } \\big ( \\frac { S A } { \\epsilon ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\big ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        363,
+                                        495,
+                                        507,
+                                        510
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". This strictly improves the previous",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                508,
+                                505,
+                                521
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        508,
+                                        505,
+                                        521
+                                    ],
+                                    "score": 1.0,
+                                    "content": "best known result due to Delayed Q-learning. It also matches the lower bound in the dependence on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                519,
+                                255,
+                                533
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        522,
+                                        112,
+                                        529
+                                    ],
+                                    "score": 0.41,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        112,
+                                        519,
+                                        115,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        116,
+                                        520,
+                                        123,
+                                        530
+                                    ],
+                                    "score": 0.72,
+                                    "content": "S",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        124,
+                                        519,
+                                        141,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        142,
+                                        520,
+                                        150,
+                                        529
+                                    ],
+                                    "score": 0.68,
+                                    "content": "A",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        151,
+                                        519,
+                                        255,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": "up to logarithmic factors.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 34.5,
+                    "bbox_fs": [
+                        105,
+                        483,
+                        507,
+                        533
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        536,
+                        505,
+                        592
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                536,
+                                505,
+                                550
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        536,
+                                        505,
+                                        550
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We point out here that the infinite-horizon setting cannot be solved by reducing to finite-horizon",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                547,
+                                504,
+                                560
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        547,
+                                        504,
+                                        560
+                                    ],
+                                    "score": 1.0,
+                                    "content": "setting. There are key technical differences between these two settings: the definition of sample",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                558,
+                                506,
+                                572
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        558,
+                                        506,
+                                        572
+                                    ],
+                                    "score": 1.0,
+                                    "content": "complexity of exploration, time-invariant policies and the error propagation structure in Q-learning.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                569,
+                                505,
+                                582
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        569,
+                                        505,
+                                        582
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In particular, the analysis techniques developed in (Jin et al., 2018) do not directly apply here. We",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                579,
+                                430,
+                                594
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        579,
+                                        430,
+                                        594
+                                    ],
+                                    "score": 1.0,
+                                    "content": "refer the readers to Section 3.2 for detailed explanations and a concrete example.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        }
+                    ],
+                    "index": 39,
+                    "bbox_fs": [
+                        105,
+                        536,
+                        506,
+                        594
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        597,
+                        505,
+                        652
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                596,
+                                505,
+                                610
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        596,
+                                        505,
+                                        610
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The rest of the paper is organized as follows. After introducing the notation used in the paper in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                608,
+                                505,
+                                620
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        608,
+                                        505,
+                                        620
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Section 2, we describe our infinite Q-learning with UCB algorithm in Section 3. We then state our",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                619,
+                                505,
+                                631
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        619,
+                                        505,
+                                        631
+                                    ],
+                                    "score": 1.0,
+                                    "content": "main theoretical results, which are in the form of PAC sample complexity bounds. In Section 4 we",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                630,
+                                505,
+                                644
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        630,
+                                        505,
+                                        644
+                                    ],
+                                    "score": 1.0,
+                                    "content": "present some interesting properties beyond sample complexity bound. Finally, we conclude the paper",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                642,
+                                159,
+                                653
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        642,
+                                        159,
+                                        653
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in Section 5.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        }
+                    ],
+                    "index": 44,
+                    "bbox_fs": [
+                        105,
+                        596,
+                        505,
+                        653
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        678,
+                        198,
+                        691
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                677,
+                                200,
+                                693
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        677,
+                                        200,
+                                        693
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2 PRELIMINARY",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        }
+                    ],
+                    "index": 47
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        709,
+                        504,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                709,
+                                506,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        709,
+                                        364,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We consider a Markov Decision Process defined by a five tuple",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        364,
+                                        710,
+                                        419,
+                                        721
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\langle S , \\mathcal { A } , p , r , \\gamma \\rangle",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        420,
+                                        709,
+                                        450,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        451,
+                                        710,
+                                        459,
+                                        720
+                                    ],
+                                    "score": 0.81,
+                                    "content": "s",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        459,
+                                        709,
+                                        506,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the state",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                720,
+                                505,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        720,
+                                        133,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "space,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        133,
+                                        721,
+                                        142,
+                                        730
+                                    ],
+                                    "score": 0.8,
+                                    "content": "\\mathcal { A }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        142,
+                                        720,
+                                        217,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the action space,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        218,
+                                        720,
+                                        255,
+                                        732
+                                    ],
+                                    "score": 0.94,
+                                    "content": "p ( s ^ { \\prime } | s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        256,
+                                        720,
+                                        355,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the transition function,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        356,
+                                        721,
+                                        428,
+                                        732
+                                    ],
+                                    "score": 0.9,
+                                    "content": "r : S \\times \\mathcal { A }  [ 0 , 1 ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        428,
+                                        720,
+                                        505,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the deterministic",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                82,
+                                505,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        82,
+                                        191,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "reward function, and",
+                                    "type": "text",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        191,
+                                        83,
+                                        235,
+                                        94
+                                    ],
+                                    "score": 0.93,
+                                    "content": "0 \\leq \\gamma < 1",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        235,
+                                        82,
+                                        388,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the discount factor for rewards. Let",
+                                    "type": "text",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        388,
+                                        82,
+                                        421,
+                                        95
+                                    ],
+                                    "score": 0.93,
+                                    "content": "S = | S |",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        421,
+                                        82,
+                                        439,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        439,
+                                        82,
+                                        475,
+                                        95
+                                    ],
+                                    "score": 0.92,
+                                    "content": "A = | { \\mathcal { A } } |",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        475,
+                                        82,
+                                        505,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "denote",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                92,
+                                347,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        92,
+                                        347,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the number of states and the number of actions respectively.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 48.5,
+                    "bbox_fs": [
+                        105,
+                        709,
+                        506,
+                        733
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        82,
+                        504,
+                        105
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                82,
+                                505,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        82,
+                                        191,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "reward function, and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        191,
+                                        83,
+                                        235,
+                                        94
+                                    ],
+                                    "score": 0.93,
+                                    "content": "0 \\leq \\gamma < 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        235,
+                                        82,
+                                        388,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the discount factor for rewards. Let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        388,
+                                        82,
+                                        421,
+                                        95
+                                    ],
+                                    "score": 0.93,
+                                    "content": "S = | S |",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        421,
+                                        82,
+                                        439,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        439,
+                                        82,
+                                        475,
+                                        95
+                                    ],
+                                    "score": 0.92,
+                                    "content": "A = | { \\mathcal { A } } |",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        475,
+                                        82,
+                                        505,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "denote",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                92,
+                                347,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        92,
+                                        347,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the number of states and the number of actions respectively.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        110,
+                        504,
+                        144
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                110,
+                                506,
+                                124
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        110,
+                                        191,
+                                        124
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Starting from a state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        191,
+                                        113,
+                                        201,
+                                        122
+                                    ],
+                                    "score": 0.86,
+                                    "content": "s _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        202,
+                                        110,
+                                        506,
+                                        124
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the agent interacts with the environment for infinite number of time steps.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                121,
+                                505,
+                                133
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        121,
+                                        278,
+                                        133
+                                    ],
+                                    "score": 1.0,
+                                    "content": "At each time step, the agent observes state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        278,
+                                        122,
+                                        307,
+                                        132
+                                    ],
+                                    "score": 0.93,
+                                    "content": "s _ { t } \\in S",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        121,
+                                        361,
+                                        133
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", picks action",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        361,
+                                        122,
+                                        391,
+                                        132
+                                    ],
+                                    "score": 0.91,
+                                    "content": "a _ { t } \\in \\mathcal A",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        392,
+                                        121,
+                                        477,
+                                        133
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and receives reward",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        477,
+                                        123,
+                                        486,
+                                        132
+                                    ],
+                                    "score": 0.85,
+                                    "content": "r _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        486,
+                                        121,
+                                        505,
+                                        133
+                                    ],
+                                    "score": 1.0,
+                                    "content": "; the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                131,
+                                262,
+                                146
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        131,
+                                        238,
+                                        146
+                                    ],
+                                    "score": 1.0,
+                                    "content": "system then transits to next state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        238,
+                                        134,
+                                        257,
+                                        144
+                                    ],
+                                    "score": 0.9,
+                                    "content": "s _ { t + 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        258,
+                                        131,
+                                        262,
+                                        146
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        148,
+                        505,
+                        216
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                147,
+                                506,
+                                163
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        147,
+                                        319,
+                                        163
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Using the notations in Strehl et al. (2006), a policy",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        319,
+                                        151,
+                                        330,
+                                        160
+                                    ],
+                                    "score": 0.86,
+                                    "content": "\\pi _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        330,
+                                        147,
+                                        506,
+                                        163
+                                    ],
+                                    "score": 1.0,
+                                    "content": "refers to the non-stationary control policy",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                159,
+                                506,
+                                173
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        159,
+                                        218,
+                                        173
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of the algorithm since step",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        218,
+                                        161,
+                                        223,
+                                        170
+                                    ],
+                                    "score": 0.62,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        223,
+                                        159,
+                                        260,
+                                        173
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". We use",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        261,
+                                        160,
+                                        290,
+                                        172
+                                    ],
+                                    "score": 0.91,
+                                    "content": "V ^ { \\pi _ { t } } ( s )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        291,
+                                        159,
+                                        463,
+                                        173
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to denote the value function under policy",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        463,
+                                        162,
+                                        473,
+                                        171
+                                    ],
+                                    "score": 0.82,
+                                    "content": "\\pi _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        474,
+                                        159,
+                                        506,
+                                        173
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", which",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                102,
+                                166,
+                                504,
+                                188
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        102,
+                                        166,
+                                        160,
+                                        188
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is defined as",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        160,
+                                        171,
+                                        360,
+                                        184
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\begin{array} { r } { V ^ { \\pi _ { t } } ( s ) = \\mathbb { E } \\bigl [ \\sum _ { i = 1 } ^ { \\infty } \\gamma ^ { i - 1 } r ( s _ { i } , \\pi _ { t + i - 1 } ( s _ { i } ) ) | s _ { 1 } = s \\bigr ] } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        361,
+                                        166,
+                                        416,
+                                        188
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". We also use",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        416,
+                                        171,
+                                        504,
+                                        183
+                                    ],
+                                    "score": 0.91,
+                                    "content": "V ^ { * } ( s ) = \\operatorname* { s u p } _ { \\pi } V ^ { \\pi } ( s )",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                181,
+                                509,
+                                211
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        181,
+                                        414,
+                                        195
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to denote the value function of the optimal policy. Accordingly, we define",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        192,
+                                        296,
+                                        206
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\begin{array} { r } { \\mathbb { E } [ \\sum _ { i = 2 } ^ { \\infty } \\gamma ^ { i - 1 } r ( s _ { i } , \\pi _ { t + i - 1 } ( s _ { i } ) ) | s _ { 1 } = \\stackrel { \\cdot } { s } , a _ { 1 } = \\stackrel { \\cdot } { a } ] } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        297,
+                                        187,
+                                        322,
+                                        211
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        323,
+                                        194,
+                                        332,
+                                        204
+                                    ],
+                                    "score": 0.26,
+                                    "content": "\\mathrm { Q }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        332,
+                                        187,
+                                        420,
+                                        211
+                                    ],
+                                    "score": 1.0,
+                                    "content": "function under policy",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        415,
+                                        183,
+                                        506,
+                                        194
+                                    ],
+                                    "score": 0.86,
+                                    "content": "Q ^ { \\pi _ { t } } ( s , a ) = r ( s , a ) +",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        420,
+                                        195,
+                                        430,
+                                        204
+                                    ],
+                                    "score": 0.64,
+                                    "content": "\\pi _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        430,
+                                        187,
+                                        434,
+                                        211
+                                    ],
+                                    "score": 1.0,
+                                    "content": ";",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        435,
+                                        194,
+                                        470,
+                                        205
+                                    ],
+                                    "score": 0.89,
+                                    "content": "Q ^ { * } ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        470,
+                                        187,
+                                        509,
+                                        211
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the Q",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                204,
+                                243,
+                                217
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        204,
+                                        227,
+                                        217
+                                    ],
+                                    "score": 1.0,
+                                    "content": "function under optimal policy",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        227,
+                                        205,
+                                        239,
+                                        214
+                                    ],
+                                    "score": 0.84,
+                                    "content": "\\pi ^ { * }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        239,
+                                        204,
+                                        243,
+                                        217
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        221,
+                        503,
+                        254
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                219,
+                                505,
+                                235
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        219,
+                                        505,
+                                        235
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We use the sample complexity of exploration defined in Kakade et al. (2003) to measure the learning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                232,
+                                505,
+                                244
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        232,
+                                        505,
+                                        244
+                                    ],
+                                    "score": 1.0,
+                                    "content": "efficiency of our algorithm. This sample complexity definition has been widely used in previous",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                243,
+                                427,
+                                255
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        243,
+                                        351,
+                                        255
+                                    ],
+                                    "score": 1.0,
+                                    "content": "works Strehl et al. (2006); Lattimore & Hutter (2012); Strehl",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        351,
+                                        244,
+                                        360,
+                                        253
+                                    ],
+                                    "score": 0.28,
+                                    "content": "\\&",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        360,
+                                        243,
+                                        427,
+                                        255
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Littman (2008).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        256,
+                        506,
+                        290
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                255,
+                                506,
+                                269
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        255,
+                                        380,
+                                        269
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Definition 1. Sample complexity of Exploration of an algorithm",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        380,
+                                        256,
+                                        402,
+                                        267
+                                    ],
+                                    "score": 0.56,
+                                    "content": "\\mathcal { A L G }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        403,
+                                        255,
+                                        506,
+                                        269
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is defined as the number",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                267,
+                                507,
+                                281
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        267,
+                                        302,
+                                        281
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of time steps t such that the non-stationary policy",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        269,
+                                        313,
+                                        278
+                                    ],
+                                    "score": 0.84,
+                                    "content": "\\pi _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        313,
+                                        267,
+                                        344,
+                                        281
+                                    ],
+                                    "score": 1.0,
+                                    "content": "at time",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        344,
+                                        269,
+                                        349,
+                                        277
+                                    ],
+                                    "score": 0.68,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        349,
+                                        267,
+                                        374,
+                                        281
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is not",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        374,
+                                        270,
+                                        379,
+                                        277
+                                    ],
+                                    "score": 0.47,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        380,
+                                        267,
+                                        479,
+                                        281
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimal for current state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        479,
+                                        269,
+                                        488,
+                                        278
+                                    ],
+                                    "score": 0.8,
+                                    "content": "s _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        489,
+                                        267,
+                                        507,
+                                        281
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", i.e.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                276,
+                                207,
+                                291
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        278,
+                                        203,
+                                        290
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\dot { V } ^ { \\pi _ { t } } \\left( s _ { t } \\right) \\dot { < } V ^ { * } \\left( s _ { t } \\right) - \\epsilon .",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        203,
+                                        276,
+                                        207,
+                                        291
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        297,
+                        504,
+                        320
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                296,
+                                505,
+                                311
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        296,
+                                        505,
+                                        311
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Roughly speaking, this measure counts the number of mistakes along the whole trajectory. We use",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                307,
+                                339,
+                                320
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        307,
+                                        339,
+                                        320
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the following definition of PAC-MDP Strehl et al. (2006).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 16.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        321,
+                        505,
+                        356
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                321,
+                                505,
+                                335
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        321,
+                                        223,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Definition 2. An algorithm",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        223,
+                                        321,
+                                        246,
+                                        332
+                                    ],
+                                    "score": 0.67,
+                                    "content": "\\mathcal { A L G }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        246,
+                                        321,
+                                        505,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is said to be PAC-MDP (Probably Approximately Correct in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                332,
+                                505,
+                                345
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        332,
+                                        225,
+                                        345
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Markov Decision Processes)",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        226,
+                                        333,
+                                        235,
+                                        344
+                                    ],
+                                    "score": 0.67,
+                                    "content": "i f ,",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        235,
+                                        332,
+                                        294,
+                                        345
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for any \u000f and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        294,
+                                        333,
+                                        300,
+                                        342
+                                    ],
+                                    "score": 0.65,
+                                    "content": "\\delta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        300,
+                                        332,
+                                        409,
+                                        345
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the sample complexity of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        409,
+                                        333,
+                                        432,
+                                        343
+                                    ],
+                                    "score": 0.61,
+                                    "content": "\\mathcal { A L G }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        432,
+                                        332,
+                                        505,
+                                        345
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is less than some",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                343,
+                                493,
+                                357
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        343,
+                                        255,
+                                        357
+                                    ],
+                                    "score": 1.0,
+                                    "content": "polynomial in the relevant quantities",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        255,
+                                        343,
+                                        363,
+                                        356
+                                    ],
+                                    "score": 0.89,
+                                    "content": "( S , A , 1 / \\epsilon , 1 / \\delta , 1 / ( 1 - \\gamma ) )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        363,
+                                        343,
+                                        465,
+                                        357
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", with probability at least",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        466,
+                                        344,
+                                        488,
+                                        354
+                                    ],
+                                    "score": 0.85,
+                                    "content": "1 - \\delta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        489,
+                                        343,
+                                        493,
+                                        357
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 19
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        362,
+                        363,
+                        374
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                361,
+                                365,
+                                376
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        361,
+                                        365,
+                                        376
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Finally, recall that Bellman equation is defined as the following:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 21
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        142,
+                        375,
+                        462,
+                        403
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                142,
+                                375,
+                                462,
+                                403
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        375,
+                                        462,
+                                        403
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\left\\{ \\begin{array} { l l } { V ^ { \\pi _ { t } } ( s ) = Q ^ { \\pi _ { t } } \\left( s , \\pi _ { t } ( s ) \\right) } \\\\ { Q ^ { \\pi _ { t } } ( s , a ) : = \\left( r _ { t } + \\gamma \\mathbb { P } V ^ { \\pi _ { t + 1 } } \\right) ( s , a ) , } \\end{array} \\right. \\quad \\left\\{ \\begin{array} { l l } { V ^ { * } ( s ) = Q ^ { * } \\left( s , \\pi ^ { * } ( s ) \\right) } \\\\ { Q ^ { * } ( s , a ) : = \\left( r _ { t } + \\gamma \\mathbb { P } V ^ { * } \\right) ( s , a ) , } \\end{array} \\right.",
+                                    "type": "interline_equation",
+                                    "image_path": "59cd62d5ec6d571803efed659b258dfba8d0141783a9422cc7a1cf15db20a44e.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 22,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                142,
+                                375,
+                                462,
+                                403
+                            ],
+                            "spans": [],
+                            "index": 22
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        103,
+                        403,
+                        493,
+                        416
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                400,
+                                493,
+                                419
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        400,
+                                        335,
+                                        419
+                                    ],
+                                    "score": 1.0,
+                                    "content": "which is frequently used in our analysis. Here we denote",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        335,
+                                        404,
+                                        493,
+                                        416
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\left[ \\mathbb { P } V ^ { \\pi _ { t } } \\right] ( s , a ) : = \\mathbb { E } _ { s ^ { \\prime } \\sim p ( \\cdot \\vert s , a ) } V ^ { \\pi _ { t + 1 } } ( s ^ { \\prime } ) .",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 23
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        430,
+                        206,
+                        443
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                428,
+                                207,
+                                445
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        428,
+                                        207,
+                                        445
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3 MAIN RESULTS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 24
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        102,
+                        454,
+                        475,
+                        467
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                453,
+                                476,
+                                469
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        453,
+                                        476,
+                                        469
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In this section, we present the UCB Q-learning algorithm and the sample complexity bound.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 25
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        478,
+                        186,
+                        490
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                478,
+                                187,
+                                491
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        478,
+                                        187,
+                                        491
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3.1 ALGORITHM",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 26
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        502,
+                        279,
+                        514
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                501,
+                                281,
+                                516
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        501,
+                                        281,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Algorithm 1 Infinite Q-learning with UCB",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 27
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        110,
+                        516,
+                        504,
+                        681
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                123,
+                                515,
+                                201,
+                                528
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        123,
+                                        515,
+                                        201,
+                                        528
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Parameters: \u000f, γ, δ",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                122,
+                                526,
+                                479,
+                                562
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        122,
+                                        526,
+                                        155,
+                                        543
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Initializ",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        155,
+                                        526,
+                                        479,
+                                        562
+                                    ],
+                                    "score": 0.69,
+                                    "content": "\\begin{array} { r l } & { \\textnormal { \\texttt { e } } Q ( s , a ) , \\hat { Q } ( s , a ) \\gets \\frac { 1 } { 1 - \\gamma } , N ( s , a ) \\gets 0 , \\epsilon _ { 1 } \\gets \\frac { \\epsilon } { 2 4 R M \\ln \\frac { 1 } { 1 - \\gamma } } , H \\gets \\frac { \\ln 1 / ( ( 1 - \\gamma ) \\epsilon _ { 1 } ) } { \\ln 1 / \\gamma } . } \\\\ & { \\cdot ( k ) = \\ln ( S A ( k + 1 ) ( k + 2 ) / \\delta ) , \\alpha _ { k } = \\frac { H + 1 } { H + k } . } \\end{array}",
+                                    "type": "inline_equation",
+                                    "image_path": "ad0c57b5739df10ef8c0d2046656de08d85d51ac78dc2acbfb1350115223ebf4.jpg"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                122,
+                                542,
+                                153,
+                                560
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        122,
+                                        542,
+                                        153,
+                                        560
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Define",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                123,
+                                557,
+                                197,
+                                570
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        123,
+                                        557,
+                                        138,
+                                        570
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        138,
+                                        559,
+                                        197,
+                                        569
+                                    ],
+                                    "score": 0.66,
+                                    "content": "t = 1 , 2 , \\dots \\mathbf { d o }",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                110,
+                                569,
+                                293,
+                                583
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        570,
+                                        123,
+                                        583
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5:",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        137,
+                                        569,
+                                        186,
+                                        583
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Take action",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        187,
+                                        569,
+                                        293,
+                                        582
+                                    ],
+                                    "score": 0.73,
+                                    "content": "a _ { t } \\gets \\arg \\operatorname* { m a x } _ { a ^ { \\prime } } \\hat { Q } ( s _ { t } , a ^ { \\prime } )",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                137,
+                                580,
+                                288,
+                                594
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        137,
+                                        580,
+                                        288,
+                                        594
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Receive reward rt and transit to st+1",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                137,
+                                590,
+                                504,
+                                670
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        137,
+                                        590,
+                                        411,
+                                        670
+                                    ],
+                                    "score": 0.48,
+                                    "content": "\\begin{array} { r l r } & { N ( s _ { t } , a _ { t } ) \\gets N ( s _ { t } , a _ { t } ) + 1 } & \\\\ & { N ( s _ { t } , a _ { t } ) \\gets N ( s _ { t } , a _ { t } ) + 1 } & \\\\ & { k \\gets N ( s _ { t } , a _ { t } ) , b _ { k } \\gets \\frac { c _ { 2 } } { 1 - \\gamma } \\sqrt { \\frac { H ( k ) } { k } } } & \\\\ & { \\hat { V } ( s _ { t + 1 } ) \\gets \\operatorname* { m a x } _ { a \\in A } \\hat { Q } ( s _ { t + 1 } , a ) } & \\\\ & { Q ( s _ { t } , a _ { t } ) \\gets ( 1 - \\alpha _ { k } ) Q ( s _ { t } , a _ { t } ) + \\alpha _ { k } \\left[ r ( s _ { t } , a _ { t } ) + b _ { k } + \\gamma \\hat { V } ( s _ { t + 1 } ) \\right] } \\\\ & { \\hat { Q } ( s _ { t } , a _ { t } ) \\gets \\operatorname* { m i n } ( \\hat { Q } ( s _ { t } , a _ { t } ) , Q ( s _ { t } , a _ { t } ) ) } & \\end{array}",
+                                    "type": "inline_equation",
+                                    "image_path": "d5388b49142af9a03fc552a4ec774a7df6c96f7f162f72703f3ded5df679058d.jpg"
+                                },
+                                {
+                                    "bbox": [
+                                        411,
+                                        608,
+                                        484,
+                                        621
+                                    ],
+                                    "score": 1.0,
+                                    "content": "t and can be set to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        484,
+                                        608,
+                                        504,
+                                        621
+                                    ],
+                                    "score": 0.88,
+                                    "content": "4 { \\sqrt { 2 } }",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                639,
+                                122,
+                                651
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        639,
+                                        122,
+                                        651
+                                    ],
+                                    "score": 1.0,
+                                    "content": "10:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                122,
+                                666,
+                                158,
+                                679
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        122,
+                                        666,
+                                        158,
+                                        679
+                                    ],
+                                    "score": 1.0,
+                                    "content": "end for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 32
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        691,
+                        505,
+                        735
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                690,
+                                507,
+                                710
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        690,
+                                        129,
+                                        710
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Here",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        129,
+                                        692,
+                                        173,
+                                        704
+                                    ],
+                                    "score": 0.93,
+                                    "content": "c _ { 2 } = 4 \\sqrt { 2 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        173,
+                                        690,
+                                        232,
+                                        710
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is a constant.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        233,
+                                        692,
+                                        338,
+                                        708
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { r } { R = \\lceil \\ln \\frac { 3 } { \\epsilon ( 1 - \\gamma ) } / ( 1 - \\gamma ) \\rceil } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        339,
+                                        690,
+                                        424,
+                                        710
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", while the choice of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        425,
+                                        694,
+                                        437,
+                                        703
+                                    ],
+                                    "score": 0.8,
+                                    "content": "M",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        437,
+                                        690,
+                                        507,
+                                        710
+                                    ],
+                                    "score": 1.0,
+                                    "content": "can be found in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                705,
+                                505,
+                                719
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        705,
+                                        162,
+                                        719
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Section. 3.3.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        162,
+                                        707,
+                                        270,
+                                        719
+                                    ],
+                                    "score": 0.75,
+                                    "content": "{ \\cal { \\left( M = 0 \\left( \\ln 1 / ( 1 - \\gamma ) \\epsilon \\right) \\right) } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        271,
+                                        705,
+                                        401,
+                                        719
+                                    ],
+                                    "score": 1.0,
+                                    "content": "). The learning rate is defined as",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        402,
+                                        706,
+                                        501,
+                                        719
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\alpha _ { k } = ( H + 1 ) / ( H + k )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        501,
+                                        705,
+                                        505,
+                                        719
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                714,
+                                366,
+                                738
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        720,
+                                        117,
+                                        730
+                                    ],
+                                    "score": 0.79,
+                                    "content": "H",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        117,
+                                        714,
+                                        168,
+                                        738
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is chosen as",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        169,
+                                        718,
+                                        222,
+                                        735
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\frac { \\ln { 1 } / ( ( 1 - \\gamma ) \\epsilon _ { 1 } ) } { \\ln { 1 } / \\gamma }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        222,
+                                        714,
+                                        287,
+                                        738
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", which satisfies",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        287,
+                                        718,
+                                        363,
+                                        735
+                                    ],
+                                    "score": 0.93,
+                                    "content": "H \\leq \\frac { \\ln 1 / ( ( 1 - \\gamma ) \\epsilon _ { 1 } ) } { 1 - \\gamma }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        363,
+                                        714,
+                                        366,
+                                        738
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 38
+                }
+            ],
+            "page_idx": 2,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        26,
+                        293,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                25,
+                                294,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        25,
+                                        294,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        751,
+                        309,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                301,
+                                750,
+                                310,
+                                762
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        301,
+                                        750,
+                                        310,
+                                        762
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        82,
+                        504,
+                        105
+                    ],
+                    "lines": [],
+                    "index": 0.5,
+                    "bbox_fs": [
+                        105,
+                        82,
+                        505,
+                        106
+                    ],
+                    "lines_deleted": true
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        110,
+                        504,
+                        144
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                110,
+                                506,
+                                124
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        110,
+                                        191,
+                                        124
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Starting from a state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        191,
+                                        113,
+                                        201,
+                                        122
+                                    ],
+                                    "score": 0.86,
+                                    "content": "s _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        202,
+                                        110,
+                                        506,
+                                        124
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the agent interacts with the environment for infinite number of time steps.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                121,
+                                505,
+                                133
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        121,
+                                        278,
+                                        133
+                                    ],
+                                    "score": 1.0,
+                                    "content": "At each time step, the agent observes state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        278,
+                                        122,
+                                        307,
+                                        132
+                                    ],
+                                    "score": 0.93,
+                                    "content": "s _ { t } \\in S",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        121,
+                                        361,
+                                        133
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", picks action",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        361,
+                                        122,
+                                        391,
+                                        132
+                                    ],
+                                    "score": 0.91,
+                                    "content": "a _ { t } \\in \\mathcal A",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        392,
+                                        121,
+                                        477,
+                                        133
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and receives reward",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        477,
+                                        123,
+                                        486,
+                                        132
+                                    ],
+                                    "score": 0.85,
+                                    "content": "r _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        486,
+                                        121,
+                                        505,
+                                        133
+                                    ],
+                                    "score": 1.0,
+                                    "content": "; the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                131,
+                                262,
+                                146
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        131,
+                                        238,
+                                        146
+                                    ],
+                                    "score": 1.0,
+                                    "content": "system then transits to next state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        238,
+                                        134,
+                                        257,
+                                        144
+                                    ],
+                                    "score": 0.9,
+                                    "content": "s _ { t + 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        258,
+                                        131,
+                                        262,
+                                        146
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 3,
+                    "bbox_fs": [
+                        105,
+                        110,
+                        506,
+                        146
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        148,
+                        505,
+                        216
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                147,
+                                506,
+                                163
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        147,
+                                        319,
+                                        163
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Using the notations in Strehl et al. (2006), a policy",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        319,
+                                        151,
+                                        330,
+                                        160
+                                    ],
+                                    "score": 0.86,
+                                    "content": "\\pi _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        330,
+                                        147,
+                                        506,
+                                        163
+                                    ],
+                                    "score": 1.0,
+                                    "content": "refers to the non-stationary control policy",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                159,
+                                506,
+                                173
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        159,
+                                        218,
+                                        173
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of the algorithm since step",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        218,
+                                        161,
+                                        223,
+                                        170
+                                    ],
+                                    "score": 0.62,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        223,
+                                        159,
+                                        260,
+                                        173
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". We use",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        261,
+                                        160,
+                                        290,
+                                        172
+                                    ],
+                                    "score": 0.91,
+                                    "content": "V ^ { \\pi _ { t } } ( s )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        291,
+                                        159,
+                                        463,
+                                        173
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to denote the value function under policy",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        463,
+                                        162,
+                                        473,
+                                        171
+                                    ],
+                                    "score": 0.82,
+                                    "content": "\\pi _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        474,
+                                        159,
+                                        506,
+                                        173
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", which",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                102,
+                                166,
+                                504,
+                                188
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        102,
+                                        166,
+                                        160,
+                                        188
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is defined as",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        160,
+                                        171,
+                                        360,
+                                        184
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\begin{array} { r } { V ^ { \\pi _ { t } } ( s ) = \\mathbb { E } \\bigl [ \\sum _ { i = 1 } ^ { \\infty } \\gamma ^ { i - 1 } r ( s _ { i } , \\pi _ { t + i - 1 } ( s _ { i } ) ) | s _ { 1 } = s \\bigr ] } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        361,
+                                        166,
+                                        416,
+                                        188
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". We also use",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        416,
+                                        171,
+                                        504,
+                                        183
+                                    ],
+                                    "score": 0.91,
+                                    "content": "V ^ { * } ( s ) = \\operatorname* { s u p } _ { \\pi } V ^ { \\pi } ( s )",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                181,
+                                509,
+                                211
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        181,
+                                        414,
+                                        195
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to denote the value function of the optimal policy. Accordingly, we define",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        192,
+                                        296,
+                                        206
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\begin{array} { r } { \\mathbb { E } [ \\sum _ { i = 2 } ^ { \\infty } \\gamma ^ { i - 1 } r ( s _ { i } , \\pi _ { t + i - 1 } ( s _ { i } ) ) | s _ { 1 } = \\stackrel { \\cdot } { s } , a _ { 1 } = \\stackrel { \\cdot } { a } ] } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        297,
+                                        187,
+                                        322,
+                                        211
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        323,
+                                        194,
+                                        332,
+                                        204
+                                    ],
+                                    "score": 0.26,
+                                    "content": "\\mathrm { Q }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        332,
+                                        187,
+                                        420,
+                                        211
+                                    ],
+                                    "score": 1.0,
+                                    "content": "function under policy",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        415,
+                                        183,
+                                        506,
+                                        194
+                                    ],
+                                    "score": 0.86,
+                                    "content": "Q ^ { \\pi _ { t } } ( s , a ) = r ( s , a ) +",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        420,
+                                        195,
+                                        430,
+                                        204
+                                    ],
+                                    "score": 0.64,
+                                    "content": "\\pi _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        430,
+                                        187,
+                                        434,
+                                        211
+                                    ],
+                                    "score": 1.0,
+                                    "content": ";",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        435,
+                                        194,
+                                        470,
+                                        205
+                                    ],
+                                    "score": 0.89,
+                                    "content": "Q ^ { * } ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        470,
+                                        187,
+                                        509,
+                                        211
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the Q",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                204,
+                                243,
+                                217
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        204,
+                                        227,
+                                        217
+                                    ],
+                                    "score": 1.0,
+                                    "content": "function under optimal policy",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        227,
+                                        205,
+                                        239,
+                                        214
+                                    ],
+                                    "score": 0.84,
+                                    "content": "\\pi ^ { * }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        239,
+                                        204,
+                                        243,
+                                        217
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 7,
+                    "bbox_fs": [
+                        102,
+                        147,
+                        509,
+                        217
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        221,
+                        503,
+                        254
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                219,
+                                505,
+                                235
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        219,
+                                        505,
+                                        235
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We use the sample complexity of exploration defined in Kakade et al. (2003) to measure the learning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                232,
+                                505,
+                                244
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        232,
+                                        505,
+                                        244
+                                    ],
+                                    "score": 1.0,
+                                    "content": "efficiency of our algorithm. This sample complexity definition has been widely used in previous",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                243,
+                                427,
+                                255
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        243,
+                                        351,
+                                        255
+                                    ],
+                                    "score": 1.0,
+                                    "content": "works Strehl et al. (2006); Lattimore & Hutter (2012); Strehl",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        351,
+                                        244,
+                                        360,
+                                        253
+                                    ],
+                                    "score": 0.28,
+                                    "content": "\\&",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        360,
+                                        243,
+                                        427,
+                                        255
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Littman (2008).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "index": 11,
+                    "bbox_fs": [
+                        105,
+                        219,
+                        505,
+                        255
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        256,
+                        506,
+                        290
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                255,
+                                506,
+                                269
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        255,
+                                        380,
+                                        269
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Definition 1. Sample complexity of Exploration of an algorithm",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        380,
+                                        256,
+                                        402,
+                                        267
+                                    ],
+                                    "score": 0.56,
+                                    "content": "\\mathcal { A L G }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        403,
+                                        255,
+                                        506,
+                                        269
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is defined as the number",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                267,
+                                507,
+                                281
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        267,
+                                        302,
+                                        281
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of time steps t such that the non-stationary policy",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        269,
+                                        313,
+                                        278
+                                    ],
+                                    "score": 0.84,
+                                    "content": "\\pi _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        313,
+                                        267,
+                                        344,
+                                        281
+                                    ],
+                                    "score": 1.0,
+                                    "content": "at time",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        344,
+                                        269,
+                                        349,
+                                        277
+                                    ],
+                                    "score": 0.68,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        349,
+                                        267,
+                                        374,
+                                        281
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is not",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        374,
+                                        270,
+                                        379,
+                                        277
+                                    ],
+                                    "score": 0.47,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        380,
+                                        267,
+                                        479,
+                                        281
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimal for current state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        479,
+                                        269,
+                                        488,
+                                        278
+                                    ],
+                                    "score": 0.8,
+                                    "content": "s _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        489,
+                                        267,
+                                        507,
+                                        281
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", i.e.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                276,
+                                207,
+                                291
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        278,
+                                        203,
+                                        290
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\dot { V } ^ { \\pi _ { t } } \\left( s _ { t } \\right) \\dot { < } V ^ { * } \\left( s _ { t } \\right) - \\epsilon .",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        203,
+                                        276,
+                                        207,
+                                        291
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 14,
+                    "bbox_fs": [
+                        105,
+                        255,
+                        507,
+                        291
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        297,
+                        504,
+                        320
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                296,
+                                505,
+                                311
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        296,
+                                        505,
+                                        311
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Roughly speaking, this measure counts the number of mistakes along the whole trajectory. We use",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                307,
+                                339,
+                                320
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        307,
+                                        339,
+                                        320
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the following definition of PAC-MDP Strehl et al. (2006).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 16.5,
+                    "bbox_fs": [
+                        105,
+                        296,
+                        505,
+                        320
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        321,
+                        505,
+                        356
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                321,
+                                505,
+                                335
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        321,
+                                        223,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Definition 2. An algorithm",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        223,
+                                        321,
+                                        246,
+                                        332
+                                    ],
+                                    "score": 0.67,
+                                    "content": "\\mathcal { A L G }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        246,
+                                        321,
+                                        505,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is said to be PAC-MDP (Probably Approximately Correct in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                332,
+                                505,
+                                345
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        332,
+                                        225,
+                                        345
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Markov Decision Processes)",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        226,
+                                        333,
+                                        235,
+                                        344
+                                    ],
+                                    "score": 0.67,
+                                    "content": "i f ,",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        235,
+                                        332,
+                                        294,
+                                        345
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for any \u000f and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        294,
+                                        333,
+                                        300,
+                                        342
+                                    ],
+                                    "score": 0.65,
+                                    "content": "\\delta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        300,
+                                        332,
+                                        409,
+                                        345
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the sample complexity of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        409,
+                                        333,
+                                        432,
+                                        343
+                                    ],
+                                    "score": 0.61,
+                                    "content": "\\mathcal { A L G }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        432,
+                                        332,
+                                        505,
+                                        345
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is less than some",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                343,
+                                493,
+                                357
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        343,
+                                        255,
+                                        357
+                                    ],
+                                    "score": 1.0,
+                                    "content": "polynomial in the relevant quantities",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        255,
+                                        343,
+                                        363,
+                                        356
+                                    ],
+                                    "score": 0.89,
+                                    "content": "( S , A , 1 / \\epsilon , 1 / \\delta , 1 / ( 1 - \\gamma ) )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        363,
+                                        343,
+                                        465,
+                                        357
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", with probability at least",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        466,
+                                        344,
+                                        488,
+                                        354
+                                    ],
+                                    "score": 0.85,
+                                    "content": "1 - \\delta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        489,
+                                        343,
+                                        493,
+                                        357
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 19,
+                    "bbox_fs": [
+                        105,
+                        321,
+                        505,
+                        357
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        362,
+                        363,
+                        374
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                361,
+                                365,
+                                376
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        361,
+                                        365,
+                                        376
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Finally, recall that Bellman equation is defined as the following:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 21,
+                    "bbox_fs": [
+                        105,
+                        361,
+                        365,
+                        376
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        142,
+                        375,
+                        462,
+                        403
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                142,
+                                375,
+                                462,
+                                403
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        375,
+                                        462,
+                                        403
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\left\\{ \\begin{array} { l l } { V ^ { \\pi _ { t } } ( s ) = Q ^ { \\pi _ { t } } \\left( s , \\pi _ { t } ( s ) \\right) } \\\\ { Q ^ { \\pi _ { t } } ( s , a ) : = \\left( r _ { t } + \\gamma \\mathbb { P } V ^ { \\pi _ { t + 1 } } \\right) ( s , a ) , } \\end{array} \\right. \\quad \\left\\{ \\begin{array} { l l } { V ^ { * } ( s ) = Q ^ { * } \\left( s , \\pi ^ { * } ( s ) \\right) } \\\\ { Q ^ { * } ( s , a ) : = \\left( r _ { t } + \\gamma \\mathbb { P } V ^ { * } \\right) ( s , a ) , } \\end{array} \\right.",
+                                    "type": "interline_equation",
+                                    "image_path": "59cd62d5ec6d571803efed659b258dfba8d0141783a9422cc7a1cf15db20a44e.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 22,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                142,
+                                375,
+                                462,
+                                403
+                            ],
+                            "spans": [],
+                            "index": 22
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        103,
+                        403,
+                        493,
+                        416
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                400,
+                                493,
+                                419
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        400,
+                                        335,
+                                        419
+                                    ],
+                                    "score": 1.0,
+                                    "content": "which is frequently used in our analysis. Here we denote",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        335,
+                                        404,
+                                        493,
+                                        416
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\left[ \\mathbb { P } V ^ { \\pi _ { t } } \\right] ( s , a ) : = \\mathbb { E } _ { s ^ { \\prime } \\sim p ( \\cdot \\vert s , a ) } V ^ { \\pi _ { t + 1 } } ( s ^ { \\prime } ) .",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 23,
+                    "bbox_fs": [
+                        104,
+                        400,
+                        493,
+                        419
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        430,
+                        206,
+                        443
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                428,
+                                207,
+                                445
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        428,
+                                        207,
+                                        445
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3 MAIN RESULTS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 24
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        102,
+                        454,
+                        475,
+                        467
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                453,
+                                476,
+                                469
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        453,
+                                        476,
+                                        469
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In this section, we present the UCB Q-learning algorithm and the sample complexity bound.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 25,
+                    "bbox_fs": [
+                        105,
+                        453,
+                        476,
+                        469
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        478,
+                        186,
+                        490
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                478,
+                                187,
+                                491
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        478,
+                                        187,
+                                        491
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3.1 ALGORITHM",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 26
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        502,
+                        279,
+                        514
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                501,
+                                281,
+                                516
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        501,
+                                        281,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Algorithm 1 Infinite Q-learning with UCB",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 27
+                },
+                {
+                    "type": "list",
+                    "bbox": [
+                        110,
+                        516,
+                        504,
+                        681
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                123,
+                                515,
+                                201,
+                                528
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        123,
+                                        515,
+                                        201,
+                                        528
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Parameters: \u000f, γ, δ",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                122,
+                                526,
+                                479,
+                                562
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        122,
+                                        526,
+                                        155,
+                                        543
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Initializ",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        155,
+                                        526,
+                                        479,
+                                        562
+                                    ],
+                                    "score": 0.69,
+                                    "content": "\\begin{array} { r l } & { \\textnormal { \\texttt { e } } Q ( s , a ) , \\hat { Q } ( s , a ) \\gets \\frac { 1 } { 1 - \\gamma } , N ( s , a ) \\gets 0 , \\epsilon _ { 1 } \\gets \\frac { \\epsilon } { 2 4 R M \\ln \\frac { 1 } { 1 - \\gamma } } , H \\gets \\frac { \\ln 1 / ( ( 1 - \\gamma ) \\epsilon _ { 1 } ) } { \\ln 1 / \\gamma } . } \\\\ & { \\cdot ( k ) = \\ln ( S A ( k + 1 ) ( k + 2 ) / \\delta ) , \\alpha _ { k } = \\frac { H + 1 } { H + k } . } \\end{array}",
+                                    "type": "inline_equation",
+                                    "image_path": "ad0c57b5739df10ef8c0d2046656de08d85d51ac78dc2acbfb1350115223ebf4.jpg"
+                                }
+                            ],
+                            "index": 29,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                122,
+                                542,
+                                153,
+                                560
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        122,
+                                        542,
+                                        153,
+                                        560
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Define",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                123,
+                                557,
+                                197,
+                                570
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        123,
+                                        557,
+                                        138,
+                                        570
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        138,
+                                        559,
+                                        197,
+                                        569
+                                    ],
+                                    "score": 0.66,
+                                    "content": "t = 1 , 2 , \\dots \\mathbf { d o }",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 31,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                110,
+                                569,
+                                293,
+                                583
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        570,
+                                        123,
+                                        583
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5:",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        137,
+                                        569,
+                                        186,
+                                        583
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Take action",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        187,
+                                        569,
+                                        293,
+                                        582
+                                    ],
+                                    "score": 0.73,
+                                    "content": "a _ { t } \\gets \\arg \\operatorname* { m a x } _ { a ^ { \\prime } } \\hat { Q } ( s _ { t } , a ^ { \\prime } )",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 32,
+                            "is_list_start_line": true,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                137,
+                                580,
+                                288,
+                                594
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        137,
+                                        580,
+                                        288,
+                                        594
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Receive reward rt and transit to st+1",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                137,
+                                590,
+                                504,
+                                670
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        137,
+                                        590,
+                                        411,
+                                        670
+                                    ],
+                                    "score": 0.48,
+                                    "content": "\\begin{array} { r l r } & { N ( s _ { t } , a _ { t } ) \\gets N ( s _ { t } , a _ { t } ) + 1 } & \\\\ & { N ( s _ { t } , a _ { t } ) \\gets N ( s _ { t } , a _ { t } ) + 1 } & \\\\ & { k \\gets N ( s _ { t } , a _ { t } ) , b _ { k } \\gets \\frac { c _ { 2 } } { 1 - \\gamma } \\sqrt { \\frac { H ( k ) } { k } } } & \\\\ & { \\hat { V } ( s _ { t + 1 } ) \\gets \\operatorname* { m a x } _ { a \\in A } \\hat { Q } ( s _ { t + 1 } , a ) } & \\\\ & { Q ( s _ { t } , a _ { t } ) \\gets ( 1 - \\alpha _ { k } ) Q ( s _ { t } , a _ { t } ) + \\alpha _ { k } \\left[ r ( s _ { t } , a _ { t } ) + b _ { k } + \\gamma \\hat { V } ( s _ { t + 1 } ) \\right] } \\\\ & { \\hat { Q } ( s _ { t } , a _ { t } ) \\gets \\operatorname* { m i n } ( \\hat { Q } ( s _ { t } , a _ { t } ) , Q ( s _ { t } , a _ { t } ) ) } & \\end{array}",
+                                    "type": "inline_equation",
+                                    "image_path": "d5388b49142af9a03fc552a4ec774a7df6c96f7f162f72703f3ded5df679058d.jpg"
+                                },
+                                {
+                                    "bbox": [
+                                        411,
+                                        608,
+                                        484,
+                                        621
+                                    ],
+                                    "score": 1.0,
+                                    "content": "t and can be set to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        484,
+                                        608,
+                                        504,
+                                        621
+                                    ],
+                                    "score": 0.88,
+                                    "content": "4 { \\sqrt { 2 } }",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                639,
+                                122,
+                                651
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        639,
+                                        122,
+                                        651
+                                    ],
+                                    "score": 1.0,
+                                    "content": "10:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34,
+                            "is_list_start_line": true,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                122,
+                                666,
+                                158,
+                                679
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        122,
+                                        666,
+                                        158,
+                                        679
+                                    ],
+                                    "score": 1.0,
+                                    "content": "end for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36,
+                            "is_list_end_line": true
+                        }
+                    ],
+                    "index": 32,
+                    "bbox_fs": [
+                        107,
+                        515,
+                        504,
+                        679
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        691,
+                        505,
+                        735
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                690,
+                                507,
+                                710
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        690,
+                                        129,
+                                        710
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Here",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        129,
+                                        692,
+                                        173,
+                                        704
+                                    ],
+                                    "score": 0.93,
+                                    "content": "c _ { 2 } = 4 \\sqrt { 2 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        173,
+                                        690,
+                                        232,
+                                        710
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is a constant.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        233,
+                                        692,
+                                        338,
+                                        708
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { r } { R = \\lceil \\ln \\frac { 3 } { \\epsilon ( 1 - \\gamma ) } / ( 1 - \\gamma ) \\rceil } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        339,
+                                        690,
+                                        424,
+                                        710
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", while the choice of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        425,
+                                        694,
+                                        437,
+                                        703
+                                    ],
+                                    "score": 0.8,
+                                    "content": "M",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        437,
+                                        690,
+                                        507,
+                                        710
+                                    ],
+                                    "score": 1.0,
+                                    "content": "can be found in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                705,
+                                505,
+                                719
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        705,
+                                        162,
+                                        719
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Section. 3.3.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        162,
+                                        707,
+                                        270,
+                                        719
+                                    ],
+                                    "score": 0.75,
+                                    "content": "{ \\cal { \\left( M = 0 \\left( \\ln 1 / ( 1 - \\gamma ) \\epsilon \\right) \\right) } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        271,
+                                        705,
+                                        401,
+                                        719
+                                    ],
+                                    "score": 1.0,
+                                    "content": "). The learning rate is defined as",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        402,
+                                        706,
+                                        501,
+                                        719
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\alpha _ { k } = ( H + 1 ) / ( H + k )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        501,
+                                        705,
+                                        505,
+                                        719
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                714,
+                                366,
+                                738
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        720,
+                                        117,
+                                        730
+                                    ],
+                                    "score": 0.79,
+                                    "content": "H",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        117,
+                                        714,
+                                        168,
+                                        738
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is chosen as",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        169,
+                                        718,
+                                        222,
+                                        735
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\frac { \\ln { 1 } / ( ( 1 - \\gamma ) \\epsilon _ { 1 } ) } { \\ln { 1 } / \\gamma }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        222,
+                                        714,
+                                        287,
+                                        738
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", which satisfies",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        287,
+                                        718,
+                                        363,
+                                        735
+                                    ],
+                                    "score": 0.93,
+                                    "content": "H \\leq \\frac { \\ln 1 / ( ( 1 - \\gamma ) \\epsilon _ { 1 } ) } { 1 - \\gamma }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        363,
+                                        714,
+                                        366,
+                                        738
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 38,
+                    "bbox_fs": [
+                        104,
+                        690,
+                        507,
+                        738
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        82,
+                        505,
+                        153
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                81,
+                                506,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        81,
+                                        506,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Our UCB Q-learning algorithm (Algorithm 1) maintains an optimistic estimation of action value",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                93,
+                                506,
+                                108
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        94,
+                                        141,
+                                        108
+                                    ],
+                                    "score": 1.0,
+                                    "content": "function",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        141,
+                                        95,
+                                        172,
+                                        107
+                                    ],
+                                    "score": 0.93,
+                                    "content": "Q ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        173,
+                                        94,
+                                        304,
+                                        108
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and its historical minimum value",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        93,
+                                        335,
+                                        107
+                                    ],
+                                    "score": 0.86,
+                                    "content": "\\hat { Q } ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        335,
+                                        94,
+                                        339,
+                                        108
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        339,
+                                        95,
+                                        374,
+                                        107
+                                    ],
+                                    "score": 0.85,
+                                    "content": "N _ { t } ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        374,
+                                        94,
+                                        506,
+                                        108
+                                    ],
+                                    "score": 1.0,
+                                    "content": "denotes the number of times that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                106,
+                                505,
+                                119
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        106,
+                                        128,
+                                        118
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        129,
+                                        106,
+                                        258,
+                                        119
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is experienced before time step",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        258,
+                                        107,
+                                        264,
+                                        117
+                                    ],
+                                    "score": 0.48,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        264,
+                                        106,
+                                        267,
+                                        119
+                                    ],
+                                    "score": 1.0,
+                                    "content": ";",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        268,
+                                        106,
+                                        306,
+                                        118
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\tau ( s , a , k )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        106,
+                                        395,
+                                        119
+                                    ],
+                                    "score": 1.0,
+                                    "content": "denotes the time step",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        396,
+                                        107,
+                                        401,
+                                        116
+                                    ],
+                                    "score": 0.75,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        401,
+                                        106,
+                                        439,
+                                        119
+                                    ],
+                                    "score": 1.0,
+                                    "content": "at which",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        440,
+                                        106,
+                                        505,
+                                        118
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( s _ { t } , a _ { t } ) = ( s , a )",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                115,
+                                505,
+                                130
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        115,
+                                        136,
+                                        130
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        136,
+                                        118,
+                                        143,
+                                        127
+                                    ],
+                                    "score": 0.82,
+                                    "content": "k",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        144,
+                                        115,
+                                        401,
+                                        130
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-th time; if this state-action pair is not visited that many times,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        402,
+                                        117,
+                                        464,
+                                        129
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\tau ( s , a , k ) = \\infty",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        465,
+                                        115,
+                                        470,
+                                        130
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        470,
+                                        118,
+                                        505,
+                                        129
+                                    ],
+                                    "score": 0.84,
+                                    "content": "Q _ { t } ( s , a )",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                128,
+                                504,
+                                144
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        128,
+                                        124,
+                                        144
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        124,
+                                        128,
+                                        158,
+                                        142
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\hat { Q } _ { t } ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        159,
+                                        128,
+                                        208,
+                                        144
+                                    ],
+                                    "score": 1.0,
+                                    "content": "denotes the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        209,
+                                        130,
+                                        218,
+                                        142
+                                    ],
+                                    "score": 0.85,
+                                    "content": "Q",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        218,
+                                        128,
+                                        236,
+                                        144
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        237,
+                                        128,
+                                        246,
+                                        142
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\hat { Q }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        246,
+                                        128,
+                                        283,
+                                        144
+                                    ],
+                                    "score": 1.0,
+                                    "content": "value of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        284,
+                                        130,
+                                        306,
+                                        142
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        128,
+                                        494,
+                                        144
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that the algorithm maintains when arriving at",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        495,
+                                        132,
+                                        504,
+                                        141
+                                    ],
+                                    "score": 0.84,
+                                    "content": "s _ { t }",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                139,
+                                159,
+                                155
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        139,
+                                        159,
+                                        155
+                                    ],
+                                    "score": 1.0,
+                                    "content": "respectively.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        }
+                    ],
+                    "index": 2.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        106,
+                        169,
+                        306,
+                        181
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                168,
+                                307,
+                                183
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        168,
+                                        307,
+                                        183
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3.2 SAMPLE COMPLEXITY OF EXPLORATION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        191,
+                        402,
+                        203
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                190,
+                                402,
+                                205
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        190,
+                                        402,
+                                        205
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Our main result is the following sample complexity of exploration bound.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        207,
+                        507,
+                        241
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                206,
+                                507,
+                                221
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        206,
+                                        194,
+                                        221
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Theorem 1. For any",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        194,
+                                        209,
+                                        218,
+                                        219
+                                    ],
+                                    "score": 0.77,
+                                    "content": "\\epsilon > 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        218,
+                                        206,
+                                        221,
+                                        221
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        221,
+                                        208,
+                                        303,
+                                        220
+                                    ],
+                                    "score": 0.6,
+                                    "content": "\\delta > 0 , 1 / 2 < \\gamma < 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        206,
+                                        374,
+                                        221
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", with probability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        375,
+                                        208,
+                                        398,
+                                        219
+                                    ],
+                                    "score": 0.76,
+                                    "content": "1 - \\delta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        398,
+                                        206,
+                                        507,
+                                        221
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the sample complexity of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                219,
+                                506,
+                                231
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        219,
+                                        322,
+                                        231
+                                    ],
+                                    "score": 1.0,
+                                    "content": "exploration (i.e., the number of time steps t such that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        322,
+                                        221,
+                                        333,
+                                        230
+                                    ],
+                                    "score": 0.86,
+                                    "content": "\\pi _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        333,
+                                        219,
+                                        358,
+                                        231
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is not",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        359,
+                                        222,
+                                        364,
+                                        229
+                                    ],
+                                    "score": 0.55,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        364,
+                                        219,
+                                        410,
+                                        231
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimal at",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        410,
+                                        221,
+                                        420,
+                                        230
+                                    ],
+                                    "score": 0.82,
+                                    "content": "s _ { t . }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        420,
+                                        219,
+                                        506,
+                                        231
+                                    ],
+                                    "score": 1.0,
+                                    "content": ") of Algorithm 1 is at",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                230,
+                                129,
+                                242
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        230,
+                                        129,
+                                        242
+                                    ],
+                                    "score": 1.0,
+                                    "content": "most",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        265,
+                        242,
+                        345,
+                        276
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                265,
+                                242,
+                                345,
+                                276
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        265,
+                                        242,
+                                        345,
+                                        276
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\tilde { \\mathcal { O } } \\left( \\frac { S A \\ln { 1 / \\delta } } { \\epsilon ^ { 2 } \\left( 1 - \\gamma \\right) ^ { 7 } } \\right) ,",
+                                    "type": "interline_equation",
+                                    "image_path": "cc2b5aa0f63178566f02139857adabb797f2f963feb35907fc51fd7501fb1693.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                265,
+                                242,
+                                345,
+                                259.0
+                            ],
+                            "spans": [],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                265,
+                                259.0,
+                                345,
+                                276.0
+                            ],
+                            "spans": [],
+                            "index": 12
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        283,
+                        375,
+                        297
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                282,
+                                376,
+                                298
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        282,
+                                        133,
+                                        298
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        133,
+                                        283,
+                                        143,
+                                        295
+                                    ],
+                                    "score": 0.79,
+                                    "content": "\\tilde { \\mathcal { O } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        143,
+                                        282,
+                                        278,
+                                        298
+                                    ],
+                                    "score": 1.0,
+                                    "content": "suppresses logarithmic factors of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        279,
+                                        284,
+                                        339,
+                                        297
+                                    ],
+                                    "score": 0.9,
+                                    "content": "1 / \\epsilon , 1 / ( 1 - \\gamma )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        339,
+                                        282,
+                                        357,
+                                        298
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        358,
+                                        284,
+                                        373,
+                                        295
+                                    ],
+                                    "score": 0.77,
+                                    "content": "S A",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        373,
+                                        282,
+                                        376,
+                                        298
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        307,
+                        505,
+                        330
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                307,
+                                506,
+                                320
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        307,
+                                        506,
+                                        320
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We first point out the obstacles for proving the theorem and reasons why the techniques in Jin et al.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                318,
+                                506,
+                                331
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        318,
+                                        506,
+                                        331
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(2018) do not directly apply here. We then give a high level description of the ideas of our approach.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 14.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        334,
+                        506,
+                        401
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                334,
+                                505,
+                                347
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        334,
+                                        505,
+                                        347
+                                    ],
+                                    "score": 1.0,
+                                    "content": "One important issue is caused by the difference in the definition of sample complexity for finite and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                345,
+                                505,
+                                358
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        345,
+                                        505,
+                                        358
+                                    ],
+                                    "score": 1.0,
+                                    "content": "infinite horizon MDP. In finite horizon settings, sample complexity (and regret) is determined in the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                354,
+                                506,
+                                371
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        354,
+                                        125,
+                                        371
+                                    ],
+                                    "score": 1.0,
+                                    "content": "first",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        125,
+                                        357,
+                                        134,
+                                        367
+                                    ],
+                                    "score": 0.79,
+                                    "content": "T",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        134,
+                                        354,
+                                        402,
+                                        371
+                                    ],
+                                    "score": 1.0,
+                                    "content": "timesteps, and only measures the performance at the initial state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        402,
+                                        358,
+                                        413,
+                                        368
+                                    ],
+                                    "score": 0.83,
+                                    "content": "s _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        413,
+                                        354,
+                                        435,
+                                        371
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(i.e.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        435,
+                                        357,
+                                        502,
+                                        369
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( V ^ { * } - V ^ { \\pi } ) ( s _ { 1 } ) )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        503,
+                                        354,
+                                        506,
+                                        371
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                367,
+                                506,
+                                381
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        367,
+                                        506,
+                                        381
+                                    ],
+                                    "score": 1.0,
+                                    "content": "However, in the infinite horizon setting, the agent may enter under-explored regions at any time",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                379,
+                                506,
+                                391
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        379,
+                                        506,
+                                        391
+                                    ],
+                                    "score": 1.0,
+                                    "content": "period, and sample complexity of exploration characterizes the performance at all states the agent",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                390,
+                                136,
+                                402
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        390,
+                                        136,
+                                        402
+                                    ],
+                                    "score": 1.0,
+                                    "content": "enters.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 18.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        406,
+                        505,
+                        484
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                407,
+                                506,
+                                419
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        407,
+                                        506,
+                                        419
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The following example clearly illustrates the key difference between infinite-horizon and finite-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                416,
+                                506,
+                                431
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        416,
+                                        296,
+                                        431
+                                    ],
+                                    "score": 1.0,
+                                    "content": "horizon. Consider an MDP with a starting state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        419,
+                                        307,
+                                        429
+                                    ],
+                                    "score": 0.85,
+                                    "content": "s _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        416,
+                                        437,
+                                        431
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where the probability of leaving",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        438,
+                                        419,
+                                        448,
+                                        429
+                                    ],
+                                    "score": 0.85,
+                                    "content": "s _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        448,
+                                        416,
+                                        458,
+                                        431
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        459,
+                                        417,
+                                        489,
+                                        430
+                                    ],
+                                    "score": 0.92,
+                                    "content": "o ( T ^ { - 1 } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        490,
+                                        416,
+                                        506,
+                                        431
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". In",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                428,
+                                505,
+                                442
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        428,
+                                        331,
+                                        442
+                                    ],
+                                    "score": 1.0,
+                                    "content": "this case, with high probability, it would take more than",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        331,
+                                        429,
+                                        340,
+                                        439
+                                    ],
+                                    "score": 0.76,
+                                    "content": "T",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        340,
+                                        428,
+                                        414,
+                                        442
+                                    ],
+                                    "score": 1.0,
+                                    "content": "timesteps to leave",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        415,
+                                        430,
+                                        425,
+                                        440
+                                    ],
+                                    "score": 0.85,
+                                    "content": "s _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        425,
+                                        428,
+                                        505,
+                                        442
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Hence, guarantees",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                440,
+                                506,
+                                452
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        440,
+                                        222,
+                                        452
+                                    ],
+                                    "score": 1.0,
+                                    "content": "about the learning in the first",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        222,
+                                        441,
+                                        231,
+                                        450
+                                    ],
+                                    "score": 0.81,
+                                    "content": "T",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        231,
+                                        440,
+                                        382,
+                                        452
+                                    ],
+                                    "score": 1.0,
+                                    "content": "timesteps or about the performance at",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        383,
+                                        441,
+                                        393,
+                                        451
+                                    ],
+                                    "score": 0.85,
+                                    "content": "s _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        393,
+                                        440,
+                                        506,
+                                        452
+                                    ],
+                                    "score": 1.0,
+                                    "content": "imply almost nothing about",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                449,
+                                505,
+                                464
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        449,
+                                        505,
+                                        464
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the number of mistakes the algorithm would make in the rest of the MDP (i.e. the sample complexity",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                461,
+                                505,
+                                474
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        461,
+                                        505,
+                                        474
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of exploration of the algorithm). As a result, the analysis for finite horizon MDPs cannot be directly",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                472,
+                                244,
+                                486
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        472,
+                                        244,
+                                        486
+                                    ],
+                                    "score": 1.0,
+                                    "content": "applied to infinite horizon setting.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        489,
+                        505,
+                        534
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                488,
+                                505,
+                                502
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        488,
+                                        505,
+                                        502
+                                    ],
+                                    "score": 1.0,
+                                    "content": "This calls for techniques for counting mistakes along the entire trajectory, such as those employed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                499,
+                                505,
+                                514
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        499,
+                                        505,
+                                        514
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by Strehl et al. (2006). In particular, we need to establish convenient sufficient conditions for being",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                511,
+                                506,
+                                524
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        514,
+                                        112,
+                                        521
+                                    ],
+                                    "score": 0.67,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        112,
+                                        511,
+                                        196,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimal at timestep",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        196,
+                                        513,
+                                        201,
+                                        521
+                                    ],
+                                    "score": 0.72,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        202,
+                                        511,
+                                        242,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        243,
+                                        513,
+                                        252,
+                                        522
+                                    ],
+                                    "score": 0.84,
+                                    "content": "s _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        252,
+                                        511,
+                                        274,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", i.e.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        275,
+                                        511,
+                                        370,
+                                        523
+                                    ],
+                                    "score": 0.92,
+                                    "content": "V ^ { \\ast } ( s _ { t } ) - V ^ { \\pi _ { t } } ( s _ { t } ) \\leq \\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        370,
+                                        511,
+                                        506,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Then, bounding the number of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                522,
+                                373,
+                                536
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        522,
+                                        373,
+                                        536
+                                    ],
+                                    "score": 1.0,
+                                    "content": "violations of such conditions gives a bound on sample complexity.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 30.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        539,
+                        505,
+                        650
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                538,
+                                505,
+                                551
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        538,
+                                        505,
+                                        551
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Another technical reason why the proof in Jin et al. (2018) cannot be directly applied to our problem",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                549,
+                                505,
+                                563
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        549,
+                                        505,
+                                        563
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the following: In finite horizon settings, Jin et al. (2018) decomposed the learning error at episode",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                560,
+                                505,
+                                574
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        562,
+                                        113,
+                                        571
+                                    ],
+                                    "score": 0.8,
+                                    "content": "k",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        114,
+                                        560,
+                                        150,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and time",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        151,
+                                        562,
+                                        158,
+                                        571
+                                    ],
+                                    "score": 0.79,
+                                    "content": "h",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        159,
+                                        560,
+                                        358,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as errors from a set of consecutive episodes before",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        358,
+                                        562,
+                                        365,
+                                        571
+                                    ],
+                                    "score": 0.81,
+                                    "content": "k",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        366,
+                                        560,
+                                        395,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": "at time",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        396,
+                                        561,
+                                        420,
+                                        572
+                                    ],
+                                    "score": 0.91,
+                                    "content": "h + 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        420,
+                                        560,
+                                        505,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": "using a clever design",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                572,
+                                506,
+                                585
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        572,
+                                        506,
+                                        585
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of learning rate. However, in the infinite horizon setting, this property does not hold. Suppose at",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                582,
+                                506,
+                                596
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        582,
+                                        126,
+                                        596
+                                    ],
+                                    "score": 1.0,
+                                    "content": "time",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        127,
+                                        584,
+                                        132,
+                                        593
+                                    ],
+                                    "score": 0.75,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        132,
+                                        582,
+                                        211,
+                                        596
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the agent is at state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        211,
+                                        585,
+                                        221,
+                                        594
+                                    ],
+                                    "score": 0.85,
+                                    "content": "s _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        221,
+                                        582,
+                                        288,
+                                        596
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and takes action",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        585,
+                                        298,
+                                        594
+                                    ],
+                                    "score": 0.84,
+                                    "content": "a _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        299,
+                                        582,
+                                        407,
+                                        596
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Then the learning error at",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        407,
+                                        584,
+                                        412,
+                                        593
+                                    ],
+                                    "score": 0.74,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        413,
+                                        582,
+                                        506,
+                                        596
+                                    ],
+                                    "score": 1.0,
+                                    "content": "only depends on those",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                594,
+                                506,
+                                606
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        594,
+                                        382,
+                                        606
+                                    ],
+                                    "score": 1.0,
+                                    "content": "previous time steps such that the agent encountered the same state as",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        382,
+                                        596,
+                                        392,
+                                        605
+                                    ],
+                                    "score": 0.86,
+                                    "content": "s _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        392,
+                                        594,
+                                        506,
+                                        606
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and took the same action as",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                604,
+                                506,
+                                618
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        606,
+                                        116,
+                                        616
+                                    ],
+                                    "score": 0.83,
+                                    "content": "a _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        117,
+                                        604,
+                                        245,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Thus the learning error at time",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        245,
+                                        606,
+                                        250,
+                                        615
+                                    ],
+                                    "score": 0.64,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        251,
+                                        604,
+                                        506,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cannot be decomposed as errors from a set of consecutive time",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                616,
+                                506,
+                                629
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        616,
+                                        157,
+                                        629
+                                    ],
+                                    "score": 1.0,
+                                    "content": "steps before",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        157,
+                                        617,
+                                        162,
+                                        626
+                                    ],
+                                    "score": 0.74,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        163,
+                                        616,
+                                        506,
+                                        629
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", but errors from a set of non-consecutive time steps without any structure. Therefore,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                627,
+                                506,
+                                640
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        627,
+                                        506,
+                                        640
+                                    ],
+                                    "score": 1.0,
+                                    "content": "we have to control the sum of learning errors over an unstructured set of time steps. This makes the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                637,
+                                215,
+                                652
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        637,
+                                        215,
+                                        652
+                                    ],
+                                    "score": 1.0,
+                                    "content": "analysis more challenging.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        }
+                    ],
+                    "index": 37.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        654,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                655,
+                                506,
+                                667
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        655,
+                                        506,
+                                        667
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Now we give a brief road map of the proof of Theorem 1. Our first goal is to establish a sufficient",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                666,
+                                506,
+                                678
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        666,
+                                        174,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "condition so that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        175,
+                                        667,
+                                        185,
+                                        677
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\pi _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        185,
+                                        666,
+                                        245,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learned at step",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        246,
+                                        667,
+                                        250,
+                                        676
+                                    ],
+                                    "score": 0.8,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        251,
+                                        666,
+                                        261,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        261,
+                                        668,
+                                        266,
+                                        676
+                                    ],
+                                    "score": 0.75,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        266,
+                                        666,
+                                        335,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimal for state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        335,
+                                        668,
+                                        344,
+                                        677
+                                    ],
+                                    "score": 0.81,
+                                    "content": "s _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        344,
+                                        666,
+                                        506,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". As an intermediate step we show that a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                676,
+                                506,
+                                690
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        676,
+                                        200,
+                                        690
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sufficient condition for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        201,
+                                        677,
+                                        292,
+                                        689
+                                    ],
+                                    "score": 0.91,
+                                    "content": "V ^ { * } ( s _ { t } ) - V ^ { \\pi _ { t } } ( s _ { t } ) \\leq \\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        292,
+                                        676,
+                                        320,
+                                        690
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        320,
+                                        677,
+                                        411,
+                                        689
+                                    ],
+                                    "score": 0.92,
+                                    "content": "V ^ { \\ast } ( s _ { t ^ { \\prime } } ) - Q ^ { \\ast } ( s _ { t ^ { \\prime } } , a _ { t ^ { \\prime } } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        412,
+                                        676,
+                                        506,
+                                        690
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is small for a few time",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                687,
+                                505,
+                                700
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        687,
+                                        128,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "steps",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        128,
+                                        687,
+                                        136,
+                                        698
+                                    ],
+                                    "score": 0.83,
+                                    "content": "t ^ { \\prime }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        136,
+                                        687,
+                                        208,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "within an interval",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        208,
+                                        689,
+                                        245,
+                                        699
+                                    ],
+                                    "score": 0.91,
+                                    "content": "[ t , t + R ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        245,
+                                        687,
+                                        333,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for a carefully chosen",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        333,
+                                        689,
+                                        342,
+                                        698
+                                    ],
+                                    "score": 0.78,
+                                    "content": "R",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        342,
+                                        687,
+                                        505,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(Condition 1). Then we show the desired",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                699,
+                                506,
+                                711
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        699,
+                                        506,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sufficient condition (Condition 2) implies Condition 1. We then bound the total number of bad time",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                708,
+                                506,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        708,
+                                        167,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "steps on which",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        168,
+                                        710,
+                                        251,
+                                        722
+                                    ],
+                                    "score": 0.91,
+                                    "content": "V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        251,
+                                        708,
+                                        506,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is large for the whole MDP; this implies a bound on the number",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                720,
+                                450,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        720,
+                                        450,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of violations of Condition 2. This in turn relies on a key technical lemma (Lemma 2).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        }
+                    ],
+                    "index": 46
+                }
+            ],
+            "page_idx": 3,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        293,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                294,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        294,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        752,
+                        308,
+                        759
+                    ],
+                    "lines": []
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        82,
+                        505,
+                        153
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                81,
+                                506,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        81,
+                                        506,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Our UCB Q-learning algorithm (Algorithm 1) maintains an optimistic estimation of action value",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                93,
+                                506,
+                                108
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        94,
+                                        141,
+                                        108
+                                    ],
+                                    "score": 1.0,
+                                    "content": "function",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        141,
+                                        95,
+                                        172,
+                                        107
+                                    ],
+                                    "score": 0.93,
+                                    "content": "Q ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        173,
+                                        94,
+                                        304,
+                                        108
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and its historical minimum value",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        93,
+                                        335,
+                                        107
+                                    ],
+                                    "score": 0.86,
+                                    "content": "\\hat { Q } ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        335,
+                                        94,
+                                        339,
+                                        108
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        339,
+                                        95,
+                                        374,
+                                        107
+                                    ],
+                                    "score": 0.85,
+                                    "content": "N _ { t } ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        374,
+                                        94,
+                                        506,
+                                        108
+                                    ],
+                                    "score": 1.0,
+                                    "content": "denotes the number of times that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                106,
+                                505,
+                                119
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        106,
+                                        128,
+                                        118
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        129,
+                                        106,
+                                        258,
+                                        119
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is experienced before time step",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        258,
+                                        107,
+                                        264,
+                                        117
+                                    ],
+                                    "score": 0.48,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        264,
+                                        106,
+                                        267,
+                                        119
+                                    ],
+                                    "score": 1.0,
+                                    "content": ";",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        268,
+                                        106,
+                                        306,
+                                        118
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\tau ( s , a , k )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        106,
+                                        395,
+                                        119
+                                    ],
+                                    "score": 1.0,
+                                    "content": "denotes the time step",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        396,
+                                        107,
+                                        401,
+                                        116
+                                    ],
+                                    "score": 0.75,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        401,
+                                        106,
+                                        439,
+                                        119
+                                    ],
+                                    "score": 1.0,
+                                    "content": "at which",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        440,
+                                        106,
+                                        505,
+                                        118
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( s _ { t } , a _ { t } ) = ( s , a )",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                115,
+                                505,
+                                130
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        115,
+                                        136,
+                                        130
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        136,
+                                        118,
+                                        143,
+                                        127
+                                    ],
+                                    "score": 0.82,
+                                    "content": "k",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        144,
+                                        115,
+                                        401,
+                                        130
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-th time; if this state-action pair is not visited that many times,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        402,
+                                        117,
+                                        464,
+                                        129
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\tau ( s , a , k ) = \\infty",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        465,
+                                        115,
+                                        470,
+                                        130
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        470,
+                                        118,
+                                        505,
+                                        129
+                                    ],
+                                    "score": 0.84,
+                                    "content": "Q _ { t } ( s , a )",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                128,
+                                504,
+                                144
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        128,
+                                        124,
+                                        144
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        124,
+                                        128,
+                                        158,
+                                        142
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\hat { Q } _ { t } ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        159,
+                                        128,
+                                        208,
+                                        144
+                                    ],
+                                    "score": 1.0,
+                                    "content": "denotes the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        209,
+                                        130,
+                                        218,
+                                        142
+                                    ],
+                                    "score": 0.85,
+                                    "content": "Q",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        218,
+                                        128,
+                                        236,
+                                        144
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        237,
+                                        128,
+                                        246,
+                                        142
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\hat { Q }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        246,
+                                        128,
+                                        283,
+                                        144
+                                    ],
+                                    "score": 1.0,
+                                    "content": "value of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        284,
+                                        130,
+                                        306,
+                                        142
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        128,
+                                        494,
+                                        144
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that the algorithm maintains when arriving at",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        495,
+                                        132,
+                                        504,
+                                        141
+                                    ],
+                                    "score": 0.84,
+                                    "content": "s _ { t }",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                139,
+                                159,
+                                155
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        139,
+                                        159,
+                                        155
+                                    ],
+                                    "score": 1.0,
+                                    "content": "respectively.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        }
+                    ],
+                    "index": 2.5,
+                    "bbox_fs": [
+                        105,
+                        81,
+                        506,
+                        155
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        106,
+                        169,
+                        306,
+                        181
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                168,
+                                307,
+                                183
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        168,
+                                        307,
+                                        183
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3.2 SAMPLE COMPLEXITY OF EXPLORATION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        191,
+                        402,
+                        203
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                190,
+                                402,
+                                205
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        190,
+                                        402,
+                                        205
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Our main result is the following sample complexity of exploration bound.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 7,
+                    "bbox_fs": [
+                        106,
+                        190,
+                        402,
+                        205
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        207,
+                        507,
+                        241
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                206,
+                                507,
+                                221
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        206,
+                                        194,
+                                        221
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Theorem 1. For any",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        194,
+                                        209,
+                                        218,
+                                        219
+                                    ],
+                                    "score": 0.77,
+                                    "content": "\\epsilon > 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        218,
+                                        206,
+                                        221,
+                                        221
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        221,
+                                        208,
+                                        303,
+                                        220
+                                    ],
+                                    "score": 0.6,
+                                    "content": "\\delta > 0 , 1 / 2 < \\gamma < 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        206,
+                                        374,
+                                        221
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", with probability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        375,
+                                        208,
+                                        398,
+                                        219
+                                    ],
+                                    "score": 0.76,
+                                    "content": "1 - \\delta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        398,
+                                        206,
+                                        507,
+                                        221
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the sample complexity of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                219,
+                                506,
+                                231
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        219,
+                                        322,
+                                        231
+                                    ],
+                                    "score": 1.0,
+                                    "content": "exploration (i.e., the number of time steps t such that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        322,
+                                        221,
+                                        333,
+                                        230
+                                    ],
+                                    "score": 0.86,
+                                    "content": "\\pi _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        333,
+                                        219,
+                                        358,
+                                        231
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is not",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        359,
+                                        222,
+                                        364,
+                                        229
+                                    ],
+                                    "score": 0.55,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        364,
+                                        219,
+                                        410,
+                                        231
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimal at",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        410,
+                                        221,
+                                        420,
+                                        230
+                                    ],
+                                    "score": 0.82,
+                                    "content": "s _ { t . }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        420,
+                                        219,
+                                        506,
+                                        231
+                                    ],
+                                    "score": 1.0,
+                                    "content": ") of Algorithm 1 is at",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                230,
+                                129,
+                                242
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        230,
+                                        129,
+                                        242
+                                    ],
+                                    "score": 1.0,
+                                    "content": "most",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 9,
+                    "bbox_fs": [
+                        105,
+                        206,
+                        507,
+                        242
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        265,
+                        242,
+                        345,
+                        276
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                265,
+                                242,
+                                345,
+                                276
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        265,
+                                        242,
+                                        345,
+                                        276
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\tilde { \\mathcal { O } } \\left( \\frac { S A \\ln { 1 / \\delta } } { \\epsilon ^ { 2 } \\left( 1 - \\gamma \\right) ^ { 7 } } \\right) ,",
+                                    "type": "interline_equation",
+                                    "image_path": "cc2b5aa0f63178566f02139857adabb797f2f963feb35907fc51fd7501fb1693.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                265,
+                                242,
+                                345,
+                                259.0
+                            ],
+                            "spans": [],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                265,
+                                259.0,
+                                345,
+                                276.0
+                            ],
+                            "spans": [],
+                            "index": 12
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        283,
+                        375,
+                        297
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                282,
+                                376,
+                                298
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        282,
+                                        133,
+                                        298
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        133,
+                                        283,
+                                        143,
+                                        295
+                                    ],
+                                    "score": 0.79,
+                                    "content": "\\tilde { \\mathcal { O } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        143,
+                                        282,
+                                        278,
+                                        298
+                                    ],
+                                    "score": 1.0,
+                                    "content": "suppresses logarithmic factors of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        279,
+                                        284,
+                                        339,
+                                        297
+                                    ],
+                                    "score": 0.9,
+                                    "content": "1 / \\epsilon , 1 / ( 1 - \\gamma )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        339,
+                                        282,
+                                        357,
+                                        298
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        358,
+                                        284,
+                                        373,
+                                        295
+                                    ],
+                                    "score": 0.77,
+                                    "content": "S A",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        373,
+                                        282,
+                                        376,
+                                        298
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 13,
+                    "bbox_fs": [
+                        106,
+                        282,
+                        376,
+                        298
+                    ]
+                },
+                {
+                    "type": "list",
+                    "bbox": [
+                        106,
+                        307,
+                        505,
+                        330
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                307,
+                                506,
+                                320
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        307,
+                                        506,
+                                        320
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We first point out the obstacles for proving the theorem and reasons why the techniques in Jin et al.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                318,
+                                506,
+                                331
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        318,
+                                        506,
+                                        331
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(2018) do not directly apply here. We then give a high level description of the ideas of our approach.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15,
+                            "is_list_start_line": true,
+                            "is_list_end_line": true
+                        }
+                    ],
+                    "index": 14.5,
+                    "bbox_fs": [
+                        106,
+                        307,
+                        506,
+                        331
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        334,
+                        506,
+                        401
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                334,
+                                505,
+                                347
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        334,
+                                        505,
+                                        347
+                                    ],
+                                    "score": 1.0,
+                                    "content": "One important issue is caused by the difference in the definition of sample complexity for finite and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                345,
+                                505,
+                                358
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        345,
+                                        505,
+                                        358
+                                    ],
+                                    "score": 1.0,
+                                    "content": "infinite horizon MDP. In finite horizon settings, sample complexity (and regret) is determined in the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                354,
+                                506,
+                                371
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        354,
+                                        125,
+                                        371
+                                    ],
+                                    "score": 1.0,
+                                    "content": "first",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        125,
+                                        357,
+                                        134,
+                                        367
+                                    ],
+                                    "score": 0.79,
+                                    "content": "T",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        134,
+                                        354,
+                                        402,
+                                        371
+                                    ],
+                                    "score": 1.0,
+                                    "content": "timesteps, and only measures the performance at the initial state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        402,
+                                        358,
+                                        413,
+                                        368
+                                    ],
+                                    "score": 0.83,
+                                    "content": "s _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        413,
+                                        354,
+                                        435,
+                                        371
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(i.e.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        435,
+                                        357,
+                                        502,
+                                        369
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( V ^ { * } - V ^ { \\pi } ) ( s _ { 1 } ) )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        503,
+                                        354,
+                                        506,
+                                        371
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                367,
+                                506,
+                                381
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        367,
+                                        506,
+                                        381
+                                    ],
+                                    "score": 1.0,
+                                    "content": "However, in the infinite horizon setting, the agent may enter under-explored regions at any time",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                379,
+                                506,
+                                391
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        379,
+                                        506,
+                                        391
+                                    ],
+                                    "score": 1.0,
+                                    "content": "period, and sample complexity of exploration characterizes the performance at all states the agent",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                390,
+                                136,
+                                402
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        390,
+                                        136,
+                                        402
+                                    ],
+                                    "score": 1.0,
+                                    "content": "enters.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 18.5,
+                    "bbox_fs": [
+                        104,
+                        334,
+                        506,
+                        402
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        406,
+                        505,
+                        484
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                407,
+                                506,
+                                419
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        407,
+                                        506,
+                                        419
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The following example clearly illustrates the key difference between infinite-horizon and finite-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                416,
+                                506,
+                                431
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        416,
+                                        296,
+                                        431
+                                    ],
+                                    "score": 1.0,
+                                    "content": "horizon. Consider an MDP with a starting state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        419,
+                                        307,
+                                        429
+                                    ],
+                                    "score": 0.85,
+                                    "content": "s _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        416,
+                                        437,
+                                        431
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where the probability of leaving",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        438,
+                                        419,
+                                        448,
+                                        429
+                                    ],
+                                    "score": 0.85,
+                                    "content": "s _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        448,
+                                        416,
+                                        458,
+                                        431
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        459,
+                                        417,
+                                        489,
+                                        430
+                                    ],
+                                    "score": 0.92,
+                                    "content": "o ( T ^ { - 1 } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        490,
+                                        416,
+                                        506,
+                                        431
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". In",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                428,
+                                505,
+                                442
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        428,
+                                        331,
+                                        442
+                                    ],
+                                    "score": 1.0,
+                                    "content": "this case, with high probability, it would take more than",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        331,
+                                        429,
+                                        340,
+                                        439
+                                    ],
+                                    "score": 0.76,
+                                    "content": "T",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        340,
+                                        428,
+                                        414,
+                                        442
+                                    ],
+                                    "score": 1.0,
+                                    "content": "timesteps to leave",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        415,
+                                        430,
+                                        425,
+                                        440
+                                    ],
+                                    "score": 0.85,
+                                    "content": "s _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        425,
+                                        428,
+                                        505,
+                                        442
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Hence, guarantees",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                440,
+                                506,
+                                452
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        440,
+                                        222,
+                                        452
+                                    ],
+                                    "score": 1.0,
+                                    "content": "about the learning in the first",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        222,
+                                        441,
+                                        231,
+                                        450
+                                    ],
+                                    "score": 0.81,
+                                    "content": "T",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        231,
+                                        440,
+                                        382,
+                                        452
+                                    ],
+                                    "score": 1.0,
+                                    "content": "timesteps or about the performance at",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        383,
+                                        441,
+                                        393,
+                                        451
+                                    ],
+                                    "score": 0.85,
+                                    "content": "s _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        393,
+                                        440,
+                                        506,
+                                        452
+                                    ],
+                                    "score": 1.0,
+                                    "content": "imply almost nothing about",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                449,
+                                505,
+                                464
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        449,
+                                        505,
+                                        464
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the number of mistakes the algorithm would make in the rest of the MDP (i.e. the sample complexity",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                461,
+                                505,
+                                474
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        461,
+                                        505,
+                                        474
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of exploration of the algorithm). As a result, the analysis for finite horizon MDPs cannot be directly",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                472,
+                                244,
+                                486
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        472,
+                                        244,
+                                        486
+                                    ],
+                                    "score": 1.0,
+                                    "content": "applied to infinite horizon setting.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 25,
+                    "bbox_fs": [
+                        104,
+                        407,
+                        506,
+                        486
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        489,
+                        505,
+                        534
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                488,
+                                505,
+                                502
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        488,
+                                        505,
+                                        502
+                                    ],
+                                    "score": 1.0,
+                                    "content": "This calls for techniques for counting mistakes along the entire trajectory, such as those employed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                499,
+                                505,
+                                514
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        499,
+                                        505,
+                                        514
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by Strehl et al. (2006). In particular, we need to establish convenient sufficient conditions for being",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                511,
+                                506,
+                                524
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        514,
+                                        112,
+                                        521
+                                    ],
+                                    "score": 0.67,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        112,
+                                        511,
+                                        196,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimal at timestep",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        196,
+                                        513,
+                                        201,
+                                        521
+                                    ],
+                                    "score": 0.72,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        202,
+                                        511,
+                                        242,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        243,
+                                        513,
+                                        252,
+                                        522
+                                    ],
+                                    "score": 0.84,
+                                    "content": "s _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        252,
+                                        511,
+                                        274,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", i.e.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        275,
+                                        511,
+                                        370,
+                                        523
+                                    ],
+                                    "score": 0.92,
+                                    "content": "V ^ { \\ast } ( s _ { t } ) - V ^ { \\pi _ { t } } ( s _ { t } ) \\leq \\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        370,
+                                        511,
+                                        506,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Then, bounding the number of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                522,
+                                373,
+                                536
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        522,
+                                        373,
+                                        536
+                                    ],
+                                    "score": 1.0,
+                                    "content": "violations of such conditions gives a bound on sample complexity.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 30.5,
+                    "bbox_fs": [
+                        105,
+                        488,
+                        506,
+                        536
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        539,
+                        505,
+                        650
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                538,
+                                505,
+                                551
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        538,
+                                        505,
+                                        551
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Another technical reason why the proof in Jin et al. (2018) cannot be directly applied to our problem",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                549,
+                                505,
+                                563
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        549,
+                                        505,
+                                        563
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the following: In finite horizon settings, Jin et al. (2018) decomposed the learning error at episode",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                560,
+                                505,
+                                574
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        562,
+                                        113,
+                                        571
+                                    ],
+                                    "score": 0.8,
+                                    "content": "k",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        114,
+                                        560,
+                                        150,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and time",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        151,
+                                        562,
+                                        158,
+                                        571
+                                    ],
+                                    "score": 0.79,
+                                    "content": "h",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        159,
+                                        560,
+                                        358,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as errors from a set of consecutive episodes before",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        358,
+                                        562,
+                                        365,
+                                        571
+                                    ],
+                                    "score": 0.81,
+                                    "content": "k",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        366,
+                                        560,
+                                        395,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": "at time",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        396,
+                                        561,
+                                        420,
+                                        572
+                                    ],
+                                    "score": 0.91,
+                                    "content": "h + 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        420,
+                                        560,
+                                        505,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": "using a clever design",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                572,
+                                506,
+                                585
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        572,
+                                        506,
+                                        585
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of learning rate. However, in the infinite horizon setting, this property does not hold. Suppose at",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                582,
+                                506,
+                                596
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        582,
+                                        126,
+                                        596
+                                    ],
+                                    "score": 1.0,
+                                    "content": "time",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        127,
+                                        584,
+                                        132,
+                                        593
+                                    ],
+                                    "score": 0.75,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        132,
+                                        582,
+                                        211,
+                                        596
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the agent is at state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        211,
+                                        585,
+                                        221,
+                                        594
+                                    ],
+                                    "score": 0.85,
+                                    "content": "s _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        221,
+                                        582,
+                                        288,
+                                        596
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and takes action",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        585,
+                                        298,
+                                        594
+                                    ],
+                                    "score": 0.84,
+                                    "content": "a _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        299,
+                                        582,
+                                        407,
+                                        596
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Then the learning error at",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        407,
+                                        584,
+                                        412,
+                                        593
+                                    ],
+                                    "score": 0.74,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        413,
+                                        582,
+                                        506,
+                                        596
+                                    ],
+                                    "score": 1.0,
+                                    "content": "only depends on those",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                594,
+                                506,
+                                606
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        594,
+                                        382,
+                                        606
+                                    ],
+                                    "score": 1.0,
+                                    "content": "previous time steps such that the agent encountered the same state as",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        382,
+                                        596,
+                                        392,
+                                        605
+                                    ],
+                                    "score": 0.86,
+                                    "content": "s _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        392,
+                                        594,
+                                        506,
+                                        606
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and took the same action as",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                604,
+                                506,
+                                618
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        606,
+                                        116,
+                                        616
+                                    ],
+                                    "score": 0.83,
+                                    "content": "a _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        117,
+                                        604,
+                                        245,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Thus the learning error at time",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        245,
+                                        606,
+                                        250,
+                                        615
+                                    ],
+                                    "score": 0.64,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        251,
+                                        604,
+                                        506,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cannot be decomposed as errors from a set of consecutive time",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                616,
+                                506,
+                                629
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        616,
+                                        157,
+                                        629
+                                    ],
+                                    "score": 1.0,
+                                    "content": "steps before",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        157,
+                                        617,
+                                        162,
+                                        626
+                                    ],
+                                    "score": 0.74,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        163,
+                                        616,
+                                        506,
+                                        629
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", but errors from a set of non-consecutive time steps without any structure. Therefore,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                627,
+                                506,
+                                640
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        627,
+                                        506,
+                                        640
+                                    ],
+                                    "score": 1.0,
+                                    "content": "we have to control the sum of learning errors over an unstructured set of time steps. This makes the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                637,
+                                215,
+                                652
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        637,
+                                        215,
+                                        652
+                                    ],
+                                    "score": 1.0,
+                                    "content": "analysis more challenging.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        }
+                    ],
+                    "index": 37.5,
+                    "bbox_fs": [
+                        105,
+                        538,
+                        506,
+                        652
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        654,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                655,
+                                506,
+                                667
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        655,
+                                        506,
+                                        667
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Now we give a brief road map of the proof of Theorem 1. Our first goal is to establish a sufficient",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                666,
+                                506,
+                                678
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        666,
+                                        174,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "condition so that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        175,
+                                        667,
+                                        185,
+                                        677
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\pi _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        185,
+                                        666,
+                                        245,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learned at step",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        246,
+                                        667,
+                                        250,
+                                        676
+                                    ],
+                                    "score": 0.8,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        251,
+                                        666,
+                                        261,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        261,
+                                        668,
+                                        266,
+                                        676
+                                    ],
+                                    "score": 0.75,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        266,
+                                        666,
+                                        335,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimal for state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        335,
+                                        668,
+                                        344,
+                                        677
+                                    ],
+                                    "score": 0.81,
+                                    "content": "s _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        344,
+                                        666,
+                                        506,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". As an intermediate step we show that a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                676,
+                                506,
+                                690
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        676,
+                                        200,
+                                        690
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sufficient condition for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        201,
+                                        677,
+                                        292,
+                                        689
+                                    ],
+                                    "score": 0.91,
+                                    "content": "V ^ { * } ( s _ { t } ) - V ^ { \\pi _ { t } } ( s _ { t } ) \\leq \\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        292,
+                                        676,
+                                        320,
+                                        690
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        320,
+                                        677,
+                                        411,
+                                        689
+                                    ],
+                                    "score": 0.92,
+                                    "content": "V ^ { \\ast } ( s _ { t ^ { \\prime } } ) - Q ^ { \\ast } ( s _ { t ^ { \\prime } } , a _ { t ^ { \\prime } } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        412,
+                                        676,
+                                        506,
+                                        690
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is small for a few time",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                687,
+                                505,
+                                700
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        687,
+                                        128,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "steps",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        128,
+                                        687,
+                                        136,
+                                        698
+                                    ],
+                                    "score": 0.83,
+                                    "content": "t ^ { \\prime }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        136,
+                                        687,
+                                        208,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "within an interval",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        208,
+                                        689,
+                                        245,
+                                        699
+                                    ],
+                                    "score": 0.91,
+                                    "content": "[ t , t + R ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        245,
+                                        687,
+                                        333,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for a carefully chosen",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        333,
+                                        689,
+                                        342,
+                                        698
+                                    ],
+                                    "score": 0.78,
+                                    "content": "R",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        342,
+                                        687,
+                                        505,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(Condition 1). Then we show the desired",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                699,
+                                506,
+                                711
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        699,
+                                        506,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sufficient condition (Condition 2) implies Condition 1. We then bound the total number of bad time",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                708,
+                                506,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        708,
+                                        167,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "steps on which",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        168,
+                                        710,
+                                        251,
+                                        722
+                                    ],
+                                    "score": 0.91,
+                                    "content": "V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        251,
+                                        708,
+                                        506,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is large for the whole MDP; this implies a bound on the number",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                720,
+                                450,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        720,
+                                        450,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of violations of Condition 2. This in turn relies on a key technical lemma (Lemma 2).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        }
+                    ],
+                    "index": 46,
+                    "bbox_fs": [
+                        105,
+                        655,
+                        506,
+                        733
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        82,
+                        505,
+                        116
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                82,
+                                505,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        82,
+                                        505,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The remaining part of this section is organized as follows. We establish the sufficient condition for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                93,
+                                505,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        96,
+                                        112,
+                                        104
+                                    ],
+                                    "score": 0.64,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        112,
+                                        93,
+                                        505,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimality in Section 3.3. The key lemma is presented in Section 3.4. Finally we prove Theorem 1",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                104,
+                                167,
+                                116
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        104,
+                                        167,
+                                        116
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in Section 3.5.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        106,
+                        129,
+                        318,
+                        141
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                129,
+                                319,
+                                142
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        129,
+                                        255,
+                                        142
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3.3 SUFFICIENT CONDITION FOR",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        255,
+                                        132,
+                                        261,
+                                        140
+                                    ],
+                                    "score": 0.67,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        261,
+                                        129,
+                                        319,
+                                        142
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-OPTIMALITY",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        149,
+                        483,
+                        163
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                148,
+                                484,
+                                165
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        148,
+                                        376,
+                                        165
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In this section, we establish a sufficient condition (Condition 2) for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        376,
+                                        153,
+                                        381,
+                                        160
+                                    ],
+                                    "score": 0.65,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        381,
+                                        148,
+                                        475,
+                                        165
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimality at time step",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        475,
+                                        152,
+                                        480,
+                                        160
+                                    ],
+                                    "score": 0.71,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        480,
+                                        148,
+                                        484,
+                                        165
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        167,
+                        506,
+                        203
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                165,
+                                506,
+                                181
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        165,
+                                        152,
+                                        181
+                                    ],
+                                    "score": 1.0,
+                                    "content": "For a fixed",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        169,
+                                        162,
+                                        178
+                                    ],
+                                    "score": 0.83,
+                                    "content": "s _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        162,
+                                        165,
+                                        204,
+                                        181
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", let TRAJ",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        204,
+                                        168,
+                                        218,
+                                        179
+                                    ],
+                                    "score": 0.66,
+                                    "content": "( R )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        219,
+                                        165,
+                                        300,
+                                        181
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be the set of length-",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        301,
+                                        168,
+                                        309,
+                                        177
+                                    ],
+                                    "score": 0.8,
+                                    "content": "R",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        310,
+                                        165,
+                                        413,
+                                        181
+                                    ],
+                                    "score": 1.0,
+                                    "content": "trajectories starting from",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        414,
+                                        170,
+                                        423,
+                                        178
+                                    ],
+                                    "score": 0.83,
+                                    "content": "s _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        423,
+                                        165,
+                                        506,
+                                        181
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Our goal is to give",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                178,
+                                505,
+                                191
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        178,
+                                        225,
+                                        191
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a sufficient condition so that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        226,
+                                        180,
+                                        236,
+                                        190
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\pi _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        236,
+                                        178,
+                                        345,
+                                        191
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the policy learned at step",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        346,
+                                        180,
+                                        351,
+                                        189
+                                    ],
+                                    "score": 0.75,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        351,
+                                        178,
+                                        364,
+                                        191
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        365,
+                                        181,
+                                        370,
+                                        188
+                                    ],
+                                    "score": 0.72,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        370,
+                                        178,
+                                        444,
+                                        191
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimal. For any",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        444,
+                                        179,
+                                        473,
+                                        190
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\epsilon _ { 2 } > 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        474,
+                                        178,
+                                        505,
+                                        191
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", define",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                187,
+                                406,
+                                206
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        189,
+                                        216,
+                                        204
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { r } { R : = \\lceil \\ln \\frac { 1 } { \\epsilon _ { 2 } ( 1 - \\gamma ) } / ( 1 - \\gamma ) \\rceil } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        217,
+                                        187,
+                                        252,
+                                        206
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Denote",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        253,
+                                        189,
+                                        335,
+                                        201
+                                    ],
+                                    "score": 0.94,
+                                    "content": "V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        336,
+                                        187,
+                                        349,
+                                        206
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        349,
+                                        190,
+                                        362,
+                                        200
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\Delta _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        362,
+                                        187,
+                                        406,
+                                        206
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". We have",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        124,
+                        209,
+                        485,
+                        372
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                124,
+                                209,
+                                485,
+                                372
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        124,
+                                        209,
+                                        485,
+                                        372
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { r l } & { \\quad V ^ { * } ( s _ { t } ) - V ^ { \\pi } ( s _ { t } ) } \\\\ & { = V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) + Q ^ { * } ( s _ { t } , a _ { t } ) - V ^ { \\pi } ( s _ { t } ) } \\\\ & { = V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) + \\gamma \\mathbb { P } ( V ^ { * } - V ^ { \\pi } ) ( s _ { t } , \\pi _ { t } ( s _ { t } ) ) } \\\\ & { = V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) + \\gamma \\sum _ { s + 1 } ^ { \\infty } p ( s _ { t + 1 } | s _ { t } , \\pi _ { t } ( s _ { t } ) ) \\cdot [ V ^ { * } ( s _ { t + 1 } ) - Q ^ { * } ( s _ { t + 1 } , a _ { t + 1 } ) ] + } \\\\ & { \\quad \\Big . \\Big . \\Big . \\Big . \\Big . \\Big . } \\\\ & { \\quad \\quad \\Big .  \\gamma _ { s + 1 , s ^ { * } + 2 } \\mathrm { ~ } p ( s _ { t + 2 } | s _ { t + 1 } , \\pi _ { t + 1 } ( s _ { t + 1 } ) ) \\cdot p ( s _ { t + 1 } | s _ { t } , \\pi _ { t } ( s _ { t } ) ) \\big [ V ^ { * } ( s _ { t + 2 } ) - Q ^ { * } ( s _ { t + 2 } , a _ { t + 2 } ) \\Big ] } \\\\ & { \\quad \\quad \\cdot \\dots } \\\\ & { \\le \\epsilon _ { 2 } + \\displaystyle \\sum _ { s ^ { \\prime } = s ^ { \\prime } } p ( t r a _ { t } ) \\cdot [ \\frac { n - 1 } { \\lambda _ { 2 } } \\gamma ^ { 2 } \\Delta _ { t + 2 } ] , } \\\\ & { \\quad \\quad \\pi _ { s \\lambda ^ { ( 2 ) } ( L ) } ^ { R , a } } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "0a9ed2938f048cb014418095c8bf22495e13c88841960e9512dce70e6eff25c2.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                124,
+                                209,
+                                485,
+                                263.3333333333333
+                            ],
+                            "spans": [],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                124,
+                                263.3333333333333,
+                                485,
+                                317.66666666666663
+                            ],
+                            "spans": [],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                124,
+                                317.66666666666663,
+                                485,
+                                371.99999999999994
+                            ],
+                            "spans": [],
+                            "index": 10
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        376,
+                        467,
+                        394
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                369,
+                                464,
+                                401
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        369,
+                                        265,
+                                        401
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where the last inequality holds because",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        265,
+                                        376,
+                                        304,
+                                        394
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\frac { \\gamma ^ { R } } { 1 - \\gamma } \\leq \\epsilon _ { 2 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        369,
+                                        456,
+                                        401
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", which follows from the definition of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        456,
+                                        381,
+                                        464,
+                                        390
+                                    ],
+                                    "score": 0.84,
+                                    "content": "R",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        401,
+                        503,
+                        428
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                103,
+                                398,
+                                504,
+                                418
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        103,
+                                        398,
+                                        239,
+                                        418
+                                    ],
+                                    "score": 1.0,
+                                    "content": "For any fixed trajectory of length",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        239,
+                                        402,
+                                        248,
+                                        412
+                                    ],
+                                    "score": 0.82,
+                                    "content": "R",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        248,
+                                        398,
+                                        302,
+                                        418
+                                    ],
+                                    "score": 1.0,
+                                    "content": "starting from",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        302,
+                                        404,
+                                        311,
+                                        413
+                                    ],
+                                    "score": 0.85,
+                                    "content": "s _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        312,
+                                        398,
+                                        404,
+                                        418
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", consider the sequence",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        404,
+                                        401,
+                                        465,
+                                        416
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\left( \\Delta _ { t ^ { \\prime } } \\right) _ { t \\leq t ^ { \\prime } < t + R }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        465,
+                                        398,
+                                        484,
+                                        418
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        484,
+                                        399,
+                                        504,
+                                        414
+                                    ],
+                                    "score": 0.91,
+                                    "content": "X _ { t } ^ { ( i ) }",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                413,
+                                402,
+                                430
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        413,
+                                        133,
+                                        430
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        133,
+                                        416,
+                                        138,
+                                        425
+                                    ],
+                                    "score": 0.74,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        138,
+                                        413,
+                                        210,
+                                        430
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-th largest item of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        210,
+                                        415,
+                                        271,
+                                        429
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\left( \\Delta _ { t ^ { \\prime } } \\right) _ { t \\leq t ^ { \\prime } < t + R }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        271,
+                                        413,
+                                        402,
+                                        430
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Rearranging Eq. (1), we obtain",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 12.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        203,
+                        434,
+                        408,
+                        469
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                203,
+                                434,
+                                408,
+                                469
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        203,
+                                        434,
+                                        408,
+                                        469
+                                    ],
+                                    "score": 0.93,
+                                    "content": "V ^ { \\ast } ( s _ { t } ) - V ^ { \\pi _ { t } } ( s _ { t } ) \\leq \\epsilon _ { 2 } + E _ { t r a j } \\left[ \\sum _ { i = 1 } ^ { R } \\gamma ^ { i - 1 } X _ { t } ^ { ( i ) } \\right] .",
+                                    "type": "interline_equation",
+                                    "image_path": "353a318648b4e83bfc1d70cd63fedbd78d74dcde5d09d9484e43d06da944118d.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                203,
+                                434,
+                                408,
+                                451.5
+                            ],
+                            "spans": [],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                203,
+                                451.5,
+                                408,
+                                469.0
+                            ],
+                            "spans": [],
+                            "index": 15
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        479,
+                        432,
+                        492
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                478,
+                                430,
+                                494
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        478,
+                                        263,
+                                        494
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We first prove that Condition 1 implies",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        264,
+                                        482,
+                                        269,
+                                        490
+                                    ],
+                                    "score": 0.76,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        269,
+                                        478,
+                                        362,
+                                        494
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimality at time step",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        363,
+                                        481,
+                                        368,
+                                        490
+                                    ],
+                                    "score": 0.77,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        368,
+                                        478,
+                                        393,
+                                        494
+                                    ],
+                                    "score": 1.0,
+                                    "content": "when",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        393,
+                                        480,
+                                        430,
+                                        492
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\epsilon _ { 2 } = \\epsilon / 3",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        496,
+                        391,
+                        517
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                102,
+                                494,
+                                387,
+                                518
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        102,
+                                        494,
+                                        179,
+                                        518
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Condition 1. Let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        180,
+                                        495,
+                                        281,
+                                        517
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\begin{array} { r } { \\xi _ { i } : = \\frac { 1 } { 2 ^ { i + 2 } } \\epsilon _ { 2 } \\left( \\ln \\frac { 1 } { 1 - \\gamma } \\right) ^ { - 1 } } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        282,
+                                        494,
+                                        316,
+                                        518
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". For all",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        316,
+                                        501,
+                                        387,
+                                        514
+                                    ],
+                                    "score": 0.88,
+                                    "content": "0 \\leq i \\leq \\lfloor \\log _ { 2 } R \\rfloor",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        274,
+                        522,
+                        336,
+                        540
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                274,
+                                522,
+                                336,
+                                540
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        274,
+                                        522,
+                                        336,
+                                        540
+                                    ],
+                                    "score": 0.9,
+                                    "content": "E [ X _ { t } ^ { ( 2 ^ { i } ) } ] \\leq \\xi _ { i } .",
+                                    "type": "interline_equation",
+                                    "image_path": "4c5556442dd84c67ed2f8017702e406cf2d4d5acde09b8b3242d907ec73dda13.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                274,
+                                522,
+                                336,
+                                540
+                            ],
+                            "spans": [],
+                            "index": 18
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        545,
+                        505,
+                        569
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                543,
+                                505,
+                                560
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        543,
+                                        198,
+                                        560
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Claim 1. If Condition",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        198,
+                                        547,
+                                        203,
+                                        556
+                                    ],
+                                    "score": 0.7,
+                                    "content": "^ { l }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        204,
+                                        543,
+                                        295,
+                                        560
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is satisfied at time step",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        295,
+                                        547,
+                                        300,
+                                        556
+                                    ],
+                                    "score": 0.51,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        301,
+                                        543,
+                                        344,
+                                        560
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the policy",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        345,
+                                        548,
+                                        355,
+                                        557
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\pi _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        356,
+                                        543,
+                                        365,
+                                        560
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        366,
+                                        548,
+                                        371,
+                                        556
+                                    ],
+                                    "score": 0.68,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        371,
+                                        543,
+                                        436,
+                                        560
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimal at state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        436,
+                                        548,
+                                        446,
+                                        557
+                                    ],
+                                    "score": 0.83,
+                                    "content": "s _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        446,
+                                        543,
+                                        464,
+                                        560
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", i.e.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        464,
+                                        545,
+                                        505,
+                                        558
+                                    ],
+                                    "score": 0.91,
+                                    "content": "V ^ { \\ast } ( s _ { t } ) -",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                554,
+                                163,
+                                571
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        557,
+                                        157,
+                                        569
+                                    ],
+                                    "score": 0.91,
+                                    "content": "V ^ { \\pi _ { t } } ( s _ { t } ) \\leq \\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        158,
+                                        554,
+                                        163,
+                                        571
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 19.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        581,
+                        505,
+                        613
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                103,
+                                579,
+                                505,
+                                618
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        103,
+                                        579,
+                                        180,
+                                        600
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Proof. Note that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        107,
+                                        596,
+                                        164,
+                                        612
+                                    ],
+                                    "score": 0.93,
+                                    "content": "E [ X _ { t } ^ { ( 2 ^ { \\lfloor \\log _ { 2 } i \\rfloor } ) } ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        165,
+                                        588,
+                                        263,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": "t. Eq. (3) implies that for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        180,
+                                        582,
+                                        200,
+                                        597
+                                    ],
+                                    "score": 0.93,
+                                    "content": "X _ { t } ^ { ( i ) }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        200,
+                                        579,
+                                        393,
+                                        600
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is monotonically decreasing with respect to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        263,
+                                        600,
+                                        317,
+                                        612
+                                    ],
+                                    "score": 0.91,
+                                    "content": "1 / 2 < \\gamma < 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        317,
+                                        588,
+                                        327,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        393,
+                                        586,
+                                        398,
+                                        595
+                                    ],
+                                    "score": 0.73,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        399,
+                                        579,
+                                        456,
+                                        600
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Therefore,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        456,
+                                        581,
+                                        505,
+                                        597
+                                    ],
+                                    "score": 0.93,
+                                    "content": "E [ X _ { t } ^ { ( i ) } ] \\ \\leq",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 21
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        144,
+                        617,
+                        466,
+                        687
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                144,
+                                617,
+                                466,
+                                687
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        144,
+                                        617,
+                                        466,
+                                        687
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { r l } & { E \\left[ \\displaystyle \\sum _ { i = 1 } ^ { R } \\gamma ^ { i - 1 } X _ { t } ^ { ( i ) } \\right] = \\displaystyle \\sum _ { i = 1 } ^ { R } \\gamma ^ { i - 1 } E [ X _ { t } ^ { ( i ) } ] \\leq \\displaystyle \\sum _ { i = 1 } ^ { R } \\gamma ^ { i - 1 } E [ X _ { t } ^ { ( 2 ^ { \\lfloor \\log _ { 2 } i \\rfloor } ) } ] } \\\\ & { \\leq \\displaystyle \\sum _ { i = 1 } ^ { R } \\gamma ^ { i - 1 } 2 ^ { - \\lfloor \\log _ { 2 } i \\rfloor - 2 } \\epsilon _ { 2 } \\left( \\ln \\frac { 1 } { 1 - \\gamma } \\right) ^ { - 1 } \\leq \\displaystyle \\sum _ { i = 1 } ^ { R } \\frac { \\gamma ^ { i - 1 } } { i } \\epsilon _ { 2 } \\left( \\ln \\frac { 1 } { 1 - \\gamma } \\right) ^ { - 1 } \\leq 2 \\epsilon _ { 2 } , } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "62ba3bea0f084d11903c964028d906643070d34916bde88924637c5e08ea73d6.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 23,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                144,
+                                617,
+                                466,
+                                640.3333333333334
+                            ],
+                            "spans": [],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                144,
+                                640.3333333333334,
+                                466,
+                                663.6666666666667
+                            ],
+                            "spans": [],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                144,
+                                663.6666666666667,
+                                466,
+                                687.0000000000001
+                            ],
+                            "spans": [],
+                            "index": 24
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        692,
+                        462,
+                        710
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                102,
+                                689,
+                                458,
+                                715
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        102,
+                                        689,
+                                        310,
+                                        715
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where the last inequality follows from the fact that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        310,
+                                        692,
+                                        405,
+                                        711
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { r } { \\sum _ { i = 1 } ^ { \\infty } \\frac { \\gamma ^ { i - 1 } } { i } = \\frac { 1 } { \\gamma } \\ln \\frac { 1 } { 1 - \\gamma } } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        405,
+                                        689,
+                                        423,
+                                        715
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        423,
+                                        695,
+                                        458,
+                                        708
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\gamma > 1 / 2",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        102,
+                        714,
+                        476,
+                        735
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                103,
+                                712,
+                                475,
+                                737
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        103,
+                                        712,
+                                        238,
+                                        737
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Combining with Eq. 2, we have,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        238,
+                                        715,
+                                        475,
+                                        736
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\begin{array} { r } { V ^ { \\ast } ( s _ { t } ) - V ^ { \\pi _ { t } } ( s _ { t } ) \\leq \\epsilon _ { 2 } + E \\left[ \\sum _ { i = 1 } ^ { R } \\gamma ^ { i - 1 } X _ { t } ^ { ( i ) } \\right] \\leq 3 \\epsilon _ { 2 } = \\epsilon . } \\end{array}",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 26
+                }
+            ],
+            "page_idx": 4,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        26,
+                        294,
+                        38
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                25,
+                                294,
+                                39
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        25,
+                                        294,
+                                        39
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        494,
+                        719,
+                        505,
+                        730
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                496,
+                                721,
+                                504,
+                                729
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        496,
+                                        721,
+                                        504,
+                                        729
+                                    ],
+                                    "score": 0.999,
+                                    "content": "□",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        751,
+                        309,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                302,
+                                750,
+                                309,
+                                762
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        302,
+                                        750,
+                                        309,
+                                        762
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        82,
+                        505,
+                        116
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                82,
+                                505,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        82,
+                                        505,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The remaining part of this section is organized as follows. We establish the sufficient condition for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                93,
+                                505,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        96,
+                                        112,
+                                        104
+                                    ],
+                                    "score": 0.64,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        112,
+                                        93,
+                                        505,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimality in Section 3.3. The key lemma is presented in Section 3.4. Finally we prove Theorem 1",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                104,
+                                167,
+                                116
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        104,
+                                        167,
+                                        116
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in Section 3.5.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1,
+                    "bbox_fs": [
+                        106,
+                        82,
+                        505,
+                        116
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        106,
+                        129,
+                        318,
+                        141
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                129,
+                                319,
+                                142
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        129,
+                                        255,
+                                        142
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3.3 SUFFICIENT CONDITION FOR",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        255,
+                                        132,
+                                        261,
+                                        140
+                                    ],
+                                    "score": 0.67,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        261,
+                                        129,
+                                        319,
+                                        142
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-OPTIMALITY",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        149,
+                        483,
+                        163
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                148,
+                                484,
+                                165
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        148,
+                                        376,
+                                        165
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In this section, we establish a sufficient condition (Condition 2) for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        376,
+                                        153,
+                                        381,
+                                        160
+                                    ],
+                                    "score": 0.65,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        381,
+                                        148,
+                                        475,
+                                        165
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimality at time step",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        475,
+                                        152,
+                                        480,
+                                        160
+                                    ],
+                                    "score": 0.71,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        480,
+                                        148,
+                                        484,
+                                        165
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 4,
+                    "bbox_fs": [
+                        105,
+                        148,
+                        484,
+                        165
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        167,
+                        506,
+                        203
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                165,
+                                506,
+                                181
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        165,
+                                        152,
+                                        181
+                                    ],
+                                    "score": 1.0,
+                                    "content": "For a fixed",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        169,
+                                        162,
+                                        178
+                                    ],
+                                    "score": 0.83,
+                                    "content": "s _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        162,
+                                        165,
+                                        204,
+                                        181
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", let TRAJ",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        204,
+                                        168,
+                                        218,
+                                        179
+                                    ],
+                                    "score": 0.66,
+                                    "content": "( R )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        219,
+                                        165,
+                                        300,
+                                        181
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be the set of length-",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        301,
+                                        168,
+                                        309,
+                                        177
+                                    ],
+                                    "score": 0.8,
+                                    "content": "R",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        310,
+                                        165,
+                                        413,
+                                        181
+                                    ],
+                                    "score": 1.0,
+                                    "content": "trajectories starting from",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        414,
+                                        170,
+                                        423,
+                                        178
+                                    ],
+                                    "score": 0.83,
+                                    "content": "s _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        423,
+                                        165,
+                                        506,
+                                        181
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Our goal is to give",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                178,
+                                505,
+                                191
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        178,
+                                        225,
+                                        191
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a sufficient condition so that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        226,
+                                        180,
+                                        236,
+                                        190
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\pi _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        236,
+                                        178,
+                                        345,
+                                        191
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the policy learned at step",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        346,
+                                        180,
+                                        351,
+                                        189
+                                    ],
+                                    "score": 0.75,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        351,
+                                        178,
+                                        364,
+                                        191
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        365,
+                                        181,
+                                        370,
+                                        188
+                                    ],
+                                    "score": 0.72,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        370,
+                                        178,
+                                        444,
+                                        191
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimal. For any",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        444,
+                                        179,
+                                        473,
+                                        190
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\epsilon _ { 2 } > 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        474,
+                                        178,
+                                        505,
+                                        191
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", define",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                187,
+                                406,
+                                206
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        189,
+                                        216,
+                                        204
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { r } { R : = \\lceil \\ln \\frac { 1 } { \\epsilon _ { 2 } ( 1 - \\gamma ) } / ( 1 - \\gamma ) \\rceil } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        217,
+                                        187,
+                                        252,
+                                        206
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Denote",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        253,
+                                        189,
+                                        335,
+                                        201
+                                    ],
+                                    "score": 0.94,
+                                    "content": "V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        336,
+                                        187,
+                                        349,
+                                        206
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        349,
+                                        190,
+                                        362,
+                                        200
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\Delta _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        362,
+                                        187,
+                                        406,
+                                        206
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". We have",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 6,
+                    "bbox_fs": [
+                        105,
+                        165,
+                        506,
+                        206
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        124,
+                        209,
+                        485,
+                        372
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                124,
+                                209,
+                                485,
+                                372
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        124,
+                                        209,
+                                        485,
+                                        372
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { r l } & { \\quad V ^ { * } ( s _ { t } ) - V ^ { \\pi } ( s _ { t } ) } \\\\ & { = V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) + Q ^ { * } ( s _ { t } , a _ { t } ) - V ^ { \\pi } ( s _ { t } ) } \\\\ & { = V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) + \\gamma \\mathbb { P } ( V ^ { * } - V ^ { \\pi } ) ( s _ { t } , \\pi _ { t } ( s _ { t } ) ) } \\\\ & { = V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) + \\gamma \\sum _ { s + 1 } ^ { \\infty } p ( s _ { t + 1 } | s _ { t } , \\pi _ { t } ( s _ { t } ) ) \\cdot [ V ^ { * } ( s _ { t + 1 } ) - Q ^ { * } ( s _ { t + 1 } , a _ { t + 1 } ) ] + } \\\\ & { \\quad \\Big . \\Big . \\Big . \\Big . \\Big . \\Big . } \\\\ & { \\quad \\quad \\Big .  \\gamma _ { s + 1 , s ^ { * } + 2 } \\mathrm { ~ } p ( s _ { t + 2 } | s _ { t + 1 } , \\pi _ { t + 1 } ( s _ { t + 1 } ) ) \\cdot p ( s _ { t + 1 } | s _ { t } , \\pi _ { t } ( s _ { t } ) ) \\big [ V ^ { * } ( s _ { t + 2 } ) - Q ^ { * } ( s _ { t + 2 } , a _ { t + 2 } ) \\Big ] } \\\\ & { \\quad \\quad \\cdot \\dots } \\\\ & { \\le \\epsilon _ { 2 } + \\displaystyle \\sum _ { s ^ { \\prime } = s ^ { \\prime } } p ( t r a _ { t } ) \\cdot [ \\frac { n - 1 } { \\lambda _ { 2 } } \\gamma ^ { 2 } \\Delta _ { t + 2 } ] , } \\\\ & { \\quad \\quad \\pi _ { s \\lambda ^ { ( 2 ) } ( L ) } ^ { R , a } } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "0a9ed2938f048cb014418095c8bf22495e13c88841960e9512dce70e6eff25c2.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                124,
+                                209,
+                                485,
+                                263.3333333333333
+                            ],
+                            "spans": [],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                124,
+                                263.3333333333333,
+                                485,
+                                317.66666666666663
+                            ],
+                            "spans": [],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                124,
+                                317.66666666666663,
+                                485,
+                                371.99999999999994
+                            ],
+                            "spans": [],
+                            "index": 10
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        376,
+                        467,
+                        394
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                369,
+                                464,
+                                401
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        369,
+                                        265,
+                                        401
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where the last inequality holds because",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        265,
+                                        376,
+                                        304,
+                                        394
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\frac { \\gamma ^ { R } } { 1 - \\gamma } \\leq \\epsilon _ { 2 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        369,
+                                        456,
+                                        401
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", which follows from the definition of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        456,
+                                        381,
+                                        464,
+                                        390
+                                    ],
+                                    "score": 0.84,
+                                    "content": "R",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 11,
+                    "bbox_fs": [
+                        105,
+                        369,
+                        464,
+                        401
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        401,
+                        503,
+                        428
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                103,
+                                398,
+                                504,
+                                418
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        103,
+                                        398,
+                                        239,
+                                        418
+                                    ],
+                                    "score": 1.0,
+                                    "content": "For any fixed trajectory of length",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        239,
+                                        402,
+                                        248,
+                                        412
+                                    ],
+                                    "score": 0.82,
+                                    "content": "R",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        248,
+                                        398,
+                                        302,
+                                        418
+                                    ],
+                                    "score": 1.0,
+                                    "content": "starting from",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        302,
+                                        404,
+                                        311,
+                                        413
+                                    ],
+                                    "score": 0.85,
+                                    "content": "s _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        312,
+                                        398,
+                                        404,
+                                        418
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", consider the sequence",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        404,
+                                        401,
+                                        465,
+                                        416
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\left( \\Delta _ { t ^ { \\prime } } \\right) _ { t \\leq t ^ { \\prime } < t + R }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        465,
+                                        398,
+                                        484,
+                                        418
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        484,
+                                        399,
+                                        504,
+                                        414
+                                    ],
+                                    "score": 0.91,
+                                    "content": "X _ { t } ^ { ( i ) }",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                413,
+                                402,
+                                430
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        413,
+                                        133,
+                                        430
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        133,
+                                        416,
+                                        138,
+                                        425
+                                    ],
+                                    "score": 0.74,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        138,
+                                        413,
+                                        210,
+                                        430
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-th largest item of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        210,
+                                        415,
+                                        271,
+                                        429
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\left( \\Delta _ { t ^ { \\prime } } \\right) _ { t \\leq t ^ { \\prime } < t + R }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        271,
+                                        413,
+                                        402,
+                                        430
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Rearranging Eq. (1), we obtain",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 12.5,
+                    "bbox_fs": [
+                        103,
+                        398,
+                        504,
+                        430
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        203,
+                        434,
+                        408,
+                        469
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                203,
+                                434,
+                                408,
+                                469
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        203,
+                                        434,
+                                        408,
+                                        469
+                                    ],
+                                    "score": 0.93,
+                                    "content": "V ^ { \\ast } ( s _ { t } ) - V ^ { \\pi _ { t } } ( s _ { t } ) \\leq \\epsilon _ { 2 } + E _ { t r a j } \\left[ \\sum _ { i = 1 } ^ { R } \\gamma ^ { i - 1 } X _ { t } ^ { ( i ) } \\right] .",
+                                    "type": "interline_equation",
+                                    "image_path": "353a318648b4e83bfc1d70cd63fedbd78d74dcde5d09d9484e43d06da944118d.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                203,
+                                434,
+                                408,
+                                451.5
+                            ],
+                            "spans": [],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                203,
+                                451.5,
+                                408,
+                                469.0
+                            ],
+                            "spans": [],
+                            "index": 15
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        479,
+                        432,
+                        492
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                478,
+                                430,
+                                494
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        478,
+                                        263,
+                                        494
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We first prove that Condition 1 implies",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        264,
+                                        482,
+                                        269,
+                                        490
+                                    ],
+                                    "score": 0.76,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        269,
+                                        478,
+                                        362,
+                                        494
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimality at time step",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        363,
+                                        481,
+                                        368,
+                                        490
+                                    ],
+                                    "score": 0.77,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        368,
+                                        478,
+                                        393,
+                                        494
+                                    ],
+                                    "score": 1.0,
+                                    "content": "when",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        393,
+                                        480,
+                                        430,
+                                        492
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\epsilon _ { 2 } = \\epsilon / 3",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 16,
+                    "bbox_fs": [
+                        105,
+                        478,
+                        430,
+                        494
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        496,
+                        391,
+                        517
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                102,
+                                494,
+                                387,
+                                518
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        102,
+                                        494,
+                                        179,
+                                        518
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Condition 1. Let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        180,
+                                        495,
+                                        281,
+                                        517
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\begin{array} { r } { \\xi _ { i } : = \\frac { 1 } { 2 ^ { i + 2 } } \\epsilon _ { 2 } \\left( \\ln \\frac { 1 } { 1 - \\gamma } \\right) ^ { - 1 } } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        282,
+                                        494,
+                                        316,
+                                        518
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". For all",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        316,
+                                        501,
+                                        387,
+                                        514
+                                    ],
+                                    "score": 0.88,
+                                    "content": "0 \\leq i \\leq \\lfloor \\log _ { 2 } R \\rfloor",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 17,
+                    "bbox_fs": [
+                        102,
+                        494,
+                        387,
+                        518
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        274,
+                        522,
+                        336,
+                        540
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                274,
+                                522,
+                                336,
+                                540
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        274,
+                                        522,
+                                        336,
+                                        540
+                                    ],
+                                    "score": 0.9,
+                                    "content": "E [ X _ { t } ^ { ( 2 ^ { i } ) } ] \\leq \\xi _ { i } .",
+                                    "type": "interline_equation",
+                                    "image_path": "4c5556442dd84c67ed2f8017702e406cf2d4d5acde09b8b3242d907ec73dda13.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                274,
+                                522,
+                                336,
+                                540
+                            ],
+                            "spans": [],
+                            "index": 18
+                        }
+                    ]
+                },
+                {
+                    "type": "list",
+                    "bbox": [
+                        106,
+                        545,
+                        505,
+                        569
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                543,
+                                505,
+                                560
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        543,
+                                        198,
+                                        560
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Claim 1. If Condition",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        198,
+                                        547,
+                                        203,
+                                        556
+                                    ],
+                                    "score": 0.7,
+                                    "content": "^ { l }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        204,
+                                        543,
+                                        295,
+                                        560
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is satisfied at time step",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        295,
+                                        547,
+                                        300,
+                                        556
+                                    ],
+                                    "score": 0.51,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        301,
+                                        543,
+                                        344,
+                                        560
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the policy",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        345,
+                                        548,
+                                        355,
+                                        557
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\pi _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        356,
+                                        543,
+                                        365,
+                                        560
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        366,
+                                        548,
+                                        371,
+                                        556
+                                    ],
+                                    "score": 0.68,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        371,
+                                        543,
+                                        436,
+                                        560
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimal at state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        436,
+                                        548,
+                                        446,
+                                        557
+                                    ],
+                                    "score": 0.83,
+                                    "content": "s _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        446,
+                                        543,
+                                        464,
+                                        560
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", i.e.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        464,
+                                        545,
+                                        505,
+                                        558
+                                    ],
+                                    "score": 0.91,
+                                    "content": "V ^ { \\ast } ( s _ { t } ) -",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 19,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                554,
+                                163,
+                                571
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        557,
+                                        157,
+                                        569
+                                    ],
+                                    "score": 0.91,
+                                    "content": "V ^ { \\pi _ { t } } ( s _ { t } ) \\leq \\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        158,
+                                        554,
+                                        163,
+                                        571
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20,
+                            "is_list_start_line": true,
+                            "is_list_end_line": true
+                        }
+                    ],
+                    "index": 19.5,
+                    "bbox_fs": [
+                        105,
+                        543,
+                        505,
+                        571
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        581,
+                        505,
+                        613
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                103,
+                                579,
+                                505,
+                                618
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        103,
+                                        579,
+                                        180,
+                                        600
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Proof. Note that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        107,
+                                        596,
+                                        164,
+                                        612
+                                    ],
+                                    "score": 0.93,
+                                    "content": "E [ X _ { t } ^ { ( 2 ^ { \\lfloor \\log _ { 2 } i \\rfloor } ) } ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        165,
+                                        588,
+                                        263,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": "t. Eq. (3) implies that for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        180,
+                                        582,
+                                        200,
+                                        597
+                                    ],
+                                    "score": 0.93,
+                                    "content": "X _ { t } ^ { ( i ) }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        200,
+                                        579,
+                                        393,
+                                        600
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is monotonically decreasing with respect to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        263,
+                                        600,
+                                        317,
+                                        612
+                                    ],
+                                    "score": 0.91,
+                                    "content": "1 / 2 < \\gamma < 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        317,
+                                        588,
+                                        327,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        393,
+                                        586,
+                                        398,
+                                        595
+                                    ],
+                                    "score": 0.73,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        399,
+                                        579,
+                                        456,
+                                        600
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Therefore,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        456,
+                                        581,
+                                        505,
+                                        597
+                                    ],
+                                    "score": 0.93,
+                                    "content": "E [ X _ { t } ^ { ( i ) } ] \\ \\leq",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 21,
+                    "bbox_fs": [
+                        103,
+                        579,
+                        505,
+                        618
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        144,
+                        617,
+                        466,
+                        687
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                144,
+                                617,
+                                466,
+                                687
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        144,
+                                        617,
+                                        466,
+                                        687
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { r l } & { E \\left[ \\displaystyle \\sum _ { i = 1 } ^ { R } \\gamma ^ { i - 1 } X _ { t } ^ { ( i ) } \\right] = \\displaystyle \\sum _ { i = 1 } ^ { R } \\gamma ^ { i - 1 } E [ X _ { t } ^ { ( i ) } ] \\leq \\displaystyle \\sum _ { i = 1 } ^ { R } \\gamma ^ { i - 1 } E [ X _ { t } ^ { ( 2 ^ { \\lfloor \\log _ { 2 } i \\rfloor } ) } ] } \\\\ & { \\leq \\displaystyle \\sum _ { i = 1 } ^ { R } \\gamma ^ { i - 1 } 2 ^ { - \\lfloor \\log _ { 2 } i \\rfloor - 2 } \\epsilon _ { 2 } \\left( \\ln \\frac { 1 } { 1 - \\gamma } \\right) ^ { - 1 } \\leq \\displaystyle \\sum _ { i = 1 } ^ { R } \\frac { \\gamma ^ { i - 1 } } { i } \\epsilon _ { 2 } \\left( \\ln \\frac { 1 } { 1 - \\gamma } \\right) ^ { - 1 } \\leq 2 \\epsilon _ { 2 } , } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "62ba3bea0f084d11903c964028d906643070d34916bde88924637c5e08ea73d6.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 23,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                144,
+                                617,
+                                466,
+                                640.3333333333334
+                            ],
+                            "spans": [],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                144,
+                                640.3333333333334,
+                                466,
+                                663.6666666666667
+                            ],
+                            "spans": [],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                144,
+                                663.6666666666667,
+                                466,
+                                687.0000000000001
+                            ],
+                            "spans": [],
+                            "index": 24
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        692,
+                        462,
+                        710
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                102,
+                                689,
+                                458,
+                                715
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        102,
+                                        689,
+                                        310,
+                                        715
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where the last inequality follows from the fact that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        310,
+                                        692,
+                                        405,
+                                        711
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { r } { \\sum _ { i = 1 } ^ { \\infty } \\frac { \\gamma ^ { i - 1 } } { i } = \\frac { 1 } { \\gamma } \\ln \\frac { 1 } { 1 - \\gamma } } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        405,
+                                        689,
+                                        423,
+                                        715
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        423,
+                                        695,
+                                        458,
+                                        708
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\gamma > 1 / 2",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 25,
+                    "bbox_fs": [
+                        102,
+                        689,
+                        458,
+                        715
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        102,
+                        714,
+                        476,
+                        735
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                103,
+                                712,
+                                475,
+                                737
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        103,
+                                        712,
+                                        238,
+                                        737
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Combining with Eq. 2, we have,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        238,
+                                        715,
+                                        475,
+                                        736
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\begin{array} { r } { V ^ { \\ast } ( s _ { t } ) - V ^ { \\pi _ { t } } ( s _ { t } ) \\leq \\epsilon _ { 2 } + E \\left[ \\sum _ { i = 1 } ^ { R } \\gamma ^ { i - 1 } X _ { t } ^ { ( i ) } \\right] \\leq 3 \\epsilon _ { 2 } = \\epsilon . } \\end{array}",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 26,
+                    "bbox_fs": [
+                        103,
+                        712,
+                        475,
+                        737
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        81,
+                        338,
+                        95
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                79,
+                                339,
+                                97
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        79,
+                                        207,
+                                        97
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Next we show that given",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        207,
+                                        83,
+                                        220,
+                                        94
+                                    ],
+                                    "score": 0.82,
+                                    "content": "i , t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        220,
+                                        79,
+                                        339,
+                                        97
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", Condition 2 implies Eq. (3).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        97,
+                        506,
+                        134
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                103,
+                                95,
+                                507,
+                                120
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        103,
+                                        95,
+                                        194,
+                                        120
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Condition 2. Define",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        194,
+                                        101,
+                                        253,
+                                        114
+                                    ],
+                                    "score": 0.91,
+                                    "content": "L = \\lfloor \\log _ { 2 } R \\rfloor",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        253,
+                                        95,
+                                        273,
+                                        120
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        273,
+                                        97,
+                                        416,
+                                        118
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\begin{array} { r } { M = \\operatorname* { m a x } \\left\\{ \\lceil 2 \\log _ { 2 } \\frac { 1 } { \\xi _ { L } ( 1 - \\gamma ) } \\rceil , 1 0 \\right\\} } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        417,
+                                        95,
+                                        439,
+                                        120
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        439,
+                                        99,
+                                        502,
+                                        115
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\begin{array} { r } { \\eta _ { j } = \\frac { \\xi _ { i } } { M } \\cdot 2 ^ { j - 1 } } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        503,
+                                        95,
+                                        507,
+                                        120
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                115,
+                                300,
+                                136
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        115,
+                                        135,
+                                        136
+                                    ],
+                                    "score": 1.0,
+                                    "content": "For all",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        140,
+                                        117,
+                                        296,
+                                        134
+                                    ],
+                                    "score": 0.75,
+                                    "content": "\\begin{array} { r } { \\because j \\le M , \\eta _ { j } \\operatorname* { P r } [ X _ { t } ^ { ( 2 ^ { i } ) } > \\eta _ { j - 1 } ] \\le \\frac { \\xi _ { i } } { M } , } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        115,
+                                        300,
+                                        136
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        136,
+                        350,
+                        148
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                136,
+                                349,
+                                149
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        136,
+                                        349,
+                                        149
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Claim 2. Given i, t, Eq. (3) holds if Condition 2 is satisfied.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        161,
+                        506,
+                        186
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                162,
+                                506,
+                                175
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        162,
+                                        273,
+                                        175
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Proof. The reason behind the choice of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        273,
+                                        163,
+                                        285,
+                                        173
+                                    ],
+                                    "score": 0.83,
+                                    "content": "M",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        285,
+                                        162,
+                                        356,
+                                        175
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is to ensure that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        357,
+                                        162,
+                                        433,
+                                        175
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\eta _ { M } > 1 / ( 1 - \\gamma )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        433,
+                                        162,
+                                        506,
+                                        175
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1. It follows that,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                173,
+                                290,
+                                186
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        173,
+                                        237,
+                                        186
+                                    ],
+                                    "score": 1.0,
+                                    "content": "assuming Condition 2 holds, for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        237,
+                                        174,
+                                        285,
+                                        186
+                                    ],
+                                    "score": 0.92,
+                                    "content": "1 \\leq j \\leq M",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        286,
+                                        173,
+                                        290,
+                                        186
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        }
+                    ],
+                    "index": 4.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        139,
+                        191,
+                        471,
+                        227
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                139,
+                                191,
+                                471,
+                                227
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        139,
+                                        191,
+                                        471,
+                                        227
+                                    ],
+                                    "score": 0.93,
+                                    "content": "E \\left[ { X _ { t } ^ { ( 2 ^ { i } ) } } \\right] = \\int _ { 0 } ^ { 1 / ( 1 - \\gamma ) } \\operatorname* { P r } \\left[ { X _ { t } ^ { ( 2 ^ { i } ) } } > x \\right] d x \\le \\eta _ { 1 } + \\sum _ { j = 2 } ^ { M } \\eta _ { j } \\operatorname* { P r } [ { X _ { t } ^ { ( 2 ^ { i } ) } } > \\eta _ { j - 1 } ] \\le \\xi _ { i } .",
+                                    "type": "interline_equation",
+                                    "image_path": "b1e98198c486d877466252bbfdd5d0afb8e4019bc37fc19f80c274168b0bb6a3.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                139,
+                                191,
+                                471,
+                                203.0
+                            ],
+                            "spans": [],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                139,
+                                203.0,
+                                471,
+                                215.0
+                            ],
+                            "spans": [],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                139,
+                                215.0,
+                                471,
+                                227.0
+                            ],
+                            "spans": [],
+                            "index": 8
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        259,
+                        505,
+                        272
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                258,
+                                506,
+                                273
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        258,
+                                        204,
+                                        273
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Therefore, if a time step",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        204,
+                                        262,
+                                        209,
+                                        270
+                                    ],
+                                    "score": 0.79,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        209,
+                                        258,
+                                        234,
+                                        273
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is not",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        234,
+                                        262,
+                                        244,
+                                        271
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\epsilon _ { 2 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        244,
+                                        258,
+                                        328,
+                                        273
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimal, there exists",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        329,
+                                        260,
+                                        399,
+                                        272
+                                    ],
+                                    "score": 0.93,
+                                    "content": "0 \\leq i < \\lfloor \\log _ { 2 } R \\rfloor",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        399,
+                                        258,
+                                        418,
+                                        273
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        418,
+                                        260,
+                                        466,
+                                        272
+                                    ],
+                                    "score": 0.91,
+                                    "content": "2 \\leq j \\leq M",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        466,
+                                        258,
+                                        506,
+                                        273
+                                    ],
+                                    "score": 1.0,
+                                    "content": "such that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        248,
+                        277,
+                        363,
+                        302
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                248,
+                                277,
+                                363,
+                                302
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        248,
+                                        277,
+                                        363,
+                                        302
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\eta _ { j } \\mathrm { P r } [ X _ { t } ^ { ( 2 ^ { i } ) } > \\eta _ { j - 1 } ] > \\frac { \\xi _ { i } } { M } .",
+                                    "type": "interline_equation",
+                                    "image_path": "7d918d021bc39256ac2de308ee455c6a54396bc36335cd0f685f840f0c5005d1.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                248,
+                                277,
+                                363,
+                                302
+                            ],
+                            "spans": [],
+                            "index": 10
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        307,
+                        506,
+                        365
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                307,
+                                506,
+                                321
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        307,
+                                        360,
+                                        321
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Now, the sample complexity can be bounded by the number of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        360,
+                                        308,
+                                        388,
+                                        320
+                                    ],
+                                    "score": 0.92,
+                                    "content": "( t , i , j )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        389,
+                                        307,
+                                        506,
+                                        321
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pairs that Eq. (4) is violated.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                318,
+                                505,
+                                332
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        318,
+                                        336,
+                                        332
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Following the approach of Strehl et al. (2006), for a fixed",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        336,
+                                        319,
+                                        357,
+                                        331
+                                    ],
+                                    "score": 0.92,
+                                    "content": "( i , j )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        357,
+                                        318,
+                                        505,
+                                        332
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-pair, instead of directly counting the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                101,
+                                330,
+                                505,
+                                351
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        101,
+                                        330,
+                                        193,
+                                        351
+                                    ],
+                                    "score": 1.0,
+                                    "content": "number of time steps",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        194,
+                                        335,
+                                        199,
+                                        344
+                                    ],
+                                    "score": 0.74,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        199,
+                                        330,
+                                        238,
+                                        351
+                                    ],
+                                    "score": 1.0,
+                                    "content": "such that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        238,
+                                        330,
+                                        343,
+                                        349
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { r } { \\operatorname* { P r } [ X _ { t } ^ { ( 2 ^ { i } ) } > \\eta _ { j - 1 } ] > \\frac { \\xi _ { i } } { M \\eta _ { j } } } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        343,
+                                        330,
+                                        505,
+                                        351
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", we count the number of time steps that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                348,
+                                409,
+                                366
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        348,
+                                        163,
+                                        365
+                                    ],
+                                    "score": 0.92,
+                                    "content": "X _ { t } ^ { ( 2 ^ { i } ) } > \\eta _ { j - 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        163,
+                                        349,
+                                        399,
+                                        366
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Lemma 1 provides an upper bound of the number of such",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        399,
+                                        353,
+                                        404,
+                                        362
+                                    ],
+                                    "score": 0.74,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        404,
+                                        349,
+                                        409,
+                                        366
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 12.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        378,
+                        192,
+                        389
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                376,
+                                193,
+                                391
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        376,
+                                        193,
+                                        391
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3.4 KEY LEMMAS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        398,
+                        506,
+                        445
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                397,
+                                507,
+                                412
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        397,
+                                        507,
+                                        412
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In this section, we present two key lemmas. Lemma 1 bounds the number of sub-optimal actions,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                410,
+                                505,
+                                422
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        410,
+                                        505,
+                                        422
+                                    ],
+                                    "score": 1.0,
+                                    "content": "which in turn, bounds the sample complexity of our algorithm. Lemma 2 bounds the weighted sum",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                421,
+                                506,
+                                435
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        421,
+                                        192,
+                                        435
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of learning error, i.e.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        192,
+                                        421,
+                                        259,
+                                        434
+                                    ],
+                                    "score": 0.92,
+                                    "content": "( \\hat { Q } _ { t } - Q ^ { * } ) ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        259,
+                                        421,
+                                        506,
+                                        435
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", with the sum and maximum of weights. Then, we show that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                433,
+                                244,
+                                445
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        433,
+                                        244,
+                                        445
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lemma 1 follows from Lemma 2.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 17.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        446,
+                        505,
+                        474
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                443,
+                                507,
+                                465
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        443,
+                                        191,
+                                        465
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lemma 1. For fixed",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        191,
+                                        450,
+                                        196,
+                                        459
+                                    ],
+                                    "score": 0.25,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        197,
+                                        443,
+                                        214,
+                                        465
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        215,
+                                        449,
+                                        240,
+                                        461
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\eta > 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        240,
+                                        443,
+                                        255,
+                                        465
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        256,
+                                        446,
+                                        275,
+                                        461
+                                    ],
+                                    "score": 0.91,
+                                    "content": "{ B } _ { \\eta } ^ { ( t ) }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        275,
+                                        443,
+                                        344,
+                                        465
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be the event that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        344,
+                                        448,
+                                        457,
+                                        463
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\begin{array} { r } { V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > \\frac { \\eta } { 1 - \\gamma } } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        458,
+                                        443,
+                                        507,
+                                        465
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in step t. If",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                461,
+                                298,
+                                475
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        462,
+                                        140,
+                                        474
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\eta > 2 \\epsilon _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        140,
+                                        461,
+                                        261,
+                                        475
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", then with probability at least",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        261,
+                                        462,
+                                        293,
+                                        474
+                                    ],
+                                    "score": 0.9,
+                                    "content": "1 - \\delta / 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        294,
+                                        461,
+                                        298,
+                                        475
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 20.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        186,
+                        479,
+                        423,
+                        514
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                186,
+                                479,
+                                423,
+                                514
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        186,
+                                        479,
+                                        423,
+                                        514
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\sum _ { t = 1 } ^ { t = \\infty } I \\left[ B _ { \\eta } ^ { ( t ) } \\right] \\leq \\frac { S A \\ln S A \\ln 1 / \\delta } { \\eta ^ { 2 } ( 1 - \\gamma ) ^ { 3 } } \\cdot p o l y l o g \\left( \\frac { 1 } { \\epsilon _ { 1 } } , \\frac { 1 } { 1 - \\gamma } \\right) ,",
+                                    "type": "interline_equation",
+                                    "image_path": "8e6137e01a7beea297bf95283d863b21a785d17463e6944e2efedb515bf7d808.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 22.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                186,
+                                479,
+                                423,
+                                496.5
+                            ],
+                            "spans": [],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                186,
+                                496.5,
+                                423,
+                                514.0
+                            ],
+                            "spans": [],
+                            "index": 23
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        519,
+                        248,
+                        532
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                520,
+                                249,
+                                533
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        520,
+                                        133,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        133,
+                                        520,
+                                        147,
+                                        532
+                                    ],
+                                    "score": 0.87,
+                                    "content": "I [ \\cdot ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        148,
+                                        520,
+                                        249,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the indicator function.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 24
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        541,
+                        440,
+                        553
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                540,
+                                440,
+                                555
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        540,
+                                        440,
+                                        555
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Before presenting Lemma 2, we define a class of sequence that occurs in the proof.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        556,
+                        504,
+                        581
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                554,
+                                506,
+                                571
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        554,
+                                        212,
+                                        571
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Definition 3. A sequence",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        212,
+                                        557,
+                                        245,
+                                        569
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( w _ { t } ) _ { t \\geq 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        245,
+                                        554,
+                                        305,
+                                        571
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is said to be a",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        557,
+                                        332,
+                                        569
+                                    ],
+                                    "score": 0.9,
+                                    "content": "( C , w )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        333,
+                                        554,
+                                        388,
+                                        571
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-sequence for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        389,
+                                        557,
+                                        427,
+                                        568
+                                    ],
+                                    "score": 0.82,
+                                    "content": "C , w > 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        427,
+                                        554,
+                                        431,
+                                        571
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        432,
+                                        557,
+                                        489,
+                                        569
+                                    ],
+                                    "score": 0.79,
+                                    "content": "i f 0 \\le w _ { t } \\le w",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        490,
+                                        554,
+                                        506,
+                                        571
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                567,
+                                227,
+                                582
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        567,
+                                        119,
+                                        582
+                                    ],
+                                    "score": 1.0,
+                                    "content": "all",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        120,
+                                        568,
+                                        142,
+                                        579
+                                    ],
+                                    "score": 0.88,
+                                    "content": "t \\geq 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        142,
+                                        567,
+                                        164,
+                                        582
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        164,
+                                        568,
+                                        222,
+                                        582
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\begin{array} { r } { \\sum _ { t \\geq 1 } w _ { t } \\leq C } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        223,
+                                        567,
+                                        227,
+                                        582
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 26.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        584,
+                        485,
+                        598
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                583,
+                                486,
+                                599
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        583,
+                                        195,
+                                        599
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lemma 2. For every",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        195,
+                                        585,
+                                        222,
+                                        597
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( C , w )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        222,
+                                        583,
+                                        264,
+                                        599
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-sequence",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        264,
+                                        585,
+                                        297,
+                                        597
+                                    ],
+                                    "score": 0.92,
+                                    "content": "( w _ { t } ) _ { t \\geq 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        297,
+                                        583,
+                                        366,
+                                        599
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", with probability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        367,
+                                        585,
+                                        400,
+                                        597
+                                    ],
+                                    "score": 0.9,
+                                    "content": "1 - \\delta / 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        400,
+                                        583,
+                                        486,
+                                        599
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the following holds:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 28
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        127,
+                        617,
+                        483,
+                        651
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                127,
+                                617,
+                                483,
+                                651
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        617,
+                                        483,
+                                        651
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\sum _ { t \\ge 1 } w _ { t } ( \\hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) \\le \\frac { C \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\frac { \\sqrt { w S A C \\ell ( C ) } } { ( 1 - \\gamma ) ^ { 2 . 5 } } + \\frac { w S A \\ln C } { ( 1 - \\gamma ) ^ { 3 } } \\ln \\frac { 1 } { ( 1 - \\gamma ) \\epsilon _ { 1 } } \\right) .",
+                                    "type": "interline_equation",
+                                    "image_path": "576704e0ba7bc113c9eb1c2218a2bd6ace18a8d09188a27f397409e00cdaad49.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 30,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                127,
+                                617,
+                                483,
+                                628.3333333333334
+                            ],
+                            "spans": [],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                628.3333333333334,
+                                483,
+                                639.6666666666667
+                            ],
+                            "spans": [],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                639.6666666666667,
+                                483,
+                                651.0000000000001
+                            ],
+                            "spans": [],
+                            "index": 31
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        664,
+                        289,
+                        681
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                133,
+                                665,
+                                228,
+                                681
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        133,
+                                        665,
+                                        228,
+                                        681
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\begin{array} { r } { \\ell ( C ) = \\iota ( C ) \\ln { \\frac { 1 } { ( 1 - \\gamma ) \\epsilon _ { 1 } } } } \\end{array}",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 32
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        689,
+                        468,
+                        702
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                688,
+                                468,
+                                703
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        688,
+                                        468,
+                                        703
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Proof of Lemma 2 is quite technical, and is therefore deferred to supplementary materials.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 33
+                }
+            ],
+            "page_idx": 5,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        26,
+                        294,
+                        38
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                25,
+                                294,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        25,
+                                        294,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        751,
+                        309,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                302,
+                                751,
+                                309,
+                                762
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        302,
+                                        751,
+                                        309,
+                                        762
+                                    ],
+                                    "score": 1.0,
+                                    "content": "6",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        494,
+                        233,
+                        505,
+                        244
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                495,
+                                234,
+                                505,
+                                245
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        495,
+                                        234,
+                                        505,
+                                        245
+                                    ],
+                                    "score": 0.998,
+                                    "content": "□",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        106,
+                        710,
+                        507,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                119,
+                                707,
+                                505,
+                                724
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        119,
+                                        707,
+                                        124,
+                                        724
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        125,
+                                        711,
+                                        186,
+                                        722
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\eta _ { M } > 1 / ( 1 - \\gamma )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        187,
+                                        707,
+                                        334,
+                                        724
+                                    ],
+                                    "score": 1.0,
+                                    "content": "can be verified by combining inequalities",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        334,
+                                        710,
+                                        415,
+                                        723
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\xi _ { i } \\cdot 2 ^ { M / 2 } \\geq 1 / ( 1 - \\gamma )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        415,
+                                        707,
+                                        431,
+                                        724
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        431,
+                                        709,
+                                        505,
+                                        722
+                                    ],
+                                    "score": 0.93,
+                                    "content": "2 ^ { M / 2 - 1 } > ( M + 1 )",
+                                    "type": "inline_equation"
+                                }
+                            ]
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                721,
+                                183,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        721,
+                                        168,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for large enough",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        168,
+                                        722,
+                                        179,
+                                        730
+                                    ],
+                                    "score": 0.8,
+                                    "content": "M",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        179,
+                                        721,
+                                        183,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        81,
+                        338,
+                        95
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                79,
+                                339,
+                                97
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        79,
+                                        207,
+                                        97
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Next we show that given",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        207,
+                                        83,
+                                        220,
+                                        94
+                                    ],
+                                    "score": 0.82,
+                                    "content": "i , t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        220,
+                                        79,
+                                        339,
+                                        97
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", Condition 2 implies Eq. (3).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        }
+                    ],
+                    "index": 0,
+                    "bbox_fs": [
+                        105,
+                        79,
+                        339,
+                        97
+                    ]
+                },
+                {
+                    "type": "list",
+                    "bbox": [
+                        106,
+                        97,
+                        506,
+                        134
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                103,
+                                95,
+                                507,
+                                120
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        103,
+                                        95,
+                                        194,
+                                        120
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Condition 2. Define",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        194,
+                                        101,
+                                        253,
+                                        114
+                                    ],
+                                    "score": 0.91,
+                                    "content": "L = \\lfloor \\log _ { 2 } R \\rfloor",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        253,
+                                        95,
+                                        273,
+                                        120
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        273,
+                                        97,
+                                        416,
+                                        118
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\begin{array} { r } { M = \\operatorname* { m a x } \\left\\{ \\lceil 2 \\log _ { 2 } \\frac { 1 } { \\xi _ { L } ( 1 - \\gamma ) } \\rceil , 1 0 \\right\\} } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        417,
+                                        95,
+                                        439,
+                                        120
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        439,
+                                        99,
+                                        502,
+                                        115
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\begin{array} { r } { \\eta _ { j } = \\frac { \\xi _ { i } } { M } \\cdot 2 ^ { j - 1 } } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        503,
+                                        95,
+                                        507,
+                                        120
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                115,
+                                300,
+                                136
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        115,
+                                        135,
+                                        136
+                                    ],
+                                    "score": 1.0,
+                                    "content": "For all",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        140,
+                                        117,
+                                        296,
+                                        134
+                                    ],
+                                    "score": 0.75,
+                                    "content": "\\begin{array} { r } { \\because j \\le M , \\eta _ { j } \\operatorname* { P r } [ X _ { t } ^ { ( 2 ^ { i } ) } > \\eta _ { j - 1 } ] \\le \\frac { \\xi _ { i } } { M } , } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        115,
+                                        300,
+                                        136
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2,
+                            "is_list_start_line": true,
+                            "is_list_end_line": true
+                        }
+                    ],
+                    "index": 1.5,
+                    "bbox_fs": [
+                        103,
+                        95,
+                        507,
+                        136
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        136,
+                        350,
+                        148
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                136,
+                                349,
+                                149
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        136,
+                                        349,
+                                        149
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Claim 2. Given i, t, Eq. (3) holds if Condition 2 is satisfied.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 3,
+                    "bbox_fs": [
+                        107,
+                        136,
+                        349,
+                        149
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        161,
+                        506,
+                        186
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                162,
+                                506,
+                                175
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        162,
+                                        273,
+                                        175
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Proof. The reason behind the choice of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        273,
+                                        163,
+                                        285,
+                                        173
+                                    ],
+                                    "score": 0.83,
+                                    "content": "M",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        285,
+                                        162,
+                                        356,
+                                        175
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is to ensure that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        357,
+                                        162,
+                                        433,
+                                        175
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\eta _ { M } > 1 / ( 1 - \\gamma )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        433,
+                                        162,
+                                        506,
+                                        175
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1. It follows that,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                173,
+                                290,
+                                186
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        173,
+                                        237,
+                                        186
+                                    ],
+                                    "score": 1.0,
+                                    "content": "assuming Condition 2 holds, for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        237,
+                                        174,
+                                        285,
+                                        186
+                                    ],
+                                    "score": 0.92,
+                                    "content": "1 \\leq j \\leq M",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        286,
+                                        173,
+                                        290,
+                                        186
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        }
+                    ],
+                    "index": 4.5,
+                    "bbox_fs": [
+                        105,
+                        162,
+                        506,
+                        186
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        139,
+                        191,
+                        471,
+                        227
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                139,
+                                191,
+                                471,
+                                227
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        139,
+                                        191,
+                                        471,
+                                        227
+                                    ],
+                                    "score": 0.93,
+                                    "content": "E \\left[ { X _ { t } ^ { ( 2 ^ { i } ) } } \\right] = \\int _ { 0 } ^ { 1 / ( 1 - \\gamma ) } \\operatorname* { P r } \\left[ { X _ { t } ^ { ( 2 ^ { i } ) } } > x \\right] d x \\le \\eta _ { 1 } + \\sum _ { j = 2 } ^ { M } \\eta _ { j } \\operatorname* { P r } [ { X _ { t } ^ { ( 2 ^ { i } ) } } > \\eta _ { j - 1 } ] \\le \\xi _ { i } .",
+                                    "type": "interline_equation",
+                                    "image_path": "b1e98198c486d877466252bbfdd5d0afb8e4019bc37fc19f80c274168b0bb6a3.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                139,
+                                191,
+                                471,
+                                203.0
+                            ],
+                            "spans": [],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                139,
+                                203.0,
+                                471,
+                                215.0
+                            ],
+                            "spans": [],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                139,
+                                215.0,
+                                471,
+                                227.0
+                            ],
+                            "spans": [],
+                            "index": 8
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        259,
+                        505,
+                        272
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                258,
+                                506,
+                                273
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        258,
+                                        204,
+                                        273
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Therefore, if a time step",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        204,
+                                        262,
+                                        209,
+                                        270
+                                    ],
+                                    "score": 0.79,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        209,
+                                        258,
+                                        234,
+                                        273
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is not",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        234,
+                                        262,
+                                        244,
+                                        271
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\epsilon _ { 2 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        244,
+                                        258,
+                                        328,
+                                        273
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimal, there exists",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        329,
+                                        260,
+                                        399,
+                                        272
+                                    ],
+                                    "score": 0.93,
+                                    "content": "0 \\leq i < \\lfloor \\log _ { 2 } R \\rfloor",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        399,
+                                        258,
+                                        418,
+                                        273
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        418,
+                                        260,
+                                        466,
+                                        272
+                                    ],
+                                    "score": 0.91,
+                                    "content": "2 \\leq j \\leq M",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        466,
+                                        258,
+                                        506,
+                                        273
+                                    ],
+                                    "score": 1.0,
+                                    "content": "such that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 9,
+                    "bbox_fs": [
+                        105,
+                        258,
+                        506,
+                        273
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        248,
+                        277,
+                        363,
+                        302
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                248,
+                                277,
+                                363,
+                                302
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        248,
+                                        277,
+                                        363,
+                                        302
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\eta _ { j } \\mathrm { P r } [ X _ { t } ^ { ( 2 ^ { i } ) } > \\eta _ { j - 1 } ] > \\frac { \\xi _ { i } } { M } .",
+                                    "type": "interline_equation",
+                                    "image_path": "7d918d021bc39256ac2de308ee455c6a54396bc36335cd0f685f840f0c5005d1.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                248,
+                                277,
+                                363,
+                                302
+                            ],
+                            "spans": [],
+                            "index": 10
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        307,
+                        506,
+                        365
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                307,
+                                506,
+                                321
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        307,
+                                        360,
+                                        321
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Now, the sample complexity can be bounded by the number of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        360,
+                                        308,
+                                        388,
+                                        320
+                                    ],
+                                    "score": 0.92,
+                                    "content": "( t , i , j )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        389,
+                                        307,
+                                        506,
+                                        321
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pairs that Eq. (4) is violated.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                318,
+                                505,
+                                332
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        318,
+                                        336,
+                                        332
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Following the approach of Strehl et al. (2006), for a fixed",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        336,
+                                        319,
+                                        357,
+                                        331
+                                    ],
+                                    "score": 0.92,
+                                    "content": "( i , j )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        357,
+                                        318,
+                                        505,
+                                        332
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-pair, instead of directly counting the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                101,
+                                330,
+                                505,
+                                351
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        101,
+                                        330,
+                                        193,
+                                        351
+                                    ],
+                                    "score": 1.0,
+                                    "content": "number of time steps",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        194,
+                                        335,
+                                        199,
+                                        344
+                                    ],
+                                    "score": 0.74,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        199,
+                                        330,
+                                        238,
+                                        351
+                                    ],
+                                    "score": 1.0,
+                                    "content": "such that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        238,
+                                        330,
+                                        343,
+                                        349
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { r } { \\operatorname* { P r } [ X _ { t } ^ { ( 2 ^ { i } ) } > \\eta _ { j - 1 } ] > \\frac { \\xi _ { i } } { M \\eta _ { j } } } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        343,
+                                        330,
+                                        505,
+                                        351
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", we count the number of time steps that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                348,
+                                409,
+                                366
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        348,
+                                        163,
+                                        365
+                                    ],
+                                    "score": 0.92,
+                                    "content": "X _ { t } ^ { ( 2 ^ { i } ) } > \\eta _ { j - 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        163,
+                                        349,
+                                        399,
+                                        366
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Lemma 1 provides an upper bound of the number of such",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        399,
+                                        353,
+                                        404,
+                                        362
+                                    ],
+                                    "score": 0.74,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        404,
+                                        349,
+                                        409,
+                                        366
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 12.5,
+                    "bbox_fs": [
+                        101,
+                        307,
+                        506,
+                        366
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        378,
+                        192,
+                        389
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                376,
+                                193,
+                                391
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        376,
+                                        193,
+                                        391
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3.4 KEY LEMMAS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        398,
+                        506,
+                        445
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                397,
+                                507,
+                                412
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        397,
+                                        507,
+                                        412
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In this section, we present two key lemmas. Lemma 1 bounds the number of sub-optimal actions,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                410,
+                                505,
+                                422
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        410,
+                                        505,
+                                        422
+                                    ],
+                                    "score": 1.0,
+                                    "content": "which in turn, bounds the sample complexity of our algorithm. Lemma 2 bounds the weighted sum",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                421,
+                                506,
+                                435
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        421,
+                                        192,
+                                        435
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of learning error, i.e.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        192,
+                                        421,
+                                        259,
+                                        434
+                                    ],
+                                    "score": 0.92,
+                                    "content": "( \\hat { Q } _ { t } - Q ^ { * } ) ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        259,
+                                        421,
+                                        506,
+                                        435
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", with the sum and maximum of weights. Then, we show that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                433,
+                                244,
+                                445
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        433,
+                                        244,
+                                        445
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lemma 1 follows from Lemma 2.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 17.5,
+                    "bbox_fs": [
+                        105,
+                        397,
+                        507,
+                        445
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        446,
+                        505,
+                        474
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                443,
+                                507,
+                                465
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        443,
+                                        191,
+                                        465
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lemma 1. For fixed",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        191,
+                                        450,
+                                        196,
+                                        459
+                                    ],
+                                    "score": 0.25,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        197,
+                                        443,
+                                        214,
+                                        465
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        215,
+                                        449,
+                                        240,
+                                        461
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\eta > 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        240,
+                                        443,
+                                        255,
+                                        465
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        256,
+                                        446,
+                                        275,
+                                        461
+                                    ],
+                                    "score": 0.91,
+                                    "content": "{ B } _ { \\eta } ^ { ( t ) }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        275,
+                                        443,
+                                        344,
+                                        465
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be the event that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        344,
+                                        448,
+                                        457,
+                                        463
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\begin{array} { r } { V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > \\frac { \\eta } { 1 - \\gamma } } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        458,
+                                        443,
+                                        507,
+                                        465
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in step t. If",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                461,
+                                298,
+                                475
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        462,
+                                        140,
+                                        474
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\eta > 2 \\epsilon _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        140,
+                                        461,
+                                        261,
+                                        475
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", then with probability at least",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        261,
+                                        462,
+                                        293,
+                                        474
+                                    ],
+                                    "score": 0.9,
+                                    "content": "1 - \\delta / 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        294,
+                                        461,
+                                        298,
+                                        475
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 20.5,
+                    "bbox_fs": [
+                        104,
+                        443,
+                        507,
+                        475
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        186,
+                        479,
+                        423,
+                        514
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                186,
+                                479,
+                                423,
+                                514
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        186,
+                                        479,
+                                        423,
+                                        514
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\sum _ { t = 1 } ^ { t = \\infty } I \\left[ B _ { \\eta } ^ { ( t ) } \\right] \\leq \\frac { S A \\ln S A \\ln 1 / \\delta } { \\eta ^ { 2 } ( 1 - \\gamma ) ^ { 3 } } \\cdot p o l y l o g \\left( \\frac { 1 } { \\epsilon _ { 1 } } , \\frac { 1 } { 1 - \\gamma } \\right) ,",
+                                    "type": "interline_equation",
+                                    "image_path": "8e6137e01a7beea297bf95283d863b21a785d17463e6944e2efedb515bf7d808.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 22.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                186,
+                                479,
+                                423,
+                                496.5
+                            ],
+                            "spans": [],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                186,
+                                496.5,
+                                423,
+                                514.0
+                            ],
+                            "spans": [],
+                            "index": 23
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        519,
+                        248,
+                        532
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                520,
+                                249,
+                                533
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        520,
+                                        133,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        133,
+                                        520,
+                                        147,
+                                        532
+                                    ],
+                                    "score": 0.87,
+                                    "content": "I [ \\cdot ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        148,
+                                        520,
+                                        249,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the indicator function.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 24,
+                    "bbox_fs": [
+                        106,
+                        520,
+                        249,
+                        533
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        541,
+                        440,
+                        553
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                540,
+                                440,
+                                555
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        540,
+                                        440,
+                                        555
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Before presenting Lemma 2, we define a class of sequence that occurs in the proof.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 25,
+                    "bbox_fs": [
+                        105,
+                        540,
+                        440,
+                        555
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        556,
+                        504,
+                        581
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                554,
+                                506,
+                                571
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        554,
+                                        212,
+                                        571
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Definition 3. A sequence",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        212,
+                                        557,
+                                        245,
+                                        569
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( w _ { t } ) _ { t \\geq 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        245,
+                                        554,
+                                        305,
+                                        571
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is said to be a",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        557,
+                                        332,
+                                        569
+                                    ],
+                                    "score": 0.9,
+                                    "content": "( C , w )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        333,
+                                        554,
+                                        388,
+                                        571
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-sequence for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        389,
+                                        557,
+                                        427,
+                                        568
+                                    ],
+                                    "score": 0.82,
+                                    "content": "C , w > 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        427,
+                                        554,
+                                        431,
+                                        571
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        432,
+                                        557,
+                                        489,
+                                        569
+                                    ],
+                                    "score": 0.79,
+                                    "content": "i f 0 \\le w _ { t } \\le w",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        490,
+                                        554,
+                                        506,
+                                        571
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                567,
+                                227,
+                                582
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        567,
+                                        119,
+                                        582
+                                    ],
+                                    "score": 1.0,
+                                    "content": "all",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        120,
+                                        568,
+                                        142,
+                                        579
+                                    ],
+                                    "score": 0.88,
+                                    "content": "t \\geq 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        142,
+                                        567,
+                                        164,
+                                        582
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        164,
+                                        568,
+                                        222,
+                                        582
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\begin{array} { r } { \\sum _ { t \\geq 1 } w _ { t } \\leq C } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        223,
+                                        567,
+                                        227,
+                                        582
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 26.5,
+                    "bbox_fs": [
+                        104,
+                        554,
+                        506,
+                        582
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        584,
+                        485,
+                        598
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                583,
+                                486,
+                                599
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        583,
+                                        195,
+                                        599
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lemma 2. For every",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        195,
+                                        585,
+                                        222,
+                                        597
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( C , w )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        222,
+                                        583,
+                                        264,
+                                        599
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-sequence",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        264,
+                                        585,
+                                        297,
+                                        597
+                                    ],
+                                    "score": 0.92,
+                                    "content": "( w _ { t } ) _ { t \\geq 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        297,
+                                        583,
+                                        366,
+                                        599
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", with probability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        367,
+                                        585,
+                                        400,
+                                        597
+                                    ],
+                                    "score": 0.9,
+                                    "content": "1 - \\delta / 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        400,
+                                        583,
+                                        486,
+                                        599
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the following holds:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 28,
+                    "bbox_fs": [
+                        104,
+                        583,
+                        486,
+                        599
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        127,
+                        617,
+                        483,
+                        651
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                127,
+                                617,
+                                483,
+                                651
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        617,
+                                        483,
+                                        651
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\sum _ { t \\ge 1 } w _ { t } ( \\hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) \\le \\frac { C \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\frac { \\sqrt { w S A C \\ell ( C ) } } { ( 1 - \\gamma ) ^ { 2 . 5 } } + \\frac { w S A \\ln C } { ( 1 - \\gamma ) ^ { 3 } } \\ln \\frac { 1 } { ( 1 - \\gamma ) \\epsilon _ { 1 } } \\right) .",
+                                    "type": "interline_equation",
+                                    "image_path": "576704e0ba7bc113c9eb1c2218a2bd6ace18a8d09188a27f397409e00cdaad49.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 30,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                127,
+                                617,
+                                483,
+                                628.3333333333334
+                            ],
+                            "spans": [],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                628.3333333333334,
+                                483,
+                                639.6666666666667
+                            ],
+                            "spans": [],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                639.6666666666667,
+                                483,
+                                651.0000000000001
+                            ],
+                            "spans": [],
+                            "index": 31
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        664,
+                        289,
+                        681
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                133,
+                                665,
+                                228,
+                                681
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        133,
+                                        665,
+                                        228,
+                                        681
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\begin{array} { r } { \\ell ( C ) = \\iota ( C ) \\ln { \\frac { 1 } { ( 1 - \\gamma ) \\epsilon _ { 1 } } } } \\end{array}",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 32,
+                    "bbox_fs": [
+                        133,
+                        665,
+                        228,
+                        681
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        689,
+                        468,
+                        702
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                688,
+                                468,
+                                703
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        688,
+                                        468,
+                                        703
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Proof of Lemma 2 is quite technical, and is therefore deferred to supplementary materials.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 33,
+                    "bbox_fs": [
+                        105,
+                        688,
+                        468,
+                        703
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        82,
+                        505,
+                        107
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                81,
+                                505,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        81,
+                                        505,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Now, we briefly explain how to prove Lemma 1 with Lemma 2. (Full proof can be found in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                93,
+                                437,
+                                109
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        94,
+                                        275,
+                                        109
+                                    ],
+                                    "score": 1.0,
+                                    "content": "supplementary materials.) Note that since",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        276,
+                                        93,
+                                        313,
+                                        107
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\hat { Q } _ { t } \\geq Q ^ { * }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        314,
+                                        94,
+                                        331,
+                                        109
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        332,
+                                        93,
+                                        433,
+                                        107
+                                    ],
+                                    "score": 0.89,
+                                    "content": "a _ { t } = \\arg \\operatorname* { m a x } _ { a } \\hat { Q } _ { t } ( s _ { t } , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        433,
+                                        94,
+                                        437,
+                                        109
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        207,
+                        109,
+                        400,
+                        124
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                207,
+                                109,
+                                400,
+                                124
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        207,
+                                        109,
+                                        400,
+                                        124
+                                    ],
+                                    "score": 0.83,
+                                    "content": "V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) \\leq \\hat { Q } _ { t } ( s _ { t } , a _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) .",
+                                    "type": "interline_equation",
+                                    "image_path": "e36c4bae9f64d8b170464eae13de7df006383d23275ffcf8d31e0711f7c4678a.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                207,
+                                109,
+                                400,
+                                124
+                            ],
+                            "spans": [],
+                            "index": 2
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        125,
+                        506,
+                        185
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                124,
+                                507,
+                                139
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        124,
+                                        201,
+                                        139
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We now consider a set",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        202,
+                                        125,
+                                        397,
+                                        138
+                                    ],
+                                    "score": 0.85,
+                                    "content": "J = \\{ t : \\ V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > \\eta ( 1 - \\gamma ) ^ { - 1 } \\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        397,
+                                        124,
+                                        472,
+                                        139
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and consider the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        472,
+                                        126,
+                                        502,
+                                        138
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( | J | , 1 )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        502,
+                                        124,
+                                        507,
+                                        139
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                135,
+                                506,
+                                149
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        135,
+                                        228,
+                                        149
+                                    ],
+                                    "score": 1.0,
+                                    "content": "weight sequence defined by",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        228,
+                                        137,
+                                        294,
+                                        149
+                                    ],
+                                    "score": 0.91,
+                                    "content": "w _ { t } ~ = ~ I \\left[ t \\in J \\right]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        294,
+                                        135,
+                                        506,
+                                        149
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". We can now apply Lemma 2 to weighted sum",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                146,
+                                506,
+                                162
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        147,
+                                        236,
+                                        162
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\begin{array} { r } { \\sum _ { t \\geq 1 } \\dot { w } _ { t } \\left[ \\bar { V } ^ { \\ast } ( s _ { t } ) - Q ^ { \\ast } ( s _ { t } , \\dot { a } _ { t } ) \\right] , } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        236,
+                                        146,
+                                        443,
+                                        162
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". On the one hand, this quantity is obviously at least",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        443,
+                                        147,
+                                        502,
+                                        160
+                                    ],
+                                    "score": 0.92,
+                                    "content": "| J | \\bar { \\eta ( 1 - \\gamma ) } ^ { - 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        503,
+                                        146,
+                                        506,
+                                        162
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                161,
+                                505,
+                                175
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        162,
+                                        408,
+                                        175
+                                    ],
+                                    "score": 1.0,
+                                    "content": "On the other hand, by lemma 2, it is upper bounded by the weighted sum of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        408,
+                                        161,
+                                        478,
+                                        174
+                                    ],
+                                    "score": 0.92,
+                                    "content": "( \\hat { Q } - Q ^ { * } ) ( s _ { t } , a _ { t } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        479,
+                                        162,
+                                        505,
+                                        175
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Thus",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                174,
+                                136,
+                                186
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        174,
+                                        136,
+                                        186
+                                    ],
+                                    "score": 1.0,
+                                    "content": "we get",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        146,
+                        186,
+                        464,
+                        219
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                146,
+                                186,
+                                464,
+                                219
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        146,
+                                        186,
+                                        464,
+                                        219
+                                    ],
+                                    "score": 0.93,
+                                    "content": "| J | \\eta ( 1 - \\gamma ) ^ { - 1 } \\leq \\frac { C \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\frac { \\sqrt { S A | J | \\ell ( | J | ) } } { ( 1 - \\gamma ) ^ { 2 . 5 } } + \\frac { w S A \\ln | J | } { ( 1 - \\gamma ) ^ { 3 } } \\ln \\frac { 1 } { ( 1 - \\gamma ) \\epsilon _ { 1 } } \\right) .",
+                                    "type": "interline_equation",
+                                    "image_path": "dc3a723cc9eab16cf16971abf7bbf69938ee49002e529fdd61110b29bb930e71.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                146,
+                                186,
+                                464,
+                                197.0
+                            ],
+                            "spans": [],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                146,
+                                197.0,
+                                464,
+                                208.0
+                            ],
+                            "spans": [],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                146,
+                                208.0,
+                                464,
+                                219.0
+                            ],
+                            "spans": [],
+                            "index": 10
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        221,
+                        505,
+                        263
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                221,
+                                505,
+                                234
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        221,
+                                        241,
+                                        234
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Now focus on the dependence on",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        242,
+                                        221,
+                                        254,
+                                        233
+                                    ],
+                                    "score": 0.89,
+                                    "content": "| J |",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        255,
+                                        221,
+                                        438,
+                                        234
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". The left-hand-side has linear dependence on",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        438,
+                                        221,
+                                        451,
+                                        234
+                                    ],
+                                    "score": 0.88,
+                                    "content": "| J |",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        452,
+                                        221,
+                                        505,
+                                        234
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", whereas the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                232,
+                                506,
+                                252
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        233,
+                                        187,
+                                        252
+                                    ],
+                                    "score": 1.0,
+                                    "content": "left-hand-side has a",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        187,
+                                        232,
+                                        231,
+                                        252
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\tilde { \\mathcal { O } } \\left( \\sqrt { | J | } \\right)",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        232,
+                                        233,
+                                        470,
+                                        252
+                                    ],
+                                    "score": 1.0,
+                                    "content": "dependence. This allows us to solve out an upper bound on",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        471,
+                                        236,
+                                        483,
+                                        248
+                                    ],
+                                    "score": 0.91,
+                                    "content": "| J |",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        484,
+                                        233,
+                                        506,
+                                        252
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                251,
+                                228,
+                                265
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        251,
+                                        208,
+                                        265
+                                    ],
+                                    "score": 1.0,
+                                    "content": "quadratic dependence on",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        208,
+                                        252,
+                                        225,
+                                        263
+                                    ],
+                                    "score": 0.87,
+                                    "content": "1 / \\eta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        225,
+                                        251,
+                                        228,
+                                        265
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        275,
+                        234,
+                        286
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                274,
+                                235,
+                                287
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        274,
+                                        235,
+                                        287
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3.5 PROOF FOR THEOREM 1",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        295,
+                        354,
+                        308
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                295,
+                                355,
+                                309
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        295,
+                                        355,
+                                        309
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We prove the theorem by stitching Lemma 1 and Condition 2.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        319,
+                        228,
+                        331
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                319,
+                                227,
+                                333
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        319,
+                                        227,
+                                        333
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Proof. (Proof for Theorem 1)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        335,
+                        449,
+                        379
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                333,
+                                450,
+                                351
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        333,
+                                        191,
+                                        351
+                                    ],
+                                    "score": 1.0,
+                                    "content": "By lemma 1, for any",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        191,
+                                        336,
+                                        419,
+                                        349
+                                    ],
+                                    "score": 0.85,
+                                    "content": "2 \\leq j \\leq M , \\sum _ { t = 1 } ^ { \\infty } I \\left[ V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > \\eta _ { j - 1 } \\right] \\leq C",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        419,
+                                        333,
+                                        450,
+                                        351
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", where",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                250,
+                                351,
+                                360,
+                                379
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        250,
+                                        351,
+                                        360,
+                                        379
+                                    ],
+                                    "score": 0.89,
+                                    "content": "C = \\frac { S A \\ln S A \\ln 1 / \\delta } { \\eta _ { j - 1 } ^ { 2 } ( 1 - \\gamma ) ^ { 5 } } \\cdot \\tilde { P } .",
+                                    "type": "inline_equation",
+                                    "image_path": "ffd9a755f0215c6d325747e98ccee281d70f6c17fc6631e7e6fc4606d3a5e751.jpg"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 17.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        381,
+                        291,
+                        401
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                101,
+                                378,
+                                288,
+                                404
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        101,
+                                        378,
+                                        128,
+                                        404
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Here",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        128,
+                                        383,
+                                        138,
+                                        395
+                                    ],
+                                    "score": 0.86,
+                                    "content": "\\tilde { P }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        138,
+                                        378,
+                                        243,
+                                        404
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is a shorthand for polylog",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        243,
+                                        381,
+                                        288,
+                                        401
+                                    ],
+                                    "score": 0.69,
+                                    "content": "\\begin{array} { r } { \\left( \\frac { 1 } { \\epsilon _ { 1 } } , \\frac { 1 } { 1 - \\gamma } \\right) } \\end{array}",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 19
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        406,
+                        506,
+                        473
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                103,
+                                403,
+                                508,
+                                426
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        103,
+                                        403,
+                                        122,
+                                        426
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        123,
+                                        406,
+                                        214,
+                                        422
+                                    ],
+                                    "score": 0.93,
+                                    "content": "A _ { t } = I [ X _ { t } ^ { ( 2 ^ { i } ) } \\geq \\eta _ { j - 1 } ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        214,
+                                        403,
+                                        363,
+                                        426
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be a Bernoulli random variable, and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        363,
+                                        410,
+                                        398,
+                                        422
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\{ \\mathcal { F } _ { t } \\} _ { t \\ge 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        398,
+                                        403,
+                                        508,
+                                        426
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be the filtration generated",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                419,
+                                507,
+                                434
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        419,
+                                        192,
+                                        434
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by random variables",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        193,
+                                        421,
+                                        287,
+                                        433
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\bar { \\{ ( s _ { \\tau } , a _ { \\tau } ) : 1 \\leq \\tau \\leq t \\} }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        287,
+                                        419,
+                                        317,
+                                        434
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Since",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        318,
+                                        421,
+                                        330,
+                                        432
+                                    ],
+                                    "score": 0.88,
+                                    "content": "A _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        330,
+                                        419,
+                                        340,
+                                        434
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        341,
+                                        421,
+                                        365,
+                                        433
+                                    ],
+                                    "score": 0.8,
+                                    "content": "\\mathcal { F } _ { t + R }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        365,
+                                        419,
+                                        455,
+                                        434
+                                    ],
+                                    "score": 1.0,
+                                    "content": "−measurable, for any",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        455,
+                                        421,
+                                        502,
+                                        432
+                                    ],
+                                    "score": 0.9,
+                                    "content": "0 \\leq k < R",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        503,
+                                        419,
+                                        507,
+                                        434
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                430,
+                                506,
+                                446
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        432,
+                                        248,
+                                        444
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\{ \\dot { A } _ { k + t R } - E [ A _ { k + t R } \\ | \\ \\mathcal { F } _ { k + t R } ] \\} _ { t \\geq 0 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        248,
+                                        430,
+                                        506,
+                                        446
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is a martingale difference sequence. For now, consider a fixed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                442,
+                                507,
+                                464
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        447,
+                                        153,
+                                        458
+                                    ],
+                                    "score": 0.9,
+                                    "content": "0 \\leq k < R",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        154,
+                                        443,
+                                        318,
+                                        462
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". By Azuma-Hoeffiding inequality, after",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        318,
+                                        443,
+                                        439,
+                                        464
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { r } { T = \\mathcal { O } \\left( \\frac { C } { 2 ^ { i } } \\cdot \\frac { M \\eta _ { j } } { \\xi _ { i } } \\ln ( R M L ) \\right) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        368,
+                                        442,
+                                        507,
+                                        462
+                                    ],
+                                    "score": 1.0,
+                                    "content": "· M ηjξ ln(RM L)\u0011 time steps (if it",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                460,
+                                231,
+                                473
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        460,
+                                        231,
+                                        473
+                                    ],
+                                    "score": 1.0,
+                                    "content": "happens that many times) with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 22
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        217,
+                        474,
+                        393,
+                        501
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                217,
+                                474,
+                                393,
+                                501
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        217,
+                                        474,
+                                        393,
+                                        501
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\operatorname* { P r } \\left[ X _ { k + t R } ^ { ( 2 ^ { i } ) } \\geq \\eta _ { j - 1 } \\right] = \\mathbb { E } [ A _ { k + t R } ] > \\frac { \\xi _ { i } } { M \\eta _ { j } } ,",
+                                    "type": "interline_equation",
+                                    "image_path": "b83b246b4683938705ff27511cfa875c502578f40906ac3c2c49408d5a5881f3.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 25,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                217,
+                                474,
+                                393,
+                                501
+                            ],
+                            "spans": [],
+                            "index": 25
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        502,
+                        387,
+                        516
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                501,
+                                388,
+                                518
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        501,
+                                        141,
+                                        518
+                                    ],
+                                    "score": 1.0,
+                                    "content": "we have",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        141,
+                                        502,
+                                        219,
+                                        516
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\textstyle \\sum _ { t } A _ { k + t R } \\geq C / 2 ^ { i }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        220,
+                                        501,
+                                        318,
+                                        518
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with probability at least",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        318,
+                                        503,
+                                        384,
+                                        515
+                                    ],
+                                    "score": 0.89,
+                                    "content": "1 - \\delta / ( 2 M R L )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        384,
+                                        501,
+                                        388,
+                                        518
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 26
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        519,
+                        506,
+                        596
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                519,
+                                506,
+                                534
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        519,
+                                        198,
+                                        534
+                                    ],
+                                    "score": 1.0,
+                                    "content": "On the other hand, if",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        198,
+                                        521,
+                                        226,
+                                        532
+                                    ],
+                                    "score": 0.9,
+                                    "content": "A _ { k + t R }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        227,
+                                        519,
+                                        298,
+                                        534
+                                    ],
+                                    "score": 1.0,
+                                    "content": "happens, within",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        298,
+                                        520,
+                                        408,
+                                        532
+                                    ],
+                                    "score": 0.92,
+                                    "content": "[ k + t R , k + t R + R - 1 ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        408,
+                                        519,
+                                        506,
+                                        534
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", there must be at least",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                529,
+                                508,
+                                545
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        531,
+                                        116,
+                                        542
+                                    ],
+                                    "score": 0.83,
+                                    "content": "2 ^ { i }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        116,
+                                        529,
+                                        202,
+                                        545
+                                    ],
+                                    "score": 1.0,
+                                    "content": "time steps at which",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        202,
+                                        532,
+                                        322,
+                                        543
+                                    ],
+                                    "score": 0.91,
+                                    "content": "V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > ^ { \\mathsf { ^ { * } } } \\eta _ { j - 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        322,
+                                        529,
+                                        468,
+                                        545
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". The latter event happens at most",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        468,
+                                        532,
+                                        477,
+                                        541
+                                    ],
+                                    "score": 0.81,
+                                    "content": "C",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        478,
+                                        529,
+                                        508,
+                                        545
+                                    ],
+                                    "score": 1.0,
+                                    "content": "times,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                102,
+                                537,
+                                510,
+                                567
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        102,
+                                        537,
+                                        124,
+                                        567
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        125,
+                                        543,
+                                        233,
+                                        555
+                                    ],
+                                    "score": 0.9,
+                                    "content": "[ k + t R , k + t R + R - 1 ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        233,
+                                        537,
+                                        293,
+                                        567
+                                    ],
+                                    "score": 1.0,
+                                    "content": "are disjoint. Tppens at most",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        302,
+                                        537,
+                                        334,
+                                        567
+                                    ],
+                                    "score": 1.0,
+                                    "content": "erefore, times f",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        334,
+                                        543,
+                                        424,
+                                        556
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\textstyle \\sum _ { t = 0 } ^ { \\infty } A _ { k + t R } \\leq C / 2 ^ { i }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        425,
+                                        537,
+                                        510,
+                                        567
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". This suggests that a union bound on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                293,
+                                555,
+                                401,
+                                566
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        293,
+                                        555,
+                                        302,
+                                        564
+                                    ],
+                                    "score": 0.83,
+                                    "content": "T",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        370,
+                                        556,
+                                        375,
+                                        564
+                                    ],
+                                    "score": 0.75,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        395,
+                                        556,
+                                        401,
+                                        566
+                                    ],
+                                    "score": 0.8,
+                                    "content": "j",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                564,
+                                506,
+                                578
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        565,
+                                        153,
+                                        576
+                                    ],
+                                    "score": 0.9,
+                                    "content": "0 \\leq k < R",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        564,
+                                        291,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", we can show that with probability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        291,
+                                        565,
+                                        348,
+                                        577
+                                    ],
+                                    "score": 0.92,
+                                    "content": "1 - \\delta / ( 2 M L )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        349,
+                                        564,
+                                        420,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", there are at most",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        420,
+                                        565,
+                                        436,
+                                        576
+                                    ],
+                                    "score": 0.78,
+                                    "content": "R T",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        436,
+                                        564,
+                                        506,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": "time steps where",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                575,
+                                461,
+                                597
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        576,
+                                        239,
+                                        596
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\mathrm { P r } \\left[ X _ { t } ^ { ( 2 ^ { i } ) } \\geq \\eta _ { j - 1 } \\right] > \\xi _ { i } / ( M \\eta _ { j } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        239,
+                                        575,
+                                        461,
+                                        597
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Thus, the number of sub-optimal steps is bounded by,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 29.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        113,
+                        604,
+                        512,
+                        734
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                113,
+                                604,
+                                512,
+                                734
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        604,
+                                        512,
+                                        734
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { r l r } {  { \\sum _ { t = 1 } ^ { \\ell - 1 } I [ V ^ { * } ( s _ { t } ) - V ^ { \\pi _ { t } } ( s _ { t } ) > \\epsilon ] } } \\\\ & { \\leq \\sum _ { t = 1 } ^ { \\infty } \\sum _ { i = 0 } ^ { L } \\sum _ { j = 2 } ^ { M } I [ \\eta _ { j } \\operatorname* { P r } [ X _ { t } ^ { ( 2 ^ { i } ) } > \\eta _ { j - 1 } ] > \\frac { \\xi _ { i } } { M } ] = \\sum _ { i = 0 } ^ { L } \\sum _ { j = 2 } ^ { M } \\sum _ { t = 1 } ^ { \\infty } I [ \\operatorname* { P r } [ X _ { t } ^ { ( 2 ^ { i } ) } > \\eta _ { j - 1 } ] > \\frac { \\xi _ { i } } { \\eta _ { j } M } ] } \\\\ & { \\leq \\sum _ { i = 0 } ^ { L } \\sum _ { j = 2 } ^ { M } \\frac { S A M R \\ln 1 / \\delta \\ln S A } { \\eta _ { j } \\xi _ { i } \\cdot 2 ^ { i } ( 1 - \\gamma ) ^ { 5 } } \\tilde { P } \\leq \\sum _ { i = 0 } ^ { L } \\frac { S A \\cdot 2 ^ { i + 4 } \\ln S A \\ln 1 / \\delta } { \\epsilon _ { 2 } ^ { 2 } ( 1 - \\gamma ) ^ { 6 } } \\tilde { P } \\mathrm { ( B y ~ d e f i n i t i o n ~ o f } \\xi _ { i } \\mathrm { ~ a n d } \\eta _ { j } ) } \\\\ & { \\leq \\frac { S A R \\ln S A \\ln 1 / \\delta } { \\epsilon _ { 2 } ^ { 2 } ( 1 - \\gamma ) ^ { 6 } } \\tilde { P } \\leq \\frac { S A \\ln S A \\ln 1 / \\delta } { \\epsilon _ { 2 } ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\tilde { P } . } & { \\mathrm { ( B y ~ d e f i n i t i o n ~ o f } \\hbar ) } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "19060e0af63eb5746ff2fa8e81a511f198a258681b5fb178d09da3690eab476b.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 34,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                113,
+                                604,
+                                512,
+                                647.3333333333334
+                            ],
+                            "spans": [],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                113,
+                                647.3333333333334,
+                                512,
+                                690.6666666666667
+                            ],
+                            "spans": [],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                113,
+                                690.6666666666667,
+                                512,
+                                734.0000000000001
+                            ],
+                            "spans": [],
+                            "index": 35
+                        }
+                    ]
+                }
+            ],
+            "page_idx": 6,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        26,
+                        294,
+                        38
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                25,
+                                294,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        25,
+                                        294,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        750,
+                        308,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                302,
+                                750,
+                                309,
+                                762
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        302,
+                                        750,
+                                        309,
+                                        762
+                                    ],
+                                    "score": 1.0,
+                                    "content": "7",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        82,
+                        505,
+                        107
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                81,
+                                505,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        81,
+                                        505,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Now, we briefly explain how to prove Lemma 1 with Lemma 2. (Full proof can be found in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                93,
+                                437,
+                                109
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        94,
+                                        275,
+                                        109
+                                    ],
+                                    "score": 1.0,
+                                    "content": "supplementary materials.) Note that since",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        276,
+                                        93,
+                                        313,
+                                        107
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\hat { Q } _ { t } \\geq Q ^ { * }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        314,
+                                        94,
+                                        331,
+                                        109
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        332,
+                                        93,
+                                        433,
+                                        107
+                                    ],
+                                    "score": 0.89,
+                                    "content": "a _ { t } = \\arg \\operatorname* { m a x } _ { a } \\hat { Q } _ { t } ( s _ { t } , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        433,
+                                        94,
+                                        437,
+                                        109
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5,
+                    "bbox_fs": [
+                        105,
+                        81,
+                        505,
+                        109
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        207,
+                        109,
+                        400,
+                        124
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                207,
+                                109,
+                                400,
+                                124
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        207,
+                                        109,
+                                        400,
+                                        124
+                                    ],
+                                    "score": 0.83,
+                                    "content": "V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) \\leq \\hat { Q } _ { t } ( s _ { t } , a _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) .",
+                                    "type": "interline_equation",
+                                    "image_path": "e36c4bae9f64d8b170464eae13de7df006383d23275ffcf8d31e0711f7c4678a.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                207,
+                                109,
+                                400,
+                                124
+                            ],
+                            "spans": [],
+                            "index": 2
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        125,
+                        506,
+                        185
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                124,
+                                507,
+                                139
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        124,
+                                        201,
+                                        139
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We now consider a set",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        202,
+                                        125,
+                                        397,
+                                        138
+                                    ],
+                                    "score": 0.85,
+                                    "content": "J = \\{ t : \\ V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > \\eta ( 1 - \\gamma ) ^ { - 1 } \\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        397,
+                                        124,
+                                        472,
+                                        139
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and consider the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        472,
+                                        126,
+                                        502,
+                                        138
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( | J | , 1 )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        502,
+                                        124,
+                                        507,
+                                        139
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                135,
+                                506,
+                                149
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        135,
+                                        228,
+                                        149
+                                    ],
+                                    "score": 1.0,
+                                    "content": "weight sequence defined by",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        228,
+                                        137,
+                                        294,
+                                        149
+                                    ],
+                                    "score": 0.91,
+                                    "content": "w _ { t } ~ = ~ I \\left[ t \\in J \\right]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        294,
+                                        135,
+                                        506,
+                                        149
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". We can now apply Lemma 2 to weighted sum",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                146,
+                                506,
+                                162
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        147,
+                                        236,
+                                        162
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\begin{array} { r } { \\sum _ { t \\geq 1 } \\dot { w } _ { t } \\left[ \\bar { V } ^ { \\ast } ( s _ { t } ) - Q ^ { \\ast } ( s _ { t } , \\dot { a } _ { t } ) \\right] , } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        236,
+                                        146,
+                                        443,
+                                        162
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". On the one hand, this quantity is obviously at least",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        443,
+                                        147,
+                                        502,
+                                        160
+                                    ],
+                                    "score": 0.92,
+                                    "content": "| J | \\bar { \\eta ( 1 - \\gamma ) } ^ { - 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        503,
+                                        146,
+                                        506,
+                                        162
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                161,
+                                505,
+                                175
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        162,
+                                        408,
+                                        175
+                                    ],
+                                    "score": 1.0,
+                                    "content": "On the other hand, by lemma 2, it is upper bounded by the weighted sum of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        408,
+                                        161,
+                                        478,
+                                        174
+                                    ],
+                                    "score": 0.92,
+                                    "content": "( \\hat { Q } - Q ^ { * } ) ( s _ { t } , a _ { t } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        479,
+                                        162,
+                                        505,
+                                        175
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Thus",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                174,
+                                136,
+                                186
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        174,
+                                        136,
+                                        186
+                                    ],
+                                    "score": 1.0,
+                                    "content": "we get",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 5,
+                    "bbox_fs": [
+                        104,
+                        124,
+                        507,
+                        186
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        146,
+                        186,
+                        464,
+                        219
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                146,
+                                186,
+                                464,
+                                219
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        146,
+                                        186,
+                                        464,
+                                        219
+                                    ],
+                                    "score": 0.93,
+                                    "content": "| J | \\eta ( 1 - \\gamma ) ^ { - 1 } \\leq \\frac { C \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\frac { \\sqrt { S A | J | \\ell ( | J | ) } } { ( 1 - \\gamma ) ^ { 2 . 5 } } + \\frac { w S A \\ln | J | } { ( 1 - \\gamma ) ^ { 3 } } \\ln \\frac { 1 } { ( 1 - \\gamma ) \\epsilon _ { 1 } } \\right) .",
+                                    "type": "interline_equation",
+                                    "image_path": "dc3a723cc9eab16cf16971abf7bbf69938ee49002e529fdd61110b29bb930e71.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                146,
+                                186,
+                                464,
+                                197.0
+                            ],
+                            "spans": [],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                146,
+                                197.0,
+                                464,
+                                208.0
+                            ],
+                            "spans": [],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                146,
+                                208.0,
+                                464,
+                                219.0
+                            ],
+                            "spans": [],
+                            "index": 10
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        221,
+                        505,
+                        263
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                221,
+                                505,
+                                234
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        221,
+                                        241,
+                                        234
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Now focus on the dependence on",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        242,
+                                        221,
+                                        254,
+                                        233
+                                    ],
+                                    "score": 0.89,
+                                    "content": "| J |",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        255,
+                                        221,
+                                        438,
+                                        234
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". The left-hand-side has linear dependence on",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        438,
+                                        221,
+                                        451,
+                                        234
+                                    ],
+                                    "score": 0.88,
+                                    "content": "| J |",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        452,
+                                        221,
+                                        505,
+                                        234
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", whereas the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                232,
+                                506,
+                                252
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        233,
+                                        187,
+                                        252
+                                    ],
+                                    "score": 1.0,
+                                    "content": "left-hand-side has a",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        187,
+                                        232,
+                                        231,
+                                        252
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\tilde { \\mathcal { O } } \\left( \\sqrt { | J | } \\right)",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        232,
+                                        233,
+                                        470,
+                                        252
+                                    ],
+                                    "score": 1.0,
+                                    "content": "dependence. This allows us to solve out an upper bound on",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        471,
+                                        236,
+                                        483,
+                                        248
+                                    ],
+                                    "score": 0.91,
+                                    "content": "| J |",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        484,
+                                        233,
+                                        506,
+                                        252
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                251,
+                                228,
+                                265
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        251,
+                                        208,
+                                        265
+                                    ],
+                                    "score": 1.0,
+                                    "content": "quadratic dependence on",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        208,
+                                        252,
+                                        225,
+                                        263
+                                    ],
+                                    "score": 0.87,
+                                    "content": "1 / \\eta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        225,
+                                        251,
+                                        228,
+                                        265
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 12,
+                    "bbox_fs": [
+                        104,
+                        221,
+                        506,
+                        265
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        275,
+                        234,
+                        286
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                274,
+                                235,
+                                287
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        274,
+                                        235,
+                                        287
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3.5 PROOF FOR THEOREM 1",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        295,
+                        354,
+                        308
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                295,
+                                355,
+                                309
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        295,
+                                        355,
+                                        309
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We prove the theorem by stitching Lemma 1 and Condition 2.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 15,
+                    "bbox_fs": [
+                        105,
+                        295,
+                        355,
+                        309
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        319,
+                        228,
+                        331
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                319,
+                                227,
+                                333
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        319,
+                                        227,
+                                        333
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Proof. (Proof for Theorem 1)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 16,
+                    "bbox_fs": [
+                        106,
+                        319,
+                        227,
+                        333
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        335,
+                        449,
+                        379
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                333,
+                                450,
+                                351
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        333,
+                                        191,
+                                        351
+                                    ],
+                                    "score": 1.0,
+                                    "content": "By lemma 1, for any",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        191,
+                                        336,
+                                        419,
+                                        349
+                                    ],
+                                    "score": 0.85,
+                                    "content": "2 \\leq j \\leq M , \\sum _ { t = 1 } ^ { \\infty } I \\left[ V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > \\eta _ { j - 1 } \\right] \\leq C",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        419,
+                                        333,
+                                        450,
+                                        351
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", where",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                250,
+                                351,
+                                360,
+                                379
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        250,
+                                        351,
+                                        360,
+                                        379
+                                    ],
+                                    "score": 0.89,
+                                    "content": "C = \\frac { S A \\ln S A \\ln 1 / \\delta } { \\eta _ { j - 1 } ^ { 2 } ( 1 - \\gamma ) ^ { 5 } } \\cdot \\tilde { P } .",
+                                    "type": "inline_equation",
+                                    "image_path": "ffd9a755f0215c6d325747e98ccee281d70f6c17fc6631e7e6fc4606d3a5e751.jpg"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 17.5,
+                    "bbox_fs": [
+                        105,
+                        333,
+                        450,
+                        379
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        381,
+                        291,
+                        401
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                101,
+                                378,
+                                288,
+                                404
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        101,
+                                        378,
+                                        128,
+                                        404
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Here",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        128,
+                                        383,
+                                        138,
+                                        395
+                                    ],
+                                    "score": 0.86,
+                                    "content": "\\tilde { P }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        138,
+                                        378,
+                                        243,
+                                        404
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is a shorthand for polylog",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        243,
+                                        381,
+                                        288,
+                                        401
+                                    ],
+                                    "score": 0.69,
+                                    "content": "\\begin{array} { r } { \\left( \\frac { 1 } { \\epsilon _ { 1 } } , \\frac { 1 } { 1 - \\gamma } \\right) } \\end{array}",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 19,
+                    "bbox_fs": [
+                        101,
+                        378,
+                        288,
+                        404
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        406,
+                        506,
+                        473
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                103,
+                                403,
+                                508,
+                                426
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        103,
+                                        403,
+                                        122,
+                                        426
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        123,
+                                        406,
+                                        214,
+                                        422
+                                    ],
+                                    "score": 0.93,
+                                    "content": "A _ { t } = I [ X _ { t } ^ { ( 2 ^ { i } ) } \\geq \\eta _ { j - 1 } ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        214,
+                                        403,
+                                        363,
+                                        426
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be a Bernoulli random variable, and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        363,
+                                        410,
+                                        398,
+                                        422
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\{ \\mathcal { F } _ { t } \\} _ { t \\ge 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        398,
+                                        403,
+                                        508,
+                                        426
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be the filtration generated",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                419,
+                                507,
+                                434
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        419,
+                                        192,
+                                        434
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by random variables",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        193,
+                                        421,
+                                        287,
+                                        433
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\bar { \\{ ( s _ { \\tau } , a _ { \\tau } ) : 1 \\leq \\tau \\leq t \\} }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        287,
+                                        419,
+                                        317,
+                                        434
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Since",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        318,
+                                        421,
+                                        330,
+                                        432
+                                    ],
+                                    "score": 0.88,
+                                    "content": "A _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        330,
+                                        419,
+                                        340,
+                                        434
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        341,
+                                        421,
+                                        365,
+                                        433
+                                    ],
+                                    "score": 0.8,
+                                    "content": "\\mathcal { F } _ { t + R }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        365,
+                                        419,
+                                        455,
+                                        434
+                                    ],
+                                    "score": 1.0,
+                                    "content": "−measurable, for any",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        455,
+                                        421,
+                                        502,
+                                        432
+                                    ],
+                                    "score": 0.9,
+                                    "content": "0 \\leq k < R",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        503,
+                                        419,
+                                        507,
+                                        434
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                430,
+                                506,
+                                446
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        432,
+                                        248,
+                                        444
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\{ \\dot { A } _ { k + t R } - E [ A _ { k + t R } \\ | \\ \\mathcal { F } _ { k + t R } ] \\} _ { t \\geq 0 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        248,
+                                        430,
+                                        506,
+                                        446
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is a martingale difference sequence. For now, consider a fixed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                442,
+                                507,
+                                464
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        447,
+                                        153,
+                                        458
+                                    ],
+                                    "score": 0.9,
+                                    "content": "0 \\leq k < R",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        154,
+                                        443,
+                                        318,
+                                        462
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". By Azuma-Hoeffiding inequality, after",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        318,
+                                        443,
+                                        439,
+                                        464
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { r } { T = \\mathcal { O } \\left( \\frac { C } { 2 ^ { i } } \\cdot \\frac { M \\eta _ { j } } { \\xi _ { i } } \\ln ( R M L ) \\right) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        368,
+                                        442,
+                                        507,
+                                        462
+                                    ],
+                                    "score": 1.0,
+                                    "content": "· M ηjξ ln(RM L)\u0011 time steps (if it",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                460,
+                                231,
+                                473
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        460,
+                                        231,
+                                        473
+                                    ],
+                                    "score": 1.0,
+                                    "content": "happens that many times) with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 22,
+                    "bbox_fs": [
+                        103,
+                        403,
+                        508,
+                        473
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        217,
+                        474,
+                        393,
+                        501
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                217,
+                                474,
+                                393,
+                                501
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        217,
+                                        474,
+                                        393,
+                                        501
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\operatorname* { P r } \\left[ X _ { k + t R } ^ { ( 2 ^ { i } ) } \\geq \\eta _ { j - 1 } \\right] = \\mathbb { E } [ A _ { k + t R } ] > \\frac { \\xi _ { i } } { M \\eta _ { j } } ,",
+                                    "type": "interline_equation",
+                                    "image_path": "b83b246b4683938705ff27511cfa875c502578f40906ac3c2c49408d5a5881f3.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 25,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                217,
+                                474,
+                                393,
+                                501
+                            ],
+                            "spans": [],
+                            "index": 25
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        502,
+                        387,
+                        516
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                501,
+                                388,
+                                518
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        501,
+                                        141,
+                                        518
+                                    ],
+                                    "score": 1.0,
+                                    "content": "we have",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        141,
+                                        502,
+                                        219,
+                                        516
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\textstyle \\sum _ { t } A _ { k + t R } \\geq C / 2 ^ { i }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        220,
+                                        501,
+                                        318,
+                                        518
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with probability at least",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        318,
+                                        503,
+                                        384,
+                                        515
+                                    ],
+                                    "score": 0.89,
+                                    "content": "1 - \\delta / ( 2 M R L )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        384,
+                                        501,
+                                        388,
+                                        518
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 26,
+                    "bbox_fs": [
+                        104,
+                        501,
+                        388,
+                        518
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        519,
+                        506,
+                        596
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                519,
+                                506,
+                                534
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        519,
+                                        198,
+                                        534
+                                    ],
+                                    "score": 1.0,
+                                    "content": "On the other hand, if",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        198,
+                                        521,
+                                        226,
+                                        532
+                                    ],
+                                    "score": 0.9,
+                                    "content": "A _ { k + t R }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        227,
+                                        519,
+                                        298,
+                                        534
+                                    ],
+                                    "score": 1.0,
+                                    "content": "happens, within",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        298,
+                                        520,
+                                        408,
+                                        532
+                                    ],
+                                    "score": 0.92,
+                                    "content": "[ k + t R , k + t R + R - 1 ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        408,
+                                        519,
+                                        506,
+                                        534
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", there must be at least",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                529,
+                                508,
+                                545
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        531,
+                                        116,
+                                        542
+                                    ],
+                                    "score": 0.83,
+                                    "content": "2 ^ { i }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        116,
+                                        529,
+                                        202,
+                                        545
+                                    ],
+                                    "score": 1.0,
+                                    "content": "time steps at which",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        202,
+                                        532,
+                                        322,
+                                        543
+                                    ],
+                                    "score": 0.91,
+                                    "content": "V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > ^ { \\mathsf { ^ { * } } } \\eta _ { j - 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        322,
+                                        529,
+                                        468,
+                                        545
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". The latter event happens at most",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        468,
+                                        532,
+                                        477,
+                                        541
+                                    ],
+                                    "score": 0.81,
+                                    "content": "C",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        478,
+                                        529,
+                                        508,
+                                        545
+                                    ],
+                                    "score": 1.0,
+                                    "content": "times,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                102,
+                                537,
+                                510,
+                                567
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        102,
+                                        537,
+                                        124,
+                                        567
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        125,
+                                        543,
+                                        233,
+                                        555
+                                    ],
+                                    "score": 0.9,
+                                    "content": "[ k + t R , k + t R + R - 1 ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        233,
+                                        537,
+                                        293,
+                                        567
+                                    ],
+                                    "score": 1.0,
+                                    "content": "are disjoint. Tppens at most",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        302,
+                                        537,
+                                        334,
+                                        567
+                                    ],
+                                    "score": 1.0,
+                                    "content": "erefore, times f",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        334,
+                                        543,
+                                        424,
+                                        556
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\textstyle \\sum _ { t = 0 } ^ { \\infty } A _ { k + t R } \\leq C / 2 ^ { i }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        425,
+                                        537,
+                                        510,
+                                        567
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". This suggests that a union bound on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                293,
+                                555,
+                                401,
+                                566
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        293,
+                                        555,
+                                        302,
+                                        564
+                                    ],
+                                    "score": 0.83,
+                                    "content": "T",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        370,
+                                        556,
+                                        375,
+                                        564
+                                    ],
+                                    "score": 0.75,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        395,
+                                        556,
+                                        401,
+                                        566
+                                    ],
+                                    "score": 0.8,
+                                    "content": "j",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                564,
+                                506,
+                                578
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        565,
+                                        153,
+                                        576
+                                    ],
+                                    "score": 0.9,
+                                    "content": "0 \\leq k < R",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        564,
+                                        291,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", we can show that with probability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        291,
+                                        565,
+                                        348,
+                                        577
+                                    ],
+                                    "score": 0.92,
+                                    "content": "1 - \\delta / ( 2 M L )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        349,
+                                        564,
+                                        420,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", there are at most",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        420,
+                                        565,
+                                        436,
+                                        576
+                                    ],
+                                    "score": 0.78,
+                                    "content": "R T",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        436,
+                                        564,
+                                        506,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": "time steps where",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                575,
+                                461,
+                                597
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        576,
+                                        239,
+                                        596
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\mathrm { P r } \\left[ X _ { t } ^ { ( 2 ^ { i } ) } \\geq \\eta _ { j - 1 } \\right] > \\xi _ { i } / ( M \\eta _ { j } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        239,
+                                        575,
+                                        461,
+                                        597
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Thus, the number of sub-optimal steps is bounded by,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 29.5,
+                    "bbox_fs": [
+                        102,
+                        519,
+                        510,
+                        597
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        113,
+                        604,
+                        512,
+                        734
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                113,
+                                604,
+                                512,
+                                734
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        604,
+                                        512,
+                                        734
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { r l r } {  { \\sum _ { t = 1 } ^ { \\ell - 1 } I [ V ^ { * } ( s _ { t } ) - V ^ { \\pi _ { t } } ( s _ { t } ) > \\epsilon ] } } \\\\ & { \\leq \\sum _ { t = 1 } ^ { \\infty } \\sum _ { i = 0 } ^ { L } \\sum _ { j = 2 } ^ { M } I [ \\eta _ { j } \\operatorname* { P r } [ X _ { t } ^ { ( 2 ^ { i } ) } > \\eta _ { j - 1 } ] > \\frac { \\xi _ { i } } { M } ] = \\sum _ { i = 0 } ^ { L } \\sum _ { j = 2 } ^ { M } \\sum _ { t = 1 } ^ { \\infty } I [ \\operatorname* { P r } [ X _ { t } ^ { ( 2 ^ { i } ) } > \\eta _ { j - 1 } ] > \\frac { \\xi _ { i } } { \\eta _ { j } M } ] } \\\\ & { \\leq \\sum _ { i = 0 } ^ { L } \\sum _ { j = 2 } ^ { M } \\frac { S A M R \\ln 1 / \\delta \\ln S A } { \\eta _ { j } \\xi _ { i } \\cdot 2 ^ { i } ( 1 - \\gamma ) ^ { 5 } } \\tilde { P } \\leq \\sum _ { i = 0 } ^ { L } \\frac { S A \\cdot 2 ^ { i + 4 } \\ln S A \\ln 1 / \\delta } { \\epsilon _ { 2 } ^ { 2 } ( 1 - \\gamma ) ^ { 6 } } \\tilde { P } \\mathrm { ( B y ~ d e f i n i t i o n ~ o f } \\xi _ { i } \\mathrm { ~ a n d } \\eta _ { j } ) } \\\\ & { \\leq \\frac { S A R \\ln S A \\ln 1 / \\delta } { \\epsilon _ { 2 } ^ { 2 } ( 1 - \\gamma ) ^ { 6 } } \\tilde { P } \\leq \\frac { S A \\ln S A \\ln 1 / \\delta } { \\epsilon _ { 2 } ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\tilde { P } . } & { \\mathrm { ( B y ~ d e f i n i t i o n ~ o f } \\hbar ) } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "19060e0af63eb5746ff2fa8e81a511f198a258681b5fb178d09da3690eab476b.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 34,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                113,
+                                604,
+                                512,
+                                647.3333333333334
+                            ],
+                            "spans": [],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                113,
+                                647.3333333333334,
+                                512,
+                                690.6666666666667
+                            ],
+                            "spans": [],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                113,
+                                690.6666666666667,
+                                512,
+                                734.0000000000001
+                            ],
+                            "spans": [],
+                            "index": 35
+                        }
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        81,
+                        505,
+                        136
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                80,
+                                506,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        80,
+                                        289,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "It should be stressed that throughout the lines,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        290,
+                                        81,
+                                        299,
+                                        92
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\tilde { P }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        299,
+                                        80,
+                                        506,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is a shorthand for an asymptotic expression, instead",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                91,
+                                505,
+                                109
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        91,
+                                        434,
+                                        109
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of an exact value. Our final choice of \u000f2 and \u000f1 are \u000f2 = \u000f3 , and \u000f1 = \u000f24RM ln",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        446,
+                                        93,
+                                        505,
+                                        105
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". It is not hard",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                428,
+                                102,
+                                442,
+                                110
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        428,
+                                        102,
+                                        442,
+                                        110
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1−γ",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                107,
+                                506,
+                                127
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        107,
+                                        150,
+                                        127
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to see that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        150,
+                                        109,
+                                        266,
+                                        124
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\ln 1 / \\epsilon _ { 1 } = \\mathrm { p o l y } ( \\ln \\textstyle \\frac { 1 } { \\epsilon } , \\ln \\frac { 1 } { 1 - \\gamma } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        267,
+                                        107,
+                                        463,
+                                        127
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". This immediately implies that with probability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        463,
+                                        110,
+                                        486,
+                                        121
+                                    ],
+                                    "score": 0.79,
+                                    "content": "1 - \\delta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        487,
+                                        107,
+                                        506,
+                                        127
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                122,
+                                324,
+                                137
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        122,
+                                        231,
+                                        137
+                                    ],
+                                    "score": 1.0,
+                                    "content": "number of time steps such that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        231,
+                                        123,
+                                        313,
+                                        136
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\left( V ^ { * } - \\dot { V } ^ { \\pi } \\right) \\left( s _ { t } \\right) > \\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        313,
+                                        122,
+                                        324,
+                                        137
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        266,
+                        140,
+                        343,
+                        168
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                266,
+                                140,
+                                343,
+                                168
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        266,
+                                        140,
+                                        343,
+                                        168
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\tilde { \\mathcal { O } } \\left( \\frac { S A \\ln 1 / \\delta } { \\epsilon ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\right) ,",
+                                    "type": "interline_equation",
+                                    "image_path": "112b2a0ff239fa280515807bb22278ab6c902bb4dd2bada09b6a5e780e0dcd78.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                266,
+                                140,
+                                343,
+                                168
+                            ],
+                            "spans": [],
+                            "index": 5
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        173,
+                        313,
+                        188
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                171,
+                                314,
+                                190
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        171,
+                                        208,
+                                        190
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where hidden factors are",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        208,
+                                        173,
+                                        309,
+                                        189
+                                    ],
+                                    "score": 0.79,
+                                    "content": "\\begin{array} { r } { \\operatorname { p o l y } ( \\ln { \\frac { 1 } { \\epsilon } } , \\ln { \\frac { 1 } { 1 - \\gamma } } , \\ln S A ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        309,
+                                        171,
+                                        314,
+                                        190
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        201,
+                        191,
+                        215
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                200,
+                                192,
+                                217
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        200,
+                                        192,
+                                        217
+                                    ],
+                                    "score": 1.0,
+                                    "content": "4 DISCUSSION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        227,
+                        505,
+                        250
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                226,
+                                506,
+                                240
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        226,
+                                        506,
+                                        240
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In this section, we discuss the implication of our results, and present some interesting properties of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                238,
+                                315,
+                                251
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        238,
+                                        315,
+                                        251
+                                    ],
+                                    "score": 1.0,
+                                    "content": "our algorithm beyond its sample complexity bound.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 8.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        263,
+                        300,
+                        274
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                263,
+                                301,
+                                276
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        263,
+                                        301,
+                                        276
+                                    ],
+                                    "score": 1.0,
+                                    "content": "4.1 COMPARISON WITH PREVIOUS RESULTS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        283,
+                        506,
+                        336
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                283,
+                                505,
+                                296
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        283,
+                                        505,
+                                        296
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lower bound To the best of our knowledge, the current best lower bound for worst-case sample",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                293,
+                                508,
+                                315
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        297,
+                                        164,
+                                        312
+                                    ],
+                                    "score": 1.0,
+                                    "content": "complexity is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        173,
+                                        293,
+                                        508,
+                                        315
+                                    ],
+                                    "score": 1.0,
+                                    "content": "\u0010 SA\u000f2(1−γ)3 ln 1/δ\u0011 due to Lattimore & Hutter (2012). The gap between our results",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                312,
+                                505,
+                                326
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        313,
+                                        309,
+                                        326
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and this lower bound lies only in the dependence on",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        309,
+                                        313,
+                                        348,
+                                        325
+                                    ],
+                                    "score": 0.93,
+                                    "content": "1 / ( 1 - \\gamma )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        348,
+                                        313,
+                                        450,
+                                        326
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and logarithmic terms of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        451,
+                                        312,
+                                        505,
+                                        325
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\mathrm { { } } ^ { \\mathrm { { 3 } } A , 1 / ( 1 - \\gamma ) }",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                323,
+                                144,
+                                337
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        323,
+                                        123,
+                                        337
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        124,
+                                        325,
+                                        138,
+                                        336
+                                    ],
+                                    "score": 0.87,
+                                    "content": "1 / \\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        139,
+                                        323,
+                                        144,
+                                        337
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 12.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        340,
+                        506,
+                        408
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                340,
+                                506,
+                                354
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        340,
+                                        506,
+                                        354
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Model-free algorithms Previously, the best sample complexity bound for a model-free algorithm",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                352,
+                                506,
+                                372
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        352,
+                                        116,
+                                        369
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        117,
+                                        352,
+                                        173,
+                                        372
+                                    ],
+                                    "score": 0.95,
+                                    "content": "\\begin{array} { r } { \\tilde { \\mathcal O } \\left( \\frac { S A } { \\epsilon ^ { 4 } ( 1 - \\gamma ) ^ { 8 } } \\right) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        174,
+                                        355,
+                                        506,
+                                        369
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(suppressing all logarithmic terms), achieved by Delayed Q-learning Strehl et al.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                102,
+                                369,
+                                508,
+                                390
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        102,
+                                        369,
+                                        345,
+                                        390
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(2006). Our results improve this upper bound by a factor of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        345,
+                                        370,
+                                        376,
+                                        387
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\frac { 1 } { \\epsilon ^ { 2 } ( 1 - \\gamma ) }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        376,
+                                        369,
+                                        508,
+                                        390
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and closes the quadratic gap in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                385,
+                                506,
+                                398
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        385,
+                                        122,
+                                        397
+                                    ],
+                                    "score": 0.87,
+                                    "content": "1 / \\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        122,
+                                        385,
+                                        506,
+                                        398
+                                    ],
+                                    "score": 1.0,
+                                    "content": "between Delayed Q-learning’s result and the lower bound. In fact, the following theorem shows",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                396,
+                                369,
+                                410
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        396,
+                                        369,
+                                        410
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that UCB Q-learning can indeed outperform Delayed Q-learning.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        411,
+                        505,
+                        453
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                409,
+                                505,
+                                424
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        409,
+                                        353,
+                                        424
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Theorem 2. There exists a family of MDPs with constant",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        354,
+                                        412,
+                                        362,
+                                        421
+                                    ],
+                                    "score": 0.77,
+                                    "content": "S",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        362,
+                                        409,
+                                        383,
+                                        424
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        383,
+                                        412,
+                                        392,
+                                        421
+                                    ],
+                                    "score": 0.71,
+                                    "content": "A",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        392,
+                                        409,
+                                        505,
+                                        424
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", in which with probability",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                422,
+                                505,
+                                442
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        425,
+                                        129,
+                                        437
+                                    ],
+                                    "score": 0.68,
+                                    "content": "1 - \\delta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        129,
+                                        423,
+                                        169,
+                                        439
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", Delayed",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        170,
+                                        426,
+                                        178,
+                                        437
+                                    ],
+                                    "score": 0.66,
+                                    "content": "Q",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        178,
+                                        423,
+                                        393,
+                                        439
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-learning incurs sample complexity of exploration of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        393,
+                                        422,
+                                        441,
+                                        442
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\Omega \\left( \\frac { \\epsilon ^ { - 3 } } { \\ln ( 1 / \\delta ) } \\right)",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        443,
+                                        425,
+                                        505,
+                                        438
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", assuming that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                440,
+                                170,
+                                453
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        440,
+                                        167,
+                                        453
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\ln ( 1 / \\delta ) < \\epsilon ^ { - 2 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        167,
+                                        440,
+                                        170,
+                                        453
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 21
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        461,
+                        432,
+                        474
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                461,
+                                433,
+                                475
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        461,
+                                        433,
+                                        475
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The construction of this hard MDP family is given in the supplementary material.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 23
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        478,
+                        506,
+                        554
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                479,
+                                505,
+                                491
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        479,
+                                        505,
+                                        491
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Model-based algorithms For model-based algorithms, better sample complexity results in infinite",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                490,
+                                506,
+                                502
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        490,
+                                        506,
+                                        502
+                                    ],
+                                    "score": 1.0,
+                                    "content": "horizon settings have been claimed Szita & Szepesvári (2010). To the best of our knowledge, the best",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                501,
+                                505,
+                                521
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        504,
+                                        325,
+                                        517
+                                    ],
+                                    "score": 1.0,
+                                    "content": "published result without further restrictions on MDPs is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        326,
+                                        501,
+                                        382,
+                                        521
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { r } { \\tilde { \\mathcal O } \\left( \\frac { S A } { \\epsilon ^ { 2 } ( 1 - \\gamma ) ^ { 6 } } \\right) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        383,
+                                        505,
+                                        505,
+                                        517
+                                    ],
+                                    "score": 1.0,
+                                    "content": "claimed by Szita & Szepesvári",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                519,
+                                506,
+                                533
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        519,
+                                        176,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(2010), which is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        176,
+                                        520,
+                                        207,
+                                        532
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( 1 - \\gamma )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        207,
+                                        519,
+                                        506,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": "smaller than our upper bound. From the space complexity point of view,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                531,
+                                505,
+                                543
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        531,
+                                        389,
+                                        543
+                                    ],
+                                    "score": 1.0,
+                                    "content": "our algorithm is much more memory-efficient. Our algorithm stores",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        390,
+                                        531,
+                                        421,
+                                        543
+                                    ],
+                                    "score": 0.92,
+                                    "content": "O ( S A )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        421,
+                                        531,
+                                        505,
+                                        543
+                                    ],
+                                    "score": 1.0,
+                                    "content": "values, whereas the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                541,
+                                479,
+                                554
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        542,
+                                        290,
+                                        554
+                                    ],
+                                    "score": 1.0,
+                                    "content": "algorithm in Szita & Szepesvári (2010) needs",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        291,
+                                        541,
+                                        325,
+                                        554
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\Omega ( S ^ { 2 } A )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        325,
+                                        542,
+                                        479,
+                                        554
+                                    ],
+                                    "score": 1.0,
+                                    "content": "memory to store the transition model.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 26.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        567,
+                        271,
+                        578
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                566,
+                                272,
+                                579
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        566,
+                                        272,
+                                        579
+                                    ],
+                                    "score": 1.0,
+                                    "content": "4.2 EXTENSION TO OTHER SETTINGS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 30
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        586,
+                        484,
+                        599
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                585,
+                                485,
+                                601
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        585,
+                                        485,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Due to length limits, detailed discussion in this section is deferred to supplementary materials.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        }
+                    ],
+                    "index": 31
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        603,
+                        505,
+                        661
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                603,
+                                505,
+                                618
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        603,
+                                        505,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Finite horizon MDP The sample complexity of exploration bounds of UCB Q-learning implies",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                613,
+                                506,
+                                631
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        615,
+                                        141,
+                                        629
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\tilde { \\mathcal { O } } \\left( \\epsilon ^ { - 2 } \\right)",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        141,
+                                        613,
+                                        265,
+                                        631
+                                    ],
+                                    "score": 1.0,
+                                    "content": "PAC sample complexity and a",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        266,
+                                        615,
+                                        304,
+                                        629
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\bar { \\mathcal { O } } \\left( T ^ { 1 / 2 } \\right)",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        613,
+                                        506,
+                                        631
+                                    ],
+                                    "score": 1.0,
+                                    "content": "regret bound in finite horizon MDPs. That is, our",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                628,
+                                505,
+                                640
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        628,
+                                        505,
+                                        640
+                                    ],
+                                    "score": 1.0,
+                                    "content": "algorithm implies a PAC algorithm for finite horizon MDPs. We are not aware of reductions of the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                637,
+                                506,
+                                653
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        637,
+                                        506,
+                                        653
+                                    ],
+                                    "score": 1.0,
+                                    "content": "opposite direction (from finite horizon sample complexity to infinite horizon sample complexity of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                649,
+                                160,
+                                663
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        649,
+                                        160,
+                                        663
+                                    ],
+                                    "score": 1.0,
+                                    "content": "exploration).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 34
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        666,
+                        505,
+                        703
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                666,
+                                505,
+                                681
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        666,
+                                        304,
+                                        681
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Regret The reason why our results can imply an",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        666,
+                                        336,
+                                        680
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\tilde { \\mathcal { O } } ( { \\sqrt { T } } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        337,
+                                        666,
+                                        451,
+                                        681
+                                    ],
+                                    "score": 1.0,
+                                    "content": "regret is that, after choosing",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        451,
+                                        670,
+                                        461,
+                                        679
+                                    ],
+                                    "score": 0.82,
+                                    "content": "\\epsilon _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        461,
+                                        666,
+                                        505,
+                                        681
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", it follows",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                679,
+                                505,
+                                693
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        680,
+                                        319,
+                                        693
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from the argument of Theorem 1 that with probability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        320,
+                                        681,
+                                        342,
+                                        691
+                                    ],
+                                    "score": 0.86,
+                                    "content": "1 - \\delta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        343,
+                                        680,
+                                        372,
+                                        693
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", for all",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        372,
+                                        679,
+                                        454,
+                                        693
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\epsilon _ { 2 } > \\tilde { \\mathcal { O } } ( \\epsilon _ { 1 } / ( 1 - \\gamma ) )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        454,
+                                        680,
+                                        505,
+                                        693
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the number",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                691,
+                                256,
+                                704
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        691,
+                                        117,
+                                        704
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        117,
+                                        693,
+                                        127,
+                                        703
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\epsilon _ { 2 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        127,
+                                        691,
+                                        256,
+                                        704
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-suboptimal steps is bounded by",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 38
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        211,
+                        708,
+                        399,
+                        736
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                211,
+                                708,
+                                399,
+                                736
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        211,
+                                        708,
+                                        399,
+                                        736
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\mathcal { O } \\left( \\frac { S A \\ln S A \\ln 1 / \\delta } { \\epsilon _ { 2 } ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\mathrm { p o l y l o g } \\left( \\frac { 1 } { \\epsilon _ { 1 } } , \\frac { 1 } { 1 - \\gamma } \\right) \\right) .",
+                                    "type": "interline_equation",
+                                    "image_path": "4312c45d17cd6e06d125f0e95014a5792379fa26cd13205bd4de52e4ac033fac.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 40,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                211,
+                                708,
+                                399,
+                                736
+                            ],
+                            "spans": [],
+                            "index": 40
+                        }
+                    ]
+                }
+            ],
+            "page_idx": 7,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        26,
+                        294,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                25,
+                                294,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        25,
+                                        294,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        494,
+                        174,
+                        505,
+                        185
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                496,
+                                176,
+                                505,
+                                185
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        496,
+                                        176,
+                                        505,
+                                        185
+                                    ],
+                                    "score": 0.999,
+                                    "content": "□",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        751,
+                        309,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                302,
+                                750,
+                                309,
+                                761
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        302,
+                                        750,
+                                        309,
+                                        761
+                                    ],
+                                    "score": 1.0,
+                                    "content": "8",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        81,
+                        505,
+                        136
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                80,
+                                506,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        80,
+                                        289,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "It should be stressed that throughout the lines,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        290,
+                                        81,
+                                        299,
+                                        92
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\tilde { P }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        299,
+                                        80,
+                                        506,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is a shorthand for an asymptotic expression, instead",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                91,
+                                505,
+                                109
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        91,
+                                        434,
+                                        109
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of an exact value. Our final choice of \u000f2 and \u000f1 are \u000f2 = \u000f3 , and \u000f1 = \u000f24RM ln",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        446,
+                                        93,
+                                        505,
+                                        105
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". It is not hard",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                428,
+                                102,
+                                442,
+                                110
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        428,
+                                        102,
+                                        442,
+                                        110
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1−γ",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                107,
+                                506,
+                                127
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        107,
+                                        150,
+                                        127
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to see that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        150,
+                                        109,
+                                        266,
+                                        124
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\ln 1 / \\epsilon _ { 1 } = \\mathrm { p o l y } ( \\ln \\textstyle \\frac { 1 } { \\epsilon } , \\ln \\frac { 1 } { 1 - \\gamma } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        267,
+                                        107,
+                                        463,
+                                        127
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". This immediately implies that with probability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        463,
+                                        110,
+                                        486,
+                                        121
+                                    ],
+                                    "score": 0.79,
+                                    "content": "1 - \\delta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        487,
+                                        107,
+                                        506,
+                                        127
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                122,
+                                324,
+                                137
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        122,
+                                        231,
+                                        137
+                                    ],
+                                    "score": 1.0,
+                                    "content": "number of time steps such that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        231,
+                                        123,
+                                        313,
+                                        136
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\left( V ^ { * } - \\dot { V } ^ { \\pi } \\right) \\left( s _ { t } \\right) > \\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        313,
+                                        122,
+                                        324,
+                                        137
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 2,
+                    "bbox_fs": [
+                        104,
+                        80,
+                        506,
+                        137
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        266,
+                        140,
+                        343,
+                        168
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                266,
+                                140,
+                                343,
+                                168
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        266,
+                                        140,
+                                        343,
+                                        168
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\tilde { \\mathcal { O } } \\left( \\frac { S A \\ln 1 / \\delta } { \\epsilon ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\right) ,",
+                                    "type": "interline_equation",
+                                    "image_path": "112b2a0ff239fa280515807bb22278ab6c902bb4dd2bada09b6a5e780e0dcd78.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                266,
+                                140,
+                                343,
+                                168
+                            ],
+                            "spans": [],
+                            "index": 5
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        173,
+                        313,
+                        188
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                171,
+                                314,
+                                190
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        171,
+                                        208,
+                                        190
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where hidden factors are",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        208,
+                                        173,
+                                        309,
+                                        189
+                                    ],
+                                    "score": 0.79,
+                                    "content": "\\begin{array} { r } { \\operatorname { p o l y } ( \\ln { \\frac { 1 } { \\epsilon } } , \\ln { \\frac { 1 } { 1 - \\gamma } } , \\ln S A ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        309,
+                                        171,
+                                        314,
+                                        190
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 6,
+                    "bbox_fs": [
+                        105,
+                        171,
+                        314,
+                        190
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        201,
+                        191,
+                        215
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                200,
+                                192,
+                                217
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        200,
+                                        192,
+                                        217
+                                    ],
+                                    "score": 1.0,
+                                    "content": "4 DISCUSSION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        227,
+                        505,
+                        250
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                226,
+                                506,
+                                240
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        226,
+                                        506,
+                                        240
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In this section, we discuss the implication of our results, and present some interesting properties of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                238,
+                                315,
+                                251
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        238,
+                                        315,
+                                        251
+                                    ],
+                                    "score": 1.0,
+                                    "content": "our algorithm beyond its sample complexity bound.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 8.5,
+                    "bbox_fs": [
+                        105,
+                        226,
+                        506,
+                        251
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        263,
+                        300,
+                        274
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                263,
+                                301,
+                                276
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        263,
+                                        301,
+                                        276
+                                    ],
+                                    "score": 1.0,
+                                    "content": "4.1 COMPARISON WITH PREVIOUS RESULTS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        283,
+                        506,
+                        336
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                283,
+                                505,
+                                296
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        283,
+                                        505,
+                                        296
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lower bound To the best of our knowledge, the current best lower bound for worst-case sample",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                293,
+                                508,
+                                315
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        297,
+                                        164,
+                                        312
+                                    ],
+                                    "score": 1.0,
+                                    "content": "complexity is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        173,
+                                        293,
+                                        508,
+                                        315
+                                    ],
+                                    "score": 1.0,
+                                    "content": "\u0010 SA\u000f2(1−γ)3 ln 1/δ\u0011 due to Lattimore & Hutter (2012). The gap between our results",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                312,
+                                505,
+                                326
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        313,
+                                        309,
+                                        326
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and this lower bound lies only in the dependence on",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        309,
+                                        313,
+                                        348,
+                                        325
+                                    ],
+                                    "score": 0.93,
+                                    "content": "1 / ( 1 - \\gamma )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        348,
+                                        313,
+                                        450,
+                                        326
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and logarithmic terms of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        451,
+                                        312,
+                                        505,
+                                        325
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\mathrm { { } } ^ { \\mathrm { { 3 } } A , 1 / ( 1 - \\gamma ) }",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                323,
+                                144,
+                                337
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        323,
+                                        123,
+                                        337
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        124,
+                                        325,
+                                        138,
+                                        336
+                                    ],
+                                    "score": 0.87,
+                                    "content": "1 / \\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        139,
+                                        323,
+                                        144,
+                                        337
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 12.5,
+                    "bbox_fs": [
+                        105,
+                        283,
+                        508,
+                        337
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        340,
+                        506,
+                        408
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                340,
+                                506,
+                                354
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        340,
+                                        506,
+                                        354
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Model-free algorithms Previously, the best sample complexity bound for a model-free algorithm",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                352,
+                                506,
+                                372
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        352,
+                                        116,
+                                        369
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        117,
+                                        352,
+                                        173,
+                                        372
+                                    ],
+                                    "score": 0.95,
+                                    "content": "\\begin{array} { r } { \\tilde { \\mathcal O } \\left( \\frac { S A } { \\epsilon ^ { 4 } ( 1 - \\gamma ) ^ { 8 } } \\right) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        174,
+                                        355,
+                                        506,
+                                        369
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(suppressing all logarithmic terms), achieved by Delayed Q-learning Strehl et al.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                102,
+                                369,
+                                508,
+                                390
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        102,
+                                        369,
+                                        345,
+                                        390
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(2006). Our results improve this upper bound by a factor of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        345,
+                                        370,
+                                        376,
+                                        387
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\frac { 1 } { \\epsilon ^ { 2 } ( 1 - \\gamma ) }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        376,
+                                        369,
+                                        508,
+                                        390
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and closes the quadratic gap in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                385,
+                                506,
+                                398
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        385,
+                                        122,
+                                        397
+                                    ],
+                                    "score": 0.87,
+                                    "content": "1 / \\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        122,
+                                        385,
+                                        506,
+                                        398
+                                    ],
+                                    "score": 1.0,
+                                    "content": "between Delayed Q-learning’s result and the lower bound. In fact, the following theorem shows",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                396,
+                                369,
+                                410
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        396,
+                                        369,
+                                        410
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that UCB Q-learning can indeed outperform Delayed Q-learning.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 17,
+                    "bbox_fs": [
+                        102,
+                        340,
+                        508,
+                        410
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        411,
+                        505,
+                        453
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                409,
+                                505,
+                                424
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        409,
+                                        353,
+                                        424
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Theorem 2. There exists a family of MDPs with constant",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        354,
+                                        412,
+                                        362,
+                                        421
+                                    ],
+                                    "score": 0.77,
+                                    "content": "S",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        362,
+                                        409,
+                                        383,
+                                        424
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        383,
+                                        412,
+                                        392,
+                                        421
+                                    ],
+                                    "score": 0.71,
+                                    "content": "A",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        392,
+                                        409,
+                                        505,
+                                        424
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", in which with probability",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                422,
+                                505,
+                                442
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        425,
+                                        129,
+                                        437
+                                    ],
+                                    "score": 0.68,
+                                    "content": "1 - \\delta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        129,
+                                        423,
+                                        169,
+                                        439
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", Delayed",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        170,
+                                        426,
+                                        178,
+                                        437
+                                    ],
+                                    "score": 0.66,
+                                    "content": "Q",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        178,
+                                        423,
+                                        393,
+                                        439
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-learning incurs sample complexity of exploration of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        393,
+                                        422,
+                                        441,
+                                        442
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\Omega \\left( \\frac { \\epsilon ^ { - 3 } } { \\ln ( 1 / \\delta ) } \\right)",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        443,
+                                        425,
+                                        505,
+                                        438
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", assuming that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                440,
+                                170,
+                                453
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        440,
+                                        167,
+                                        453
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\ln ( 1 / \\delta ) < \\epsilon ^ { - 2 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        167,
+                                        440,
+                                        170,
+                                        453
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 21,
+                    "bbox_fs": [
+                        105,
+                        409,
+                        505,
+                        453
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        461,
+                        432,
+                        474
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                461,
+                                433,
+                                475
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        461,
+                                        433,
+                                        475
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The construction of this hard MDP family is given in the supplementary material.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 23,
+                    "bbox_fs": [
+                        105,
+                        461,
+                        433,
+                        475
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        478,
+                        506,
+                        554
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                479,
+                                505,
+                                491
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        479,
+                                        505,
+                                        491
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Model-based algorithms For model-based algorithms, better sample complexity results in infinite",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                490,
+                                506,
+                                502
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        490,
+                                        506,
+                                        502
+                                    ],
+                                    "score": 1.0,
+                                    "content": "horizon settings have been claimed Szita & Szepesvári (2010). To the best of our knowledge, the best",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                501,
+                                505,
+                                521
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        504,
+                                        325,
+                                        517
+                                    ],
+                                    "score": 1.0,
+                                    "content": "published result without further restrictions on MDPs is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        326,
+                                        501,
+                                        382,
+                                        521
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { r } { \\tilde { \\mathcal O } \\left( \\frac { S A } { \\epsilon ^ { 2 } ( 1 - \\gamma ) ^ { 6 } } \\right) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        383,
+                                        505,
+                                        505,
+                                        517
+                                    ],
+                                    "score": 1.0,
+                                    "content": "claimed by Szita & Szepesvári",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                519,
+                                506,
+                                533
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        519,
+                                        176,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(2010), which is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        176,
+                                        520,
+                                        207,
+                                        532
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( 1 - \\gamma )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        207,
+                                        519,
+                                        506,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": "smaller than our upper bound. From the space complexity point of view,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                531,
+                                505,
+                                543
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        531,
+                                        389,
+                                        543
+                                    ],
+                                    "score": 1.0,
+                                    "content": "our algorithm is much more memory-efficient. Our algorithm stores",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        390,
+                                        531,
+                                        421,
+                                        543
+                                    ],
+                                    "score": 0.92,
+                                    "content": "O ( S A )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        421,
+                                        531,
+                                        505,
+                                        543
+                                    ],
+                                    "score": 1.0,
+                                    "content": "values, whereas the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                541,
+                                479,
+                                554
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        542,
+                                        290,
+                                        554
+                                    ],
+                                    "score": 1.0,
+                                    "content": "algorithm in Szita & Szepesvári (2010) needs",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        291,
+                                        541,
+                                        325,
+                                        554
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\Omega ( S ^ { 2 } A )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        325,
+                                        542,
+                                        479,
+                                        554
+                                    ],
+                                    "score": 1.0,
+                                    "content": "memory to store the transition model.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 26.5,
+                    "bbox_fs": [
+                        104,
+                        479,
+                        506,
+                        554
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        567,
+                        271,
+                        578
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                566,
+                                272,
+                                579
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        566,
+                                        272,
+                                        579
+                                    ],
+                                    "score": 1.0,
+                                    "content": "4.2 EXTENSION TO OTHER SETTINGS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 30
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        586,
+                        484,
+                        599
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                585,
+                                485,
+                                601
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        585,
+                                        485,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Due to length limits, detailed discussion in this section is deferred to supplementary materials.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        }
+                    ],
+                    "index": 31,
+                    "bbox_fs": [
+                        105,
+                        585,
+                        485,
+                        601
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        603,
+                        505,
+                        661
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                603,
+                                505,
+                                618
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        603,
+                                        505,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Finite horizon MDP The sample complexity of exploration bounds of UCB Q-learning implies",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                613,
+                                506,
+                                631
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        615,
+                                        141,
+                                        629
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\tilde { \\mathcal { O } } \\left( \\epsilon ^ { - 2 } \\right)",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        141,
+                                        613,
+                                        265,
+                                        631
+                                    ],
+                                    "score": 1.0,
+                                    "content": "PAC sample complexity and a",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        266,
+                                        615,
+                                        304,
+                                        629
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\bar { \\mathcal { O } } \\left( T ^ { 1 / 2 } \\right)",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        613,
+                                        506,
+                                        631
+                                    ],
+                                    "score": 1.0,
+                                    "content": "regret bound in finite horizon MDPs. That is, our",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                628,
+                                505,
+                                640
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        628,
+                                        505,
+                                        640
+                                    ],
+                                    "score": 1.0,
+                                    "content": "algorithm implies a PAC algorithm for finite horizon MDPs. We are not aware of reductions of the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                637,
+                                506,
+                                653
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        637,
+                                        506,
+                                        653
+                                    ],
+                                    "score": 1.0,
+                                    "content": "opposite direction (from finite horizon sample complexity to infinite horizon sample complexity of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                649,
+                                160,
+                                663
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        649,
+                                        160,
+                                        663
+                                    ],
+                                    "score": 1.0,
+                                    "content": "exploration).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 34,
+                    "bbox_fs": [
+                        104,
+                        603,
+                        506,
+                        663
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        666,
+                        505,
+                        703
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                666,
+                                505,
+                                681
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        666,
+                                        304,
+                                        681
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Regret The reason why our results can imply an",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        666,
+                                        336,
+                                        680
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\tilde { \\mathcal { O } } ( { \\sqrt { T } } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        337,
+                                        666,
+                                        451,
+                                        681
+                                    ],
+                                    "score": 1.0,
+                                    "content": "regret is that, after choosing",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        451,
+                                        670,
+                                        461,
+                                        679
+                                    ],
+                                    "score": 0.82,
+                                    "content": "\\epsilon _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        461,
+                                        666,
+                                        505,
+                                        681
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", it follows",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                679,
+                                505,
+                                693
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        680,
+                                        319,
+                                        693
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from the argument of Theorem 1 that with probability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        320,
+                                        681,
+                                        342,
+                                        691
+                                    ],
+                                    "score": 0.86,
+                                    "content": "1 - \\delta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        343,
+                                        680,
+                                        372,
+                                        693
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", for all",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        372,
+                                        679,
+                                        454,
+                                        693
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\epsilon _ { 2 } > \\tilde { \\mathcal { O } } ( \\epsilon _ { 1 } / ( 1 - \\gamma ) )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        454,
+                                        680,
+                                        505,
+                                        693
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the number",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                691,
+                                256,
+                                704
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        691,
+                                        117,
+                                        704
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        117,
+                                        693,
+                                        127,
+                                        703
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\epsilon _ { 2 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        127,
+                                        691,
+                                        256,
+                                        704
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-suboptimal steps is bounded by",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 38,
+                    "bbox_fs": [
+                        105,
+                        666,
+                        505,
+                        704
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        211,
+                        708,
+                        399,
+                        736
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                211,
+                                708,
+                                399,
+                                736
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        211,
+                                        708,
+                                        399,
+                                        736
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\mathcal { O } \\left( \\frac { S A \\ln S A \\ln 1 / \\delta } { \\epsilon _ { 2 } ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\mathrm { p o l y l o g } \\left( \\frac { 1 } { \\epsilon _ { 1 } } , \\frac { 1 } { 1 - \\gamma } \\right) \\right) .",
+                                    "type": "interline_equation",
+                                    "image_path": "4312c45d17cd6e06d125f0e95014a5792379fa26cd13205bd4de52e4ac033fac.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 40,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                211,
+                                708,
+                                399,
+                                736
+                            ],
+                            "spans": [],
+                            "index": 40
+                        }
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        82,
+                        504,
+                        105
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                81,
+                                505,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        81,
+                                        446,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In contrast, Delayed Q-learning Strehl et al. (2006) can only give an upper bound on",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        447,
+                                        84,
+                                        456,
+                                        93
+                                    ],
+                                    "score": 0.84,
+                                    "content": "\\epsilon _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        456,
+                                        81,
+                                        505,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-suboptimal",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                93,
+                                235,
+                                107
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        93,
+                                        221,
+                                        107
+                                    ],
+                                    "score": 1.0,
+                                    "content": "steps after setting parameter",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        221,
+                                        96,
+                                        231,
+                                        105
+                                    ],
+                                    "score": 0.84,
+                                    "content": "\\epsilon _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        231,
+                                        93,
+                                        235,
+                                        107
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        120,
+                        195,
+                        133
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                119,
+                                198,
+                                136
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        119,
+                                        198,
+                                        136
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5 CONCLUSION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        145,
+                        505,
+                        220
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                146,
+                                505,
+                                157
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        146,
+                                        505,
+                                        157
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Infinite-horizon MDP with discounted reward is a setting that is arguably more difficult than other",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                101,
+                                157,
+                                506,
+                                190
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        101,
+                                        157,
+                                        383,
+                                        190
+                                    ],
+                                    "score": 1.0,
+                                    "content": "popular settings, such as finite-horizon MDP. Previously, the best samby model-free reinforcement learning algorithms in this setting is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        383,
+                                        168,
+                                        434,
+                                        184
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\tilde { \\cal O } \\big ( { \\textstyle \\frac { S A } { \\epsilon ^ { 4 } ( 1 - \\gamma _ { _ { - } } ) ^ { 8 } } } \\big )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        434,
+                                        157,
+                                        506,
+                                        190
+                                    ],
+                                    "score": 1.0,
+                                    "content": "y bound achieved, due to Delayed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                182,
+                                506,
+                                195
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        182,
+                                        506,
+                                        195
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Q-learning Strehl et al. (2006). In this paper, we propose a variant of Q-learning that incorporates",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                102,
+                                188,
+                                509,
+                                214
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        102,
+                                        188,
+                                        380,
+                                        214
+                                    ],
+                                    "score": 1.0,
+                                    "content": "upper confidence bound, and show that it has a sample complexity of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        381,
+                                        193,
+                                        431,
+                                        209
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { r } { \\tilde { \\mathcal { O } } \\big ( \\frac { S A } { \\epsilon ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\big ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        432,
+                                        188,
+                                        509,
+                                        214
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". This matches the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                207,
+                                419,
+                                221
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        207,
+                                        278,
+                                        221
+                                    ],
+                                    "score": 1.0,
+                                    "content": "best lower bound except in dependence on",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        278,
+                                        208,
+                                        320,
+                                        220
+                                    ],
+                                    "score": 0.93,
+                                    "content": "1 / ( 1 - \\gamma )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        320,
+                                        207,
+                                        419,
+                                        221
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and logarithmic factors.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        236,
+                        242,
+                        248
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                236,
+                                243,
+                                250
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        236,
+                                        243,
+                                        250
+                                    ],
+                                    "score": 1.0,
+                                    "content": "6 ACKNOWLEDGEMENTS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        260,
+                        504,
+                        294
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                260,
+                                505,
+                                273
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        260,
+                                        505,
+                                        273
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The authors thank Chi Jin and Chongjie Zhang for helpful discussions. This work is supported",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                270,
+                                506,
+                                284
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        270,
+                                        506,
+                                        284
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by National Basic Research Program of China (973 Program) (grant no. 2015CB352502), NSFC",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                282,
+                                425,
+                                296
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        282,
+                                        425,
+                                        296
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(61573026), BJNSF (L172037) and Beijing Acedemy of Artificial Intelligence.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        310,
+                        176,
+                        322
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                311,
+                                176,
+                                323
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        311,
+                                        176,
+                                        323
+                                    ],
+                                    "score": 1.0,
+                                    "content": "REFERENCES",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        329,
+                        504,
+                        351
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                327,
+                                505,
+                                343
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        327,
+                                        505,
+                                        343
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Mohammad Gheshlaghi Azar, Remi Munos, Mohammad Ghavamzadeh, and Hilbert Kappen. Speedy",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                339,
+                                409,
+                                352
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        339,
+                                        409,
+                                        352
+                                    ],
+                                    "score": 1.0,
+                                    "content": "q-learning. In Advances in neural information processing systems, 2011.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 13.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        358,
+                        504,
+                        381
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                356,
+                                506,
+                                371
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        356,
+                                        506,
+                                        371
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Mohammad Gheshlaghi Azar, Ian Osband, and Rémi Munos. Minimax regret bounds for reinforce-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                369,
+                                340,
+                                382
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        369,
+                                        340,
+                                        382
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ment learning. arXiv preprint arXiv:1703.05449, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 15.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        387,
+                        506,
+                        432
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                387,
+                                506,
+                                400
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        387,
+                                        506,
+                                        400
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Ronen I. Brafman and Moshe Tennenholtz. R-max - a general polynomial time algorithm for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                399,
+                                506,
+                                411
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        399,
+                                        506,
+                                        411
+                                    ],
+                                    "score": 1.0,
+                                    "content": "near-optimal reinforcement learning. J. Mach. Learn. Res., 3:213–231, March 2003. ISSN",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                410,
+                                506,
+                                422
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        410,
+                                        506,
+                                        422
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1532-4435. doi: 10.1162/153244303765208377. URL https://doi.org/10.1162/",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                421,
+                                230,
+                                433
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        421,
+                                        230,
+                                        433
+                                    ],
+                                    "score": 1.0,
+                                    "content": "153244303765208377.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 18.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        439,
+                        504,
+                        473
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                439,
+                                506,
+                                452
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        439,
+                                        506,
+                                        452
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Christoph Dann, Tor Lattimore, and Emma Brunskill. Unifying pac and regret: Uniform pac bounds",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                449,
+                                506,
+                                464
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        449,
+                                        506,
+                                        464
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for episodic reinforcement learning. In Advances in Neural Information Processing Systems, pp.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                462,
+                                191,
+                                473
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        462,
+                                        191,
+                                        473
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5713–5723, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 22
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        479,
+                        504,
+                        502
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                478,
+                                505,
+                                494
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        478,
+                                        505,
+                                        494
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Eyal Even-Dar and Yishay Mansour. Learning rates for q-learning. Journal of Machine Learning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                491,
+                                237,
+                                502
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        491,
+                                        237,
+                                        502
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Research, 5(Dec):1–25, 2003.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 24.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        509,
+                        504,
+                        533
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                509,
+                                505,
+                                522
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        509,
+                                        505,
+                                        522
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Thomas Jaksch, Ronald Ortner, and Peter Auer. Near-optimal regret bounds for reinforcement",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                520,
+                                426,
+                                533
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        520,
+                                        426,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning. Journal of Machine Learning Research, 11(Apr):1563–1600, 2010.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 26.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        539,
+                        504,
+                        563
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                539,
+                                505,
+                                552
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        539,
+                                        505,
+                                        552
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Chi Jin, Zeyuan Allen-Zhu, Sebastien Bubeck, and Michael I Jordan. Is q-learning provably efficient?",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                550,
+                                430,
+                                562
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        550,
+                                        430,
+                                        562
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In Advances in Neural Information Processing Systems, pp. 4864–4874, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 28.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        569,
+                        505,
+                        592
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                568,
+                                506,
+                                582
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        568,
+                                        506,
+                                        582
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sham Machandranath Kakade et al. On the sample complexity of reinforcement learning. PhD thesis,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                580,
+                                303,
+                                591
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        580,
+                                        303,
+                                        591
+                                    ],
+                                    "score": 1.0,
+                                    "content": "University of London London, England, 2003.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        }
+                    ],
+                    "index": 30.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        598,
+                        504,
+                        622
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                597,
+                                505,
+                                612
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        597,
+                                        505,
+                                        612
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Tor Lattimore and Marcus Hutter. Pac bounds for discounted mdps. In International Conference on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                609,
+                                357,
+                                622
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        609,
+                                        357,
+                                        622
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Algorithmic Learning Theory, pp. 320–334. Springer, 2012.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 32.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        627,
+                        505,
+                        662
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                627,
+                                505,
+                                641
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        627,
+                                        505,
+                                        641
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Volodymyr Mnih, Koray Kavukcuoglu, David Silver, Alex Graves, Ioannis Antonoglou, Daan",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                639,
+                                505,
+                                652
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        639,
+                                        505,
+                                        652
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Wierstra, and Martin Riedmiller. Playing atari with deep reinforcement learning. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                651,
+                                214,
+                                661
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        651,
+                                        214,
+                                        661
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1312.5602, 2013.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 35
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        668,
+                        504,
+                        703
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                668,
+                                505,
+                                682
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        668,
+                                        505,
+                                        682
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Volodymyr Mnih, Adria Puigdomenech Badia, Mehdi Mirza, Alex Graves, Timothy Lillicrap, Tim",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                680,
+                                505,
+                                692
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        680,
+                                        505,
+                                        692
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Harley, David Silver, and Koray Kavukcuoglu. Asynchronous methods for deep reinforcement",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                690,
+                                444,
+                                703
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        690,
+                                        444,
+                                        703
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning. In International conference on machine learning, pp. 1928–1937, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 38
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        709,
+                        502,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                708,
+                                505,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        708,
+                                        505,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "John Schulman, Sergey Levine, Pieter Abbeel, Michael Jordan, and Philipp Moritz. Trust region",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                720,
+                                495,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        720,
+                                        495,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "policy optimization. In International Conference on Machine Learning, pp. 1889–1897, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        }
+                    ],
+                    "index": 40.5
+                }
+            ],
+            "page_idx": 8,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        108,
+                        27,
+                        293,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                294,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        294,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        751,
+                        309,
+                        759
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                302,
+                                751,
+                                309,
+                                762
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        302,
+                                        751,
+                                        309,
+                                        762
+                                    ],
+                                    "score": 1.0,
+                                    "content": "9",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        82,
+                        504,
+                        105
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                81,
+                                505,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        81,
+                                        446,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In contrast, Delayed Q-learning Strehl et al. (2006) can only give an upper bound on",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        447,
+                                        84,
+                                        456,
+                                        93
+                                    ],
+                                    "score": 0.84,
+                                    "content": "\\epsilon _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        456,
+                                        81,
+                                        505,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-suboptimal",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                93,
+                                235,
+                                107
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        93,
+                                        221,
+                                        107
+                                    ],
+                                    "score": 1.0,
+                                    "content": "steps after setting parameter",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        221,
+                                        96,
+                                        231,
+                                        105
+                                    ],
+                                    "score": 0.84,
+                                    "content": "\\epsilon _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        231,
+                                        93,
+                                        235,
+                                        107
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5,
+                    "bbox_fs": [
+                        105,
+                        81,
+                        505,
+                        107
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        120,
+                        195,
+                        133
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                119,
+                                198,
+                                136
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        119,
+                                        198,
+                                        136
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5 CONCLUSION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        145,
+                        505,
+                        220
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                146,
+                                505,
+                                157
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        146,
+                                        505,
+                                        157
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Infinite-horizon MDP with discounted reward is a setting that is arguably more difficult than other",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                101,
+                                157,
+                                506,
+                                190
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        101,
+                                        157,
+                                        383,
+                                        190
+                                    ],
+                                    "score": 1.0,
+                                    "content": "popular settings, such as finite-horizon MDP. Previously, the best samby model-free reinforcement learning algorithms in this setting is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        383,
+                                        168,
+                                        434,
+                                        184
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\tilde { \\cal O } \\big ( { \\textstyle \\frac { S A } { \\epsilon ^ { 4 } ( 1 - \\gamma _ { _ { - } } ) ^ { 8 } } } \\big )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        434,
+                                        157,
+                                        506,
+                                        190
+                                    ],
+                                    "score": 1.0,
+                                    "content": "y bound achieved, due to Delayed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                182,
+                                506,
+                                195
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        182,
+                                        506,
+                                        195
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Q-learning Strehl et al. (2006). In this paper, we propose a variant of Q-learning that incorporates",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                102,
+                                188,
+                                509,
+                                214
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        102,
+                                        188,
+                                        380,
+                                        214
+                                    ],
+                                    "score": 1.0,
+                                    "content": "upper confidence bound, and show that it has a sample complexity of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        381,
+                                        193,
+                                        431,
+                                        209
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { r } { \\tilde { \\mathcal { O } } \\big ( \\frac { S A } { \\epsilon ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\big ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        432,
+                                        188,
+                                        509,
+                                        214
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". This matches the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                207,
+                                419,
+                                221
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        207,
+                                        278,
+                                        221
+                                    ],
+                                    "score": 1.0,
+                                    "content": "best lower bound except in dependence on",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        278,
+                                        208,
+                                        320,
+                                        220
+                                    ],
+                                    "score": 0.93,
+                                    "content": "1 / ( 1 - \\gamma )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        320,
+                                        207,
+                                        419,
+                                        221
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and logarithmic factors.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 5,
+                    "bbox_fs": [
+                        101,
+                        146,
+                        509,
+                        221
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        236,
+                        242,
+                        248
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                236,
+                                243,
+                                250
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        236,
+                                        243,
+                                        250
+                                    ],
+                                    "score": 1.0,
+                                    "content": "6 ACKNOWLEDGEMENTS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        260,
+                        504,
+                        294
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                260,
+                                505,
+                                273
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        260,
+                                        505,
+                                        273
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The authors thank Chi Jin and Chongjie Zhang for helpful discussions. This work is supported",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                270,
+                                506,
+                                284
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        270,
+                                        506,
+                                        284
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by National Basic Research Program of China (973 Program) (grant no. 2015CB352502), NSFC",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                282,
+                                425,
+                                296
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        282,
+                                        425,
+                                        296
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(61573026), BJNSF (L172037) and Beijing Acedemy of Artificial Intelligence.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 10,
+                    "bbox_fs": [
+                        105,
+                        260,
+                        506,
+                        296
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        310,
+                        176,
+                        322
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                311,
+                                176,
+                                323
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        311,
+                                        176,
+                                        323
+                                    ],
+                                    "score": 1.0,
+                                    "content": "REFERENCES",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        329,
+                        504,
+                        351
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                327,
+                                505,
+                                343
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        327,
+                                        505,
+                                        343
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Mohammad Gheshlaghi Azar, Remi Munos, Mohammad Ghavamzadeh, and Hilbert Kappen. Speedy",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                339,
+                                409,
+                                352
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        339,
+                                        409,
+                                        352
+                                    ],
+                                    "score": 1.0,
+                                    "content": "q-learning. In Advances in neural information processing systems, 2011.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 13.5,
+                    "bbox_fs": [
+                        105,
+                        327,
+                        505,
+                        352
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        358,
+                        504,
+                        381
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                356,
+                                506,
+                                371
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        356,
+                                        506,
+                                        371
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Mohammad Gheshlaghi Azar, Ian Osband, and Rémi Munos. Minimax regret bounds for reinforce-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                369,
+                                340,
+                                382
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        369,
+                                        340,
+                                        382
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ment learning. arXiv preprint arXiv:1703.05449, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 15.5,
+                    "bbox_fs": [
+                        105,
+                        356,
+                        506,
+                        382
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        387,
+                        506,
+                        432
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                387,
+                                506,
+                                400
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        387,
+                                        506,
+                                        400
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Ronen I. Brafman and Moshe Tennenholtz. R-max - a general polynomial time algorithm for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                399,
+                                506,
+                                411
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        399,
+                                        506,
+                                        411
+                                    ],
+                                    "score": 1.0,
+                                    "content": "near-optimal reinforcement learning. J. Mach. Learn. Res., 3:213–231, March 2003. ISSN",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                410,
+                                506,
+                                422
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        410,
+                                        506,
+                                        422
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1532-4435. doi: 10.1162/153244303765208377. URL https://doi.org/10.1162/",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                421,
+                                230,
+                                433
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        421,
+                                        230,
+                                        433
+                                    ],
+                                    "score": 1.0,
+                                    "content": "153244303765208377.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 18.5,
+                    "bbox_fs": [
+                        105,
+                        387,
+                        506,
+                        433
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        439,
+                        504,
+                        473
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                439,
+                                506,
+                                452
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        439,
+                                        506,
+                                        452
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Christoph Dann, Tor Lattimore, and Emma Brunskill. Unifying pac and regret: Uniform pac bounds",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                449,
+                                506,
+                                464
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        449,
+                                        506,
+                                        464
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for episodic reinforcement learning. In Advances in Neural Information Processing Systems, pp.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                462,
+                                191,
+                                473
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        462,
+                                        191,
+                                        473
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5713–5723, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 22,
+                    "bbox_fs": [
+                        106,
+                        439,
+                        506,
+                        473
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        479,
+                        504,
+                        502
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                478,
+                                505,
+                                494
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        478,
+                                        505,
+                                        494
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Eyal Even-Dar and Yishay Mansour. Learning rates for q-learning. Journal of Machine Learning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                491,
+                                237,
+                                502
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        491,
+                                        237,
+                                        502
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Research, 5(Dec):1–25, 2003.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 24.5,
+                    "bbox_fs": [
+                        105,
+                        478,
+                        505,
+                        502
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        509,
+                        504,
+                        533
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                509,
+                                505,
+                                522
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        509,
+                                        505,
+                                        522
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Thomas Jaksch, Ronald Ortner, and Peter Auer. Near-optimal regret bounds for reinforcement",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                520,
+                                426,
+                                533
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        520,
+                                        426,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning. Journal of Machine Learning Research, 11(Apr):1563–1600, 2010.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 26.5,
+                    "bbox_fs": [
+                        106,
+                        509,
+                        505,
+                        533
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        539,
+                        504,
+                        563
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                539,
+                                505,
+                                552
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        539,
+                                        505,
+                                        552
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Chi Jin, Zeyuan Allen-Zhu, Sebastien Bubeck, and Michael I Jordan. Is q-learning provably efficient?",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                550,
+                                430,
+                                562
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        550,
+                                        430,
+                                        562
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In Advances in Neural Information Processing Systems, pp. 4864–4874, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 28.5,
+                    "bbox_fs": [
+                        106,
+                        539,
+                        505,
+                        562
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        569,
+                        505,
+                        592
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                568,
+                                506,
+                                582
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        568,
+                                        506,
+                                        582
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sham Machandranath Kakade et al. On the sample complexity of reinforcement learning. PhD thesis,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                580,
+                                303,
+                                591
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        580,
+                                        303,
+                                        591
+                                    ],
+                                    "score": 1.0,
+                                    "content": "University of London London, England, 2003.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        }
+                    ],
+                    "index": 30.5,
+                    "bbox_fs": [
+                        106,
+                        568,
+                        506,
+                        591
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        598,
+                        504,
+                        622
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                597,
+                                505,
+                                612
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        597,
+                                        505,
+                                        612
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Tor Lattimore and Marcus Hutter. Pac bounds for discounted mdps. In International Conference on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                609,
+                                357,
+                                622
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        609,
+                                        357,
+                                        622
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Algorithmic Learning Theory, pp. 320–334. Springer, 2012.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 32.5,
+                    "bbox_fs": [
+                        106,
+                        597,
+                        505,
+                        622
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        627,
+                        505,
+                        662
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                627,
+                                505,
+                                641
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        627,
+                                        505,
+                                        641
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Volodymyr Mnih, Koray Kavukcuoglu, David Silver, Alex Graves, Ioannis Antonoglou, Daan",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                639,
+                                505,
+                                652
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        639,
+                                        505,
+                                        652
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Wierstra, and Martin Riedmiller. Playing atari with deep reinforcement learning. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                651,
+                                214,
+                                661
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        651,
+                                        214,
+                                        661
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1312.5602, 2013.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 35,
+                    "bbox_fs": [
+                        106,
+                        627,
+                        505,
+                        661
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        668,
+                        504,
+                        703
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                668,
+                                505,
+                                682
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        668,
+                                        505,
+                                        682
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Volodymyr Mnih, Adria Puigdomenech Badia, Mehdi Mirza, Alex Graves, Timothy Lillicrap, Tim",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                680,
+                                505,
+                                692
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        680,
+                                        505,
+                                        692
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Harley, David Silver, and Koray Kavukcuoglu. Asynchronous methods for deep reinforcement",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                690,
+                                444,
+                                703
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        690,
+                                        444,
+                                        703
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning. In International conference on machine learning, pp. 1928–1937, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 38,
+                    "bbox_fs": [
+                        106,
+                        668,
+                        505,
+                        703
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        709,
+                        502,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                708,
+                                505,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        708,
+                                        505,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "John Schulman, Sergey Levine, Pieter Abbeel, Michael Jordan, and Philipp Moritz. Trust region",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                720,
+                                495,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        720,
+                                        495,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "policy optimization. In International Conference on Machine Learning, pp. 1889–1897, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        }
+                    ],
+                    "index": 40.5,
+                    "bbox_fs": [
+                        105,
+                        708,
+                        505,
+                        732
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        82,
+                        504,
+                        116
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                81,
+                                506,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        81,
+                                        506,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Aaron Sidford, Mengdi Wang, Xian Wu, Lin Yang, and Yinyu Ye. Near-optimal time and sample",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                95,
+                                505,
+                                105
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        95,
+                                        505,
+                                        105
+                                    ],
+                                    "score": 1.0,
+                                    "content": "complexities for solving markov decision processes with a generative model. In Advances in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                103,
+                                374,
+                                118
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        103,
+                                        374,
+                                        118
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Neural Information Processing Systems, pp. 5186–5196, 2018a.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        123,
+                        505,
+                        168
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                124,
+                                505,
+                                136
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        124,
+                                        505,
+                                        136
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Aaron Sidford, Mengdi Wang, Xian Wu, and Yinyu Ye. Variance reduced value iteration and faster",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                134,
+                                505,
+                                146
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        134,
+                                        505,
+                                        146
+                                    ],
+                                    "score": 1.0,
+                                    "content": "algorithms for solving markov decision processes. In Proceedings of the Twenty-Ninth Annual",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                145,
+                                505,
+                                159
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        145,
+                                        505,
+                                        159
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ACM-SIAM Symposium on Discrete Algorithms, pp. 770–787. Society for Industrial and Applied",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                156,
+                                202,
+                                168
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        156,
+                                        202,
+                                        168
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Mathematics, 2018b.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 4.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        174,
+                        503,
+                        198
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                176,
+                                505,
+                                187
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        176,
+                                        505,
+                                        187
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Alexander L Strehl and Michael L Littman. An analysis of model-based interval estimation for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                186,
+                                501,
+                                198
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        186,
+                                        501,
+                                        198
+                                    ],
+                                    "score": 1.0,
+                                    "content": "markov decision processes. Journal of Computer and System Sciences, 74(8):1309–1331, 2008.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 7.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        204,
+                        506,
+                        239
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                205,
+                                506,
+                                217
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        205,
+                                        506,
+                                        217
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Alexander L Strehl, Lihong Li, Eric Wiewiora, John Langford, and Michael L Littman. Pac model-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                217,
+                                505,
+                                229
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        217,
+                                        505,
+                                        229
+                                    ],
+                                    "score": 1.0,
+                                    "content": "free reinforcement learning. In Proceedings of the 23rd international conference on Machine",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                227,
+                                262,
+                                239
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        227,
+                                        262,
+                                        239
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning, pp. 881–888. ACM, 2006.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        245,
+                        505,
+                        280
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                246,
+                                504,
+                                258
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        246,
+                                        504,
+                                        258
+                                    ],
+                                    "score": 1.0,
+                                    "content": "István Szita and Csaba Szepesvári. Model-based reinforcement learning with nearly tight exploration",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                256,
+                                505,
+                                271
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        256,
+                                        505,
+                                        271
+                                    ],
+                                    "score": 1.0,
+                                    "content": "complexity bounds. In Proceedings of the 27th International Conference on Machine Learning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                268,
+                                254,
+                                281
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        268,
+                                        254,
+                                        281
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(ICML-10), pp. 1031–1038, 2010.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        300,
+                        232,
+                        313
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                299,
+                                233,
+                                315
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        299,
+                                        233,
+                                        315
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A PROOF OF LEMMA 1",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        323,
+                        505,
+                        351
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                321,
+                                507,
+                                342
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        321,
+                                        215,
+                                        342
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lemma 1. For fixed t and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        215,
+                                        326,
+                                        240,
+                                        338
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\eta > 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        240,
+                                        321,
+                                        255,
+                                        342
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        256,
+                                        323,
+                                        275,
+                                        338
+                                    ],
+                                    "score": 0.92,
+                                    "content": "B _ { \\eta } ^ { ( t ) }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        275,
+                                        321,
+                                        344,
+                                        342
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be the event that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        344,
+                                        325,
+                                        457,
+                                        340
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { r } { V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > \\frac { \\eta } { 1 - \\gamma } } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        458,
+                                        321,
+                                        507,
+                                        342
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in step t. If",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                338,
+                                297,
+                                353
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        339,
+                                        139,
+                                        351
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\eta > 2 \\epsilon _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        140,
+                                        338,
+                                        261,
+                                        353
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", then with probability at least",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        261,
+                                        339,
+                                        294,
+                                        351
+                                    ],
+                                    "score": 0.9,
+                                    "content": "1 - \\delta / 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        294,
+                                        338,
+                                        297,
+                                        353
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 16.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        186,
+                        356,
+                        423,
+                        390
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                186,
+                                356,
+                                423,
+                                390
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        186,
+                                        356,
+                                        423,
+                                        390
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\sum _ { t = 1 } ^ { t = \\infty } I \\left[ B _ { \\eta } ^ { ( t ) } \\right] \\leq \\frac { S A \\ln S A \\ln 1 / \\delta } { \\eta ^ { 2 } ( 1 - \\gamma ) ^ { 3 } } \\cdot p o l y l o g \\left( \\frac { 1 } { \\epsilon _ { 1 } } , \\frac { 1 } { 1 - \\gamma } \\right) ,",
+                                    "type": "interline_equation",
+                                    "image_path": "0b9f09a826319782774c08f51f81a7e3a19a570518937c623163e273091ef961.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                186,
+                                356,
+                                423,
+                                373.0
+                            ],
+                            "spans": [],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                186,
+                                373.0,
+                                423,
+                                390.0
+                            ],
+                            "spans": [],
+                            "index": 19
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        395,
+                        248,
+                        407
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                395,
+                                249,
+                                408
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        395,
+                                        133,
+                                        408
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        133,
+                                        395,
+                                        147,
+                                        407
+                                    ],
+                                    "score": 0.87,
+                                    "content": "I [ \\cdot ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        148,
+                                        395,
+                                        249,
+                                        408
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the indicator function.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 20
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        418,
+                        431,
+                        432
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                418,
+                                432,
+                                433
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        418,
+                                        162,
+                                        433
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Proof. When",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        163,
+                                        420,
+                                        187,
+                                        431
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\eta > 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        188,
+                                        418,
+                                        403,
+                                        433
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the lemma holds trivially. Now consider the case that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        403,
+                                        420,
+                                        428,
+                                        431
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\eta \\leq 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        428,
+                                        418,
+                                        432,
+                                        433
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 21
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        435,
+                        430,
+                        450
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                433,
+                                427,
+                                452
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        433,
+                                        122,
+                                        452
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        122,
+                                        435,
+                                        279,
+                                        451
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\begin{array} { r } { I = \\{ t \\colon V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > \\frac { \\eta } { 1 - \\gamma } \\} } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        280,
+                                        433,
+                                        404,
+                                        452
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". By lemma 2, with probability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        404,
+                                        437,
+                                        427,
+                                        447
+                                    ],
+                                    "score": 0.84,
+                                    "content": "1 - \\delta",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 22
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        138,
+                        457,
+                        472,
+                        592
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                138,
+                                457,
+                                472,
+                                592
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        138,
+                                        457,
+                                        472,
+                                        592
+                                    ],
+                                    "score": 0.95,
+                                    "content": "\\begin{array} { r l } & { \\frac { \\eta | I | } { 1 - \\gamma } \\leq \\displaystyle \\sum _ { t \\in I } \\left( V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) \\right) \\leq \\displaystyle \\sum _ { t \\in I } \\left[ \\left( \\hat { Q } _ { t } - Q ^ { * } \\right) ( s _ { t } , a _ { t } ) \\right] } \\\\ & { \\qquad \\leq \\displaystyle \\frac { | I | \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\frac { 1 } { ( 1 - \\gamma ) ^ { 5 / 2 } } \\sqrt { S A | I | \\ell | ( I | ) } + \\frac { S A } { ( 1 - \\gamma ) ^ { 3 } } \\ln | I | \\ln \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\right) } \\\\ & { \\qquad \\leq \\displaystyle \\frac { | I | \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\ln \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\cdot \\left( \\frac { \\sqrt { S A | I | \\ln \\frac { S A | I | } { \\delta } } } { ( 1 - \\gamma ) ^ { 5 / 2 } } + \\frac { S A \\ln | I | } { ( 1 - \\gamma ) ^ { 3 } } \\right) \\right) } \\\\ & { \\qquad \\leq \\displaystyle \\frac { | I | \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\sqrt { \\ln \\frac { 1 } { \\delta } } \\ln \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\cdot \\left( \\frac { \\sqrt { S A | I | \\ln S A | I | } } { ( 1 - \\gamma ) ^ { 5 / 2 } } + \\frac { S A \\ln | I | } { ( 1 - \\gamma ) ^ { 3 } } \\right) \\right) } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "c3600e24303e29ac9ff643f0f4892a82d147d38d65c5111e6d8ac103703617e6.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 24,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                138,
+                                457,
+                                472,
+                                502.0
+                            ],
+                            "spans": [],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                138,
+                                502.0,
+                                472,
+                                547.0
+                            ],
+                            "spans": [],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                138,
+                                547.0,
+                                472,
+                                592.0
+                            ],
+                            "spans": [],
+                            "index": 25
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        617,
+                        487,
+                        634
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                616,
+                                488,
+                                635
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        616,
+                                        160,
+                                        635
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Suppose that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        160,
+                                        617,
+                                        247,
+                                        634
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { r } { | I | = \\frac { S A k ^ { 2 } } { \\eta ^ { 2 } ( 1 - \\gamma ) ^ { 3 } } \\ln S A } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        247,
+                                        616,
+                                        288,
+                                        635
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", for some",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        288,
+                                        619,
+                                        313,
+                                        630
+                                    ],
+                                    "score": 0.9,
+                                    "content": "k > 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        313,
+                                        616,
+                                        471,
+                                        635
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Then it follows that for some constant",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        472,
+                                        620,
+                                        484,
+                                        631
+                                    ],
+                                    "score": 0.88,
+                                    "content": "C _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        484,
+                                        616,
+                                        488,
+                                        635
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 26
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        128,
+                        639,
+                        483,
+                        733
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                128,
+                                639,
+                                483,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        639,
+                                        483,
+                                        733
+                                    ],
+                                    "score": 0.95,
+                                    "content": "\\begin{array} { r l } & { \\frac { \\eta | I | } { 1 - \\gamma } = \\cfrac { k ^ { 2 } S A \\ln S A } { ( 1 - \\gamma ) ^ { 4 } \\eta } \\leq 2 \\cfrac { ( \\eta - \\epsilon _ { 1 } ) | I | } { 1 - \\gamma } } \\\\ & { \\qquad \\leq C _ { 1 } \\sqrt { \\ln \\frac { 1 } { \\delta } } \\ln \\cfrac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\left( \\cfrac { \\sqrt { S A | I | \\ln \\left( S A | I | \\right) } } { ( 1 - \\gamma ) ^ { 5 / 2 } } + \\cfrac { S A \\ln | I | } { ( 1 - \\gamma ) ^ { 3 } } \\right) } \\\\ & { \\qquad \\leq C _ { 1 } \\sqrt { \\ln \\frac { 1 } { \\delta } } \\ln \\cfrac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\left( \\cfrac { S A k } { \\eta ( 1 - \\gamma ) ^ { 4 } } \\sqrt { \\ln S A \\cdot ( \\ln S A + \\ln | I | ) } + \\cfrac { S A \\ln | I | } { ( 1 - \\gamma ) ^ { 3 } } \\right) . } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "c06bd9e11a4120e53c0b8d2cd822906d72211ae50589d30086bcbaef0151ca3a.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 28,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                128,
+                                639,
+                                483,
+                                670.3333333333334
+                            ],
+                            "spans": [],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                670.3333333333334,
+                                483,
+                                701.6666666666667
+                            ],
+                            "spans": [],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                701.6666666666667,
+                                483,
+                                733.0000000000001
+                            ],
+                            "spans": [],
+                            "index": 29
+                        }
+                    ]
+                }
+            ],
+            "page_idx": 9,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        294,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                294,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        294,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        311,
+                        761
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                312,
+                                764
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        312,
+                                        764
+                                    ],
+                                    "score": 1.0,
+                                    "content": "10",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        82,
+                        504,
+                        116
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                81,
+                                506,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        81,
+                                        506,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Aaron Sidford, Mengdi Wang, Xian Wu, Lin Yang, and Yinyu Ye. Near-optimal time and sample",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                95,
+                                505,
+                                105
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        95,
+                                        505,
+                                        105
+                                    ],
+                                    "score": 1.0,
+                                    "content": "complexities for solving markov decision processes with a generative model. In Advances in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                103,
+                                374,
+                                118
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        103,
+                                        374,
+                                        118
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Neural Information Processing Systems, pp. 5186–5196, 2018a.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1,
+                    "bbox_fs": [
+                        106,
+                        81,
+                        506,
+                        118
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        123,
+                        505,
+                        168
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                124,
+                                505,
+                                136
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        124,
+                                        505,
+                                        136
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Aaron Sidford, Mengdi Wang, Xian Wu, and Yinyu Ye. Variance reduced value iteration and faster",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                134,
+                                505,
+                                146
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        134,
+                                        505,
+                                        146
+                                    ],
+                                    "score": 1.0,
+                                    "content": "algorithms for solving markov decision processes. In Proceedings of the Twenty-Ninth Annual",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                145,
+                                505,
+                                159
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        145,
+                                        505,
+                                        159
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ACM-SIAM Symposium on Discrete Algorithms, pp. 770–787. Society for Industrial and Applied",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                156,
+                                202,
+                                168
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        156,
+                                        202,
+                                        168
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Mathematics, 2018b.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 4.5,
+                    "bbox_fs": [
+                        106,
+                        124,
+                        505,
+                        168
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        174,
+                        503,
+                        198
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                176,
+                                505,
+                                187
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        176,
+                                        505,
+                                        187
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Alexander L Strehl and Michael L Littman. An analysis of model-based interval estimation for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                186,
+                                501,
+                                198
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        186,
+                                        501,
+                                        198
+                                    ],
+                                    "score": 1.0,
+                                    "content": "markov decision processes. Journal of Computer and System Sciences, 74(8):1309–1331, 2008.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 7.5,
+                    "bbox_fs": [
+                        107,
+                        176,
+                        505,
+                        198
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        204,
+                        506,
+                        239
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                205,
+                                506,
+                                217
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        205,
+                                        506,
+                                        217
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Alexander L Strehl, Lihong Li, Eric Wiewiora, John Langford, and Michael L Littman. Pac model-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                217,
+                                505,
+                                229
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        217,
+                                        505,
+                                        229
+                                    ],
+                                    "score": 1.0,
+                                    "content": "free reinforcement learning. In Proceedings of the 23rd international conference on Machine",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                227,
+                                262,
+                                239
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        227,
+                                        262,
+                                        239
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning, pp. 881–888. ACM, 2006.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 10,
+                    "bbox_fs": [
+                        106,
+                        205,
+                        506,
+                        239
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        245,
+                        505,
+                        280
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                246,
+                                504,
+                                258
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        246,
+                                        504,
+                                        258
+                                    ],
+                                    "score": 1.0,
+                                    "content": "István Szita and Csaba Szepesvári. Model-based reinforcement learning with nearly tight exploration",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                256,
+                                505,
+                                271
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        256,
+                                        505,
+                                        271
+                                    ],
+                                    "score": 1.0,
+                                    "content": "complexity bounds. In Proceedings of the 27th International Conference on Machine Learning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                268,
+                                254,
+                                281
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        268,
+                                        254,
+                                        281
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(ICML-10), pp. 1031–1038, 2010.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 13,
+                    "bbox_fs": [
+                        106,
+                        246,
+                        505,
+                        281
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        300,
+                        232,
+                        313
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                299,
+                                233,
+                                315
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        299,
+                                        233,
+                                        315
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A PROOF OF LEMMA 1",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        323,
+                        505,
+                        351
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                321,
+                                507,
+                                342
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        321,
+                                        215,
+                                        342
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lemma 1. For fixed t and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        215,
+                                        326,
+                                        240,
+                                        338
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\eta > 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        240,
+                                        321,
+                                        255,
+                                        342
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        256,
+                                        323,
+                                        275,
+                                        338
+                                    ],
+                                    "score": 0.92,
+                                    "content": "B _ { \\eta } ^ { ( t ) }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        275,
+                                        321,
+                                        344,
+                                        342
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be the event that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        344,
+                                        325,
+                                        457,
+                                        340
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { r } { V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > \\frac { \\eta } { 1 - \\gamma } } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        458,
+                                        321,
+                                        507,
+                                        342
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in step t. If",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                338,
+                                297,
+                                353
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        339,
+                                        139,
+                                        351
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\eta > 2 \\epsilon _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        140,
+                                        338,
+                                        261,
+                                        353
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", then with probability at least",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        261,
+                                        339,
+                                        294,
+                                        351
+                                    ],
+                                    "score": 0.9,
+                                    "content": "1 - \\delta / 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        294,
+                                        338,
+                                        297,
+                                        353
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 16.5,
+                    "bbox_fs": [
+                        104,
+                        321,
+                        507,
+                        353
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        186,
+                        356,
+                        423,
+                        390
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                186,
+                                356,
+                                423,
+                                390
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        186,
+                                        356,
+                                        423,
+                                        390
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\sum _ { t = 1 } ^ { t = \\infty } I \\left[ B _ { \\eta } ^ { ( t ) } \\right] \\leq \\frac { S A \\ln S A \\ln 1 / \\delta } { \\eta ^ { 2 } ( 1 - \\gamma ) ^ { 3 } } \\cdot p o l y l o g \\left( \\frac { 1 } { \\epsilon _ { 1 } } , \\frac { 1 } { 1 - \\gamma } \\right) ,",
+                                    "type": "interline_equation",
+                                    "image_path": "0b9f09a826319782774c08f51f81a7e3a19a570518937c623163e273091ef961.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                186,
+                                356,
+                                423,
+                                373.0
+                            ],
+                            "spans": [],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                186,
+                                373.0,
+                                423,
+                                390.0
+                            ],
+                            "spans": [],
+                            "index": 19
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        395,
+                        248,
+                        407
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                395,
+                                249,
+                                408
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        395,
+                                        133,
+                                        408
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        133,
+                                        395,
+                                        147,
+                                        407
+                                    ],
+                                    "score": 0.87,
+                                    "content": "I [ \\cdot ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        148,
+                                        395,
+                                        249,
+                                        408
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the indicator function.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 20,
+                    "bbox_fs": [
+                        106,
+                        395,
+                        249,
+                        408
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        418,
+                        431,
+                        432
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                418,
+                                432,
+                                433
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        418,
+                                        162,
+                                        433
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Proof. When",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        163,
+                                        420,
+                                        187,
+                                        431
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\eta > 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        188,
+                                        418,
+                                        403,
+                                        433
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the lemma holds trivially. Now consider the case that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        403,
+                                        420,
+                                        428,
+                                        431
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\eta \\leq 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        428,
+                                        418,
+                                        432,
+                                        433
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 21,
+                    "bbox_fs": [
+                        105,
+                        418,
+                        432,
+                        433
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        435,
+                        430,
+                        450
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                433,
+                                427,
+                                452
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        433,
+                                        122,
+                                        452
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        122,
+                                        435,
+                                        279,
+                                        451
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\begin{array} { r } { I = \\{ t \\colon V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > \\frac { \\eta } { 1 - \\gamma } \\} } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        280,
+                                        433,
+                                        404,
+                                        452
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". By lemma 2, with probability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        404,
+                                        437,
+                                        427,
+                                        447
+                                    ],
+                                    "score": 0.84,
+                                    "content": "1 - \\delta",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 22,
+                    "bbox_fs": [
+                        105,
+                        433,
+                        427,
+                        452
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        138,
+                        457,
+                        472,
+                        592
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                138,
+                                457,
+                                472,
+                                592
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        138,
+                                        457,
+                                        472,
+                                        592
+                                    ],
+                                    "score": 0.95,
+                                    "content": "\\begin{array} { r l } & { \\frac { \\eta | I | } { 1 - \\gamma } \\leq \\displaystyle \\sum _ { t \\in I } \\left( V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) \\right) \\leq \\displaystyle \\sum _ { t \\in I } \\left[ \\left( \\hat { Q } _ { t } - Q ^ { * } \\right) ( s _ { t } , a _ { t } ) \\right] } \\\\ & { \\qquad \\leq \\displaystyle \\frac { | I | \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\frac { 1 } { ( 1 - \\gamma ) ^ { 5 / 2 } } \\sqrt { S A | I | \\ell | ( I | ) } + \\frac { S A } { ( 1 - \\gamma ) ^ { 3 } } \\ln | I | \\ln \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\right) } \\\\ & { \\qquad \\leq \\displaystyle \\frac { | I | \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\ln \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\cdot \\left( \\frac { \\sqrt { S A | I | \\ln \\frac { S A | I | } { \\delta } } } { ( 1 - \\gamma ) ^ { 5 / 2 } } + \\frac { S A \\ln | I | } { ( 1 - \\gamma ) ^ { 3 } } \\right) \\right) } \\\\ & { \\qquad \\leq \\displaystyle \\frac { | I | \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\sqrt { \\ln \\frac { 1 } { \\delta } } \\ln \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\cdot \\left( \\frac { \\sqrt { S A | I | \\ln S A | I | } } { ( 1 - \\gamma ) ^ { 5 / 2 } } + \\frac { S A \\ln | I | } { ( 1 - \\gamma ) ^ { 3 } } \\right) \\right) } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "c3600e24303e29ac9ff643f0f4892a82d147d38d65c5111e6d8ac103703617e6.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 24,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                138,
+                                457,
+                                472,
+                                502.0
+                            ],
+                            "spans": [],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                138,
+                                502.0,
+                                472,
+                                547.0
+                            ],
+                            "spans": [],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                138,
+                                547.0,
+                                472,
+                                592.0
+                            ],
+                            "spans": [],
+                            "index": 25
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        617,
+                        487,
+                        634
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                616,
+                                488,
+                                635
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        616,
+                                        160,
+                                        635
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Suppose that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        160,
+                                        617,
+                                        247,
+                                        634
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { r } { | I | = \\frac { S A k ^ { 2 } } { \\eta ^ { 2 } ( 1 - \\gamma ) ^ { 3 } } \\ln S A } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        247,
+                                        616,
+                                        288,
+                                        635
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", for some",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        288,
+                                        619,
+                                        313,
+                                        630
+                                    ],
+                                    "score": 0.9,
+                                    "content": "k > 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        313,
+                                        616,
+                                        471,
+                                        635
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Then it follows that for some constant",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        472,
+                                        620,
+                                        484,
+                                        631
+                                    ],
+                                    "score": 0.88,
+                                    "content": "C _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        484,
+                                        616,
+                                        488,
+                                        635
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 26,
+                    "bbox_fs": [
+                        106,
+                        616,
+                        488,
+                        635
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        128,
+                        639,
+                        483,
+                        733
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                128,
+                                639,
+                                483,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        639,
+                                        483,
+                                        733
+                                    ],
+                                    "score": 0.95,
+                                    "content": "\\begin{array} { r l } & { \\frac { \\eta | I | } { 1 - \\gamma } = \\cfrac { k ^ { 2 } S A \\ln S A } { ( 1 - \\gamma ) ^ { 4 } \\eta } \\leq 2 \\cfrac { ( \\eta - \\epsilon _ { 1 } ) | I | } { 1 - \\gamma } } \\\\ & { \\qquad \\leq C _ { 1 } \\sqrt { \\ln \\frac { 1 } { \\delta } } \\ln \\cfrac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\left( \\cfrac { \\sqrt { S A | I | \\ln \\left( S A | I | \\right) } } { ( 1 - \\gamma ) ^ { 5 / 2 } } + \\cfrac { S A \\ln | I | } { ( 1 - \\gamma ) ^ { 3 } } \\right) } \\\\ & { \\qquad \\leq C _ { 1 } \\sqrt { \\ln \\frac { 1 } { \\delta } } \\ln \\cfrac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\left( \\cfrac { S A k } { \\eta ( 1 - \\gamma ) ^ { 4 } } \\sqrt { \\ln S A \\cdot ( \\ln S A + \\ln | I | ) } + \\cfrac { S A \\ln | I | } { ( 1 - \\gamma ) ^ { 3 } } \\right) . } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "c06bd9e11a4120e53c0b8d2cd822906d72211ae50589d30086bcbaef0151ca3a.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 28,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                128,
+                                639,
+                                483,
+                                670.3333333333334
+                            ],
+                            "spans": [],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                670.3333333333334,
+                                483,
+                                701.6666666666667
+                            ],
+                            "spans": [],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                701.6666666666667,
+                                483,
+                                733.0000000000001
+                            ],
+                            "spans": [],
+                            "index": 29
+                        }
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        82,
+                        147,
+                        94
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                82,
+                                148,
+                                94
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        82,
+                                        148,
+                                        94
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Therefore",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        150,
+                        97,
+                        461,
+                        217
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                150,
+                                97,
+                                461,
+                                217
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        150,
+                                        97,
+                                        461,
+                                        217
+                                    ],
+                                    "score": 0.95,
+                                    "content": "\\begin{array} { r l } & { k ^ { 2 } \\ln ( S A ) \\le C _ { 1 } \\sqrt { \\ln \\displaystyle \\frac { 1 } { \\delta } } \\ln \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\left( k \\left( \\ln S A + \\ln | I | \\right) + \\eta ( 1 - \\gamma ) \\ln | I | \\right) } \\\\ & { \\qquad \\le k C _ { 1 } \\sqrt { \\ln \\displaystyle \\frac { 1 } { \\delta } } \\ln \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\cdot \\left( \\ln S A + 2 \\ln | I | \\right) } \\\\ & { \\qquad \\le k C _ { 1 } \\sqrt { \\ln \\displaystyle \\frac { 1 } { \\delta } } \\ln \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\cdot \\left( 3 \\ln S A + 4 \\ln k + 6 \\ln \\frac { 1 } { \\eta ( 1 - \\gamma ) } \\right) } \\\\ & { \\qquad \\le 6 k C _ { 1 } \\sqrt { \\ln \\displaystyle \\frac { 1 } { \\delta } } \\ln ^ { 2 } \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\left( \\ln S A + \\ln \\epsilon k \\right) . } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "bae465b19e019059a91e97016934af5f7bf0c47e9357a7ca6741dfa6dd715015.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                150,
+                                97,
+                                461,
+                                137.0
+                            ],
+                            "spans": [],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                150,
+                                137.0,
+                                461,
+                                177.0
+                            ],
+                            "spans": [],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                150,
+                                177.0,
+                                461,
+                                217.0
+                            ],
+                            "spans": [],
+                            "index": 3
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        222,
+                        303,
+                        241
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                100,
+                                220,
+                                307,
+                                246
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        100,
+                                        220,
+                                        122,
+                                        246
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        123,
+                                        222,
+                                        275,
+                                        243
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { r } { C ^ { \\prime } = \\operatorname* { m a x } \\lbrace 2 , 6 C _ { 1 } \\sqrt { \\ln \\frac { 1 } { \\delta } } \\ln ^ { 2 } \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\rbrace } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        275,
+                                        220,
+                                        307,
+                                        246
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Then",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        268,
+                        246,
+                        343,
+                        262
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                268,
+                                246,
+                                343,
+                                262
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        268,
+                                        246,
+                                        343,
+                                        262
+                                    ],
+                                    "score": 0.89,
+                                    "content": "k \\leq C ^ { \\prime } ( 2 + \\ln k ) .",
+                                    "type": "interline_equation",
+                                    "image_path": "6648dce62ed22bd5032b6259b54c85d35efee676cf37255340a1199f339eda3d.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                268,
+                                246,
+                                343,
+                                262
+                            ],
+                            "spans": [],
+                            "index": 5
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        266,
+                        201,
+                        278
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                265,
+                                202,
+                                280
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        265,
+                                        116,
+                                        280
+                                    ],
+                                    "score": 1.0,
+                                    "content": "If",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        116,
+                                        267,
+                                        178,
+                                        278
+                                    ],
+                                    "score": 0.91,
+                                    "content": "k \\geq 1 0 C ^ { \\prime } \\ln C ^ { \\prime }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        178,
+                                        265,
+                                        202,
+                                        280
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", then",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        209,
+                        282,
+                        401,
+                        315
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                209,
+                                282,
+                                401,
+                                315
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        209,
+                                        282,
+                                        401,
+                                        315
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\begin{array} { c } { k - C ^ { \\prime } \\left( 2 + \\ln k \\right) \\geq 8 C ^ { \\prime } \\ln C ^ { \\prime } - ( 2 + \\ln 1 0 ) C ^ { \\prime } } \\\\ { \\geq 4 C ^ { \\prime } \\left( 2 \\ln C ^ { \\prime } - 4 \\right) \\geq 0 , } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "4ae996b10596e3c7079276b4b960d96f44d70fb21ef5f209a0ea7326b6d16c83.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                209,
+                                282,
+                                401,
+                                298.5
+                            ],
+                            "spans": [],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                209,
+                                298.5,
+                                401,
+                                315.0
+                            ],
+                            "spans": [],
+                            "index": 8
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        318,
+                        326,
+                        330
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                317,
+                                325,
+                                332
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        317,
+                                        294,
+                                        332
+                                    ],
+                                    "score": 1.0,
+                                    "content": "which means violation of (9). Therefore, since",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        294,
+                                        318,
+                                        325,
+                                        330
+                                    ],
+                                    "score": 0.91,
+                                    "content": "C ^ { \\prime } \\geq 2",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        193,
+                        334,
+                        417,
+                        361
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                193,
+                                334,
+                                417,
+                                361
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        193,
+                                        334,
+                                        417,
+                                        361
+                                    ],
+                                    "score": 0.9,
+                                    "content": "k \\leq 1 0 C ^ { \\prime } \\ln C ^ { \\prime } \\leq 3 6 0 C _ { 1 } ^ { 2 } \\operatorname* { m a x } \\{ \\ln ^ { 4 } { \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } } , 2 0 \\ln 2 \\} .",
+                                    "type": "interline_equation",
+                                    "image_path": "3659eb39bbdbcc0c60a416911c59460e57107ec3dbd0e6f62d3b7b93a525422e.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                193,
+                                334,
+                                417,
+                                361
+                            ],
+                            "spans": [],
+                            "index": 10
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        366,
+                        217,
+                        377
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                364,
+                                217,
+                                379
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        364,
+                                        217,
+                                        379
+                                    ],
+                                    "score": 1.0,
+                                    "content": "It immediately follows that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        210,
+                        382,
+                        401,
+                        440
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                210,
+                                382,
+                                401,
+                                440
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        210,
+                                        382,
+                                        401,
+                                        440
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { r l r } {  { \\vert I \\vert = \\frac { S A k ^ { 2 } } { \\eta ^ { 2 } ( 1 - \\gamma ) ^ { 3 } } \\ln S A } } \\\\ & { \\leq \\frac { S A \\ln S A } { \\eta ^ { 2 } ( 1 - \\gamma ) ^ { 5 } } \\cdot \\ln \\frac { 1 } { \\delta } \\cdot \\mathcal { O } ( \\ln ^ { 8 } \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } ) . } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "ad528682451c2a80d59b5c6f1508b5b7b9f26c92e6092f8aeb71c929441cec39.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                210,
+                                382,
+                                401,
+                                401.3333333333333
+                            ],
+                            "spans": [],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                210,
+                                401.3333333333333,
+                                401,
+                                420.66666666666663
+                            ],
+                            "spans": [],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                210,
+                                420.66666666666663,
+                                401,
+                                439.99999999999994
+                            ],
+                            "spans": [],
+                            "index": 14
+                        }
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        477,
+                        233,
+                        490
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                476,
+                                233,
+                                492
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        476,
+                                        233,
+                                        492
+                                    ],
+                                    "score": 1.0,
+                                    "content": "B PROOF OF LEMMA 2",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        103,
+                        501,
+                        484,
+                        515
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                501,
+                                486,
+                                516
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        501,
+                                        195,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lemma 2. For every",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        195,
+                                        502,
+                                        222,
+                                        514
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( C , w )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        223,
+                                        501,
+                                        264,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-sequence",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        264,
+                                        502,
+                                        297,
+                                        515
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( w _ { t } ) _ { t \\geq 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        297,
+                                        501,
+                                        366,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", with probability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        367,
+                                        502,
+                                        399,
+                                        514
+                                    ],
+                                    "score": 0.89,
+                                    "content": "1 - \\delta / 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        400,
+                                        501,
+                                        486,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the following holds:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        128,
+                        534,
+                        482,
+                        568
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                128,
+                                534,
+                                482,
+                                568
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        534,
+                                        482,
+                                        568
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\sum _ { t \\ge 1 } w _ { t } ( \\hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) \\le \\frac { C \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\frac { \\sqrt { w S A C \\ell ( C ) } } { ( 1 - \\gamma ) ^ { 2 . 5 } } + \\frac { w S A \\ln C } { ( 1 - \\gamma ) ^ { 3 } } \\ln \\frac { 1 } { ( 1 - \\gamma ) \\epsilon _ { 1 } } \\right) .",
+                                    "type": "interline_equation",
+                                    "image_path": "ff487b4def18b98c770f155f72c7d52760fabc4d6097e5e050552ffa5fb8baab.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                128,
+                                534,
+                                482,
+                                545.3333333333334
+                            ],
+                            "spans": [],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                545.3333333333334,
+                                482,
+                                556.6666666666667
+                            ],
+                            "spans": [],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                556.6666666666667,
+                                482,
+                                568.0000000000001
+                            ],
+                            "spans": [],
+                            "index": 19
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        580,
+                        289,
+                        596
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                102,
+                                577,
+                                294,
+                                601
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        102,
+                                        577,
+                                        133,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        133,
+                                        580,
+                                        228,
+                                        596
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\begin{array} { r } { \\ell ( C ) = \\iota ( C ) \\ln { \\frac { 1 } { ( 1 - \\gamma ) \\epsilon _ { 1 } } } } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        229,
+                                        577,
+                                        294,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is a log-factor.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 20
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        598,
+                        381,
+                        610
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                597,
+                                381,
+                                613
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        597,
+                                        381,
+                                        613
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Fact 1. (1) The following statement holds throughout the algorithm,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 21
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        251,
+                        615,
+                        359,
+                        632
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                251,
+                                615,
+                                359,
+                                632
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        251,
+                                        615,
+                                        359,
+                                        632
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\hat { Q } _ { p + 1 } ( s , a ) \\leq Q _ { p + 1 } ( s , a ) .",
+                                    "type": "interline_equation",
+                                    "image_path": "33f263fc3dd14df50727d4ef76ef6c4ffe1d222ffa11393ce94b14974de75afd.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 22,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                251,
+                                615,
+                                359,
+                                632
+                            ],
+                            "spans": [],
+                            "index": 22
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        636,
+                        277,
+                        648
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                635,
+                                278,
+                                649
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        635,
+                                        153,
+                                        649
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(2) For any",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        639,
+                                        159,
+                                        648
+                                    ],
+                                    "score": 0.54,
+                                    "content": "p",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        160,
+                                        635,
+                                        210,
+                                        649
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", there exists",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        210,
+                                        636,
+                                        238,
+                                        648
+                                    ],
+                                    "score": 0.92,
+                                    "content": "p ^ { \\prime } \\leq p",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        238,
+                                        635,
+                                        278,
+                                        649
+                                    ],
+                                    "score": 1.0,
+                                    "content": "such that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 23
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        250,
+                        653,
+                        360,
+                        669
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                250,
+                                653,
+                                360,
+                                669
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        250,
+                                        653,
+                                        360,
+                                        669
+                                    ],
+                                    "score": 0.91,
+                                    "content": "{ \\hat { Q } } _ { p + 1 } ( s , a ) \\geq Q _ { p ^ { \\prime } + 1 } ( s , a ) .",
+                                    "type": "interline_equation",
+                                    "image_path": "6fac3e0bba44afb720a787e2593dcafd19d5e03a7a0d6878331dbb6aecc146fa.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 24,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                250,
+                                653,
+                                360,
+                                669
+                            ],
+                            "spans": [],
+                            "index": 24
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        680,
+                        420,
+                        693
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                680,
+                                420,
+                                694
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        680,
+                                        420,
+                                        694
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Proof. Both properties are results of the update rule at line 11 of Algorithm 1.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        705,
+                        357,
+                        718
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                704,
+                                357,
+                                720
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        704,
+                                        357,
+                                        720
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Before proving lemma 2, we will prove two auxiliary lemmas.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 26
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        720,
+                        305,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                719,
+                                307,
+                                735
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        719,
+                                        289,
+                                        735
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lemma 3. The following properties hold for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        720,
+                                        300,
+                                        732
+                                    ],
+                                    "score": 0.86,
+                                    "content": "\\alpha _ { t } ^ { i }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        300,
+                                        719,
+                                        307,
+                                        735
+                                    ],
+                                    "score": 1.0,
+                                    "content": ":",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 27
+                }
+            ],
+            "page_idx": 10,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        106,
+                        26,
+                        294,
+                        38
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                25,
+                                294,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        25,
+                                        294,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        310,
+                        761
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                312,
+                                764
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        312,
+                                        764
+                                    ],
+                                    "score": 1.0,
+                                    "content": "11",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        494,
+                        681,
+                        505,
+                        692
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                496,
+                                683,
+                                504,
+                                691
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        496,
+                                        683,
+                                        504,
+                                        691
+                                    ],
+                                    "score": 0.997,
+                                    "content": "□",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        494,
+                        449,
+                        505,
+                        460
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                496,
+                                451,
+                                505,
+                                461
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        496,
+                                        451,
+                                        505,
+                                        461
+                                    ],
+                                    "score": 1.0,
+                                    "content": "□",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        82,
+                        147,
+                        94
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                82,
+                                148,
+                                94
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        82,
+                                        148,
+                                        94
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Therefore",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        }
+                    ],
+                    "index": 0,
+                    "bbox_fs": [
+                        106,
+                        82,
+                        148,
+                        94
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        150,
+                        97,
+                        461,
+                        217
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                150,
+                                97,
+                                461,
+                                217
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        150,
+                                        97,
+                                        461,
+                                        217
+                                    ],
+                                    "score": 0.95,
+                                    "content": "\\begin{array} { r l } & { k ^ { 2 } \\ln ( S A ) \\le C _ { 1 } \\sqrt { \\ln \\displaystyle \\frac { 1 } { \\delta } } \\ln \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\left( k \\left( \\ln S A + \\ln | I | \\right) + \\eta ( 1 - \\gamma ) \\ln | I | \\right) } \\\\ & { \\qquad \\le k C _ { 1 } \\sqrt { \\ln \\displaystyle \\frac { 1 } { \\delta } } \\ln \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\cdot \\left( \\ln S A + 2 \\ln | I | \\right) } \\\\ & { \\qquad \\le k C _ { 1 } \\sqrt { \\ln \\displaystyle \\frac { 1 } { \\delta } } \\ln \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\cdot \\left( 3 \\ln S A + 4 \\ln k + 6 \\ln \\frac { 1 } { \\eta ( 1 - \\gamma ) } \\right) } \\\\ & { \\qquad \\le 6 k C _ { 1 } \\sqrt { \\ln \\displaystyle \\frac { 1 } { \\delta } } \\ln ^ { 2 } \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\left( \\ln S A + \\ln \\epsilon k \\right) . } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "bae465b19e019059a91e97016934af5f7bf0c47e9357a7ca6741dfa6dd715015.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                150,
+                                97,
+                                461,
+                                137.0
+                            ],
+                            "spans": [],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                150,
+                                137.0,
+                                461,
+                                177.0
+                            ],
+                            "spans": [],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                150,
+                                177.0,
+                                461,
+                                217.0
+                            ],
+                            "spans": [],
+                            "index": 3
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        222,
+                        303,
+                        241
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                100,
+                                220,
+                                307,
+                                246
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        100,
+                                        220,
+                                        122,
+                                        246
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        123,
+                                        222,
+                                        275,
+                                        243
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { r } { C ^ { \\prime } = \\operatorname* { m a x } \\lbrace 2 , 6 C _ { 1 } \\sqrt { \\ln \\frac { 1 } { \\delta } } \\ln ^ { 2 } \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\rbrace } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        275,
+                                        220,
+                                        307,
+                                        246
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Then",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 4,
+                    "bbox_fs": [
+                        100,
+                        220,
+                        307,
+                        246
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        268,
+                        246,
+                        343,
+                        262
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                268,
+                                246,
+                                343,
+                                262
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        268,
+                                        246,
+                                        343,
+                                        262
+                                    ],
+                                    "score": 0.89,
+                                    "content": "k \\leq C ^ { \\prime } ( 2 + \\ln k ) .",
+                                    "type": "interline_equation",
+                                    "image_path": "6648dce62ed22bd5032b6259b54c85d35efee676cf37255340a1199f339eda3d.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                268,
+                                246,
+                                343,
+                                262
+                            ],
+                            "spans": [],
+                            "index": 5
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        266,
+                        201,
+                        278
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                265,
+                                202,
+                                280
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        265,
+                                        116,
+                                        280
+                                    ],
+                                    "score": 1.0,
+                                    "content": "If",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        116,
+                                        267,
+                                        178,
+                                        278
+                                    ],
+                                    "score": 0.91,
+                                    "content": "k \\geq 1 0 C ^ { \\prime } \\ln C ^ { \\prime }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        178,
+                                        265,
+                                        202,
+                                        280
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", then",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 6,
+                    "bbox_fs": [
+                        105,
+                        265,
+                        202,
+                        280
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        209,
+                        282,
+                        401,
+                        315
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                209,
+                                282,
+                                401,
+                                315
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        209,
+                                        282,
+                                        401,
+                                        315
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\begin{array} { c } { k - C ^ { \\prime } \\left( 2 + \\ln k \\right) \\geq 8 C ^ { \\prime } \\ln C ^ { \\prime } - ( 2 + \\ln 1 0 ) C ^ { \\prime } } \\\\ { \\geq 4 C ^ { \\prime } \\left( 2 \\ln C ^ { \\prime } - 4 \\right) \\geq 0 , } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "4ae996b10596e3c7079276b4b960d96f44d70fb21ef5f209a0ea7326b6d16c83.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                209,
+                                282,
+                                401,
+                                298.5
+                            ],
+                            "spans": [],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                209,
+                                298.5,
+                                401,
+                                315.0
+                            ],
+                            "spans": [],
+                            "index": 8
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        318,
+                        326,
+                        330
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                317,
+                                325,
+                                332
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        317,
+                                        294,
+                                        332
+                                    ],
+                                    "score": 1.0,
+                                    "content": "which means violation of (9). Therefore, since",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        294,
+                                        318,
+                                        325,
+                                        330
+                                    ],
+                                    "score": 0.91,
+                                    "content": "C ^ { \\prime } \\geq 2",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 9,
+                    "bbox_fs": [
+                        105,
+                        317,
+                        325,
+                        332
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        193,
+                        334,
+                        417,
+                        361
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                193,
+                                334,
+                                417,
+                                361
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        193,
+                                        334,
+                                        417,
+                                        361
+                                    ],
+                                    "score": 0.9,
+                                    "content": "k \\leq 1 0 C ^ { \\prime } \\ln C ^ { \\prime } \\leq 3 6 0 C _ { 1 } ^ { 2 } \\operatorname* { m a x } \\{ \\ln ^ { 4 } { \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } } , 2 0 \\ln 2 \\} .",
+                                    "type": "interline_equation",
+                                    "image_path": "3659eb39bbdbcc0c60a416911c59460e57107ec3dbd0e6f62d3b7b93a525422e.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                193,
+                                334,
+                                417,
+                                361
+                            ],
+                            "spans": [],
+                            "index": 10
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        366,
+                        217,
+                        377
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                364,
+                                217,
+                                379
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        364,
+                                        217,
+                                        379
+                                    ],
+                                    "score": 1.0,
+                                    "content": "It immediately follows that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 11,
+                    "bbox_fs": [
+                        105,
+                        364,
+                        217,
+                        379
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        210,
+                        382,
+                        401,
+                        440
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                210,
+                                382,
+                                401,
+                                440
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        210,
+                                        382,
+                                        401,
+                                        440
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { r l r } {  { \\vert I \\vert = \\frac { S A k ^ { 2 } } { \\eta ^ { 2 } ( 1 - \\gamma ) ^ { 3 } } \\ln S A } } \\\\ & { \\leq \\frac { S A \\ln S A } { \\eta ^ { 2 } ( 1 - \\gamma ) ^ { 5 } } \\cdot \\ln \\frac { 1 } { \\delta } \\cdot \\mathcal { O } ( \\ln ^ { 8 } \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } ) . } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "ad528682451c2a80d59b5c6f1508b5b7b9f26c92e6092f8aeb71c929441cec39.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                210,
+                                382,
+                                401,
+                                401.3333333333333
+                            ],
+                            "spans": [],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                210,
+                                401.3333333333333,
+                                401,
+                                420.66666666666663
+                            ],
+                            "spans": [],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                210,
+                                420.66666666666663,
+                                401,
+                                439.99999999999994
+                            ],
+                            "spans": [],
+                            "index": 14
+                        }
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        477,
+                        233,
+                        490
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                476,
+                                233,
+                                492
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        476,
+                                        233,
+                                        492
+                                    ],
+                                    "score": 1.0,
+                                    "content": "B PROOF OF LEMMA 2",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        103,
+                        501,
+                        484,
+                        515
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                501,
+                                486,
+                                516
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        501,
+                                        195,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lemma 2. For every",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        195,
+                                        502,
+                                        222,
+                                        514
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( C , w )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        223,
+                                        501,
+                                        264,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-sequence",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        264,
+                                        502,
+                                        297,
+                                        515
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( w _ { t } ) _ { t \\geq 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        297,
+                                        501,
+                                        366,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", with probability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        367,
+                                        502,
+                                        399,
+                                        514
+                                    ],
+                                    "score": 0.89,
+                                    "content": "1 - \\delta / 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        400,
+                                        501,
+                                        486,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the following holds:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 16,
+                    "bbox_fs": [
+                        105,
+                        501,
+                        486,
+                        516
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        128,
+                        534,
+                        482,
+                        568
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                128,
+                                534,
+                                482,
+                                568
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        534,
+                                        482,
+                                        568
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\sum _ { t \\ge 1 } w _ { t } ( \\hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) \\le \\frac { C \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\frac { \\sqrt { w S A C \\ell ( C ) } } { ( 1 - \\gamma ) ^ { 2 . 5 } } + \\frac { w S A \\ln C } { ( 1 - \\gamma ) ^ { 3 } } \\ln \\frac { 1 } { ( 1 - \\gamma ) \\epsilon _ { 1 } } \\right) .",
+                                    "type": "interline_equation",
+                                    "image_path": "ff487b4def18b98c770f155f72c7d52760fabc4d6097e5e050552ffa5fb8baab.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                128,
+                                534,
+                                482,
+                                545.3333333333334
+                            ],
+                            "spans": [],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                545.3333333333334,
+                                482,
+                                556.6666666666667
+                            ],
+                            "spans": [],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                556.6666666666667,
+                                482,
+                                568.0000000000001
+                            ],
+                            "spans": [],
+                            "index": 19
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        580,
+                        289,
+                        596
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                102,
+                                577,
+                                294,
+                                601
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        102,
+                                        577,
+                                        133,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        133,
+                                        580,
+                                        228,
+                                        596
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\begin{array} { r } { \\ell ( C ) = \\iota ( C ) \\ln { \\frac { 1 } { ( 1 - \\gamma ) \\epsilon _ { 1 } } } } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        229,
+                                        577,
+                                        294,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is a log-factor.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 20,
+                    "bbox_fs": [
+                        102,
+                        577,
+                        294,
+                        601
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        598,
+                        381,
+                        610
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                597,
+                                381,
+                                613
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        597,
+                                        381,
+                                        613
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Fact 1. (1) The following statement holds throughout the algorithm,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 21,
+                    "bbox_fs": [
+                        105,
+                        597,
+                        381,
+                        613
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        251,
+                        615,
+                        359,
+                        632
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                251,
+                                615,
+                                359,
+                                632
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        251,
+                                        615,
+                                        359,
+                                        632
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\hat { Q } _ { p + 1 } ( s , a ) \\leq Q _ { p + 1 } ( s , a ) .",
+                                    "type": "interline_equation",
+                                    "image_path": "33f263fc3dd14df50727d4ef76ef6c4ffe1d222ffa11393ce94b14974de75afd.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 22,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                251,
+                                615,
+                                359,
+                                632
+                            ],
+                            "spans": [],
+                            "index": 22
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        636,
+                        277,
+                        648
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                635,
+                                278,
+                                649
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        635,
+                                        153,
+                                        649
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(2) For any",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        639,
+                                        159,
+                                        648
+                                    ],
+                                    "score": 0.54,
+                                    "content": "p",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        160,
+                                        635,
+                                        210,
+                                        649
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", there exists",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        210,
+                                        636,
+                                        238,
+                                        648
+                                    ],
+                                    "score": 0.92,
+                                    "content": "p ^ { \\prime } \\leq p",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        238,
+                                        635,
+                                        278,
+                                        649
+                                    ],
+                                    "score": 1.0,
+                                    "content": "such that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 23,
+                    "bbox_fs": [
+                        105,
+                        635,
+                        278,
+                        649
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        250,
+                        653,
+                        360,
+                        669
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                250,
+                                653,
+                                360,
+                                669
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        250,
+                                        653,
+                                        360,
+                                        669
+                                    ],
+                                    "score": 0.91,
+                                    "content": "{ \\hat { Q } } _ { p + 1 } ( s , a ) \\geq Q _ { p ^ { \\prime } + 1 } ( s , a ) .",
+                                    "type": "interline_equation",
+                                    "image_path": "6fac3e0bba44afb720a787e2593dcafd19d5e03a7a0d6878331dbb6aecc146fa.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 24,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                250,
+                                653,
+                                360,
+                                669
+                            ],
+                            "spans": [],
+                            "index": 24
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        680,
+                        420,
+                        693
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                680,
+                                420,
+                                694
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        680,
+                                        420,
+                                        694
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Proof. Both properties are results of the update rule at line 11 of Algorithm 1.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 25,
+                    "bbox_fs": [
+                        106,
+                        680,
+                        420,
+                        694
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        705,
+                        357,
+                        718
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                704,
+                                357,
+                                720
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        704,
+                                        357,
+                                        720
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Before proving lemma 2, we will prove two auxiliary lemmas.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 26,
+                    "bbox_fs": [
+                        105,
+                        704,
+                        357,
+                        720
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        720,
+                        305,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                719,
+                                307,
+                                735
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        719,
+                                        289,
+                                        735
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lemma 3. The following properties hold for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        720,
+                                        300,
+                                        732
+                                    ],
+                                    "score": 0.86,
+                                    "content": "\\alpha _ { t } ^ { i }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        300,
+                                        719,
+                                        307,
+                                        735
+                                    ],
+                                    "score": 1.0,
+                                    "content": ":",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 27,
+                    "bbox_fs": [
+                        106,
+                        719,
+                        307,
+                        735
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        129,
+                        79,
+                        353,
+                        101
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                127,
+                                78,
+                                356,
+                                102
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        78,
+                                        142,
+                                        102
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        142,
+                                        80,
+                                        259,
+                                        101
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\begin{array} { r } { \\sqrt { \\frac { 1 } { t } } \\leq \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\sqrt { \\frac { 1 } { i } } \\leq 2 \\sqrt { \\frac { 1 } { t } } } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        260,
+                                        78,
+                                        298,
+                                        102
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for every",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        299,
+                                        84,
+                                        349,
+                                        97
+                                    ],
+                                    "score": 0.58,
+                                    "content": "t \\geq 1 , c > 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        349,
+                                        78,
+                                        356,
+                                        102
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        129,
+                        106,
+                        374,
+                        123
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                126,
+                                104,
+                                372,
+                                125
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        104,
+                                        142,
+                                        125
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        142,
+                                        108,
+                                        216,
+                                        122
+                                    ],
+                                    "score": 0.84,
+                                    "content": "\\begin{array} { r } { \\operatorname* { m a x } _ { i \\in [ t ] } \\alpha _ { t } ^ { i } \\leq \\frac { 2 H } { t } } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        217,
+                                        104,
+                                        235,
+                                        125
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        236,
+                                        107,
+                                        309,
+                                        122
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\begin{array} { r } { \\sum _ { i = 1 } ^ { t } ( \\alpha _ { t } ^ { i } ) ^ { 2 } \\le \\frac { 2 H } { t } } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        310,
+                                        104,
+                                        348,
+                                        125
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for every",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        348,
+                                        109,
+                                        372,
+                                        121
+                                    ],
+                                    "score": 0.68,
+                                    "content": "t \\geq 1",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        129,
+                        128,
+                        294,
+                        142
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                127,
+                                126,
+                                292,
+                                145
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        126,
+                                        142,
+                                        145
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        142,
+                                        129,
+                                        228,
+                                        142
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\textstyle \\sum _ { t = i } ^ { \\infty } \\alpha _ { t } ^ { i } = 1 + 1 / H",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        228,
+                                        126,
+                                        269,
+                                        145
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", for every",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        269,
+                                        130,
+                                        292,
+                                        141
+                                    ],
+                                    "score": 0.83,
+                                    "content": "i \\geq 1",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        180,
+                        181,
+                        192
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                179,
+                                182,
+                                192
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        179,
+                                        182,
+                                        192
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Proof. Recall that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        179,
+                        195,
+                        432,
+                        230
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                179,
+                                195,
+                                432,
+                                230
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        179,
+                                        195,
+                                        432,
+                                        230
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\alpha _ { t } = \\frac { H + 1 } { H + t } , \\quad \\alpha _ { t } ^ { 0 } = \\prod _ { j = 1 } ^ { t } ( 1 - \\alpha _ { j } ) , \\quad \\alpha _ { t } ^ { i } = \\alpha _ { i } \\prod _ { j = i + 1 } ^ { t } ( 1 - \\alpha _ { j } ) .",
+                                    "type": "interline_equation",
+                                    "image_path": "242c5979af7b492fba1d80135236539576c26cc515f271d589d39be0ce0b496a.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                179,
+                                195,
+                                432,
+                                206.66666666666666
+                            ],
+                            "spans": [],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                179,
+                                206.66666666666666,
+                                432,
+                                218.33333333333331
+                            ],
+                            "spans": [],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                179,
+                                218.33333333333331,
+                                432,
+                                229.99999999999997
+                            ],
+                            "spans": [],
+                            "index": 6
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        233,
+                        420,
+                        245
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                230,
+                                421,
+                                249
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        230,
+                                        421,
+                                        249
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Properties 1-3 are proven by Jin et al. (2018). Now we prove the last property.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        250,
+                        176,
+                        262
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                249,
+                                177,
+                                263
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        249,
+                                        177,
+                                        263
+                                    ],
+                                    "score": 1.0,
+                                    "content": "On the one hand,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        219,
+                        259,
+                        390,
+                        293
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                219,
+                                259,
+                                390,
+                                293
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        219,
+                                        259,
+                                        390,
+                                        293
+                                    ],
+                                    "score": 0.95,
+                                    "content": "\\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\sqrt { \\frac { \\iota ( i ) } { i } } \\leq \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\sqrt { \\frac { \\iota ( t ) } { i } } \\leq 2 \\sqrt { \\frac { \\iota ( t ) } { t } } ,",
+                                    "type": "interline_equation",
+                                    "image_path": "07ae804a6b110033f8bf12b32de163cad5567ec4167d97952b977363794b7bc4.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                219,
+                                259,
+                                390,
+                                276.0
+                            ],
+                            "spans": [],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                219,
+                                276.0,
+                                390,
+                                293.0
+                            ],
+                            "spans": [],
+                            "index": 10
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        294,
+                        306,
+                        306
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                292,
+                                307,
+                                308
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        292,
+                                        307,
+                                        308
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where the last inequality follows from property 1.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        310,
+                        505,
+                        333
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                308,
+                                505,
+                                324
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        308,
+                                        282,
+                                        324
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The left-hand side is proven by induction on",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        283,
+                                        312,
+                                        288,
+                                        321
+                                    ],
+                                    "score": 0.7,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        288,
+                                        308,
+                                        388,
+                                        324
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". For the base case, when",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        388,
+                                        311,
+                                        444,
+                                        323
+                                    ],
+                                    "score": 0.91,
+                                    "content": "t = 1 , \\alpha _ { t } ^ { t } = 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        444,
+                                        308,
+                                        464,
+                                        324
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". For",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        464,
+                                        311,
+                                        487,
+                                        322
+                                    ],
+                                    "score": 0.88,
+                                    "content": "t \\geq 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        488,
+                                        308,
+                                        505,
+                                        324
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", we",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                320,
+                                342,
+                                335
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        320,
+                                        128,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "have",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        128,
+                                        321,
+                                        207,
+                                        335
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\alpha _ { t } ^ { i } = ( 1 - \\alpha _ { t } ) \\dot { \\alpha _ { t - 1 } ^ { i } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        207,
+                                        320,
+                                        222,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        222,
+                                        322,
+                                        279,
+                                        333
+                                    ],
+                                    "score": 0.9,
+                                    "content": "1 \\leq i \\leq t - 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        280,
+                                        320,
+                                        342,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". It follows that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 12.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        122,
+                        337,
+                        487,
+                        372
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                122,
+                                337,
+                                487,
+                                372
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        122,
+                                        337,
+                                        487,
+                                        372
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\sqrt { \\frac { \\iota ( i ) } { i } } = \\alpha _ { t } \\sqrt { \\frac { \\iota ( t ) } { t } } + ( 1 - \\alpha _ { t } ) \\sum _ { i = 1 } ^ { t - 1 } \\alpha _ { t - 1 } ^ { i } \\sqrt { \\frac { \\iota ( i ) } { i } } \\geq \\alpha _ { t } \\sqrt { \\frac { \\iota ( t ) } { t } } + ( 1 - \\alpha _ { t } ) \\sqrt { \\frac { \\iota ( t - 1 ) } { t - 1 } } .",
+                                    "type": "interline_equation",
+                                    "image_path": "ab4e05f21481995ad7b6907c39b07eca8dcf1b1707af7599ec0fb0ba9984a116.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                122,
+                                337,
+                                487,
+                                348.6666666666667
+                            ],
+                            "spans": [],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                122,
+                                348.6666666666667,
+                                487,
+                                360.33333333333337
+                            ],
+                            "spans": [],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                122,
+                                360.33333333333337,
+                                487,
+                                372.00000000000006
+                            ],
+                            "spans": [],
+                            "index": 16
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        375,
+                        441,
+                        388
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                375,
+                                441,
+                                389
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        375,
+                                        167,
+                                        389
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Since function",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        167,
+                                        375,
+                                        222,
+                                        388
+                                    ],
+                                    "score": 0.94,
+                                    "content": "f ( t ) = \\iota ( t ) / t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        222,
+                                        375,
+                                        352,
+                                        389
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is monotonically decreasing for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        352,
+                                        376,
+                                        402,
+                                        387
+                                    ],
+                                    "score": 0.92,
+                                    "content": "t \\geq 1 , c \\geq 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        402,
+                                        375,
+                                        441,
+                                        389
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", we have",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        155,
+                        390,
+                        455,
+                        419
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                155,
+                                390,
+                                455,
+                                419
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        155,
+                                        390,
+                                        455,
+                                        419
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\alpha _ { t } \\sqrt { \\frac { \\iota ( t ) } { t } } + ( 1 - \\alpha _ { t } ) \\sqrt { \\frac { \\iota ( t - 1 ) } { t - 1 } } \\geq \\alpha _ { t } \\sqrt { \\frac { \\iota ( t ) } { t } } + ( 1 - \\alpha _ { t } ) \\sqrt { \\frac { \\iota ( t ) } { t } } \\geq \\sqrt { \\frac { \\iota ( t ) } { t } } .",
+                                    "type": "interline_equation",
+                                    "image_path": "7a7308ee3372dff7c4a6c3cae36090077c647b119d15a408f894359ff305977f.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                155,
+                                390,
+                                455,
+                                419
+                            ],
+                            "spans": [],
+                            "index": 18
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        438,
+                        405,
+                        452
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                438,
+                                406,
+                                454
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        438,
+                                        253,
+                                        454
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lemma 4. With probability at least",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        253,
+                                        439,
+                                        286,
+                                        452
+                                    ],
+                                    "score": 0.91,
+                                    "content": "1 - \\delta / 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        286,
+                                        438,
+                                        317,
+                                        454
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", for all",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        317,
+                                        440,
+                                        342,
+                                        451
+                                    ],
+                                    "score": 0.92,
+                                    "content": "p \\geq 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        342,
+                                        438,
+                                        360,
+                                        454
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        361,
+                                        440,
+                                        383,
+                                        452
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        383,
+                                        438,
+                                        406,
+                                        454
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-pair,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 19
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        170,
+                        455,
+                        439,
+                        506
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                170,
+                                455,
+                                439,
+                                506
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        170,
+                                        455,
+                                        439,
+                                        506
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\begin{array} { r l } & { 0 \\le ( Q _ { p } - Q ^ { * } ) ( s , a ) \\le \\displaystyle \\frac { \\alpha _ { t } ^ { 0 } } { 1 - \\gamma } + \\displaystyle \\sum _ { i = 1 } ^ { t } \\gamma \\alpha _ { t } ^ { i } ( { \\hat { V } } _ { t _ { i } } - V ^ { * } ) ( s _ { t _ { i } + 1 } ) + \\beta _ { t } , } \\\\ & { 0 \\le ( { \\hat { Q } } _ { p } - Q ^ { * } ) ( s , a ) , } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "bf1a7588fbf4d42939d18d2d26129510541081c72f7d186c33706ba60d0c68e1.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                170,
+                                455,
+                                439,
+                                472.0
+                            ],
+                            "spans": [],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                170,
+                                472.0,
+                                439,
+                                489.0
+                            ],
+                            "spans": [],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                170,
+                                489.0,
+                                439,
+                                506.0
+                            ],
+                            "spans": [],
+                            "index": 22
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        510,
+                        386,
+                        524
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                507,
+                                387,
+                                527
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        507,
+                                        133,
+                                        527
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        133,
+                                        511,
+                                        246,
+                                        524
+                                    ],
+                                    "score": 0.89,
+                                    "content": "t = N _ { p } ( s , a ) , t _ { i } = \\tau ( s , a , i )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        246,
+                                        507,
+                                        264,
+                                        527
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        265,
+                                        509,
+                                        383,
+                                        524
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\beta _ { t } = c _ { 3 } \\sqrt { H \\iota ( t ) / ( ( 1 - \\gamma ) ^ { 2 } t ) }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        383,
+                                        507,
+                                        387,
+                                        527
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 23
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        534,
+                        181,
+                        546
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                533,
+                                182,
+                                547
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        533,
+                                        182,
+                                        547
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Proof. Recall that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 24
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        212,
+                        544,
+                        398,
+                        579
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                212,
+                                544,
+                                398,
+                                579
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        212,
+                                        544,
+                                        398,
+                                        579
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\alpha _ { t } ^ { 0 } = \\prod _ { j = 1 } ^ { t } ( 1 - \\alpha _ { j } ) , \\quad \\alpha _ { t } ^ { i } = \\alpha _ { i } \\prod _ { j = i + 1 } ^ { t } ( 1 - \\alpha _ { j } ) .",
+                                    "type": "interline_equation",
+                                    "image_path": "88278a9f30fd7a368323e468f5e3ad316e4a238d906d20218881efa56614124b.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 25.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                212,
+                                544,
+                                398,
+                                561.5
+                            ],
+                            "spans": [],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                212,
+                                561.5,
+                                398,
+                                579.0
+                            ],
+                            "spans": [],
+                            "index": 26
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        581,
+                        457,
+                        593
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                580,
+                                458,
+                                595
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        580,
+                                        423,
+                                        595
+                                    ],
+                                    "score": 1.0,
+                                    "content": "From the update rule, it can be seen that our algorithm maintains the following",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        423,
+                                        581,
+                                        453,
+                                        593
+                                    ],
+                                    "score": 0.92,
+                                    "content": "Q ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        454,
+                                        580,
+                                        458,
+                                        595
+                                    ],
+                                    "score": 1.0,
+                                    "content": ":",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 27
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        182,
+                        596,
+                        429,
+                        630
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                182,
+                                596,
+                                429,
+                                630
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        182,
+                                        596,
+                                        429,
+                                        630
+                                    ],
+                                    "score": 0.94,
+                                    "content": "Q _ { p } ( s , a ) = \\alpha _ { t } ^ { 0 } \\frac { 1 } { 1 - \\gamma } + \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\left[ r ( s , a ) + b _ { i } + \\gamma \\hat { V } _ { t _ { i } } ( s _ { t _ { i } + 1 } ) \\right] .",
+                                    "type": "interline_equation",
+                                    "image_path": "1b23fc9ed7edc8e4d294bbfadc8232c0e3a3f7ae514e3b0f9f7eb6f05a9180e4.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 29,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                182,
+                                596,
+                                429,
+                                607.3333333333334
+                            ],
+                            "spans": [],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                182,
+                                607.3333333333334,
+                                429,
+                                618.6666666666667
+                            ],
+                            "spans": [],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                182,
+                                618.6666666666667,
+                                429,
+                                630.0000000000001
+                            ],
+                            "spans": [],
+                            "index": 30
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        633,
+                        248,
+                        645
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                632,
+                                249,
+                                647
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        632,
+                                        249,
+                                        647
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Bellman optimality equation gives:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        }
+                    ],
+                    "index": 31
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        140,
+                        648,
+                        470,
+                        682
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                140,
+                                648,
+                                470,
+                                682
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        140,
+                                        648,
+                                        470,
+                                        682
+                                    ],
+                                    "score": 0.93,
+                                    "content": "Q ^ { * } ( s , a ) = r ( s , a ) + \\gamma \\mathbb { P } V ^ { * } ( s , a ) = \\alpha _ { t } ^ { 0 } Q ^ { * } ( s , a ) + \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\left[ r ( s , a ) + \\gamma \\mathbb { P } V ^ { * } ( s , a ) \\right] .",
+                                    "type": "interline_equation",
+                                    "image_path": "7f3af02c43fff8510d8c8a82457783c482e400b5602396a1f237a333d06d0211.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 33,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                140,
+                                648,
+                                470,
+                                659.3333333333334
+                            ],
+                            "spans": [],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                140,
+                                659.3333333333334,
+                                470,
+                                670.6666666666667
+                            ],
+                            "spans": [],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                140,
+                                670.6666666666667,
+                                470,
+                                682.0000000000001
+                            ],
+                            "spans": [],
+                            "index": 34
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        685,
+                        250,
+                        697
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                683,
+                                250,
+                                699
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        683,
+                                        250,
+                                        699
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Subtracting the two equations gives",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        }
+                    ],
+                    "index": 35
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        111,
+                        700,
+                        514,
+                        734
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                111,
+                                700,
+                                514,
+                                734
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        700,
+                                        514,
+                                        734
+                                    ],
+                                    "score": 0.9,
+                                    "content": "Q _ { p } - Q ^ { * } ) ( s , a ) = \\alpha _ { t } ^ { 0 } ( \\frac { 1 } { 1 - \\gamma } - Q ^ { * } ( s , a ) ) + \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\left[ b _ { i } + \\gamma \\left( V _ { t _ { i } } - V ^ { * } \\right) \\left( s _ { t _ { i } + 1 } \\right) + \\gamma \\left( V ^ { * } \\left( s _ { t _ { i } + 1 } \\right) - \\mathbb { P } V ^ { * } \\right) \\right] ,",
+                                    "type": "interline_equation",
+                                    "image_path": "4daae5a78519cf382ebb3c39463504ef4bdc6c481b0042a0fad9b5891adc01b0.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 37,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                111,
+                                700,
+                                514,
+                                711.3333333333334
+                            ],
+                            "spans": [],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                111,
+                                711.3333333333334,
+                                514,
+                                722.6666666666667
+                            ],
+                            "spans": [],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                111,
+                                722.6666666666667,
+                                514,
+                                734.0000000000001
+                            ],
+                            "spans": [],
+                            "index": 38
+                        }
+                    ]
+                }
+            ],
+            "page_idx": 11,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        106,
+                        26,
+                        294,
+                        38
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                25,
+                                294,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        25,
+                                        294,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        494,
+                        422,
+                        505,
+                        432
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                495,
+                                423,
+                                505,
+                                433
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        495,
+                                        423,
+                                        505,
+                                        433
+                                    ],
+                                    "score": 0.998,
+                                    "content": "□",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        311,
+                        761
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                312,
+                                764
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        312,
+                                        764
+                                    ],
+                                    "score": 1.0,
+                                    "content": "12",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        129,
+                        79,
+                        353,
+                        101
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                127,
+                                78,
+                                356,
+                                102
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        78,
+                                        142,
+                                        102
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        142,
+                                        80,
+                                        259,
+                                        101
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\begin{array} { r } { \\sqrt { \\frac { 1 } { t } } \\leq \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\sqrt { \\frac { 1 } { i } } \\leq 2 \\sqrt { \\frac { 1 } { t } } } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        260,
+                                        78,
+                                        298,
+                                        102
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for every",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        299,
+                                        84,
+                                        349,
+                                        97
+                                    ],
+                                    "score": 0.58,
+                                    "content": "t \\geq 1 , c > 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        349,
+                                        78,
+                                        356,
+                                        102
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        }
+                    ],
+                    "index": 0,
+                    "bbox_fs": [
+                        127,
+                        78,
+                        356,
+                        102
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        129,
+                        106,
+                        374,
+                        123
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                126,
+                                104,
+                                372,
+                                125
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        104,
+                                        142,
+                                        125
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        142,
+                                        108,
+                                        216,
+                                        122
+                                    ],
+                                    "score": 0.84,
+                                    "content": "\\begin{array} { r } { \\operatorname* { m a x } _ { i \\in [ t ] } \\alpha _ { t } ^ { i } \\leq \\frac { 2 H } { t } } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        217,
+                                        104,
+                                        235,
+                                        125
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        236,
+                                        107,
+                                        309,
+                                        122
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\begin{array} { r } { \\sum _ { i = 1 } ^ { t } ( \\alpha _ { t } ^ { i } ) ^ { 2 } \\le \\frac { 2 H } { t } } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        310,
+                                        104,
+                                        348,
+                                        125
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for every",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        348,
+                                        109,
+                                        372,
+                                        121
+                                    ],
+                                    "score": 0.68,
+                                    "content": "t \\geq 1",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 1,
+                    "bbox_fs": [
+                        126,
+                        104,
+                        372,
+                        125
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        129,
+                        128,
+                        294,
+                        142
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                127,
+                                126,
+                                292,
+                                145
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        126,
+                                        142,
+                                        145
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        142,
+                                        129,
+                                        228,
+                                        142
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\textstyle \\sum _ { t = i } ^ { \\infty } \\alpha _ { t } ^ { i } = 1 + 1 / H",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        228,
+                                        126,
+                                        269,
+                                        145
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", for every",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        269,
+                                        130,
+                                        292,
+                                        141
+                                    ],
+                                    "score": 0.83,
+                                    "content": "i \\geq 1",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 2,
+                    "bbox_fs": [
+                        127,
+                        126,
+                        292,
+                        145
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        180,
+                        181,
+                        192
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                179,
+                                182,
+                                192
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        179,
+                                        182,
+                                        192
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Proof. Recall that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 3,
+                    "bbox_fs": [
+                        106,
+                        179,
+                        182,
+                        192
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        179,
+                        195,
+                        432,
+                        230
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                179,
+                                195,
+                                432,
+                                230
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        179,
+                                        195,
+                                        432,
+                                        230
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\alpha _ { t } = \\frac { H + 1 } { H + t } , \\quad \\alpha _ { t } ^ { 0 } = \\prod _ { j = 1 } ^ { t } ( 1 - \\alpha _ { j } ) , \\quad \\alpha _ { t } ^ { i } = \\alpha _ { i } \\prod _ { j = i + 1 } ^ { t } ( 1 - \\alpha _ { j } ) .",
+                                    "type": "interline_equation",
+                                    "image_path": "242c5979af7b492fba1d80135236539576c26cc515f271d589d39be0ce0b496a.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                179,
+                                195,
+                                432,
+                                206.66666666666666
+                            ],
+                            "spans": [],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                179,
+                                206.66666666666666,
+                                432,
+                                218.33333333333331
+                            ],
+                            "spans": [],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                179,
+                                218.33333333333331,
+                                432,
+                                229.99999999999997
+                            ],
+                            "spans": [],
+                            "index": 6
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        233,
+                        420,
+                        245
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                230,
+                                421,
+                                249
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        230,
+                                        421,
+                                        249
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Properties 1-3 are proven by Jin et al. (2018). Now we prove the last property.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 7,
+                    "bbox_fs": [
+                        104,
+                        230,
+                        421,
+                        249
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        250,
+                        176,
+                        262
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                249,
+                                177,
+                                263
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        249,
+                                        177,
+                                        263
+                                    ],
+                                    "score": 1.0,
+                                    "content": "On the one hand,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 8,
+                    "bbox_fs": [
+                        106,
+                        249,
+                        177,
+                        263
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        219,
+                        259,
+                        390,
+                        293
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                219,
+                                259,
+                                390,
+                                293
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        219,
+                                        259,
+                                        390,
+                                        293
+                                    ],
+                                    "score": 0.95,
+                                    "content": "\\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\sqrt { \\frac { \\iota ( i ) } { i } } \\leq \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\sqrt { \\frac { \\iota ( t ) } { i } } \\leq 2 \\sqrt { \\frac { \\iota ( t ) } { t } } ,",
+                                    "type": "interline_equation",
+                                    "image_path": "07ae804a6b110033f8bf12b32de163cad5567ec4167d97952b977363794b7bc4.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                219,
+                                259,
+                                390,
+                                276.0
+                            ],
+                            "spans": [],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                219,
+                                276.0,
+                                390,
+                                293.0
+                            ],
+                            "spans": [],
+                            "index": 10
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        294,
+                        306,
+                        306
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                292,
+                                307,
+                                308
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        292,
+                                        307,
+                                        308
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where the last inequality follows from property 1.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 11,
+                    "bbox_fs": [
+                        105,
+                        292,
+                        307,
+                        308
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        310,
+                        505,
+                        333
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                308,
+                                505,
+                                324
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        308,
+                                        282,
+                                        324
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The left-hand side is proven by induction on",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        283,
+                                        312,
+                                        288,
+                                        321
+                                    ],
+                                    "score": 0.7,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        288,
+                                        308,
+                                        388,
+                                        324
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". For the base case, when",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        388,
+                                        311,
+                                        444,
+                                        323
+                                    ],
+                                    "score": 0.91,
+                                    "content": "t = 1 , \\alpha _ { t } ^ { t } = 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        444,
+                                        308,
+                                        464,
+                                        324
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". For",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        464,
+                                        311,
+                                        487,
+                                        322
+                                    ],
+                                    "score": 0.88,
+                                    "content": "t \\geq 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        488,
+                                        308,
+                                        505,
+                                        324
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", we",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                320,
+                                342,
+                                335
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        320,
+                                        128,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "have",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        128,
+                                        321,
+                                        207,
+                                        335
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\alpha _ { t } ^ { i } = ( 1 - \\alpha _ { t } ) \\dot { \\alpha _ { t - 1 } ^ { i } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        207,
+                                        320,
+                                        222,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        222,
+                                        322,
+                                        279,
+                                        333
+                                    ],
+                                    "score": 0.9,
+                                    "content": "1 \\leq i \\leq t - 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        280,
+                                        320,
+                                        342,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". It follows that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 12.5,
+                    "bbox_fs": [
+                        105,
+                        308,
+                        505,
+                        335
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        122,
+                        337,
+                        487,
+                        372
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                122,
+                                337,
+                                487,
+                                372
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        122,
+                                        337,
+                                        487,
+                                        372
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\sqrt { \\frac { \\iota ( i ) } { i } } = \\alpha _ { t } \\sqrt { \\frac { \\iota ( t ) } { t } } + ( 1 - \\alpha _ { t } ) \\sum _ { i = 1 } ^ { t - 1 } \\alpha _ { t - 1 } ^ { i } \\sqrt { \\frac { \\iota ( i ) } { i } } \\geq \\alpha _ { t } \\sqrt { \\frac { \\iota ( t ) } { t } } + ( 1 - \\alpha _ { t } ) \\sqrt { \\frac { \\iota ( t - 1 ) } { t - 1 } } .",
+                                    "type": "interline_equation",
+                                    "image_path": "ab4e05f21481995ad7b6907c39b07eca8dcf1b1707af7599ec0fb0ba9984a116.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                122,
+                                337,
+                                487,
+                                348.6666666666667
+                            ],
+                            "spans": [],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                122,
+                                348.6666666666667,
+                                487,
+                                360.33333333333337
+                            ],
+                            "spans": [],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                122,
+                                360.33333333333337,
+                                487,
+                                372.00000000000006
+                            ],
+                            "spans": [],
+                            "index": 16
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        375,
+                        441,
+                        388
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                375,
+                                441,
+                                389
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        375,
+                                        167,
+                                        389
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Since function",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        167,
+                                        375,
+                                        222,
+                                        388
+                                    ],
+                                    "score": 0.94,
+                                    "content": "f ( t ) = \\iota ( t ) / t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        222,
+                                        375,
+                                        352,
+                                        389
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is monotonically decreasing for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        352,
+                                        376,
+                                        402,
+                                        387
+                                    ],
+                                    "score": 0.92,
+                                    "content": "t \\geq 1 , c \\geq 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        402,
+                                        375,
+                                        441,
+                                        389
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", we have",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 17,
+                    "bbox_fs": [
+                        106,
+                        375,
+                        441,
+                        389
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        155,
+                        390,
+                        455,
+                        419
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                155,
+                                390,
+                                455,
+                                419
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        155,
+                                        390,
+                                        455,
+                                        419
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\alpha _ { t } \\sqrt { \\frac { \\iota ( t ) } { t } } + ( 1 - \\alpha _ { t } ) \\sqrt { \\frac { \\iota ( t - 1 ) } { t - 1 } } \\geq \\alpha _ { t } \\sqrt { \\frac { \\iota ( t ) } { t } } + ( 1 - \\alpha _ { t } ) \\sqrt { \\frac { \\iota ( t ) } { t } } \\geq \\sqrt { \\frac { \\iota ( t ) } { t } } .",
+                                    "type": "interline_equation",
+                                    "image_path": "7a7308ee3372dff7c4a6c3cae36090077c647b119d15a408f894359ff305977f.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                155,
+                                390,
+                                455,
+                                419
+                            ],
+                            "spans": [],
+                            "index": 18
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        438,
+                        405,
+                        452
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                438,
+                                406,
+                                454
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        438,
+                                        253,
+                                        454
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lemma 4. With probability at least",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        253,
+                                        439,
+                                        286,
+                                        452
+                                    ],
+                                    "score": 0.91,
+                                    "content": "1 - \\delta / 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        286,
+                                        438,
+                                        317,
+                                        454
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", for all",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        317,
+                                        440,
+                                        342,
+                                        451
+                                    ],
+                                    "score": 0.92,
+                                    "content": "p \\geq 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        342,
+                                        438,
+                                        360,
+                                        454
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        361,
+                                        440,
+                                        383,
+                                        452
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        383,
+                                        438,
+                                        406,
+                                        454
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-pair,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 19,
+                    "bbox_fs": [
+                        106,
+                        438,
+                        406,
+                        454
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        170,
+                        455,
+                        439,
+                        506
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                170,
+                                455,
+                                439,
+                                506
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        170,
+                                        455,
+                                        439,
+                                        506
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\begin{array} { r l } & { 0 \\le ( Q _ { p } - Q ^ { * } ) ( s , a ) \\le \\displaystyle \\frac { \\alpha _ { t } ^ { 0 } } { 1 - \\gamma } + \\displaystyle \\sum _ { i = 1 } ^ { t } \\gamma \\alpha _ { t } ^ { i } ( { \\hat { V } } _ { t _ { i } } - V ^ { * } ) ( s _ { t _ { i } + 1 } ) + \\beta _ { t } , } \\\\ & { 0 \\le ( { \\hat { Q } } _ { p } - Q ^ { * } ) ( s , a ) , } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "bf1a7588fbf4d42939d18d2d26129510541081c72f7d186c33706ba60d0c68e1.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                170,
+                                455,
+                                439,
+                                472.0
+                            ],
+                            "spans": [],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                170,
+                                472.0,
+                                439,
+                                489.0
+                            ],
+                            "spans": [],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                170,
+                                489.0,
+                                439,
+                                506.0
+                            ],
+                            "spans": [],
+                            "index": 22
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        510,
+                        386,
+                        524
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                507,
+                                387,
+                                527
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        507,
+                                        133,
+                                        527
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        133,
+                                        511,
+                                        246,
+                                        524
+                                    ],
+                                    "score": 0.89,
+                                    "content": "t = N _ { p } ( s , a ) , t _ { i } = \\tau ( s , a , i )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        246,
+                                        507,
+                                        264,
+                                        527
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        265,
+                                        509,
+                                        383,
+                                        524
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\beta _ { t } = c _ { 3 } \\sqrt { H \\iota ( t ) / ( ( 1 - \\gamma ) ^ { 2 } t ) }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        383,
+                                        507,
+                                        387,
+                                        527
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 23,
+                    "bbox_fs": [
+                        105,
+                        507,
+                        387,
+                        527
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        534,
+                        181,
+                        546
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                533,
+                                182,
+                                547
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        533,
+                                        182,
+                                        547
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Proof. Recall that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 24,
+                    "bbox_fs": [
+                        105,
+                        533,
+                        182,
+                        547
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        212,
+                        544,
+                        398,
+                        579
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                212,
+                                544,
+                                398,
+                                579
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        212,
+                                        544,
+                                        398,
+                                        579
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\alpha _ { t } ^ { 0 } = \\prod _ { j = 1 } ^ { t } ( 1 - \\alpha _ { j } ) , \\quad \\alpha _ { t } ^ { i } = \\alpha _ { i } \\prod _ { j = i + 1 } ^ { t } ( 1 - \\alpha _ { j } ) .",
+                                    "type": "interline_equation",
+                                    "image_path": "88278a9f30fd7a368323e468f5e3ad316e4a238d906d20218881efa56614124b.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 25.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                212,
+                                544,
+                                398,
+                                561.5
+                            ],
+                            "spans": [],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                212,
+                                561.5,
+                                398,
+                                579.0
+                            ],
+                            "spans": [],
+                            "index": 26
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        581,
+                        457,
+                        593
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                580,
+                                458,
+                                595
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        580,
+                                        423,
+                                        595
+                                    ],
+                                    "score": 1.0,
+                                    "content": "From the update rule, it can be seen that our algorithm maintains the following",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        423,
+                                        581,
+                                        453,
+                                        593
+                                    ],
+                                    "score": 0.92,
+                                    "content": "Q ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        454,
+                                        580,
+                                        458,
+                                        595
+                                    ],
+                                    "score": 1.0,
+                                    "content": ":",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 27,
+                    "bbox_fs": [
+                        105,
+                        580,
+                        458,
+                        595
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        182,
+                        596,
+                        429,
+                        630
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                182,
+                                596,
+                                429,
+                                630
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        182,
+                                        596,
+                                        429,
+                                        630
+                                    ],
+                                    "score": 0.94,
+                                    "content": "Q _ { p } ( s , a ) = \\alpha _ { t } ^ { 0 } \\frac { 1 } { 1 - \\gamma } + \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\left[ r ( s , a ) + b _ { i } + \\gamma \\hat { V } _ { t _ { i } } ( s _ { t _ { i } + 1 } ) \\right] .",
+                                    "type": "interline_equation",
+                                    "image_path": "1b23fc9ed7edc8e4d294bbfadc8232c0e3a3f7ae514e3b0f9f7eb6f05a9180e4.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 29,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                182,
+                                596,
+                                429,
+                                607.3333333333334
+                            ],
+                            "spans": [],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                182,
+                                607.3333333333334,
+                                429,
+                                618.6666666666667
+                            ],
+                            "spans": [],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                182,
+                                618.6666666666667,
+                                429,
+                                630.0000000000001
+                            ],
+                            "spans": [],
+                            "index": 30
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        633,
+                        248,
+                        645
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                632,
+                                249,
+                                647
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        632,
+                                        249,
+                                        647
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Bellman optimality equation gives:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        }
+                    ],
+                    "index": 31,
+                    "bbox_fs": [
+                        105,
+                        632,
+                        249,
+                        647
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        140,
+                        648,
+                        470,
+                        682
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                140,
+                                648,
+                                470,
+                                682
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        140,
+                                        648,
+                                        470,
+                                        682
+                                    ],
+                                    "score": 0.93,
+                                    "content": "Q ^ { * } ( s , a ) = r ( s , a ) + \\gamma \\mathbb { P } V ^ { * } ( s , a ) = \\alpha _ { t } ^ { 0 } Q ^ { * } ( s , a ) + \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\left[ r ( s , a ) + \\gamma \\mathbb { P } V ^ { * } ( s , a ) \\right] .",
+                                    "type": "interline_equation",
+                                    "image_path": "7f3af02c43fff8510d8c8a82457783c482e400b5602396a1f237a333d06d0211.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 33,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                140,
+                                648,
+                                470,
+                                659.3333333333334
+                            ],
+                            "spans": [],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                140,
+                                659.3333333333334,
+                                470,
+                                670.6666666666667
+                            ],
+                            "spans": [],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                140,
+                                670.6666666666667,
+                                470,
+                                682.0000000000001
+                            ],
+                            "spans": [],
+                            "index": 34
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        685,
+                        250,
+                        697
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                683,
+                                250,
+                                699
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        683,
+                                        250,
+                                        699
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Subtracting the two equations gives",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        }
+                    ],
+                    "index": 35,
+                    "bbox_fs": [
+                        106,
+                        683,
+                        250,
+                        699
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        111,
+                        700,
+                        514,
+                        734
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                111,
+                                700,
+                                514,
+                                734
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        700,
+                                        514,
+                                        734
+                                    ],
+                                    "score": 0.9,
+                                    "content": "Q _ { p } - Q ^ { * } ) ( s , a ) = \\alpha _ { t } ^ { 0 } ( \\frac { 1 } { 1 - \\gamma } - Q ^ { * } ( s , a ) ) + \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\left[ b _ { i } + \\gamma \\left( V _ { t _ { i } } - V ^ { * } \\right) \\left( s _ { t _ { i } + 1 } \\right) + \\gamma \\left( V ^ { * } \\left( s _ { t _ { i } + 1 } \\right) - \\mathbb { P } V ^ { * } \\right) \\right] ,",
+                                    "type": "interline_equation",
+                                    "image_path": "4daae5a78519cf382ebb3c39463504ef4bdc6c481b0042a0fad9b5891adc01b0.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 37,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                111,
+                                700,
+                                514,
+                                711.3333333333334
+                            ],
+                            "spans": [],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                111,
+                                711.3333333333334,
+                                514,
+                                722.6666666666667
+                            ],
+                            "spans": [],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                111,
+                                722.6666666666667,
+                                514,
+                                734.0000000000001
+                            ],
+                            "spans": [],
+                            "index": 38
+                        }
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        82,
+                        506,
+                        115
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                81,
+                                506,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        81,
+                                        254,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The identity above holds for arbitrary",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        254,
+                                        85,
+                                        271,
+                                        93
+                                    ],
+                                    "score": 0.31,
+                                    "content": "p , s",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        271,
+                                        81,
+                                        288,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        288,
+                                        85,
+                                        294,
+                                        92
+                                    ],
+                                    "score": 0.73,
+                                    "content": "a",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        295,
+                                        81,
+                                        332,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Now fix",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        333,
+                                        83,
+                                        357,
+                                        93
+                                    ],
+                                    "score": 0.89,
+                                    "content": "s \\in S",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        357,
+                                        81,
+                                        360,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        361,
+                                        83,
+                                        387,
+                                        93
+                                    ],
+                                    "score": 0.88,
+                                    "content": "a \\in A",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        387,
+                                        81,
+                                        404,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        405,
+                                        83,
+                                        430,
+                                        94
+                                    ],
+                                    "score": 0.9,
+                                    "content": "p \\in \\mathbb N",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        430,
+                                        81,
+                                        450,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        450,
+                                        83,
+                                        502,
+                                        95
+                                    ],
+                                    "score": 0.93,
+                                    "content": "t = N _ { p } ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        502,
+                                        81,
+                                        506,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                93,
+                                507,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        93,
+                                        163,
+                                        106
+                                    ],
+                                    "score": 0.93,
+                                    "content": "t _ { i } = \\tau ( s , a , i )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        163,
+                                        93,
+                                        185,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". The",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        186,
+                                        94,
+                                        209,
+                                        104
+                                    ],
+                                    "score": 0.9,
+                                    "content": "t = 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        209,
+                                        93,
+                                        313,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "case is trivial; we assume",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        314,
+                                        94,
+                                        337,
+                                        105
+                                    ],
+                                    "score": 0.9,
+                                    "content": "t \\geq 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        337,
+                                        93,
+                                        496,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "below. Now consider an arbitrary fixed",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        496,
+                                        95,
+                                        503,
+                                        104
+                                    ],
+                                    "score": 0.83,
+                                    "content": "k",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        503,
+                                        93,
+                                        507,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                103,
+                                137,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        103,
+                                        137,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Define",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        206,
+                        115,
+                        404,
+                        137
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                206,
+                                115,
+                                404,
+                                137
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        206,
+                                        115,
+                                        404,
+                                        137
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\Delta _ { i } = \\left( \\alpha _ { k } ^ { i } \\cdot I [ t _ { i } < \\infty ] \\cdot \\left( \\mathbb { P } V ^ { * } - \\mathbb { \\hat { P } } _ { t _ { i } } V ^ { * } \\right) ( s , a ) \\right)",
+                                    "type": "interline_equation",
+                                    "image_path": "7ed6137165be41b2ad3ac59dec10e06c5f86c9778d1953d9a7904ac5097d5be4.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                206,
+                                115,
+                                404,
+                                137
+                            ],
+                            "spans": [],
+                            "index": 3
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        138,
+                        507,
+                        174
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                137,
+                                506,
+                                152
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        137,
+                                        124,
+                                        152
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        124,
+                                        139,
+                                        135,
+                                        149
+                                    ],
+                                    "score": 0.86,
+                                    "content": "F _ { i }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        135,
+                                        137,
+                                        168,
+                                        152
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        168,
+                                        140,
+                                        176,
+                                        149
+                                    ],
+                                    "score": 0.81,
+                                    "content": "\\sigma",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        176,
+                                        137,
+                                        336,
+                                        152
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-Field generated by random variables",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        337,
+                                        139,
+                                        413,
+                                        150
+                                    ],
+                                    "score": 0.88,
+                                    "content": "( s _ { 1 } , a _ { 1 } , . . . , s _ { t _ { i } } , a _ { t _ { i } } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        414,
+                                        137,
+                                        506,
+                                        152
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". It can be seen that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                144,
+                                507,
+                                167
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        150,
+                                        166,
+                                        162
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\mathbb { E } \\left[ \\Delta _ { i } | F _ { i } \\right] = 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        167,
+                                        144,
+                                        196,
+                                        167
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", while",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        197,
+                                        150,
+                                        209,
+                                        160
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\Delta _ { i }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        210,
+                                        144,
+                                        281,
+                                        167
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is measurable in",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        281,
+                                        150,
+                                        302,
+                                        162
+                                    ],
+                                    "score": 0.92,
+                                    "content": "F _ { i + 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        144,
+                                        358,
+                                        167
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Also, since",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        358,
+                                        150,
+                                        447,
+                                        163
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\textstyle 0 \\leq V ^ { \\ast } ( s , { \\bar { a } } ) \\leq { \\frac { 1 } { 1 - \\gamma } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        447,
+                                        144,
+                                        452,
+                                        167
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        452,
+                                        149,
+                                        502,
+                                        164
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\begin{array} { r } { | \\Delta _ { i } | \\le \\frac { 2 } { 1 - \\gamma } } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        503,
+                                        144,
+                                        507,
+                                        167
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                160,
+                                457,
+                                175
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        160,
+                                        150,
+                                        175
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Therefore,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        151,
+                                        163,
+                                        163,
+                                        173
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\Delta _ { i }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        163,
+                                        160,
+                                        457,
+                                        175
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is a martingale difference sequence; by the Azuma-Hoeffding inequality,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        183,
+                        175,
+                        428,
+                        210
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                183,
+                                175,
+                                428,
+                                210
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        183,
+                                        175,
+                                        428,
+                                        210
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\mathrm { P r } \\left[ \\left| \\sum _ { i = 1 } ^ { k } \\Delta _ { i } \\right| > \\eta \\right] \\leq 2 \\exp \\left\\{ - \\frac { \\eta ^ { 2 } } { 8 \\left( 1 - \\gamma \\right) ^ { - 2 } \\sum _ { i = 1 } ^ { k } ( \\alpha _ { k } ^ { i } ) ^ { 2 } } \\right\\} .",
+                                    "type": "interline_equation",
+                                    "image_path": "e1fd0592f2fbfb43a68fa1b2348697afc8a3b51894eb01a3c12dfc2769dfd098.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                183,
+                                175,
+                                428,
+                                186.66666666666666
+                            ],
+                            "spans": [],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                183,
+                                186.66666666666666,
+                                428,
+                                198.33333333333331
+                            ],
+                            "spans": [],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                183,
+                                198.33333333333331,
+                                428,
+                                209.99999999999997
+                            ],
+                            "spans": [],
+                            "index": 9
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        211,
+                        421,
+                        224
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                210,
+                                421,
+                                225
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        210,
+                                        159,
+                                        225
+                                    ],
+                                    "score": 1.0,
+                                    "content": "By choosing",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        159,
+                                        214,
+                                        165,
+                                        223
+                                    ],
+                                    "score": 0.76,
+                                    "content": "\\eta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        166,
+                                        210,
+                                        307,
+                                        225
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", we can show that with probability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        212,
+                                        416,
+                                        223
+                                    ],
+                                    "score": 0.9,
+                                    "content": "1 - \\delta / \\left[ S A ( k + 1 ) ( k + 2 ) \\right]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        417,
+                                        210,
+                                        421,
+                                        225
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        148,
+                        241,
+                        461,
+                        279
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                148,
+                                241,
+                                461,
+                                279
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        148,
+                                        241,
+                                        461,
+                                        279
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\left| \\sum _ { i = 1 } ^ { k } \\Delta _ { i } \\right| \\leq \\frac { 2 \\sqrt { 2 } } { 1 - \\gamma } \\cdot \\sqrt { \\sum _ { i = 1 } ^ { k } ( \\alpha _ { k } ^ { i } ) ^ { 2 } \\cdot \\ln \\frac { 2 ( k + 1 ) ( k + 2 ) S A } { \\delta } } \\leq \\frac { c _ { 2 } } { 1 - \\gamma } \\sqrt { \\frac { H \\iota ( k ) } { k } } .",
+                                    "type": "interline_equation",
+                                    "image_path": "4635fc976e34fd23da44f8967bc69d839d0dafaecc85d492653e8f8184e7782e.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                148,
+                                241,
+                                461,
+                                253.66666666666666
+                            ],
+                            "spans": [],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                148,
+                                253.66666666666666,
+                                461,
+                                266.3333333333333
+                            ],
+                            "spans": [],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                148,
+                                266.3333333333333,
+                                461,
+                                279.0
+                            ],
+                            "spans": [],
+                            "index": 13
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        281,
+                        506,
+                        306
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                276,
+                                502,
+                                299
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        276,
+                                        128,
+                                        299
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Here",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        128,
+                                        282,
+                                        170,
+                                        294
+                                    ],
+                                    "score": 0.89,
+                                    "content": "c _ { 2 } = 4 \\sqrt { 2 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        171,
+                                        276,
+                                        174,
+                                        299
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        174,
+                                        281,
+                                        270,
+                                        296
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { r } { \\iota ( k ) = \\ln { \\frac { ( k + 1 ) ( k + 2 ) S A } { \\delta } } } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        270,
+                                        276,
+                                        375,
+                                        299
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". By a union bound for all",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        375,
+                                        284,
+                                        381,
+                                        293
+                                    ],
+                                    "score": 0.81,
+                                    "content": "k",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        382,
+                                        276,
+                                        478,
+                                        299
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", this holds for arbitrary",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        478,
+                                        284,
+                                        502,
+                                        294
+                                    ],
+                                    "score": 0.89,
+                                    "content": "k > 0",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                293,
+                                328,
+                                307
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        293,
+                                        143,
+                                        307
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arbitrary",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        143,
+                                        295,
+                                        198,
+                                        305
+                                    ],
+                                    "score": 0.33,
+                                    "content": "s \\in S , a \\in A",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        198,
+                                        293,
+                                        328,
+                                        307
+                                    ],
+                                    "score": 1.0,
+                                    "content": "simultaneously with probability",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 14.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        205,
+                        307,
+                        404,
+                        341
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                205,
+                                307,
+                                404,
+                                341
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        205,
+                                        307,
+                                        404,
+                                        341
+                                    ],
+                                    "score": 0.93,
+                                    "content": "1 - \\sum _ { s ^ { \\prime } \\in S , a ^ { \\prime } \\in A } \\sum _ { k = 1 } ^ { \\infty } \\frac { \\delta } { 2 S A ( k + 1 ) ( k + 2 ) } = 1 - \\frac { \\delta } { 2 } .",
+                                    "type": "interline_equation",
+                                    "image_path": "d36f303c3c54ca211346b95b702c878d2e496acc0473679ca8912f1c49bc42a5.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                205,
+                                307,
+                                404,
+                                324.0
+                            ],
+                            "spans": [],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                205,
+                                324.0,
+                                404,
+                                341.0
+                            ],
+                            "spans": [],
+                            "index": 17
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        343,
+                        504,
+                        366
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                341,
+                                505,
+                                356
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        341,
+                                        371,
+                                        356
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Therefore, we conclude that (16) holds for the random variable",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        371,
+                                        343,
+                                        425,
+                                        356
+                                    ],
+                                    "score": 0.93,
+                                    "content": "t = N _ { p } ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        426,
+                                        341,
+                                        473,
+                                        356
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and for all",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        474,
+                                        346,
+                                        480,
+                                        355
+                                    ],
+                                    "score": 0.77,
+                                    "content": "p",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        480,
+                                        341,
+                                        505,
+                                        356
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                354,
+                                220,
+                                366
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        354,
+                                        153,
+                                        366
+                                    ],
+                                    "score": 1.0,
+                                    "content": "probability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        354,
+                                        186,
+                                        366
+                                    ],
+                                    "score": 0.91,
+                                    "content": "1 - \\delta / 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        186,
+                                        354,
+                                        220,
+                                        366
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as well.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 18.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        373,
+                        418,
+                        391
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                371,
+                                416,
+                                392
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        376,
+                                        336,
+                                        389
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Proof of the right hand side of (13): We also know that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        337,
+                                        371,
+                                        416,
+                                        392
+                                    ],
+                                    "score": 0.68,
+                                    "content": "\\begin{array} { r } { ( b _ { k } = \\frac { c _ { 2 } } { 1 - \\gamma } \\sqrt { \\frac { H \\iota ( k ) } { k } } ) } \\end{array}",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 20
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        208,
+                        393,
+                        401,
+                        427
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                208,
+                                393,
+                                401,
+                                427
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        208,
+                                        393,
+                                        401,
+                                        427
+                                    ],
+                                    "score": 0.86,
+                                    "content": "\\frac { c _ { 2 } } { 1 - \\gamma } \\sqrt { \\frac { H \\iota ( k ) } { k } } \\leq \\sum _ { i = 1 } ^ { k } \\alpha _ { k } ^ { i } b _ { i } \\leq \\frac { 2 c _ { 2 } } { 1 - \\gamma } \\sqrt { \\frac { H \\iota ( k ) } { k } } .",
+                                    "type": "interline_equation",
+                                    "image_path": "881fb37a93a36ca33279a8cb7352a55121d9d63aa62473943680b180547b1336.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                208,
+                                393,
+                                401,
+                                410.0
+                            ],
+                            "spans": [],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                208,
+                                410.0,
+                                401,
+                                427.0
+                            ],
+                            "spans": [],
+                            "index": 22
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        428,
+                        206,
+                        440
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                427,
+                                207,
+                                442
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        427,
+                                        207,
+                                        442
+                                    ],
+                                    "score": 1.0,
+                                    "content": "It is implied by (16) that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 23
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        149,
+                        442,
+                        462,
+                        510
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                149,
+                                442,
+                                462,
+                                510
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        149,
+                                        442,
+                                        462,
+                                        510
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\begin{array} { r l } & { ( Q _ { p } - Q ^ { * } ) ( s , a ) \\leq \\displaystyle \\frac { \\alpha _ { t } ^ { 0 } } { 1 - \\gamma } + \\gamma \\left| \\displaystyle \\sum _ { i = 1 } ^ { t } \\Delta _ { i } \\right| + \\displaystyle \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\left[ \\gamma ( \\hat { V } _ { t _ { i } } - V ^ { * } ) ( x _ { t _ { i } + 1 } ) + b _ { i } \\right] } \\\\ & { \\qquad \\leq \\displaystyle \\frac { \\alpha _ { t } ^ { 0 } } { 1 - \\gamma } + \\displaystyle \\frac { 3 c _ { 2 } } { 1 - \\gamma } \\sqrt { \\frac { H \\iota ( t ) } { t } } + \\displaystyle \\sum _ { i = 1 } ^ { t } \\gamma \\alpha _ { t } ^ { i } ( \\hat { V } ^ { t _ { i } } - V ^ { * } ) ( x _ { t _ { i } + 1 } ) } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "d2bbc005947d28dd95e009c07818fe62e6d9b1e5309a47331c5537b6fbe06992.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 25,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                149,
+                                442,
+                                462,
+                                464.6666666666667
+                            ],
+                            "spans": [],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                149,
+                                464.6666666666667,
+                                462,
+                                487.33333333333337
+                            ],
+                            "spans": [],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                149,
+                                487.33333333333337,
+                                462,
+                                510.00000000000006
+                            ],
+                            "spans": [],
+                            "index": 26
+                        }
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        218,
+                        523,
+                        403,
+                        556
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                218,
+                                523,
+                                403,
+                                556
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        218,
+                                        523,
+                                        403,
+                                        556
+                                    ],
+                                    "score": 0.38,
+                                    "content": "\\leq \\frac { \\alpha _ { t } ^ { 0 } } { 1 - \\gamma } + \\sum _ { i = 1 } ^ { t } \\gamma \\alpha _ { t } ^ { i } ( { \\hat { V } } ^ { t _ { i } } - V ^ { * } ) ( x _ { t _ { i } + 1 } ) + \\beta _ { t } .",
+                                    "type": "interline_equation",
+                                    "image_path": "53eab3d1f26c37eff9f588636d51ccb07f492de053eae442ba9c0192a7489963.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 27.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                218,
+                                523,
+                                403,
+                                539.5
+                            ],
+                            "spans": [],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                218,
+                                539.5,
+                                403,
+                                556.0
+                            ],
+                            "spans": [],
+                            "index": 28
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        558,
+                        343,
+                        573
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                557,
+                                343,
+                                574
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        557,
+                                        146,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Note that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        146,
+                                        559,
+                                        262,
+                                        573
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\beta _ { t } = c _ { 3 } ( 1 - \\gamma ) ^ { - 1 } \\sqrt { H \\iota ( t ) / t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        262,
+                                        557,
+                                        266,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": ";",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        266,
+                                        558,
+                                        341,
+                                        572
+                                    ],
+                                    "score": 0.73,
+                                    "content": "c _ { 3 } = 3 c _ { 2 } = 1 2 { \\sqrt { 2 } } .",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        341,
+                                        557,
+                                        343,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 29
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        576,
+                        505,
+                        600
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                576,
+                                506,
+                                589
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        576,
+                                        506,
+                                        589
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Proof of the left hand side of (13): Now, we assume that event that (16) holds. We assert that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                587,
+                                453,
+                                601
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        588,
+                                        146,
+                                        600
+                                    ],
+                                    "score": 0.92,
+                                    "content": "Q _ { p } \\geq Q ^ { * }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        146,
+                                        587,
+                                        174,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for all",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        174,
+                                        588,
+                                        197,
+                                        600
+                                    ],
+                                    "score": 0.92,
+                                    "content": "( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        197,
+                                        587,
+                                        215,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        215,
+                                        588,
+                                        242,
+                                        600
+                                    ],
+                                    "score": 0.92,
+                                    "content": "p \\leq p ^ { \\prime }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        243,
+                                        587,
+                                        398,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". This assertion is obviously true when",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        398,
+                                        588,
+                                        425,
+                                        599
+                                    ],
+                                    "score": 0.93,
+                                    "content": "p ^ { \\prime } = 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        425,
+                                        587,
+                                        453,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Then",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        }
+                    ],
+                    "index": 30.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        163,
+                        601,
+                        447,
+                        671
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                163,
+                                601,
+                                447,
+                                671
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        163,
+                                        601,
+                                        447,
+                                        671
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { c l } { ( Q _ { p } - Q ^ { * } ) ( s , a ) \\geq - \\gamma \\displaystyle \\left| \\displaystyle \\sum _ { i = 1 } ^ { t } \\Delta _ { i } \\right| + \\displaystyle \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\left[ \\gamma ( \\hat { V } _ { t _ { i } } - V ^ { * } ) ( x _ { t _ { i } + 1 } ) + b _ { i } \\right] } \\\\ { \\geq \\displaystyle \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } b _ { i } - \\gamma \\displaystyle \\left| \\displaystyle \\sum _ { i = 1 } ^ { t } \\Delta _ { i } \\right| \\geq 0 . } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "70ff20e4e31a1bb0299ebb34008753b3eaca5c5e3da766015eda50bc514d5a51.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 33,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                163,
+                                601,
+                                447,
+                                624.3333333333334
+                            ],
+                            "spans": [],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                163,
+                                624.3333333333334,
+                                447,
+                                647.6666666666667
+                            ],
+                            "spans": [],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                163,
+                                647.6666666666667,
+                                447,
+                                671.0000000000001
+                            ],
+                            "spans": [],
+                            "index": 34
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        671,
+                        425,
+                        684
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                670,
+                                425,
+                                685
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        670,
+                                        238,
+                                        685
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Therefore the assertion holds for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        239,
+                                        672,
+                                        265,
+                                        683
+                                    ],
+                                    "score": 0.91,
+                                    "content": "p ^ { \\prime } + 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        266,
+                                        670,
+                                        415,
+                                        685
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as well. By induction, it holds for all",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        415,
+                                        674,
+                                        421,
+                                        683
+                                    ],
+                                    "score": 0.79,
+                                    "content": "p",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        421,
+                                        670,
+                                        425,
+                                        685
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        }
+                    ],
+                    "index": 35
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        689,
+                        505,
+                        717
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                688,
+                                505,
+                                703
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        688,
+                                        280,
+                                        703
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We now see that (13) holds for probability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        281,
+                                        690,
+                                        313,
+                                        702
+                                    ],
+                                    "score": 0.91,
+                                    "content": "1 - \\delta / 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        314,
+                                        688,
+                                        342,
+                                        703
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for all",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        342,
+                                        691,
+                                        368,
+                                        702
+                                    ],
+                                    "score": 0.77,
+                                    "content": "p , s , a",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        369,
+                                        688,
+                                        397,
+                                        703
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Since",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        398,
+                                        688,
+                                        433,
+                                        703
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\hat { Q } _ { p } ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        434,
+                                        688,
+                                        505,
+                                        703
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is always greater",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                702,
+                                503,
+                                718
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        702,
+                                        126,
+                                        718
+                                    ],
+                                    "score": 1.0,
+                                    "content": "than",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        126,
+                                        703,
+                                        164,
+                                        716
+                                    ],
+                                    "score": 0.93,
+                                    "content": "Q _ { p ^ { \\prime } } ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        165,
+                                        702,
+                                        203,
+                                        718
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for some",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        204,
+                                        703,
+                                        231,
+                                        715
+                                    ],
+                                    "score": 0.92,
+                                    "content": "p ^ { \\prime } \\leq p",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        231,
+                                        702,
+                                        290,
+                                        718
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", we know that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        291,
+                                        703,
+                                        425,
+                                        716
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\hat { Q } _ { p } ( s , a ) \\geq Q _ { p ^ { \\prime } } ( s , a ) \\geq Q ^ { * } ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        425,
+                                        702,
+                                        503,
+                                        718
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", thus proving (14).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 36.5
+                }
+            ],
+            "page_idx": 12,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        26,
+                        294,
+                        38
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                25,
+                                294,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        25,
+                                        294,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        311,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                312,
+                                764
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        312,
+                                        764
+                                    ],
+                                    "score": 1.0,
+                                    "content": "13",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        494,
+                        721,
+                        504,
+                        731
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                497,
+                                723,
+                                504,
+                                730
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        497,
+                                        723,
+                                        504,
+                                        730
+                                    ],
+                                    "score": 0.996,
+                                    "content": "□",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        82,
+                        506,
+                        115
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                81,
+                                506,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        81,
+                                        254,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The identity above holds for arbitrary",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        254,
+                                        85,
+                                        271,
+                                        93
+                                    ],
+                                    "score": 0.31,
+                                    "content": "p , s",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        271,
+                                        81,
+                                        288,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        288,
+                                        85,
+                                        294,
+                                        92
+                                    ],
+                                    "score": 0.73,
+                                    "content": "a",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        295,
+                                        81,
+                                        332,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Now fix",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        333,
+                                        83,
+                                        357,
+                                        93
+                                    ],
+                                    "score": 0.89,
+                                    "content": "s \\in S",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        357,
+                                        81,
+                                        360,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        361,
+                                        83,
+                                        387,
+                                        93
+                                    ],
+                                    "score": 0.88,
+                                    "content": "a \\in A",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        387,
+                                        81,
+                                        404,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        405,
+                                        83,
+                                        430,
+                                        94
+                                    ],
+                                    "score": 0.9,
+                                    "content": "p \\in \\mathbb N",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        430,
+                                        81,
+                                        450,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        450,
+                                        83,
+                                        502,
+                                        95
+                                    ],
+                                    "score": 0.93,
+                                    "content": "t = N _ { p } ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        502,
+                                        81,
+                                        506,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                93,
+                                507,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        93,
+                                        163,
+                                        106
+                                    ],
+                                    "score": 0.93,
+                                    "content": "t _ { i } = \\tau ( s , a , i )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        163,
+                                        93,
+                                        185,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". The",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        186,
+                                        94,
+                                        209,
+                                        104
+                                    ],
+                                    "score": 0.9,
+                                    "content": "t = 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        209,
+                                        93,
+                                        313,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "case is trivial; we assume",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        314,
+                                        94,
+                                        337,
+                                        105
+                                    ],
+                                    "score": 0.9,
+                                    "content": "t \\geq 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        337,
+                                        93,
+                                        496,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "below. Now consider an arbitrary fixed",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        496,
+                                        95,
+                                        503,
+                                        104
+                                    ],
+                                    "score": 0.83,
+                                    "content": "k",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        503,
+                                        93,
+                                        507,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                103,
+                                137,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        103,
+                                        137,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Define",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1,
+                    "bbox_fs": [
+                        105,
+                        81,
+                        507,
+                        117
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        206,
+                        115,
+                        404,
+                        137
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                206,
+                                115,
+                                404,
+                                137
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        206,
+                                        115,
+                                        404,
+                                        137
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\Delta _ { i } = \\left( \\alpha _ { k } ^ { i } \\cdot I [ t _ { i } < \\infty ] \\cdot \\left( \\mathbb { P } V ^ { * } - \\mathbb { \\hat { P } } _ { t _ { i } } V ^ { * } \\right) ( s , a ) \\right)",
+                                    "type": "interline_equation",
+                                    "image_path": "7ed6137165be41b2ad3ac59dec10e06c5f86c9778d1953d9a7904ac5097d5be4.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                206,
+                                115,
+                                404,
+                                137
+                            ],
+                            "spans": [],
+                            "index": 3
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        138,
+                        507,
+                        174
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                137,
+                                506,
+                                152
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        137,
+                                        124,
+                                        152
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        124,
+                                        139,
+                                        135,
+                                        149
+                                    ],
+                                    "score": 0.86,
+                                    "content": "F _ { i }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        135,
+                                        137,
+                                        168,
+                                        152
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        168,
+                                        140,
+                                        176,
+                                        149
+                                    ],
+                                    "score": 0.81,
+                                    "content": "\\sigma",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        176,
+                                        137,
+                                        336,
+                                        152
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-Field generated by random variables",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        337,
+                                        139,
+                                        413,
+                                        150
+                                    ],
+                                    "score": 0.88,
+                                    "content": "( s _ { 1 } , a _ { 1 } , . . . , s _ { t _ { i } } , a _ { t _ { i } } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        414,
+                                        137,
+                                        506,
+                                        152
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". It can be seen that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                144,
+                                507,
+                                167
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        150,
+                                        166,
+                                        162
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\mathbb { E } \\left[ \\Delta _ { i } | F _ { i } \\right] = 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        167,
+                                        144,
+                                        196,
+                                        167
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", while",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        197,
+                                        150,
+                                        209,
+                                        160
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\Delta _ { i }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        210,
+                                        144,
+                                        281,
+                                        167
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is measurable in",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        281,
+                                        150,
+                                        302,
+                                        162
+                                    ],
+                                    "score": 0.92,
+                                    "content": "F _ { i + 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        144,
+                                        358,
+                                        167
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Also, since",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        358,
+                                        150,
+                                        447,
+                                        163
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\textstyle 0 \\leq V ^ { \\ast } ( s , { \\bar { a } } ) \\leq { \\frac { 1 } { 1 - \\gamma } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        447,
+                                        144,
+                                        452,
+                                        167
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        452,
+                                        149,
+                                        502,
+                                        164
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\begin{array} { r } { | \\Delta _ { i } | \\le \\frac { 2 } { 1 - \\gamma } } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        503,
+                                        144,
+                                        507,
+                                        167
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                160,
+                                457,
+                                175
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        160,
+                                        150,
+                                        175
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Therefore,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        151,
+                                        163,
+                                        163,
+                                        173
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\Delta _ { i }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        163,
+                                        160,
+                                        457,
+                                        175
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is a martingale difference sequence; by the Azuma-Hoeffding inequality,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 5,
+                    "bbox_fs": [
+                        105,
+                        137,
+                        507,
+                        175
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        183,
+                        175,
+                        428,
+                        210
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                183,
+                                175,
+                                428,
+                                210
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        183,
+                                        175,
+                                        428,
+                                        210
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\mathrm { P r } \\left[ \\left| \\sum _ { i = 1 } ^ { k } \\Delta _ { i } \\right| > \\eta \\right] \\leq 2 \\exp \\left\\{ - \\frac { \\eta ^ { 2 } } { 8 \\left( 1 - \\gamma \\right) ^ { - 2 } \\sum _ { i = 1 } ^ { k } ( \\alpha _ { k } ^ { i } ) ^ { 2 } } \\right\\} .",
+                                    "type": "interline_equation",
+                                    "image_path": "e1fd0592f2fbfb43a68fa1b2348697afc8a3b51894eb01a3c12dfc2769dfd098.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                183,
+                                175,
+                                428,
+                                186.66666666666666
+                            ],
+                            "spans": [],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                183,
+                                186.66666666666666,
+                                428,
+                                198.33333333333331
+                            ],
+                            "spans": [],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                183,
+                                198.33333333333331,
+                                428,
+                                209.99999999999997
+                            ],
+                            "spans": [],
+                            "index": 9
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        211,
+                        421,
+                        224
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                210,
+                                421,
+                                225
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        210,
+                                        159,
+                                        225
+                                    ],
+                                    "score": 1.0,
+                                    "content": "By choosing",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        159,
+                                        214,
+                                        165,
+                                        223
+                                    ],
+                                    "score": 0.76,
+                                    "content": "\\eta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        166,
+                                        210,
+                                        307,
+                                        225
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", we can show that with probability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        212,
+                                        416,
+                                        223
+                                    ],
+                                    "score": 0.9,
+                                    "content": "1 - \\delta / \\left[ S A ( k + 1 ) ( k + 2 ) \\right]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        417,
+                                        210,
+                                        421,
+                                        225
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 10,
+                    "bbox_fs": [
+                        106,
+                        210,
+                        421,
+                        225
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        148,
+                        241,
+                        461,
+                        279
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                148,
+                                241,
+                                461,
+                                279
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        148,
+                                        241,
+                                        461,
+                                        279
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\left| \\sum _ { i = 1 } ^ { k } \\Delta _ { i } \\right| \\leq \\frac { 2 \\sqrt { 2 } } { 1 - \\gamma } \\cdot \\sqrt { \\sum _ { i = 1 } ^ { k } ( \\alpha _ { k } ^ { i } ) ^ { 2 } \\cdot \\ln \\frac { 2 ( k + 1 ) ( k + 2 ) S A } { \\delta } } \\leq \\frac { c _ { 2 } } { 1 - \\gamma } \\sqrt { \\frac { H \\iota ( k ) } { k } } .",
+                                    "type": "interline_equation",
+                                    "image_path": "4635fc976e34fd23da44f8967bc69d839d0dafaecc85d492653e8f8184e7782e.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                148,
+                                241,
+                                461,
+                                253.66666666666666
+                            ],
+                            "spans": [],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                148,
+                                253.66666666666666,
+                                461,
+                                266.3333333333333
+                            ],
+                            "spans": [],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                148,
+                                266.3333333333333,
+                                461,
+                                279.0
+                            ],
+                            "spans": [],
+                            "index": 13
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        281,
+                        506,
+                        306
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                276,
+                                502,
+                                299
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        276,
+                                        128,
+                                        299
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Here",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        128,
+                                        282,
+                                        170,
+                                        294
+                                    ],
+                                    "score": 0.89,
+                                    "content": "c _ { 2 } = 4 \\sqrt { 2 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        171,
+                                        276,
+                                        174,
+                                        299
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        174,
+                                        281,
+                                        270,
+                                        296
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { r } { \\iota ( k ) = \\ln { \\frac { ( k + 1 ) ( k + 2 ) S A } { \\delta } } } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        270,
+                                        276,
+                                        375,
+                                        299
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". By a union bound for all",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        375,
+                                        284,
+                                        381,
+                                        293
+                                    ],
+                                    "score": 0.81,
+                                    "content": "k",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        382,
+                                        276,
+                                        478,
+                                        299
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", this holds for arbitrary",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        478,
+                                        284,
+                                        502,
+                                        294
+                                    ],
+                                    "score": 0.89,
+                                    "content": "k > 0",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                293,
+                                328,
+                                307
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        293,
+                                        143,
+                                        307
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arbitrary",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        143,
+                                        295,
+                                        198,
+                                        305
+                                    ],
+                                    "score": 0.33,
+                                    "content": "s \\in S , a \\in A",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        198,
+                                        293,
+                                        328,
+                                        307
+                                    ],
+                                    "score": 1.0,
+                                    "content": "simultaneously with probability",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 14.5,
+                    "bbox_fs": [
+                        104,
+                        276,
+                        502,
+                        307
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        205,
+                        307,
+                        404,
+                        341
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                205,
+                                307,
+                                404,
+                                341
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        205,
+                                        307,
+                                        404,
+                                        341
+                                    ],
+                                    "score": 0.93,
+                                    "content": "1 - \\sum _ { s ^ { \\prime } \\in S , a ^ { \\prime } \\in A } \\sum _ { k = 1 } ^ { \\infty } \\frac { \\delta } { 2 S A ( k + 1 ) ( k + 2 ) } = 1 - \\frac { \\delta } { 2 } .",
+                                    "type": "interline_equation",
+                                    "image_path": "d36f303c3c54ca211346b95b702c878d2e496acc0473679ca8912f1c49bc42a5.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                205,
+                                307,
+                                404,
+                                324.0
+                            ],
+                            "spans": [],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                205,
+                                324.0,
+                                404,
+                                341.0
+                            ],
+                            "spans": [],
+                            "index": 17
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        343,
+                        504,
+                        366
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                341,
+                                505,
+                                356
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        341,
+                                        371,
+                                        356
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Therefore, we conclude that (16) holds for the random variable",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        371,
+                                        343,
+                                        425,
+                                        356
+                                    ],
+                                    "score": 0.93,
+                                    "content": "t = N _ { p } ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        426,
+                                        341,
+                                        473,
+                                        356
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and for all",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        474,
+                                        346,
+                                        480,
+                                        355
+                                    ],
+                                    "score": 0.77,
+                                    "content": "p",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        480,
+                                        341,
+                                        505,
+                                        356
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                354,
+                                220,
+                                366
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        354,
+                                        153,
+                                        366
+                                    ],
+                                    "score": 1.0,
+                                    "content": "probability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        354,
+                                        186,
+                                        366
+                                    ],
+                                    "score": 0.91,
+                                    "content": "1 - \\delta / 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        186,
+                                        354,
+                                        220,
+                                        366
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as well.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 18.5,
+                    "bbox_fs": [
+                        105,
+                        341,
+                        505,
+                        366
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        373,
+                        418,
+                        391
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                371,
+                                416,
+                                392
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        376,
+                                        336,
+                                        389
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Proof of the right hand side of (13): We also know that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        337,
+                                        371,
+                                        416,
+                                        392
+                                    ],
+                                    "score": 0.68,
+                                    "content": "\\begin{array} { r } { ( b _ { k } = \\frac { c _ { 2 } } { 1 - \\gamma } \\sqrt { \\frac { H \\iota ( k ) } { k } } ) } \\end{array}",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 20,
+                    "bbox_fs": [
+                        105,
+                        371,
+                        416,
+                        392
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        208,
+                        393,
+                        401,
+                        427
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                208,
+                                393,
+                                401,
+                                427
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        208,
+                                        393,
+                                        401,
+                                        427
+                                    ],
+                                    "score": 0.86,
+                                    "content": "\\frac { c _ { 2 } } { 1 - \\gamma } \\sqrt { \\frac { H \\iota ( k ) } { k } } \\leq \\sum _ { i = 1 } ^ { k } \\alpha _ { k } ^ { i } b _ { i } \\leq \\frac { 2 c _ { 2 } } { 1 - \\gamma } \\sqrt { \\frac { H \\iota ( k ) } { k } } .",
+                                    "type": "interline_equation",
+                                    "image_path": "881fb37a93a36ca33279a8cb7352a55121d9d63aa62473943680b180547b1336.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                208,
+                                393,
+                                401,
+                                410.0
+                            ],
+                            "spans": [],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                208,
+                                410.0,
+                                401,
+                                427.0
+                            ],
+                            "spans": [],
+                            "index": 22
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        428,
+                        206,
+                        440
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                427,
+                                207,
+                                442
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        427,
+                                        207,
+                                        442
+                                    ],
+                                    "score": 1.0,
+                                    "content": "It is implied by (16) that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 23,
+                    "bbox_fs": [
+                        105,
+                        427,
+                        207,
+                        442
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        149,
+                        442,
+                        462,
+                        510
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                149,
+                                442,
+                                462,
+                                510
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        149,
+                                        442,
+                                        462,
+                                        510
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\begin{array} { r l } & { ( Q _ { p } - Q ^ { * } ) ( s , a ) \\leq \\displaystyle \\frac { \\alpha _ { t } ^ { 0 } } { 1 - \\gamma } + \\gamma \\left| \\displaystyle \\sum _ { i = 1 } ^ { t } \\Delta _ { i } \\right| + \\displaystyle \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\left[ \\gamma ( \\hat { V } _ { t _ { i } } - V ^ { * } ) ( x _ { t _ { i } + 1 } ) + b _ { i } \\right] } \\\\ & { \\qquad \\leq \\displaystyle \\frac { \\alpha _ { t } ^ { 0 } } { 1 - \\gamma } + \\displaystyle \\frac { 3 c _ { 2 } } { 1 - \\gamma } \\sqrt { \\frac { H \\iota ( t ) } { t } } + \\displaystyle \\sum _ { i = 1 } ^ { t } \\gamma \\alpha _ { t } ^ { i } ( \\hat { V } ^ { t _ { i } } - V ^ { * } ) ( x _ { t _ { i } + 1 } ) } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "d2bbc005947d28dd95e009c07818fe62e6d9b1e5309a47331c5537b6fbe06992.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 25,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                149,
+                                442,
+                                462,
+                                464.6666666666667
+                            ],
+                            "spans": [],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                149,
+                                464.6666666666667,
+                                462,
+                                487.33333333333337
+                            ],
+                            "spans": [],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                149,
+                                487.33333333333337,
+                                462,
+                                510.00000000000006
+                            ],
+                            "spans": [],
+                            "index": 26
+                        }
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        218,
+                        523,
+                        403,
+                        556
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                218,
+                                523,
+                                403,
+                                556
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        218,
+                                        523,
+                                        403,
+                                        556
+                                    ],
+                                    "score": 0.38,
+                                    "content": "\\leq \\frac { \\alpha _ { t } ^ { 0 } } { 1 - \\gamma } + \\sum _ { i = 1 } ^ { t } \\gamma \\alpha _ { t } ^ { i } ( { \\hat { V } } ^ { t _ { i } } - V ^ { * } ) ( x _ { t _ { i } + 1 } ) + \\beta _ { t } .",
+                                    "type": "interline_equation",
+                                    "image_path": "53eab3d1f26c37eff9f588636d51ccb07f492de053eae442ba9c0192a7489963.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 27.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                218,
+                                523,
+                                403,
+                                539.5
+                            ],
+                            "spans": [],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                218,
+                                539.5,
+                                403,
+                                556.0
+                            ],
+                            "spans": [],
+                            "index": 28
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        558,
+                        343,
+                        573
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                557,
+                                343,
+                                574
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        557,
+                                        146,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Note that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        146,
+                                        559,
+                                        262,
+                                        573
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\beta _ { t } = c _ { 3 } ( 1 - \\gamma ) ^ { - 1 } \\sqrt { H \\iota ( t ) / t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        262,
+                                        557,
+                                        266,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": ";",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        266,
+                                        558,
+                                        341,
+                                        572
+                                    ],
+                                    "score": 0.73,
+                                    "content": "c _ { 3 } = 3 c _ { 2 } = 1 2 { \\sqrt { 2 } } .",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        341,
+                                        557,
+                                        343,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 29,
+                    "bbox_fs": [
+                        105,
+                        557,
+                        343,
+                        574
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        576,
+                        505,
+                        600
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                576,
+                                506,
+                                589
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        576,
+                                        506,
+                                        589
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Proof of the left hand side of (13): Now, we assume that event that (16) holds. We assert that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                587,
+                                453,
+                                601
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        588,
+                                        146,
+                                        600
+                                    ],
+                                    "score": 0.92,
+                                    "content": "Q _ { p } \\geq Q ^ { * }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        146,
+                                        587,
+                                        174,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for all",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        174,
+                                        588,
+                                        197,
+                                        600
+                                    ],
+                                    "score": 0.92,
+                                    "content": "( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        197,
+                                        587,
+                                        215,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        215,
+                                        588,
+                                        242,
+                                        600
+                                    ],
+                                    "score": 0.92,
+                                    "content": "p \\leq p ^ { \\prime }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        243,
+                                        587,
+                                        398,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". This assertion is obviously true when",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        398,
+                                        588,
+                                        425,
+                                        599
+                                    ],
+                                    "score": 0.93,
+                                    "content": "p ^ { \\prime } = 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        425,
+                                        587,
+                                        453,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Then",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        }
+                    ],
+                    "index": 30.5,
+                    "bbox_fs": [
+                        105,
+                        576,
+                        506,
+                        601
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        163,
+                        601,
+                        447,
+                        671
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                163,
+                                601,
+                                447,
+                                671
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        163,
+                                        601,
+                                        447,
+                                        671
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { c l } { ( Q _ { p } - Q ^ { * } ) ( s , a ) \\geq - \\gamma \\displaystyle \\left| \\displaystyle \\sum _ { i = 1 } ^ { t } \\Delta _ { i } \\right| + \\displaystyle \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\left[ \\gamma ( \\hat { V } _ { t _ { i } } - V ^ { * } ) ( x _ { t _ { i } + 1 } ) + b _ { i } \\right] } \\\\ { \\geq \\displaystyle \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } b _ { i } - \\gamma \\displaystyle \\left| \\displaystyle \\sum _ { i = 1 } ^ { t } \\Delta _ { i } \\right| \\geq 0 . } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "70ff20e4e31a1bb0299ebb34008753b3eaca5c5e3da766015eda50bc514d5a51.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 33,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                163,
+                                601,
+                                447,
+                                624.3333333333334
+                            ],
+                            "spans": [],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                163,
+                                624.3333333333334,
+                                447,
+                                647.6666666666667
+                            ],
+                            "spans": [],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                163,
+                                647.6666666666667,
+                                447,
+                                671.0000000000001
+                            ],
+                            "spans": [],
+                            "index": 34
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        671,
+                        425,
+                        684
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                670,
+                                425,
+                                685
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        670,
+                                        238,
+                                        685
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Therefore the assertion holds for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        239,
+                                        672,
+                                        265,
+                                        683
+                                    ],
+                                    "score": 0.91,
+                                    "content": "p ^ { \\prime } + 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        266,
+                                        670,
+                                        415,
+                                        685
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as well. By induction, it holds for all",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        415,
+                                        674,
+                                        421,
+                                        683
+                                    ],
+                                    "score": 0.79,
+                                    "content": "p",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        421,
+                                        670,
+                                        425,
+                                        685
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        }
+                    ],
+                    "index": 35,
+                    "bbox_fs": [
+                        105,
+                        670,
+                        425,
+                        685
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        689,
+                        505,
+                        717
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                688,
+                                505,
+                                703
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        688,
+                                        280,
+                                        703
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We now see that (13) holds for probability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        281,
+                                        690,
+                                        313,
+                                        702
+                                    ],
+                                    "score": 0.91,
+                                    "content": "1 - \\delta / 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        314,
+                                        688,
+                                        342,
+                                        703
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for all",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        342,
+                                        691,
+                                        368,
+                                        702
+                                    ],
+                                    "score": 0.77,
+                                    "content": "p , s , a",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        369,
+                                        688,
+                                        397,
+                                        703
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Since",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        398,
+                                        688,
+                                        433,
+                                        703
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\hat { Q } _ { p } ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        434,
+                                        688,
+                                        505,
+                                        703
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is always greater",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                702,
+                                503,
+                                718
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        702,
+                                        126,
+                                        718
+                                    ],
+                                    "score": 1.0,
+                                    "content": "than",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        126,
+                                        703,
+                                        164,
+                                        716
+                                    ],
+                                    "score": 0.93,
+                                    "content": "Q _ { p ^ { \\prime } } ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        165,
+                                        702,
+                                        203,
+                                        718
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for some",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        204,
+                                        703,
+                                        231,
+                                        715
+                                    ],
+                                    "score": 0.92,
+                                    "content": "p ^ { \\prime } \\leq p",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        231,
+                                        702,
+                                        290,
+                                        718
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", we know that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        291,
+                                        703,
+                                        425,
+                                        716
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\hat { Q } _ { p } ( s , a ) \\geq Q _ { p ^ { \\prime } } ( s , a ) \\geq Q ^ { * } ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        425,
+                                        702,
+                                        503,
+                                        718
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", thus proving (14).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 36.5,
+                    "bbox_fs": [
+                        105,
+                        688,
+                        505,
+                        718
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        81,
+                        505,
+                        107
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                79,
+                                505,
+                                97
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        79,
+                                        350,
+                                        97
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We now give a proof for lemma 2. Recall the definition for a",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        351,
+                                        83,
+                                        378,
+                                        94
+                                    ],
+                                    "score": 0.92,
+                                    "content": "( C , w )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        378,
+                                        79,
+                                        471,
+                                        97
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-sequence. A sequence",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        472,
+                                        82,
+                                        505,
+                                        95
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( w _ { t } ) _ { t \\geq 1 }",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                92,
+                                483,
+                                108
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        92,
+                                        164,
+                                        108
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is said to be a",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        164,
+                                        94,
+                                        191,
+                                        106
+                                    ],
+                                    "score": 0.95,
+                                    "content": "( C , w )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        191,
+                                        92,
+                                        246,
+                                        108
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-sequence for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        246,
+                                        94,
+                                        285,
+                                        105
+                                    ],
+                                    "score": 0.92,
+                                    "content": "C , w > 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        285,
+                                        92,
+                                        297,
+                                        108
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", if",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        298,
+                                        94,
+                                        348,
+                                        105
+                                    ],
+                                    "score": 0.92,
+                                    "content": "0 \\leq w _ { t } \\leq w",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        349,
+                                        92,
+                                        376,
+                                        108
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for all",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        376,
+                                        94,
+                                        399,
+                                        105
+                                    ],
+                                    "score": 0.89,
+                                    "content": "t \\geq 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        399,
+                                        92,
+                                        420,
+                                        108
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        420,
+                                        93,
+                                        478,
+                                        108
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\textstyle \\sum _ { t \\geq 1 } w _ { t } \\leq C",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        479,
+                                        92,
+                                        483,
+                                        108
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        118,
+                        313,
+                        131
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                118,
+                                312,
+                                132
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        118,
+                                        152,
+                                        132
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Proof. Let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        152,
+                                        119,
+                                        216,
+                                        131
+                                    ],
+                                    "score": 0.95,
+                                    "content": "n _ { t } = N _ { t } ( s _ { t } , a _ { t } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        217,
+                                        118,
+                                        312,
+                                        132
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for simplicity; we have",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        158,
+                        134,
+                        451,
+                        226
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                158,
+                                134,
+                                451,
+                                226
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        158,
+                                        134,
+                                        451,
+                                        226
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { r l } {  { \\sum _ { t \\geq 1 } w _ { t } ( \\hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) } } \\\\ & { \\leq \\sum _ { t \\geq 1 } w _ { t } ( Q _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) } \\\\ & { \\leq \\sum _ { t \\geq 1 } w _ { t } [ \\cfrac { \\alpha _ { n _ { t } } ^ { 0 } } { 1 - \\gamma } + \\beta _ { n _ { t } } + \\gamma \\sum _ { i = 1 } ^ { n _ { t } } \\alpha _ { n _ { t } } ^ { i } ( \\hat { V } _ { \\tau ( s _ { t } , a _ { t } , i ) } - V ^ { * } ) ( s _ { \\tau ( s _ { t } , a _ { t } , i ) + 1 } ) ] } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "56de998ef0518be48301779db9712c42690034bbbfeba7d7ae47e786453e29e7.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                158,
+                                134,
+                                451,
+                                164.66666666666666
+                            ],
+                            "spans": [],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                158,
+                                164.66666666666666,
+                                451,
+                                195.33333333333331
+                            ],
+                            "spans": [],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                158,
+                                195.33333333333331,
+                                451,
+                                225.99999999999997
+                            ],
+                            "spans": [],
+                            "index": 5
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        230,
+                        505,
+                        254
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                228,
+                                507,
+                                246
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        228,
+                                        295,
+                                        246
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The last inequality is due to lemma 4. Note that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        230,
+                                        362,
+                                        244
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\alpha _ { n _ { t } } ^ { 0 } = \\mathbb { I } [ n _ { t } = 0 ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        362,
+                                        228,
+                                        507,
+                                        246
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the first term in the summation can",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                240,
+                                170,
+                                255
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        240,
+                                        170,
+                                        255
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be bounded by,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 6.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        256,
+                        256,
+                        354,
+                        290
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                256,
+                                256,
+                                354,
+                                290
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        256,
+                                        256,
+                                        354,
+                                        290
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\sum _ { t \\geq 1 } w _ { t } \\frac { \\alpha _ { n _ { t } } ^ { 0 } } { 1 - \\gamma } \\leq \\frac { S A w } { 1 - \\gamma } .",
+                                    "type": "interline_equation",
+                                    "image_path": "fb8a30f2f69b0a0ef551b8c5d16a0c30b4272df4f37761a5fa9bb9799022d5bd.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                256,
+                                256,
+                                354,
+                                273.0
+                            ],
+                            "spans": [],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                256,
+                                273.0,
+                                354,
+                                290.0
+                            ],
+                            "spans": [],
+                            "index": 9
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        299,
+                        382,
+                        313
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                299,
+                                383,
+                                313
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        299,
+                                        217,
+                                        313
+                                    ],
+                                    "score": 1.0,
+                                    "content": "For the second term, define",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        218,
+                                        300,
+                                        314,
+                                        312
+                                    ],
+                                    "score": 0.93,
+                                    "content": "u ( s , a ) = \\operatorname* { s u p } _ { t } N _ { t } ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        315,
+                                        299,
+                                        383,
+                                        313
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".2 It follows that,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        207,
+                        317,
+                        402,
+                        438
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                207,
+                                317,
+                                402,
+                                438
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        207,
+                                        317,
+                                        402,
+                                        438
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { l } { \\displaystyle \\sum _ { t \\geq 1 } w _ { t } \\beta _ { n _ { t } } = \\sum _ { s , o } ^ { u ( s , o ) } w _ { \\tau ( s , a , i ) } \\beta _ { i } } \\\\ { \\displaystyle \\qquad \\leq \\sum _ { s , a } ( 1 - \\gamma ) ^ { - 1 } c _ { 3 } \\sum _ { i = 1 } ^ { C _ { s , a } / w } \\sqrt { \\frac { H \\iota ( i ) } { i } } w } \\\\ { \\displaystyle \\qquad \\leq 2 \\sum _ { s , a } ( 1 - \\gamma ) ^ { - 1 } c _ { 3 } \\sqrt { \\iota ( C ) H C _ { s , a } w } } \\\\ { \\displaystyle \\qquad \\leq 2 c _ { 3 } ( 1 - \\gamma ) ^ { - 1 } \\sqrt { w S A H C \\iota ( C ) } . } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "bce9df1dbdecfd18cd0fbd700e55e9d74ea6aeee786233ea436d7b29badc95fc.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                207,
+                                317,
+                                402,
+                                334.2857142857143
+                            ],
+                            "spans": [],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                207,
+                                334.2857142857143,
+                                402,
+                                351.57142857142856
+                            ],
+                            "spans": [],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                207,
+                                351.57142857142856,
+                                402,
+                                368.85714285714283
+                            ],
+                            "spans": [],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                207,
+                                368.85714285714283,
+                                402,
+                                386.1428571428571
+                            ],
+                            "spans": [],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                207,
+                                386.1428571428571,
+                                402,
+                                403.4285714285714
+                            ],
+                            "spans": [],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                207,
+                                403.4285714285714,
+                                402,
+                                420.71428571428567
+                            ],
+                            "spans": [],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                207,
+                                420.71428571428567,
+                                402,
+                                437.99999999999994
+                            ],
+                            "spans": [],
+                            "index": 17
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        440,
+                        506,
+                        466
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                436,
+                                507,
+                                458
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        436,
+                                        136,
+                                        458
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        136,
+                                        441,
+                                        254,
+                                        455
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\begin{array} { r } { C _ { s , a } = \\sum _ { t \\geq 1 , ( s _ { t } , a _ { t } ) = ( s , a ) } w _ { t } } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        254,
+                                        436,
+                                        507,
+                                        458
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Inequality (19) follows from rearrangement inequality, since",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                451,
+                                450,
+                                468
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        453,
+                                        135,
+                                        466
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\iota ( x ) / x",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        136,
+                                        451,
+                                        450,
+                                        468
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is monotonically decreasing. Inequality (21) follows from Jensen’s inequality.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 18.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        470,
+                        289,
+                        482
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                469,
+                                289,
+                                483
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        469,
+                                        289,
+                                        483
+                                    ],
+                                    "score": 1.0,
+                                    "content": "For the third term of the summation, we have",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 20
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        198,
+                        485,
+                        414,
+                        573
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                198,
+                                485,
+                                414,
+                                573
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        198,
+                                        485,
+                                        414,
+                                        573
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { c } { { \\displaystyle \\sum _ { t \\ge 1 } w _ { t } \\sum _ { i = 1 } ^ { n _ { t } } \\alpha _ { n _ { t } } ^ { i } \\left( \\hat { V } _ { \\tau ( s _ { t } , a _ { t } , i ) } - V ^ { * } \\right) \\left( s _ { \\tau ( s _ { t } , a _ { t } , i ) + 1 } \\right) } } \\\\ { { \\displaystyle \\le \\sum _ { t ^ { \\prime } \\ge 1 } \\left( \\hat { V } _ { t ^ { \\prime } } - V ^ { * } \\right) \\left( s _ { t ^ { \\prime } + 1 } \\right) \\left( \\sum _ { t = t ^ { \\prime } + 1 } ^ { \\infty } \\alpha _ { n _ { t } } ^ { n _ { t ^ { \\prime } } } w _ { t } \\right) . } } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "a3e0c01b442b6f3c208a66bd1e6c84604cad0908954b7748b2f4faaaf3ab9889.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 23,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                198,
+                                485,
+                                414,
+                                502.6
+                            ],
+                            "spans": [],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                198,
+                                502.6,
+                                414,
+                                520.2
+                            ],
+                            "spans": [],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                198,
+                                520.2,
+                                414,
+                                537.8000000000001
+                            ],
+                            "spans": [],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                198,
+                                537.8000000000001,
+                                414,
+                                555.4000000000001
+                            ],
+                            "spans": [],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                198,
+                                555.4000000000001,
+                                414,
+                                573.0000000000001
+                            ],
+                            "spans": [],
+                            "index": 25
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        591,
+                        135,
+                        602
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                589,
+                                136,
+                                604
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        589,
+                                        136,
+                                        604
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Define",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 26
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        233,
+                        598,
+                        377,
+                        651
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                233,
+                                598,
+                                377,
+                                651
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        233,
+                                        598,
+                                        377,
+                                        651
+                                    ],
+                                    "score": 0.94,
+                                    "content": "w _ { t ^ { \\prime } + 1 } ^ { \\prime } = \\left( \\sum _ { \\stackrel { t = t ^ { \\prime } + 1 } { ( s _ { t } , a _ { t } ) = ( s _ { t } ^ { \\prime } , a _ { t } ^ { \\prime } ) } } ^ { \\infty } \\alpha _ { n _ { t } } ^ { n _ { t ^ { \\prime } } } w _ { t } \\right) .",
+                                    "type": "interline_equation",
+                                    "image_path": "90d6cf339da0fc0bd898216b68464ffc95f01fd8012796a3a8c23865fc73b784.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 27.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                233,
+                                598,
+                                377,
+                                624.5
+                            ],
+                            "spans": [],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                233,
+                                624.5,
+                                377,
+                                651.0
+                            ],
+                            "spans": [],
+                            "index": 28
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        659,
+                        504,
+                        682
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                657,
+                                506,
+                                675
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        657,
+                                        165,
+                                        675
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We claim that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        165,
+                                        660,
+                                        187,
+                                        673
+                                    ],
+                                    "score": 0.92,
+                                    "content": "w _ { t + 1 } ^ { \\prime }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        187,
+                                        657,
+                                        205,
+                                        675
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is a",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        205,
+                                        659,
+                                        267,
+                                        673
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\textstyle ( C , ( 1 + { \\frac { 1 } { H } } ) w )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        267,
+                                        657,
+                                        506,
+                                        675
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-sequence. We now prove this claim. By lemma 3, for any",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                668,
+                                138,
+                                685
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        671,
+                                        132,
+                                        682
+                                    ],
+                                    "score": 0.88,
+                                    "content": "t ^ { \\prime } \\geq 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        133,
+                                        668,
+                                        138,
+                                        685
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 29.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        227,
+                        680,
+                        383,
+                        714
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                227,
+                                680,
+                                383,
+                                714
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        227,
+                                        680,
+                                        383,
+                                        714
+                                    ],
+                                    "score": 0.94,
+                                    "content": "w _ { t ^ { \\prime } + 1 } ^ { \\prime } \\leq w \\sum _ { j = n _ { t ^ { \\prime } } } ^ { \\infty } \\alpha _ { j } ^ { n _ { t ^ { \\prime } } } = ( 1 + 1 / H ) w .",
+                                    "type": "interline_equation",
+                                    "image_path": "4253341d3793835fab3da24d7c177c2e36a4c25bd994300d52241f505a8a3adc.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 31.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                227,
+                                680,
+                                383,
+                                697.0
+                            ],
+                            "spans": [],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                227,
+                                697.0,
+                                383,
+                                714.0
+                            ],
+                            "spans": [],
+                            "index": 32
+                        }
+                    ]
+                }
+            ],
+            "page_idx": 13,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        26,
+                        294,
+                        38
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                25,
+                                294,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        25,
+                                        294,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        311,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                312,
+                                764
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        312,
+                                        764
+                                    ],
+                                    "score": 1.0,
+                                    "content": "14",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        118,
+                        720,
+                        394,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                119,
+                                720,
+                                394,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        119,
+                                        721,
+                                        149,
+                                        732
+                                    ],
+                                    "score": 0.89,
+                                    "content": "^ 2 u ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        150,
+                                        720,
+                                        234,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "could be infinity when",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        234,
+                                        722,
+                                        255,
+                                        732
+                                    ],
+                                    "score": 0.89,
+                                    "content": "( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        255,
+                                        720,
+                                        394,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is visited for infinite number of times.",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        81,
+                        505,
+                        107
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                79,
+                                505,
+                                97
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        79,
+                                        350,
+                                        97
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We now give a proof for lemma 2. Recall the definition for a",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        351,
+                                        83,
+                                        378,
+                                        94
+                                    ],
+                                    "score": 0.92,
+                                    "content": "( C , w )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        378,
+                                        79,
+                                        471,
+                                        97
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-sequence. A sequence",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        472,
+                                        82,
+                                        505,
+                                        95
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( w _ { t } ) _ { t \\geq 1 }",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                92,
+                                483,
+                                108
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        92,
+                                        164,
+                                        108
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is said to be a",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        164,
+                                        94,
+                                        191,
+                                        106
+                                    ],
+                                    "score": 0.95,
+                                    "content": "( C , w )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        191,
+                                        92,
+                                        246,
+                                        108
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-sequence for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        246,
+                                        94,
+                                        285,
+                                        105
+                                    ],
+                                    "score": 0.92,
+                                    "content": "C , w > 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        285,
+                                        92,
+                                        297,
+                                        108
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", if",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        298,
+                                        94,
+                                        348,
+                                        105
+                                    ],
+                                    "score": 0.92,
+                                    "content": "0 \\leq w _ { t } \\leq w",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        349,
+                                        92,
+                                        376,
+                                        108
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for all",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        376,
+                                        94,
+                                        399,
+                                        105
+                                    ],
+                                    "score": 0.89,
+                                    "content": "t \\geq 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        399,
+                                        92,
+                                        420,
+                                        108
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        420,
+                                        93,
+                                        478,
+                                        108
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\textstyle \\sum _ { t \\geq 1 } w _ { t } \\leq C",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        479,
+                                        92,
+                                        483,
+                                        108
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5,
+                    "bbox_fs": [
+                        105,
+                        79,
+                        505,
+                        108
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        118,
+                        313,
+                        131
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                118,
+                                312,
+                                132
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        118,
+                                        152,
+                                        132
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Proof. Let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        152,
+                                        119,
+                                        216,
+                                        131
+                                    ],
+                                    "score": 0.95,
+                                    "content": "n _ { t } = N _ { t } ( s _ { t } , a _ { t } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        217,
+                                        118,
+                                        312,
+                                        132
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for simplicity; we have",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 2,
+                    "bbox_fs": [
+                        106,
+                        118,
+                        312,
+                        132
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        158,
+                        134,
+                        451,
+                        226
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                158,
+                                134,
+                                451,
+                                226
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        158,
+                                        134,
+                                        451,
+                                        226
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { r l } {  { \\sum _ { t \\geq 1 } w _ { t } ( \\hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) } } \\\\ & { \\leq \\sum _ { t \\geq 1 } w _ { t } ( Q _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) } \\\\ & { \\leq \\sum _ { t \\geq 1 } w _ { t } [ \\cfrac { \\alpha _ { n _ { t } } ^ { 0 } } { 1 - \\gamma } + \\beta _ { n _ { t } } + \\gamma \\sum _ { i = 1 } ^ { n _ { t } } \\alpha _ { n _ { t } } ^ { i } ( \\hat { V } _ { \\tau ( s _ { t } , a _ { t } , i ) } - V ^ { * } ) ( s _ { \\tau ( s _ { t } , a _ { t } , i ) + 1 } ) ] } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "56de998ef0518be48301779db9712c42690034bbbfeba7d7ae47e786453e29e7.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                158,
+                                134,
+                                451,
+                                164.66666666666666
+                            ],
+                            "spans": [],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                158,
+                                164.66666666666666,
+                                451,
+                                195.33333333333331
+                            ],
+                            "spans": [],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                158,
+                                195.33333333333331,
+                                451,
+                                225.99999999999997
+                            ],
+                            "spans": [],
+                            "index": 5
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        230,
+                        505,
+                        254
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                228,
+                                507,
+                                246
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        228,
+                                        295,
+                                        246
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The last inequality is due to lemma 4. Note that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        230,
+                                        362,
+                                        244
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\alpha _ { n _ { t } } ^ { 0 } = \\mathbb { I } [ n _ { t } = 0 ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        362,
+                                        228,
+                                        507,
+                                        246
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the first term in the summation can",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                240,
+                                170,
+                                255
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        240,
+                                        170,
+                                        255
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be bounded by,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 6.5,
+                    "bbox_fs": [
+                        104,
+                        228,
+                        507,
+                        255
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        256,
+                        256,
+                        354,
+                        290
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                256,
+                                256,
+                                354,
+                                290
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        256,
+                                        256,
+                                        354,
+                                        290
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\sum _ { t \\geq 1 } w _ { t } \\frac { \\alpha _ { n _ { t } } ^ { 0 } } { 1 - \\gamma } \\leq \\frac { S A w } { 1 - \\gamma } .",
+                                    "type": "interline_equation",
+                                    "image_path": "fb8a30f2f69b0a0ef551b8c5d16a0c30b4272df4f37761a5fa9bb9799022d5bd.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                256,
+                                256,
+                                354,
+                                273.0
+                            ],
+                            "spans": [],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                256,
+                                273.0,
+                                354,
+                                290.0
+                            ],
+                            "spans": [],
+                            "index": 9
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        299,
+                        382,
+                        313
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                299,
+                                383,
+                                313
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        299,
+                                        217,
+                                        313
+                                    ],
+                                    "score": 1.0,
+                                    "content": "For the second term, define",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        218,
+                                        300,
+                                        314,
+                                        312
+                                    ],
+                                    "score": 0.93,
+                                    "content": "u ( s , a ) = \\operatorname* { s u p } _ { t } N _ { t } ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        315,
+                                        299,
+                                        383,
+                                        313
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".2 It follows that,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 10,
+                    "bbox_fs": [
+                        105,
+                        299,
+                        383,
+                        313
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        207,
+                        317,
+                        402,
+                        438
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                207,
+                                317,
+                                402,
+                                438
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        207,
+                                        317,
+                                        402,
+                                        438
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { l } { \\displaystyle \\sum _ { t \\geq 1 } w _ { t } \\beta _ { n _ { t } } = \\sum _ { s , o } ^ { u ( s , o ) } w _ { \\tau ( s , a , i ) } \\beta _ { i } } \\\\ { \\displaystyle \\qquad \\leq \\sum _ { s , a } ( 1 - \\gamma ) ^ { - 1 } c _ { 3 } \\sum _ { i = 1 } ^ { C _ { s , a } / w } \\sqrt { \\frac { H \\iota ( i ) } { i } } w } \\\\ { \\displaystyle \\qquad \\leq 2 \\sum _ { s , a } ( 1 - \\gamma ) ^ { - 1 } c _ { 3 } \\sqrt { \\iota ( C ) H C _ { s , a } w } } \\\\ { \\displaystyle \\qquad \\leq 2 c _ { 3 } ( 1 - \\gamma ) ^ { - 1 } \\sqrt { w S A H C \\iota ( C ) } . } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "bce9df1dbdecfd18cd0fbd700e55e9d74ea6aeee786233ea436d7b29badc95fc.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                207,
+                                317,
+                                402,
+                                334.2857142857143
+                            ],
+                            "spans": [],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                207,
+                                334.2857142857143,
+                                402,
+                                351.57142857142856
+                            ],
+                            "spans": [],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                207,
+                                351.57142857142856,
+                                402,
+                                368.85714285714283
+                            ],
+                            "spans": [],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                207,
+                                368.85714285714283,
+                                402,
+                                386.1428571428571
+                            ],
+                            "spans": [],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                207,
+                                386.1428571428571,
+                                402,
+                                403.4285714285714
+                            ],
+                            "spans": [],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                207,
+                                403.4285714285714,
+                                402,
+                                420.71428571428567
+                            ],
+                            "spans": [],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                207,
+                                420.71428571428567,
+                                402,
+                                437.99999999999994
+                            ],
+                            "spans": [],
+                            "index": 17
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        440,
+                        506,
+                        466
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                436,
+                                507,
+                                458
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        436,
+                                        136,
+                                        458
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        136,
+                                        441,
+                                        254,
+                                        455
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\begin{array} { r } { C _ { s , a } = \\sum _ { t \\geq 1 , ( s _ { t } , a _ { t } ) = ( s , a ) } w _ { t } } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        254,
+                                        436,
+                                        507,
+                                        458
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Inequality (19) follows from rearrangement inequality, since",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                451,
+                                450,
+                                468
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        453,
+                                        135,
+                                        466
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\iota ( x ) / x",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        136,
+                                        451,
+                                        450,
+                                        468
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is monotonically decreasing. Inequality (21) follows from Jensen’s inequality.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 18.5,
+                    "bbox_fs": [
+                        104,
+                        436,
+                        507,
+                        468
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        470,
+                        289,
+                        482
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                469,
+                                289,
+                                483
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        469,
+                                        289,
+                                        483
+                                    ],
+                                    "score": 1.0,
+                                    "content": "For the third term of the summation, we have",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 20,
+                    "bbox_fs": [
+                        105,
+                        469,
+                        289,
+                        483
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        198,
+                        485,
+                        414,
+                        573
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                198,
+                                485,
+                                414,
+                                573
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        198,
+                                        485,
+                                        414,
+                                        573
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { c } { { \\displaystyle \\sum _ { t \\ge 1 } w _ { t } \\sum _ { i = 1 } ^ { n _ { t } } \\alpha _ { n _ { t } } ^ { i } \\left( \\hat { V } _ { \\tau ( s _ { t } , a _ { t } , i ) } - V ^ { * } \\right) \\left( s _ { \\tau ( s _ { t } , a _ { t } , i ) + 1 } \\right) } } \\\\ { { \\displaystyle \\le \\sum _ { t ^ { \\prime } \\ge 1 } \\left( \\hat { V } _ { t ^ { \\prime } } - V ^ { * } \\right) \\left( s _ { t ^ { \\prime } + 1 } \\right) \\left( \\sum _ { t = t ^ { \\prime } + 1 } ^ { \\infty } \\alpha _ { n _ { t } } ^ { n _ { t ^ { \\prime } } } w _ { t } \\right) . } } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "a3e0c01b442b6f3c208a66bd1e6c84604cad0908954b7748b2f4faaaf3ab9889.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 23,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                198,
+                                485,
+                                414,
+                                502.6
+                            ],
+                            "spans": [],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                198,
+                                502.6,
+                                414,
+                                520.2
+                            ],
+                            "spans": [],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                198,
+                                520.2,
+                                414,
+                                537.8000000000001
+                            ],
+                            "spans": [],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                198,
+                                537.8000000000001,
+                                414,
+                                555.4000000000001
+                            ],
+                            "spans": [],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                198,
+                                555.4000000000001,
+                                414,
+                                573.0000000000001
+                            ],
+                            "spans": [],
+                            "index": 25
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        591,
+                        135,
+                        602
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                589,
+                                136,
+                                604
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        589,
+                                        136,
+                                        604
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Define",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 26,
+                    "bbox_fs": [
+                        105,
+                        589,
+                        136,
+                        604
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        233,
+                        598,
+                        377,
+                        651
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                233,
+                                598,
+                                377,
+                                651
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        233,
+                                        598,
+                                        377,
+                                        651
+                                    ],
+                                    "score": 0.94,
+                                    "content": "w _ { t ^ { \\prime } + 1 } ^ { \\prime } = \\left( \\sum _ { \\stackrel { t = t ^ { \\prime } + 1 } { ( s _ { t } , a _ { t } ) = ( s _ { t } ^ { \\prime } , a _ { t } ^ { \\prime } ) } } ^ { \\infty } \\alpha _ { n _ { t } } ^ { n _ { t ^ { \\prime } } } w _ { t } \\right) .",
+                                    "type": "interline_equation",
+                                    "image_path": "90d6cf339da0fc0bd898216b68464ffc95f01fd8012796a3a8c23865fc73b784.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 27.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                233,
+                                598,
+                                377,
+                                624.5
+                            ],
+                            "spans": [],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                233,
+                                624.5,
+                                377,
+                                651.0
+                            ],
+                            "spans": [],
+                            "index": 28
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        659,
+                        504,
+                        682
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                657,
+                                506,
+                                675
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        657,
+                                        165,
+                                        675
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We claim that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        165,
+                                        660,
+                                        187,
+                                        673
+                                    ],
+                                    "score": 0.92,
+                                    "content": "w _ { t + 1 } ^ { \\prime }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        187,
+                                        657,
+                                        205,
+                                        675
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is a",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        205,
+                                        659,
+                                        267,
+                                        673
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\textstyle ( C , ( 1 + { \\frac { 1 } { H } } ) w )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        267,
+                                        657,
+                                        506,
+                                        675
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-sequence. We now prove this claim. By lemma 3, for any",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                668,
+                                138,
+                                685
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        671,
+                                        132,
+                                        682
+                                    ],
+                                    "score": 0.88,
+                                    "content": "t ^ { \\prime } \\geq 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        133,
+                                        668,
+                                        138,
+                                        685
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 29.5,
+                    "bbox_fs": [
+                        104,
+                        657,
+                        506,
+                        685
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        227,
+                        680,
+                        383,
+                        714
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                227,
+                                680,
+                                383,
+                                714
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        227,
+                                        680,
+                                        383,
+                                        714
+                                    ],
+                                    "score": 0.94,
+                                    "content": "w _ { t ^ { \\prime } + 1 } ^ { \\prime } \\leq w \\sum _ { j = n _ { t ^ { \\prime } } } ^ { \\infty } \\alpha _ { j } ^ { n _ { t ^ { \\prime } } } = ( 1 + 1 / H ) w .",
+                                    "type": "interline_equation",
+                                    "image_path": "4253341d3793835fab3da24d7c177c2e36a4c25bd994300d52241f505a8a3adc.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 31.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                227,
+                                680,
+                                383,
+                                697.0
+                            ],
+                            "spans": [],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                227,
+                                697.0,
+                                383,
+                                714.0
+                            ],
+                            "spans": [],
+                            "index": 32
+                        }
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        81,
+                        505,
+                        106
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                101,
+                                74,
+                                509,
+                                101
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        101,
+                                        74,
+                                        120,
+                                        101
+                                    ],
+                                    "score": 1.0,
+                                    "content": "By",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        120,
+                                        80,
+                                        177,
+                                        96
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\textstyle \\sum _ { j = 0 } ^ { i } \\alpha _ { i } ^ { j } = 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        177,
+                                        74,
+                                        214,
+                                        101
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", we have",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        214,
+                                        82,
+                                        339,
+                                        96
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { r } { \\sum _ { t ^ { \\prime } \\geq 1 } w _ { t ^ { \\prime } + 1 } ^ { \\prime } \\leq \\sum _ { t \\geq 1 } w _ { t } \\leq C . } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        339,
+                                        74,
+                                        509,
+                                        101
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". This proves the assertion. It follows from",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                92,
+                                145,
+                                109
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        92,
+                                        145,
+                                        109
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(22) that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        169,
+                        110,
+                        438,
+                        267
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                169,
+                                110,
+                                438,
+                                267
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        169,
+                                        110,
+                                        438,
+                                        267
+                                    ],
+                                    "score": 0.95,
+                                    "content": "\\begin{array} { r l } & { \\quad \\underset { t \\geq 1 } { \\sum \\sigma } u _ { t + 1 } ^ { \\prime } \\left( \\hat { V } _ { t } - V ^ { * } \\right) \\left( s _ { t + 1 } \\right) } \\\\ & { = \\underset { t \\geq 1 } { \\sum \\sigma } u _ { t + 1 } ^ { \\prime } \\left( \\hat { V } _ { t + 1 } - V ^ { * } \\right) \\left( s _ { t + 1 } \\right) + \\underset { t \\geq 1 } { \\sum \\sigma } u _ { t + 1 } ^ { \\prime } \\left( \\hat { V } _ { t } - \\hat { V } _ { t + 1 } \\right) \\left( s _ { t + 1 } \\right) } \\\\ & { \\quad \\leq \\underset { t \\geq 1 } { \\sum \\sigma } u _ { t + 1 } ^ { \\prime } \\left( \\hat { V } _ { t + 1 } - V ^ { * } \\right) \\left( s _ { t + 1 } \\right) + \\underset { t \\geq 1 } { \\sum \\sigma } u _ { t + 1 } ^ { \\prime } \\left( 2 \\alpha _ { n _ { t } + 1 } \\frac { 1 } { 1 - \\gamma } \\right) } \\\\ & { \\quad \\leq \\underset { t \\geq 1 } { \\sum \\sigma } w _ { t + 1 } ^ { \\prime } \\left( \\hat { V } _ { t + 1 } - V ^ { * } \\right) \\left( s _ { t + 1 } \\right) + \\mathcal { O } \\left( \\frac { w S A H } { 1 - \\gamma } \\ln { C } \\right) } \\\\ & { \\quad \\leq \\underset { t \\geq 1 } { \\sum \\sigma } w _ { t + 1 } ^ { \\prime } \\left( \\hat { Q } _ { t + 1 } - Q ^ { * } \\right) \\left( s _ { t + 1 } , a _ { t + 1 } \\right) + \\mathcal { O } \\left( \\frac { w S A H } { 1 - \\gamma } \\ln { C } \\right) } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "a1c63f8ce8866bfa935cc54ba0fa4060644052edbd98620aad79e7ef97f0f148.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                169,
+                                110,
+                                438,
+                                162.33333333333334
+                            ],
+                            "spans": [],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                169,
+                                162.33333333333334,
+                                438,
+                                214.66666666666669
+                            ],
+                            "spans": [],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                169,
+                                214.66666666666669,
+                                438,
+                                267.0
+                            ],
+                            "spans": [],
+                            "index": 4
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        270,
+                        503,
+                        307
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                270,
+                                504,
+                                282
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        270,
+                                        504,
+                                        282
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Inequality (25) comes from the update rule of our algorithm. Inequality (26) comes from the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                277,
+                                505,
+                                297
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        277,
+                                        144,
+                                        297
+                                    ],
+                                    "score": 1.0,
+                                    "content": "fact that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        144,
+                                        281,
+                                        277,
+                                        293
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\dot { \\alpha } _ { t } = ( H + 1 ) / ( H + t ) \\overset { \\cdot } { \\leq } H / t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        277,
+                                        277,
+                                        473,
+                                        297
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and Jensen’s Inequality. More specifically, let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        473,
+                                        281,
+                                        505,
+                                        295
+                                    ],
+                                    "score": 0.91,
+                                    "content": "C _ { s , a } ^ { \\prime } =",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                292,
+                                303,
+                                309
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        293,
+                                        193,
+                                        308
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\scriptstyle \\sum _ { t \\geq 1 , ( s _ { t } , a _ { t } = s , a } w _ { t + 1 } ^ { \\prime }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        193,
+                                        292,
+                                        197,
+                                        309
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        198,
+                                        294,
+                                        273,
+                                        306
+                                    ],
+                                    "score": 0.83,
+                                    "content": "w ^ { \\prime } = w ( 1 + 1 / H )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        274,
+                                        292,
+                                        303,
+                                        309
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Then",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        148,
+                        311,
+                        462,
+                        351
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                148,
+                                311,
+                                462,
+                                351
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        148,
+                                        311,
+                                        462,
+                                        351
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\sum _ { t \\geq 1 } w _ { t + 1 } ^ { \\prime } \\alpha _ { n _ { t } + 1 } \\leq \\sum _ { s , a } \\sum _ { n = 1 } ^ { C _ { s , a } ^ { \\prime } / w ^ { \\prime } } w ^ { \\prime } \\frac { H } { n } \\leq \\sum _ { s , a } H w ^ { \\prime } \\ln ( C _ { s , a } ^ { \\prime } / w ) \\leq 2 S A H w \\ln C .",
+                                    "type": "interline_equation",
+                                    "image_path": "9834ce9a1e7dc58cf0a708f75e6b5b858bcdc589ad24752ed45e1722a959c115.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                148,
+                                311,
+                                462,
+                                324.3333333333333
+                            ],
+                            "spans": [],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                148,
+                                324.3333333333333,
+                                462,
+                                337.66666666666663
+                            ],
+                            "spans": [],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                148,
+                                337.66666666666663,
+                                462,
+                                350.99999999999994
+                            ],
+                            "spans": [],
+                            "index": 10
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        360,
+                        289,
+                        372
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                358,
+                                290,
+                                375
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        358,
+                                        290,
+                                        375
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Putting (18), (21) and (27) together, we have,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        117,
+                        389,
+                        477,
+                        453
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                117,
+                                389,
+                                477,
+                                453
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        389,
+                                        477,
+                                        453
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\begin{array} { r l } & { \\displaystyle \\sum _ { t \\geq 1 } w _ { t } ( \\hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) } \\\\ & { \\leq 2 c _ { 3 } \\frac { \\sqrt { w S A H C \\iota ( C ) } } { 1 - \\gamma } + \\mathcal { O } \\left( \\frac { w S A H } { 1 - \\gamma } \\ln C \\right) + \\gamma \\displaystyle \\sum _ { t \\geq 1 } w _ { t + 1 } ^ { \\prime } \\left( \\hat { Q } _ { t + 1 } - Q ^ { * } \\right) ( s _ { t + 1 } , a _ { t + 1 } ) . } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "fca33e0caf6dada43c874ac741c299779e61219671c7f66b39e75e1f2d6533ae.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                117,
+                                389,
+                                477,
+                                410.3333333333333
+                            ],
+                            "spans": [],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                410.3333333333333,
+                                477,
+                                431.66666666666663
+                            ],
+                            "spans": [],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                431.66666666666663,
+                                477,
+                                452.99999999999994
+                            ],
+                            "spans": [],
+                            "index": 14
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        456,
+                        507,
+                        518
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                455,
+                                506,
+                                469
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        455,
+                                        506,
+                                        469
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Observe that the third term is another weighted sum with the same form as (17). Therefore, we",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                468,
+                                506,
+                                480
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        468,
+                                        506,
+                                        480
+                                    ],
+                                    "score": 1.0,
+                                    "content": "can unroll this term repetitively with changing weight sequences.Suppose that our original weight",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                102,
+                                475,
+                                508,
+                                497
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        102,
+                                        475,
+                                        217,
+                                        497
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sequence is also denoted by",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        218,
+                                        478,
+                                        260,
+                                        493
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\{ \\bar { w _ { t } ^ { ( 0 ) } } \\} _ { t \\ge 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        261,
+                                        475,
+                                        288,
+                                        497
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", while",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        479,
+                                        331,
+                                        494
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\{ w _ { t } ^ { ( k ) } \\} _ { t \\ge 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        331,
+                                        475,
+                                        508,
+                                        497
+                                    ],
+                                    "score": 1.0,
+                                    "content": "denotes the weight sequence after unrolling",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                491,
+                                508,
+                                510
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        491,
+                                        120,
+                                        510
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        121,
+                                        496,
+                                        128,
+                                        505
+                                    ],
+                                    "score": 0.81,
+                                    "content": "k",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        128,
+                                        491,
+                                        172,
+                                        510
+                                    ],
+                                    "score": 1.0,
+                                    "content": "times. Let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        173,
+                                        494,
+                                        192,
+                                        506
+                                    ],
+                                    "score": 0.9,
+                                    "content": "w ^ { ( k ) }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        192,
+                                        491,
+                                        205,
+                                        510
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        206,
+                                        493,
+                                        270,
+                                        507
+                                    ],
+                                    "score": 0.93,
+                                    "content": "w \\cdot \\left( 1 + 1 / H \\right) ^ { k }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        270,
+                                        491,
+                                        362,
+                                        510
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Then we can see that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        363,
+                                        492,
+                                        406,
+                                        508
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\{ w _ { t } ^ { ( k ) } \\} _ { t \\ge 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        406,
+                                        491,
+                                        424,
+                                        510
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is a",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        424,
+                                        494,
+                                        462,
+                                        507
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( C , w ^ { ( k ) } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        462,
+                                        491,
+                                        508,
+                                        510
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-sequence.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                506,
+                                277,
+                                518
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        506,
+                                        214,
+                                        518
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Suppose that we unroll for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        215,
+                                        507,
+                                        225,
+                                        516
+                                    ],
+                                    "score": 0.81,
+                                    "content": "H",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        225,
+                                        506,
+                                        277,
+                                        518
+                                    ],
+                                    "score": 1.0,
+                                    "content": "times. Then",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        125,
+                        522,
+                        487,
+                        617
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                125,
+                                522,
+                                487,
+                                617
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        125,
+                                        522,
+                                        487,
+                                        617
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { r l } & { \\displaystyle \\sum _ { t \\geq 1 } w _ { t } ( \\hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) } \\\\ & { \\leq 2 c _ { 3 } \\frac { \\sqrt { w ^ { ( H ) } S A H C \\iota ( C ) } } { ( 1 - \\gamma ) ^ { 2 } } + \\mathcal { O } \\left( \\frac { w ^ { ( H ) } S A H } { ( 1 - \\gamma ) ^ { 2 } } \\ln C \\right) + \\gamma ^ { H } \\displaystyle \\sum _ { t \\geq 1 } w _ { t } ^ { ( H ) } \\left( \\hat { Q } _ { t } - Q ^ { * } \\right) ( s _ { t } , a _ { t } ) } \\\\ & { \\leq 2 c _ { 3 } \\frac { \\sqrt { w ^ { ( H ) } S A H C \\iota ( C ) } } { ( 1 - \\gamma ) ^ { 2 } } + \\mathcal { O } \\left( \\frac { w ^ { ( H ) } S A H } { ( 1 - \\gamma ) ^ { 2 } } \\ln C \\right) + \\gamma ^ { H } \\frac { C } { 1 - \\gamma } . } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "4b3ee4cb41b96d3c4f223bc4146fc59bb343a3cac7f567861e3ed3154212ede1.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                125,
+                                522,
+                                487,
+                                553.6666666666666
+                            ],
+                            "spans": [],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                125,
+                                553.6666666666666,
+                                487,
+                                585.3333333333333
+                            ],
+                            "spans": [],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                125,
+                                585.3333333333333,
+                                487,
+                                616.9999999999999
+                            ],
+                            "spans": [],
+                            "index": 22
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        633,
+                        506,
+                        665
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                102,
+                                629,
+                                508,
+                                653
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        102,
+                                        629,
+                                        136,
+                                        653
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We set",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        136,
+                                        633,
+                                        280,
+                                        651
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { r } { H = \\frac { \\ln 1 / ( ( 1 - \\gamma ) \\epsilon _ { 1 } ) } { \\ln 1 / \\gamma } \\leq \\frac { \\ln 1 / ( ( 1 - \\gamma ) \\epsilon _ { 1 } ) } { 1 - \\gamma } , } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        280,
+                                        629,
+                                        342,
+                                        653
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". It follows that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        342,
+                                        635,
+                                        483,
+                                        649
+                                    ],
+                                    "score": 0.92,
+                                    "content": "w ^ { ( H ) } = ( 1 + 1 / H ) ^ { H } w ^ { ( 0 ) } \\leq e w ^ { ( 0 ) }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        484,
+                                        629,
+                                        508,
+                                        653
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                102,
+                                646,
+                                402,
+                                668
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        102,
+                                        646,
+                                        159,
+                                        668
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that γH C1−γ",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        124,
+                                        650,
+                                        185,
+                                        666
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\gamma ^ { H } \\frac { C } { 1 - \\gamma } \\leq C \\epsilon _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        185,
+                                        649,
+                                        226,
+                                        665
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Also, let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        226,
+                                        650,
+                                        352,
+                                        664
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\ell ( C ) = \\iota ( C ) \\ln ( ( 1 - \\gamma ) ^ { - 1 } \\epsilon _ { 1 } ^ { - 1 } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        353,
+                                        649,
+                                        402,
+                                        665
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Therefore,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 23.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        113,
+                        682,
+                        482,
+                        716
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                113,
+                                682,
+                                482,
+                                716
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        682,
+                                        482,
+                                        716
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\sum _ { t \\geq 1 } w _ { t } ( \\hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) \\leq \\frac { C \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\frac { \\sqrt { w S A C \\ell ( C ) } } { ( 1 - \\gamma ) ^ { 2 . 5 } } + \\frac { w S A } { ( 1 - \\gamma ) ^ { 3 } } \\ln C \\ln \\frac { 1 } { ( 1 - \\gamma ) \\epsilon _ { 1 } } \\right) .",
+                                    "type": "interline_equation",
+                                    "image_path": "11b4d3a7f4cf29588edd0397db246aa8a18f798a841609b619f1a546acf17d46.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 25,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                113,
+                                682,
+                                482,
+                                716
+                            ],
+                            "spans": [],
+                            "index": 25
+                        }
+                    ]
+                }
+            ],
+            "page_idx": 14,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        106,
+                        26,
+                        294,
+                        38
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                25,
+                                294,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        25,
+                                        294,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        311,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                312,
+                                764
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        312,
+                                        764
+                                    ],
+                                    "score": 1.0,
+                                    "content": "15",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        494,
+                        721,
+                        504,
+                        731
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                496,
+                                723,
+                                504,
+                                730
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        496,
+                                        723,
+                                        504,
+                                        730
+                                    ],
+                                    "score": 0.998,
+                                    "content": "□",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        81,
+                        505,
+                        106
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                101,
+                                74,
+                                509,
+                                101
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        101,
+                                        74,
+                                        120,
+                                        101
+                                    ],
+                                    "score": 1.0,
+                                    "content": "By",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        120,
+                                        80,
+                                        177,
+                                        96
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\textstyle \\sum _ { j = 0 } ^ { i } \\alpha _ { i } ^ { j } = 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        177,
+                                        74,
+                                        214,
+                                        101
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", we have",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        214,
+                                        82,
+                                        339,
+                                        96
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { r } { \\sum _ { t ^ { \\prime } \\geq 1 } w _ { t ^ { \\prime } + 1 } ^ { \\prime } \\leq \\sum _ { t \\geq 1 } w _ { t } \\leq C . } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        339,
+                                        74,
+                                        509,
+                                        101
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". This proves the assertion. It follows from",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                92,
+                                145,
+                                109
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        92,
+                                        145,
+                                        109
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(22) that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5,
+                    "bbox_fs": [
+                        101,
+                        74,
+                        509,
+                        109
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        169,
+                        110,
+                        438,
+                        267
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                169,
+                                110,
+                                438,
+                                267
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        169,
+                                        110,
+                                        438,
+                                        267
+                                    ],
+                                    "score": 0.95,
+                                    "content": "\\begin{array} { r l } & { \\quad \\underset { t \\geq 1 } { \\sum \\sigma } u _ { t + 1 } ^ { \\prime } \\left( \\hat { V } _ { t } - V ^ { * } \\right) \\left( s _ { t + 1 } \\right) } \\\\ & { = \\underset { t \\geq 1 } { \\sum \\sigma } u _ { t + 1 } ^ { \\prime } \\left( \\hat { V } _ { t + 1 } - V ^ { * } \\right) \\left( s _ { t + 1 } \\right) + \\underset { t \\geq 1 } { \\sum \\sigma } u _ { t + 1 } ^ { \\prime } \\left( \\hat { V } _ { t } - \\hat { V } _ { t + 1 } \\right) \\left( s _ { t + 1 } \\right) } \\\\ & { \\quad \\leq \\underset { t \\geq 1 } { \\sum \\sigma } u _ { t + 1 } ^ { \\prime } \\left( \\hat { V } _ { t + 1 } - V ^ { * } \\right) \\left( s _ { t + 1 } \\right) + \\underset { t \\geq 1 } { \\sum \\sigma } u _ { t + 1 } ^ { \\prime } \\left( 2 \\alpha _ { n _ { t } + 1 } \\frac { 1 } { 1 - \\gamma } \\right) } \\\\ & { \\quad \\leq \\underset { t \\geq 1 } { \\sum \\sigma } w _ { t + 1 } ^ { \\prime } \\left( \\hat { V } _ { t + 1 } - V ^ { * } \\right) \\left( s _ { t + 1 } \\right) + \\mathcal { O } \\left( \\frac { w S A H } { 1 - \\gamma } \\ln { C } \\right) } \\\\ & { \\quad \\leq \\underset { t \\geq 1 } { \\sum \\sigma } w _ { t + 1 } ^ { \\prime } \\left( \\hat { Q } _ { t + 1 } - Q ^ { * } \\right) \\left( s _ { t + 1 } , a _ { t + 1 } \\right) + \\mathcal { O } \\left( \\frac { w S A H } { 1 - \\gamma } \\ln { C } \\right) } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "a1c63f8ce8866bfa935cc54ba0fa4060644052edbd98620aad79e7ef97f0f148.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                169,
+                                110,
+                                438,
+                                162.33333333333334
+                            ],
+                            "spans": [],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                169,
+                                162.33333333333334,
+                                438,
+                                214.66666666666669
+                            ],
+                            "spans": [],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                169,
+                                214.66666666666669,
+                                438,
+                                267.0
+                            ],
+                            "spans": [],
+                            "index": 4
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        270,
+                        503,
+                        307
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                270,
+                                504,
+                                282
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        270,
+                                        504,
+                                        282
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Inequality (25) comes from the update rule of our algorithm. Inequality (26) comes from the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                277,
+                                505,
+                                297
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        277,
+                                        144,
+                                        297
+                                    ],
+                                    "score": 1.0,
+                                    "content": "fact that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        144,
+                                        281,
+                                        277,
+                                        293
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\dot { \\alpha } _ { t } = ( H + 1 ) / ( H + t ) \\overset { \\cdot } { \\leq } H / t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        277,
+                                        277,
+                                        473,
+                                        297
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and Jensen’s Inequality. More specifically, let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        473,
+                                        281,
+                                        505,
+                                        295
+                                    ],
+                                    "score": 0.91,
+                                    "content": "C _ { s , a } ^ { \\prime } =",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                292,
+                                303,
+                                309
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        293,
+                                        193,
+                                        308
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\scriptstyle \\sum _ { t \\geq 1 , ( s _ { t } , a _ { t } = s , a } w _ { t + 1 } ^ { \\prime }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        193,
+                                        292,
+                                        197,
+                                        309
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        198,
+                                        294,
+                                        273,
+                                        306
+                                    ],
+                                    "score": 0.83,
+                                    "content": "w ^ { \\prime } = w ( 1 + 1 / H )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        274,
+                                        292,
+                                        303,
+                                        309
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Then",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 6,
+                    "bbox_fs": [
+                        104,
+                        270,
+                        505,
+                        309
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        148,
+                        311,
+                        462,
+                        351
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                148,
+                                311,
+                                462,
+                                351
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        148,
+                                        311,
+                                        462,
+                                        351
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\sum _ { t \\geq 1 } w _ { t + 1 } ^ { \\prime } \\alpha _ { n _ { t } + 1 } \\leq \\sum _ { s , a } \\sum _ { n = 1 } ^ { C _ { s , a } ^ { \\prime } / w ^ { \\prime } } w ^ { \\prime } \\frac { H } { n } \\leq \\sum _ { s , a } H w ^ { \\prime } \\ln ( C _ { s , a } ^ { \\prime } / w ) \\leq 2 S A H w \\ln C .",
+                                    "type": "interline_equation",
+                                    "image_path": "9834ce9a1e7dc58cf0a708f75e6b5b858bcdc589ad24752ed45e1722a959c115.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                148,
+                                311,
+                                462,
+                                324.3333333333333
+                            ],
+                            "spans": [],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                148,
+                                324.3333333333333,
+                                462,
+                                337.66666666666663
+                            ],
+                            "spans": [],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                148,
+                                337.66666666666663,
+                                462,
+                                350.99999999999994
+                            ],
+                            "spans": [],
+                            "index": 10
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        360,
+                        289,
+                        372
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                358,
+                                290,
+                                375
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        358,
+                                        290,
+                                        375
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Putting (18), (21) and (27) together, we have,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 11,
+                    "bbox_fs": [
+                        105,
+                        358,
+                        290,
+                        375
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        117,
+                        389,
+                        477,
+                        453
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                117,
+                                389,
+                                477,
+                                453
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        389,
+                                        477,
+                                        453
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\begin{array} { r l } & { \\displaystyle \\sum _ { t \\geq 1 } w _ { t } ( \\hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) } \\\\ & { \\leq 2 c _ { 3 } \\frac { \\sqrt { w S A H C \\iota ( C ) } } { 1 - \\gamma } + \\mathcal { O } \\left( \\frac { w S A H } { 1 - \\gamma } \\ln C \\right) + \\gamma \\displaystyle \\sum _ { t \\geq 1 } w _ { t + 1 } ^ { \\prime } \\left( \\hat { Q } _ { t + 1 } - Q ^ { * } \\right) ( s _ { t + 1 } , a _ { t + 1 } ) . } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "fca33e0caf6dada43c874ac741c299779e61219671c7f66b39e75e1f2d6533ae.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                117,
+                                389,
+                                477,
+                                410.3333333333333
+                            ],
+                            "spans": [],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                410.3333333333333,
+                                477,
+                                431.66666666666663
+                            ],
+                            "spans": [],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                431.66666666666663,
+                                477,
+                                452.99999999999994
+                            ],
+                            "spans": [],
+                            "index": 14
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        456,
+                        507,
+                        518
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                455,
+                                506,
+                                469
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        455,
+                                        506,
+                                        469
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Observe that the third term is another weighted sum with the same form as (17). Therefore, we",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                468,
+                                506,
+                                480
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        468,
+                                        506,
+                                        480
+                                    ],
+                                    "score": 1.0,
+                                    "content": "can unroll this term repetitively with changing weight sequences.Suppose that our original weight",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                102,
+                                475,
+                                508,
+                                497
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        102,
+                                        475,
+                                        217,
+                                        497
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sequence is also denoted by",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        218,
+                                        478,
+                                        260,
+                                        493
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\{ \\bar { w _ { t } ^ { ( 0 ) } } \\} _ { t \\ge 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        261,
+                                        475,
+                                        288,
+                                        497
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", while",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        479,
+                                        331,
+                                        494
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\{ w _ { t } ^ { ( k ) } \\} _ { t \\ge 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        331,
+                                        475,
+                                        508,
+                                        497
+                                    ],
+                                    "score": 1.0,
+                                    "content": "denotes the weight sequence after unrolling",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                491,
+                                508,
+                                510
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        491,
+                                        120,
+                                        510
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        121,
+                                        496,
+                                        128,
+                                        505
+                                    ],
+                                    "score": 0.81,
+                                    "content": "k",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        128,
+                                        491,
+                                        172,
+                                        510
+                                    ],
+                                    "score": 1.0,
+                                    "content": "times. Let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        173,
+                                        494,
+                                        192,
+                                        506
+                                    ],
+                                    "score": 0.9,
+                                    "content": "w ^ { ( k ) }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        192,
+                                        491,
+                                        205,
+                                        510
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        206,
+                                        493,
+                                        270,
+                                        507
+                                    ],
+                                    "score": 0.93,
+                                    "content": "w \\cdot \\left( 1 + 1 / H \\right) ^ { k }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        270,
+                                        491,
+                                        362,
+                                        510
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Then we can see that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        363,
+                                        492,
+                                        406,
+                                        508
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\{ w _ { t } ^ { ( k ) } \\} _ { t \\ge 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        406,
+                                        491,
+                                        424,
+                                        510
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is a",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        424,
+                                        494,
+                                        462,
+                                        507
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( C , w ^ { ( k ) } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        462,
+                                        491,
+                                        508,
+                                        510
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-sequence.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                506,
+                                277,
+                                518
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        506,
+                                        214,
+                                        518
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Suppose that we unroll for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        215,
+                                        507,
+                                        225,
+                                        516
+                                    ],
+                                    "score": 0.81,
+                                    "content": "H",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        225,
+                                        506,
+                                        277,
+                                        518
+                                    ],
+                                    "score": 1.0,
+                                    "content": "times. Then",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 17,
+                    "bbox_fs": [
+                        102,
+                        455,
+                        508,
+                        518
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        125,
+                        522,
+                        487,
+                        617
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                125,
+                                522,
+                                487,
+                                617
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        125,
+                                        522,
+                                        487,
+                                        617
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { r l } & { \\displaystyle \\sum _ { t \\geq 1 } w _ { t } ( \\hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) } \\\\ & { \\leq 2 c _ { 3 } \\frac { \\sqrt { w ^ { ( H ) } S A H C \\iota ( C ) } } { ( 1 - \\gamma ) ^ { 2 } } + \\mathcal { O } \\left( \\frac { w ^ { ( H ) } S A H } { ( 1 - \\gamma ) ^ { 2 } } \\ln C \\right) + \\gamma ^ { H } \\displaystyle \\sum _ { t \\geq 1 } w _ { t } ^ { ( H ) } \\left( \\hat { Q } _ { t } - Q ^ { * } \\right) ( s _ { t } , a _ { t } ) } \\\\ & { \\leq 2 c _ { 3 } \\frac { \\sqrt { w ^ { ( H ) } S A H C \\iota ( C ) } } { ( 1 - \\gamma ) ^ { 2 } } + \\mathcal { O } \\left( \\frac { w ^ { ( H ) } S A H } { ( 1 - \\gamma ) ^ { 2 } } \\ln C \\right) + \\gamma ^ { H } \\frac { C } { 1 - \\gamma } . } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "4b3ee4cb41b96d3c4f223bc4146fc59bb343a3cac7f567861e3ed3154212ede1.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                125,
+                                522,
+                                487,
+                                553.6666666666666
+                            ],
+                            "spans": [],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                125,
+                                553.6666666666666,
+                                487,
+                                585.3333333333333
+                            ],
+                            "spans": [],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                125,
+                                585.3333333333333,
+                                487,
+                                616.9999999999999
+                            ],
+                            "spans": [],
+                            "index": 22
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        633,
+                        506,
+                        665
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                102,
+                                629,
+                                508,
+                                653
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        102,
+                                        629,
+                                        136,
+                                        653
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We set",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        136,
+                                        633,
+                                        280,
+                                        651
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { r } { H = \\frac { \\ln 1 / ( ( 1 - \\gamma ) \\epsilon _ { 1 } ) } { \\ln 1 / \\gamma } \\leq \\frac { \\ln 1 / ( ( 1 - \\gamma ) \\epsilon _ { 1 } ) } { 1 - \\gamma } , } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        280,
+                                        629,
+                                        342,
+                                        653
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". It follows that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        342,
+                                        635,
+                                        483,
+                                        649
+                                    ],
+                                    "score": 0.92,
+                                    "content": "w ^ { ( H ) } = ( 1 + 1 / H ) ^ { H } w ^ { ( 0 ) } \\leq e w ^ { ( 0 ) }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        484,
+                                        629,
+                                        508,
+                                        653
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                102,
+                                646,
+                                402,
+                                668
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        102,
+                                        646,
+                                        159,
+                                        668
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that γH C1−γ",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        124,
+                                        650,
+                                        185,
+                                        666
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\gamma ^ { H } \\frac { C } { 1 - \\gamma } \\leq C \\epsilon _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        185,
+                                        649,
+                                        226,
+                                        665
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Also, let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        226,
+                                        650,
+                                        352,
+                                        664
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\ell ( C ) = \\iota ( C ) \\ln ( ( 1 - \\gamma ) ^ { - 1 } \\epsilon _ { 1 } ^ { - 1 } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        353,
+                                        649,
+                                        402,
+                                        665
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Therefore,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 23.5,
+                    "bbox_fs": [
+                        102,
+                        629,
+                        508,
+                        668
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        113,
+                        682,
+                        482,
+                        716
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                113,
+                                682,
+                                482,
+                                716
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        682,
+                                        482,
+                                        716
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\sum _ { t \\geq 1 } w _ { t } ( \\hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) \\leq \\frac { C \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\frac { \\sqrt { w S A C \\ell ( C ) } } { ( 1 - \\gamma ) ^ { 2 . 5 } } + \\frac { w S A } { ( 1 - \\gamma ) ^ { 3 } } \\ln C \\ln \\frac { 1 } { ( 1 - \\gamma ) \\epsilon _ { 1 } } \\right) .",
+                                    "type": "interline_equation",
+                                    "image_path": "11b4d3a7f4cf29588edd0397db246aa8a18f798a841609b619f1a546acf17d46.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 25,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                113,
+                                682,
+                                482,
+                                716
+                            ],
+                            "spans": [],
+                            "index": 25
+                        }
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        81,
+                        295,
+                        94
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                80,
+                                297,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        80,
+                                        297,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "C EXTENSION TO OTHER SETTINGS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        105,
+                        506,
+                        150
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                105,
+                                505,
+                                118
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        105,
+                                        505,
+                                        118
+                                    ],
+                                    "score": 1.0,
+                                    "content": "First we define a mapping from a finite horizon MDP to an infinite horizon MDP so that our algorithm",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                116,
+                                504,
+                                129
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        116,
+                                        312,
+                                        129
+                                    ],
+                                    "score": 1.0,
+                                    "content": "can be applied. For an arbitrary finite horizon MDP",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        312,
+                                        117,
+                                        465,
+                                        129
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\mathcal { M } = ( S , A , H , r _ { h } ( s _ { \\perp } a ) , p _ { h } ( s ^ { \\prime } \\mid s , a ) )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        465,
+                                        116,
+                                        493,
+                                        129
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        494,
+                                        117,
+                                        504,
+                                        127
+                                    ],
+                                    "score": 0.79,
+                                    "content": "H",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                127,
+                                504,
+                                140
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        127,
+                                        363,
+                                        140
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the length of episode, the corresponding infinite horizon MDP",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        364,
+                                        129,
+                                        504,
+                                        140
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\mathcal { M } = ( S , A , \\gamma , \\bar { r } ( \\bar { s } , \\bar { a } ) , \\bar { p } ( \\bar { s } ^ { \\prime } \\mid \\bar { s } , \\bar { a } ) )",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                138,
+                                162,
+                                151
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        138,
+                                        162,
+                                        151
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is defined as,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 2.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        131,
+                        157,
+                        505,
+                        226
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                131,
+                                157,
+                                226,
+                                187
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        131,
+                                        157,
+                                        226,
+                                        187
+                                    ],
+                                    "score": 0.37,
+                                    "content": "\\begin{array} { l } { { \\bullet \\ { \\bar { S } } = S \\times H , { \\bar { A } } = A ; } } \\\\ { { \\bullet \\ \\gamma = ( 1 - 1 / H ) ; } } \\end{array}",
+                                    "type": "inline_equation",
+                                    "image_path": "6163bc4f633c8d81c5759aacc60e20932b8157511f7dd0e021ff4e1df174dd54.jpg"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                131,
+                                188,
+                                505,
+                                201
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        131,
+                                        188,
+                                        185,
+                                        201
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• for a state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        186,
+                                        192,
+                                        191,
+                                        199
+                                    ],
+                                    "score": 0.76,
+                                    "content": "s",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        192,
+                                        188,
+                                        221,
+                                        201
+                                    ],
+                                    "score": 1.0,
+                                    "content": "at step",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        222,
+                                        190,
+                                        228,
+                                        199
+                                    ],
+                                    "score": 0.83,
+                                    "content": "h",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        229,
+                                        188,
+                                        245,
+                                        201
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        246,
+                                        190,
+                                        263,
+                                        201
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\bar { s } _ { s , h }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        263,
+                                        188,
+                                        438,
+                                        201
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be the corresponding state. For any action",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        439,
+                                        192,
+                                        445,
+                                        199
+                                    ],
+                                    "score": 0.77,
+                                    "content": "a",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        446,
+                                        188,
+                                        505,
+                                        201
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and next state",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                198,
+                                507,
+                                216
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        201,
+                                        151,
+                                        211
+                                    ],
+                                    "score": 0.84,
+                                    "content": "s ^ { \\prime }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        151,
+                                        198,
+                                        183,
+                                        216
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", define",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        183,
+                                        201,
+                                        303,
+                                        213
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\bar { r } ( \\bar { s } _ { s , h } , a ) = \\gamma ^ { H - h + 1 } r _ { h } ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        198,
+                                        322,
+                                        216
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        323,
+                                        201,
+                                        466,
+                                        213
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\bar { p } ( \\bar { s } _ { s ^ { \\prime } , h + 1 } \\mid \\bar { s } _ { s , h } , a ) = p _ { h } ( s ^ { \\prime } \\mid s , h )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        466,
+                                        198,
+                                        507,
+                                        216
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". And for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                211,
+                                497,
+                                226
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        213,
+                                        172,
+                                        223
+                                    ],
+                                    "score": 0.88,
+                                    "content": "h = H",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        172,
+                                        211,
+                                        189,
+                                        226
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", set",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        190,
+                                        213,
+                                        247,
+                                        225
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\bar { r } ( \\bar { s } _ { s , h } , a ) = 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        247,
+                                        211,
+                                        265,
+                                        226
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        265,
+                                        213,
+                                        384,
+                                        225
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\bar { p } ( \\bar { s } _ { s ^ { \\prime } , 1 } \\mid \\bar { s } _ { s , h } , a ) = I [ s ^ { \\prime } = s _ { 1 } ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        384,
+                                        211,
+                                        482,
+                                        226
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for a fixed starting state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        482,
+                                        214,
+                                        492,
+                                        223
+                                    ],
+                                    "score": 0.84,
+                                    "content": "s _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        493,
+                                        211,
+                                        497,
+                                        226
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 6.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        233,
+                        506,
+                        297
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                233,
+                                506,
+                                247
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        233,
+                                        122,
+                                        247
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        122,
+                                        234,
+                                        133,
+                                        245
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\bar { V } _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        133,
+                                        233,
+                                        231,
+                                        247
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be the value function in",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        231,
+                                        234,
+                                        244,
+                                        245
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\bar { \\mathcal { M } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        244,
+                                        233,
+                                        275,
+                                        247
+                                    ],
+                                    "score": 1.0,
+                                    "content": "at time",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        275,
+                                        235,
+                                        281,
+                                        244
+                                    ],
+                                    "score": 0.76,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        281,
+                                        233,
+                                        298,
+                                        247
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        299,
+                                        234,
+                                        312,
+                                        247
+                                    ],
+                                    "score": 0.91,
+                                    "content": "V _ { h } ^ { k }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        313,
+                                        233,
+                                        398,
+                                        247
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the value function in",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        399,
+                                        235,
+                                        412,
+                                        245
+                                    ],
+                                    "score": 0.82,
+                                    "content": "\\mathcal { M }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        412,
+                                        233,
+                                        456,
+                                        247
+                                    ],
+                                    "score": 1.0,
+                                    "content": "at episode",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        456,
+                                        235,
+                                        462,
+                                        244
+                                    ],
+                                    "score": 0.78,
+                                    "content": "k",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        463,
+                                        233,
+                                        485,
+                                        247
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", step",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        485,
+                                        235,
+                                        492,
+                                        244
+                                    ],
+                                    "score": 0.76,
+                                    "content": "h",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        492,
+                                        233,
+                                        506,
+                                        247
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". It",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                245,
+                                507,
+                                265
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        245,
+                                        157,
+                                        265
+                                    ],
+                                    "score": 1.0,
+                                    "content": "follows that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        158,
+                                        246,
+                                        264,
+                                        263
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { r } { \\bar { V } ^ { \\ast } ( \\bar { s } _ { s _ { 1 } , 1 } ) = \\frac { \\gamma ^ { H } } { 1 - \\gamma ^ { H } } V _ { 1 } ^ { \\ast } ( s _ { 1 } ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        265,
+                                        245,
+                                        422,
+                                        265
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". And the policy mapping is defined as",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        422,
+                                        249,
+                                        489,
+                                        262
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\pi _ { h } ( s ) = \\bar { \\pi } ( \\bar { s } _ { s , h } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        490,
+                                        245,
+                                        507,
+                                        265
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                262,
+                                506,
+                                276
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        262,
+                                        133,
+                                        276
+                                    ],
+                                    "score": 1.0,
+                                    "content": "policy",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        133,
+                                        264,
+                                        141,
+                                        273
+                                    ],
+                                    "score": 0.78,
+                                    "content": "\\bar { \\pi }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        141,
+                                        262,
+                                        152,
+                                        276
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        262,
+                                        165,
+                                        273
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\bar { \\mathcal { M } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        165,
+                                        262,
+                                        268,
+                                        276
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Value functions in MDP",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        268,
+                                        263,
+                                        281,
+                                        273
+                                    ],
+                                    "score": 0.78,
+                                    "content": "\\mathcal { M }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        281,
+                                        262,
+                                        299,
+                                        276
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        299,
+                                        262,
+                                        312,
+                                        273
+                                    ],
+                                    "score": 0.86,
+                                    "content": "\\bar { \\mathcal { M } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        313,
+                                        262,
+                                        465,
+                                        276
+                                    ],
+                                    "score": 1.0,
+                                    "content": "are closely related in a sense that, any",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        465,
+                                        266,
+                                        470,
+                                        273
+                                    ],
+                                    "score": 0.68,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        471,
+                                        262,
+                                        506,
+                                        276
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimal",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                273,
+                                506,
+                                287
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        273,
+                                        133,
+                                        287
+                                    ],
+                                    "score": 1.0,
+                                    "content": "policy",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        133,
+                                        275,
+                                        141,
+                                        284
+                                    ],
+                                    "score": 0.79,
+                                    "content": "\\bar { \\pi }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        141,
+                                        273,
+                                        153,
+                                        287
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        273,
+                                        166,
+                                        284
+                                    ],
+                                    "score": 0.82,
+                                    "content": "\\bar { \\mathcal { M } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        166,
+                                        273,
+                                        248,
+                                        287
+                                    ],
+                                    "score": 1.0,
+                                    "content": "corresponding to an",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        249,
+                                        273,
+                                        279,
+                                        286
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( \\epsilon / \\gamma ^ { H } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        279,
+                                        273,
+                                        340,
+                                        287
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimal policy",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        341,
+                                        276,
+                                        348,
+                                        284
+                                    ],
+                                    "score": 0.75,
+                                    "content": "\\pi",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        349,
+                                        273,
+                                        360,
+                                        287
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        360,
+                                        275,
+                                        373,
+                                        284
+                                    ],
+                                    "score": 0.83,
+                                    "content": "\\mathcal { M }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        373,
+                                        273,
+                                        506,
+                                        287
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(see section C.1 for proof). Note",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                283,
+                                313,
+                                298
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        283,
+                                        144,
+                                        298
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that here",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        144,
+                                        284,
+                                        257,
+                                        297
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\gamma ^ { H } = ( 1 - \\dot { 1 } / H ) ^ { \\tilde { H } } = \\mathcal { O } ( \\dot { 1 } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        257,
+                                        283,
+                                        313,
+                                        298
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is a constant.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        302,
+                        506,
+                        357
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                299,
+                                507,
+                                335
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        299,
+                                        141,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "For any visited a",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        141,
+                                        305,
+                                        166,
+                                        315
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\epsilon > 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        212,
+                                        299,
+                                        289,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "g our algorithm on  times, and at most",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        291,
+                                        303,
+                                        302,
+                                        315
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\bar { M }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        299,
+                                        319,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        319,
+                                        302,
+                                        364,
+                                        317
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\tilde { \\mathcal O } \\big ( \\frac { 3 S A H ^ { 9 } } { \\epsilon ^ { 2 } } \\big )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        364,
+                                        299,
+                                        370,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tt",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        376,
+                                        299,
+                                        483,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "me steps, the starting state -optimal. If we select the p",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        484,
+                                        307,
+                                        494,
+                                        316
+                                    ],
+                                    "score": 0.85,
+                                    "content": "s _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        494,
+                                        299,
+                                        507,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "iscy",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                167,
+                                317,
+                                376,
+                                332
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        167,
+                                        317,
+                                        212,
+                                        332
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\tilde { \\mathcal O } \\big ( { \\textstyle { \\frac { 3 S A H ^ { 8 } } { \\epsilon ^ { 2 } } } } \\big )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        290,
+                                        319,
+                                        306,
+                                        331
+                                    ],
+                                    "score": 0.72,
+                                    "content": "1 / 3",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        371,
+                                        321,
+                                        376,
+                                        329
+                                    ],
+                                    "score": 0.71,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                329,
+                                506,
+                                346
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        329,
+                                        254,
+                                        346
+                                    ],
+                                    "score": 1.0,
+                                    "content": "uniformly randomly from the policy",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        255,
+                                        331,
+                                        282,
+                                        342
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\pi ^ { t H + 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        282,
+                                        329,
+                                        298,
+                                        346
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        298,
+                                        331,
+                                        355,
+                                        344
+                                    ],
+                                    "score": 0.93,
+                                    "content": "0 \\leq t < T / H",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        356,
+                                        329,
+                                        457,
+                                        346
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", with probability at least",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        457,
+                                        331,
+                                        473,
+                                        344
+                                    ],
+                                    "score": 0.44,
+                                    "content": "2 / 3",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        474,
+                                        329,
+                                        506,
+                                        346
+                                    ],
+                                    "score": 1.0,
+                                    "content": "we can",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                343,
+                                507,
+                                359
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        343,
+                                        133,
+                                        359
+                                    ],
+                                    "score": 1.0,
+                                    "content": "get an",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        133,
+                                        347,
+                                        138,
+                                        354
+                                    ],
+                                    "score": 0.65,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        138,
+                                        343,
+                                        362,
+                                        359
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimal policy. Therefore the PAC sample complexity is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        362,
+                                        343,
+                                        396,
+                                        358
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\tilde { \\mathcal { O } } \\left( \\epsilon ^ { - 2 } \\right)",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        397,
+                                        343,
+                                        446,
+                                        359
+                                    ],
+                                    "score": 1.0,
+                                    "content": "after hiding",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        446,
+                                        344,
+                                        479,
+                                        356
+                                    ],
+                                    "score": 0.91,
+                                    "content": "S , A , H",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        479,
+                                        343,
+                                        507,
+                                        359
+                                    ],
+                                    "score": 1.0,
+                                    "content": "terms.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 15.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        361,
+                        351,
+                        373
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                358,
+                                352,
+                                376
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        358,
+                                        301,
+                                        376
+                                    ],
+                                    "score": 1.0,
+                                    "content": "On the other hand, we want to show that for any",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        301,
+                                        362,
+                                        311,
+                                        371
+                                    ],
+                                    "score": 0.83,
+                                    "content": "K",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        312,
+                                        358,
+                                        352,
+                                        376
+                                    ],
+                                    "score": 1.0,
+                                    "content": "episodes,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        209,
+                        377,
+                        401,
+                        414
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                209,
+                                377,
+                                401,
+                                414
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        209,
+                                        377,
+                                        401,
+                                        414
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\mathrm { R e g r e t } ( T ) = \\sum _ { k = 1 } ^ { T / H } \\left[ V ^ { * } ( s _ { 1 } ) - V _ { 1 } ^ { k } ( s _ { 1 } ) \\right] \\propto T ^ { 1 / 2 } .",
+                                    "type": "interline_equation",
+                                    "image_path": "dfeb0feb59d694c97b8d3ad8daa0ee95cb21f9b5f8a16f568ba86cb50b2a11bd.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                209,
+                                377,
+                                401,
+                                395.5
+                            ],
+                            "spans": [],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                209,
+                                395.5,
+                                401,
+                                414.0
+                            ],
+                            "spans": [],
+                            "index": 20
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        423,
+                        506,
+                        458
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                422,
+                                505,
+                                437
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        422,
+                                        505,
+                                        437
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The reason why our algorithm can have a better reduction from regret to PAC is that, after choosing",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                434,
+                                506,
+                                448
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        438,
+                                        116,
+                                        447
+                                    ],
+                                    "score": 0.79,
+                                    "content": "\\epsilon _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        116,
+                                        435,
+                                        350,
+                                        448
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", it follows from the argument of theorem 1 that for all",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        351,
+                                        434,
+                                        438,
+                                        448
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\epsilon _ { 2 } > \\tilde { \\mathcal { O } } ( \\epsilon _ { 1 } / ( 1 - \\gamma ) )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        438,
+                                        435,
+                                        506,
+                                        448
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the number of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                446,
+                                246,
+                                460
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        448,
+                                        116,
+                                        458
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\epsilon _ { 2 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        117,
+                                        446,
+                                        246,
+                                        460
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-suboptimal steps is bounded by",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 22
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        213,
+                        462,
+                        397,
+                        490
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                213,
+                                462,
+                                397,
+                                490
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        213,
+                                        462,
+                                        397,
+                                        490
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\mathcal { O } \\left( \\frac { S A \\ln S A \\ln 1 / \\delta } { \\epsilon _ { 2 } ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\mathrm { p o l y l o g } \\left( \\frac { 1 } { \\epsilon _ { 1 } } , \\frac { 1 } { 1 - \\gamma } \\right) \\right)",
+                                    "type": "interline_equation",
+                                    "image_path": "fc17daba551915b444155b637b9972b89541ce4691b2e2c14706d565e8c89847.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 24,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                213,
+                                462,
+                                397,
+                                490
+                            ],
+                            "spans": [],
+                            "index": 24
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        494,
+                        505,
+                        517
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                493,
+                                505,
+                                507
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        493,
+                                        171,
+                                        507
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with probability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        171,
+                                        494,
+                                        192,
+                                        505
+                                    ],
+                                    "score": 0.77,
+                                    "content": "1 - \\delta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        192,
+                                        493,
+                                        447,
+                                        507
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". In contrast, delayed Q-learning can only give an upper bound on",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        447,
+                                        496,
+                                        457,
+                                        505
+                                    ],
+                                    "score": 0.84,
+                                    "content": "\\epsilon _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        457,
+                                        493,
+                                        505,
+                                        507
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-suboptimal",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                504,
+                                235,
+                                519
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        504,
+                                        221,
+                                        519
+                                    ],
+                                    "score": 1.0,
+                                    "content": "steps after setting parameter",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        221,
+                                        507,
+                                        230,
+                                        516
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\epsilon _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        231,
+                                        504,
+                                        235,
+                                        519
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 25.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        522,
+                        505,
+                        551
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                521,
+                                505,
+                                537
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        521,
+                                        159,
+                                        537
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Formally, let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        159,
+                                        523,
+                                        258,
+                                        536
+                                    ],
+                                    "score": 0.91,
+                                    "content": "X _ { k } = V ^ { \\ast } ( s _ { 1 } ) - V _ { 1 } ^ { k } ( s _ { 1 } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        258,
+                                        521,
+                                        320,
+                                        537
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be the regret of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        321,
+                                        524,
+                                        327,
+                                        533
+                                    ],
+                                    "score": 0.83,
+                                    "content": "k",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        327,
+                                        521,
+                                        407,
+                                        537
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-th episode. For any",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        407,
+                                        524,
+                                        415,
+                                        533
+                                    ],
+                                    "score": 0.81,
+                                    "content": "T",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        416,
+                                        521,
+                                        432,
+                                        537
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", set",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        433,
+                                        522,
+                                        487,
+                                        536
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\epsilon = \\sqrt { S A / T }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        488,
+                                        521,
+                                        505,
+                                        537
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                534,
+                                360,
+                                554
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        535,
+                                        189,
+                                        549
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\epsilon _ { 2 } = \\tilde { \\mathcal { O } } ( \\epsilon _ { 1 } / ( 1 - \\gamma ) )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        189,
+                                        534,
+                                        209,
+                                        554
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        209,
+                                        536,
+                                        293,
+                                        551
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\begin{array} { r } { M = \\lceil \\log _ { 2 } \\frac { 1 } { \\epsilon _ { 2 } ( 1 - \\gamma ) } \\rceil } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        293,
+                                        534,
+                                        360,
+                                        554
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". It follows that,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 27.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        191,
+                        556,
+                        420,
+                        648
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                191,
+                                556,
+                                420,
+                                648
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        191,
+                                        556,
+                                        420,
+                                        648
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { r l r } {  { \\operatorname { R e g r e t } ( T ) \\le T \\epsilon _ { 2 } + \\sum _ { i = 1 } ^ { M } ( | k : \\{ X _ { k } \\ge \\epsilon _ { 2 } \\cdot 2 ^ { i - 1 } \\} | ) \\epsilon _ { 2 } \\cdot 2 ^ { i } } } \\\\ & { } & \\\\ & { } & { \\le \\tilde { \\mathcal { O } } ( T \\epsilon _ { 2 } + \\sum _ { i = 1 } ^ { M } \\frac { S A \\ln 1 / \\delta } { \\epsilon _ { 2 } \\cdot 2 ^ { i - 2 } } ) } \\\\ & { } & { \\le \\tilde { \\mathcal { O } } ( \\sqrt { S A T } \\ln 1 / \\delta ) } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "1d7fa9ef3cc29e1e3ac2d0a868dec889d151fa6dfb8e0d2bbd8979285d9e7f25.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 31.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                191,
+                                556,
+                                420,
+                                571.3333333333334
+                            ],
+                            "spans": [],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                191,
+                                571.3333333333334,
+                                420,
+                                586.6666666666667
+                            ],
+                            "spans": [],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                191,
+                                586.6666666666667,
+                                420,
+                                602.0000000000001
+                            ],
+                            "spans": [],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                191,
+                                602.0000000000001,
+                                420,
+                                617.3333333333335
+                            ],
+                            "spans": [],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                191,
+                                617.3333333333335,
+                                420,
+                                632.6666666666669
+                            ],
+                            "spans": [],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                191,
+                                632.6666666666669,
+                                420,
+                                648.0000000000002
+                            ],
+                            "spans": [],
+                            "index": 34
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        652,
+                        504,
+                        677
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                650,
+                                505,
+                                666
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        650,
+                                        171,
+                                        666
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with probability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        171,
+                                        653,
+                                        194,
+                                        663
+                                    ],
+                                    "score": 0.71,
+                                    "content": "1 - \\delta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        194,
+                                        650,
+                                        250,
+                                        666
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Note that the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        250,
+                                        651,
+                                        260,
+                                        663
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\tilde { \\mathcal { O } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        260,
+                                        650,
+                                        353,
+                                        666
+                                    ],
+                                    "score": 1.0,
+                                    "content": "notation hides the poly",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        353,
+                                        653,
+                                        438,
+                                        666
+                                    ],
+                                    "score": 0.87,
+                                    "content": "( 1 / ( 1 - \\gamma ) , \\log { 1 / \\epsilon _ { 1 } } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        438,
+                                        650,
+                                        505,
+                                        666
+                                    ],
+                                    "score": 1.0,
+                                    "content": "which is, by our",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                663,
+                                267,
+                                677
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        663,
+                                        169,
+                                        677
+                                    ],
+                                    "score": 1.0,
+                                    "content": "reduction, poly",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        169,
+                                        664,
+                                        262,
+                                        676
+                                    ],
+                                    "score": 0.9,
+                                    "content": "( H , \\log T , \\log S , \\log A )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        263,
+                                        663,
+                                        267,
+                                        677
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 35.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        106,
+                        689,
+                        319,
+                        700
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                689,
+                                319,
+                                702
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        689,
+                                        319,
+                                        702
+                                    ],
+                                    "score": 1.0,
+                                    "content": "C.1 CONNECTION BETWEEN VALUE FUNCTIONS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 37
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        708,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                707,
+                                505,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        707,
+                                        275,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Recall that our MDP mapping from",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        275,
+                                        709,
+                                        454,
+                                        722
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\begin{array} { r c l } { \\mathcal { M } } & { = } & { ( S , A , H , r _ { h } ( s , a ) , p _ { h } ( s ^ { \\prime } \\mathrm { ~  ~ \\chi ~ } | \\mathrm { ~  ~ \\chi ~ } s , a ) ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        455,
+                                        707,
+                                        473,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        474,
+                                        708,
+                                        505,
+                                        721
+                                    ],
+                                    "score": 0.8,
+                                    "content": "\\begin{array} { r l } { \\bar { \\mathcal { M } } } & { { } = } \\end{array}",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                719,
+                                279,
+                                734
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        720,
+                                        221,
+                                        732
+                                    ],
+                                    "score": 0.9,
+                                    "content": "( \\bar { S } , \\bar { A } , \\gamma , \\bar { r } ( \\bar { s } , \\bar { a } ) , \\bar { p } ( \\bar { s } ^ { \\prime } \\mid \\bar { s } , \\bar { a } ) )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        222,
+                                        719,
+                                        279,
+                                        734
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is defined as,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 38.5
+                }
+            ],
+            "page_idx": 15,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        26,
+                        294,
+                        38
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                25,
+                                294,
+                                39
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        25,
+                                        294,
+                                        39
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        311,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                312,
+                                764
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        312,
+                                        764
+                                    ],
+                                    "score": 1.0,
+                                    "content": "16",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        81,
+                        295,
+                        94
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                80,
+                                297,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        80,
+                                        297,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "C EXTENSION TO OTHER SETTINGS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        105,
+                        506,
+                        150
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                105,
+                                505,
+                                118
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        105,
+                                        505,
+                                        118
+                                    ],
+                                    "score": 1.0,
+                                    "content": "First we define a mapping from a finite horizon MDP to an infinite horizon MDP so that our algorithm",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                116,
+                                504,
+                                129
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        116,
+                                        312,
+                                        129
+                                    ],
+                                    "score": 1.0,
+                                    "content": "can be applied. For an arbitrary finite horizon MDP",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        312,
+                                        117,
+                                        465,
+                                        129
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\mathcal { M } = ( S , A , H , r _ { h } ( s _ { \\perp } a ) , p _ { h } ( s ^ { \\prime } \\mid s , a ) )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        465,
+                                        116,
+                                        493,
+                                        129
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        494,
+                                        117,
+                                        504,
+                                        127
+                                    ],
+                                    "score": 0.79,
+                                    "content": "H",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                127,
+                                504,
+                                140
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        127,
+                                        363,
+                                        140
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the length of episode, the corresponding infinite horizon MDP",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        364,
+                                        129,
+                                        504,
+                                        140
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\mathcal { M } = ( S , A , \\gamma , \\bar { r } ( \\bar { s } , \\bar { a } ) , \\bar { p } ( \\bar { s } ^ { \\prime } \\mid \\bar { s } , \\bar { a } ) )",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                138,
+                                162,
+                                151
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        138,
+                                        162,
+                                        151
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is defined as,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 2.5,
+                    "bbox_fs": [
+                        104,
+                        105,
+                        505,
+                        151
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        131,
+                        157,
+                        505,
+                        226
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                131,
+                                157,
+                                226,
+                                187
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        131,
+                                        157,
+                                        226,
+                                        187
+                                    ],
+                                    "score": 0.37,
+                                    "content": "\\begin{array} { l } { { \\bullet \\ { \\bar { S } } = S \\times H , { \\bar { A } } = A ; } } \\\\ { { \\bullet \\ \\gamma = ( 1 - 1 / H ) ; } } \\end{array}",
+                                    "type": "inline_equation",
+                                    "image_path": "6163bc4f633c8d81c5759aacc60e20932b8157511f7dd0e021ff4e1df174dd54.jpg"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                131,
+                                188,
+                                505,
+                                201
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        131,
+                                        188,
+                                        185,
+                                        201
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• for a state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        186,
+                                        192,
+                                        191,
+                                        199
+                                    ],
+                                    "score": 0.76,
+                                    "content": "s",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        192,
+                                        188,
+                                        221,
+                                        201
+                                    ],
+                                    "score": 1.0,
+                                    "content": "at step",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        222,
+                                        190,
+                                        228,
+                                        199
+                                    ],
+                                    "score": 0.83,
+                                    "content": "h",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        229,
+                                        188,
+                                        245,
+                                        201
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        246,
+                                        190,
+                                        263,
+                                        201
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\bar { s } _ { s , h }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        263,
+                                        188,
+                                        438,
+                                        201
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be the corresponding state. For any action",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        439,
+                                        192,
+                                        445,
+                                        199
+                                    ],
+                                    "score": 0.77,
+                                    "content": "a",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        446,
+                                        188,
+                                        505,
+                                        201
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and next state",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                198,
+                                507,
+                                216
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        201,
+                                        151,
+                                        211
+                                    ],
+                                    "score": 0.84,
+                                    "content": "s ^ { \\prime }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        151,
+                                        198,
+                                        183,
+                                        216
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", define",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        183,
+                                        201,
+                                        303,
+                                        213
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\bar { r } ( \\bar { s } _ { s , h } , a ) = \\gamma ^ { H - h + 1 } r _ { h } ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        198,
+                                        322,
+                                        216
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        323,
+                                        201,
+                                        466,
+                                        213
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\bar { p } ( \\bar { s } _ { s ^ { \\prime } , h + 1 } \\mid \\bar { s } _ { s , h } , a ) = p _ { h } ( s ^ { \\prime } \\mid s , h )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        466,
+                                        198,
+                                        507,
+                                        216
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". And for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                211,
+                                497,
+                                226
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        213,
+                                        172,
+                                        223
+                                    ],
+                                    "score": 0.88,
+                                    "content": "h = H",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        172,
+                                        211,
+                                        189,
+                                        226
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", set",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        190,
+                                        213,
+                                        247,
+                                        225
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\bar { r } ( \\bar { s } _ { s , h } , a ) = 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        247,
+                                        211,
+                                        265,
+                                        226
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        265,
+                                        213,
+                                        384,
+                                        225
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\bar { p } ( \\bar { s } _ { s ^ { \\prime } , 1 } \\mid \\bar { s } _ { s , h } , a ) = I [ s ^ { \\prime } = s _ { 1 } ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        384,
+                                        211,
+                                        482,
+                                        226
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for a fixed starting state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        482,
+                                        214,
+                                        492,
+                                        223
+                                    ],
+                                    "score": 0.84,
+                                    "content": "s _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        493,
+                                        211,
+                                        497,
+                                        226
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 6.5,
+                    "bbox_fs": [
+                        131,
+                        157,
+                        507,
+                        226
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        233,
+                        506,
+                        297
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                233,
+                                506,
+                                247
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        233,
+                                        122,
+                                        247
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        122,
+                                        234,
+                                        133,
+                                        245
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\bar { V } _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        133,
+                                        233,
+                                        231,
+                                        247
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be the value function in",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        231,
+                                        234,
+                                        244,
+                                        245
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\bar { \\mathcal { M } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        244,
+                                        233,
+                                        275,
+                                        247
+                                    ],
+                                    "score": 1.0,
+                                    "content": "at time",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        275,
+                                        235,
+                                        281,
+                                        244
+                                    ],
+                                    "score": 0.76,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        281,
+                                        233,
+                                        298,
+                                        247
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        299,
+                                        234,
+                                        312,
+                                        247
+                                    ],
+                                    "score": 0.91,
+                                    "content": "V _ { h } ^ { k }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        313,
+                                        233,
+                                        398,
+                                        247
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the value function in",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        399,
+                                        235,
+                                        412,
+                                        245
+                                    ],
+                                    "score": 0.82,
+                                    "content": "\\mathcal { M }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        412,
+                                        233,
+                                        456,
+                                        247
+                                    ],
+                                    "score": 1.0,
+                                    "content": "at episode",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        456,
+                                        235,
+                                        462,
+                                        244
+                                    ],
+                                    "score": 0.78,
+                                    "content": "k",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        463,
+                                        233,
+                                        485,
+                                        247
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", step",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        485,
+                                        235,
+                                        492,
+                                        244
+                                    ],
+                                    "score": 0.76,
+                                    "content": "h",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        492,
+                                        233,
+                                        506,
+                                        247
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". It",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                245,
+                                507,
+                                265
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        245,
+                                        157,
+                                        265
+                                    ],
+                                    "score": 1.0,
+                                    "content": "follows that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        158,
+                                        246,
+                                        264,
+                                        263
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { r } { \\bar { V } ^ { \\ast } ( \\bar { s } _ { s _ { 1 } , 1 } ) = \\frac { \\gamma ^ { H } } { 1 - \\gamma ^ { H } } V _ { 1 } ^ { \\ast } ( s _ { 1 } ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        265,
+                                        245,
+                                        422,
+                                        265
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". And the policy mapping is defined as",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        422,
+                                        249,
+                                        489,
+                                        262
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\pi _ { h } ( s ) = \\bar { \\pi } ( \\bar { s } _ { s , h } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        490,
+                                        245,
+                                        507,
+                                        265
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                262,
+                                506,
+                                276
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        262,
+                                        133,
+                                        276
+                                    ],
+                                    "score": 1.0,
+                                    "content": "policy",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        133,
+                                        264,
+                                        141,
+                                        273
+                                    ],
+                                    "score": 0.78,
+                                    "content": "\\bar { \\pi }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        141,
+                                        262,
+                                        152,
+                                        276
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        262,
+                                        165,
+                                        273
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\bar { \\mathcal { M } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        165,
+                                        262,
+                                        268,
+                                        276
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Value functions in MDP",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        268,
+                                        263,
+                                        281,
+                                        273
+                                    ],
+                                    "score": 0.78,
+                                    "content": "\\mathcal { M }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        281,
+                                        262,
+                                        299,
+                                        276
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        299,
+                                        262,
+                                        312,
+                                        273
+                                    ],
+                                    "score": 0.86,
+                                    "content": "\\bar { \\mathcal { M } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        313,
+                                        262,
+                                        465,
+                                        276
+                                    ],
+                                    "score": 1.0,
+                                    "content": "are closely related in a sense that, any",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        465,
+                                        266,
+                                        470,
+                                        273
+                                    ],
+                                    "score": 0.68,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        471,
+                                        262,
+                                        506,
+                                        276
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimal",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                273,
+                                506,
+                                287
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        273,
+                                        133,
+                                        287
+                                    ],
+                                    "score": 1.0,
+                                    "content": "policy",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        133,
+                                        275,
+                                        141,
+                                        284
+                                    ],
+                                    "score": 0.79,
+                                    "content": "\\bar { \\pi }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        141,
+                                        273,
+                                        153,
+                                        287
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        273,
+                                        166,
+                                        284
+                                    ],
+                                    "score": 0.82,
+                                    "content": "\\bar { \\mathcal { M } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        166,
+                                        273,
+                                        248,
+                                        287
+                                    ],
+                                    "score": 1.0,
+                                    "content": "corresponding to an",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        249,
+                                        273,
+                                        279,
+                                        286
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( \\epsilon / \\gamma ^ { H } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        279,
+                                        273,
+                                        340,
+                                        287
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimal policy",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        341,
+                                        276,
+                                        348,
+                                        284
+                                    ],
+                                    "score": 0.75,
+                                    "content": "\\pi",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        349,
+                                        273,
+                                        360,
+                                        287
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        360,
+                                        275,
+                                        373,
+                                        284
+                                    ],
+                                    "score": 0.83,
+                                    "content": "\\mathcal { M }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        373,
+                                        273,
+                                        506,
+                                        287
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(see section C.1 for proof). Note",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                283,
+                                313,
+                                298
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        283,
+                                        144,
+                                        298
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that here",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        144,
+                                        284,
+                                        257,
+                                        297
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\gamma ^ { H } = ( 1 - \\dot { 1 } / H ) ^ { \\tilde { H } } = \\mathcal { O } ( \\dot { 1 } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        257,
+                                        283,
+                                        313,
+                                        298
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is a constant.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 11,
+                    "bbox_fs": [
+                        104,
+                        233,
+                        507,
+                        298
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        302,
+                        506,
+                        357
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                299,
+                                507,
+                                335
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        299,
+                                        141,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "For any visited a",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        141,
+                                        305,
+                                        166,
+                                        315
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\epsilon > 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        212,
+                                        299,
+                                        289,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "g our algorithm on  times, and at most",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        291,
+                                        303,
+                                        302,
+                                        315
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\bar { M }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        299,
+                                        319,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        319,
+                                        302,
+                                        364,
+                                        317
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\tilde { \\mathcal O } \\big ( \\frac { 3 S A H ^ { 9 } } { \\epsilon ^ { 2 } } \\big )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        364,
+                                        299,
+                                        370,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tt",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        376,
+                                        299,
+                                        483,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "me steps, the starting state -optimal. If we select the p",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        484,
+                                        307,
+                                        494,
+                                        316
+                                    ],
+                                    "score": 0.85,
+                                    "content": "s _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        494,
+                                        299,
+                                        507,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "iscy",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                167,
+                                317,
+                                376,
+                                332
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        167,
+                                        317,
+                                        212,
+                                        332
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\tilde { \\mathcal O } \\big ( { \\textstyle { \\frac { 3 S A H ^ { 8 } } { \\epsilon ^ { 2 } } } } \\big )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        290,
+                                        319,
+                                        306,
+                                        331
+                                    ],
+                                    "score": 0.72,
+                                    "content": "1 / 3",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        371,
+                                        321,
+                                        376,
+                                        329
+                                    ],
+                                    "score": 0.71,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                329,
+                                506,
+                                346
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        329,
+                                        254,
+                                        346
+                                    ],
+                                    "score": 1.0,
+                                    "content": "uniformly randomly from the policy",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        255,
+                                        331,
+                                        282,
+                                        342
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\pi ^ { t H + 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        282,
+                                        329,
+                                        298,
+                                        346
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        298,
+                                        331,
+                                        355,
+                                        344
+                                    ],
+                                    "score": 0.93,
+                                    "content": "0 \\leq t < T / H",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        356,
+                                        329,
+                                        457,
+                                        346
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", with probability at least",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        457,
+                                        331,
+                                        473,
+                                        344
+                                    ],
+                                    "score": 0.44,
+                                    "content": "2 / 3",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        474,
+                                        329,
+                                        506,
+                                        346
+                                    ],
+                                    "score": 1.0,
+                                    "content": "we can",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                343,
+                                507,
+                                359
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        343,
+                                        133,
+                                        359
+                                    ],
+                                    "score": 1.0,
+                                    "content": "get an",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        133,
+                                        347,
+                                        138,
+                                        354
+                                    ],
+                                    "score": 0.65,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        138,
+                                        343,
+                                        362,
+                                        359
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimal policy. Therefore the PAC sample complexity is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        362,
+                                        343,
+                                        396,
+                                        358
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\tilde { \\mathcal { O } } \\left( \\epsilon ^ { - 2 } \\right)",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        397,
+                                        343,
+                                        446,
+                                        359
+                                    ],
+                                    "score": 1.0,
+                                    "content": "after hiding",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        446,
+                                        344,
+                                        479,
+                                        356
+                                    ],
+                                    "score": 0.91,
+                                    "content": "S , A , H",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        479,
+                                        343,
+                                        507,
+                                        359
+                                    ],
+                                    "score": 1.0,
+                                    "content": "terms.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 15.5,
+                    "bbox_fs": [
+                        104,
+                        299,
+                        507,
+                        359
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        361,
+                        351,
+                        373
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                358,
+                                352,
+                                376
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        358,
+                                        301,
+                                        376
+                                    ],
+                                    "score": 1.0,
+                                    "content": "On the other hand, we want to show that for any",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        301,
+                                        362,
+                                        311,
+                                        371
+                                    ],
+                                    "score": 0.83,
+                                    "content": "K",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        312,
+                                        358,
+                                        352,
+                                        376
+                                    ],
+                                    "score": 1.0,
+                                    "content": "episodes,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 18,
+                    "bbox_fs": [
+                        105,
+                        358,
+                        352,
+                        376
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        209,
+                        377,
+                        401,
+                        414
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                209,
+                                377,
+                                401,
+                                414
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        209,
+                                        377,
+                                        401,
+                                        414
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\mathrm { R e g r e t } ( T ) = \\sum _ { k = 1 } ^ { T / H } \\left[ V ^ { * } ( s _ { 1 } ) - V _ { 1 } ^ { k } ( s _ { 1 } ) \\right] \\propto T ^ { 1 / 2 } .",
+                                    "type": "interline_equation",
+                                    "image_path": "dfeb0feb59d694c97b8d3ad8daa0ee95cb21f9b5f8a16f568ba86cb50b2a11bd.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                209,
+                                377,
+                                401,
+                                395.5
+                            ],
+                            "spans": [],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                209,
+                                395.5,
+                                401,
+                                414.0
+                            ],
+                            "spans": [],
+                            "index": 20
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        423,
+                        506,
+                        458
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                422,
+                                505,
+                                437
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        422,
+                                        505,
+                                        437
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The reason why our algorithm can have a better reduction from regret to PAC is that, after choosing",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                434,
+                                506,
+                                448
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        438,
+                                        116,
+                                        447
+                                    ],
+                                    "score": 0.79,
+                                    "content": "\\epsilon _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        116,
+                                        435,
+                                        350,
+                                        448
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", it follows from the argument of theorem 1 that for all",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        351,
+                                        434,
+                                        438,
+                                        448
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\epsilon _ { 2 } > \\tilde { \\mathcal { O } } ( \\epsilon _ { 1 } / ( 1 - \\gamma ) )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        438,
+                                        435,
+                                        506,
+                                        448
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the number of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                446,
+                                246,
+                                460
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        448,
+                                        116,
+                                        458
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\epsilon _ { 2 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        117,
+                                        446,
+                                        246,
+                                        460
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-suboptimal steps is bounded by",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 22,
+                    "bbox_fs": [
+                        105,
+                        422,
+                        506,
+                        460
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        213,
+                        462,
+                        397,
+                        490
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                213,
+                                462,
+                                397,
+                                490
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        213,
+                                        462,
+                                        397,
+                                        490
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\mathcal { O } \\left( \\frac { S A \\ln S A \\ln 1 / \\delta } { \\epsilon _ { 2 } ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\mathrm { p o l y l o g } \\left( \\frac { 1 } { \\epsilon _ { 1 } } , \\frac { 1 } { 1 - \\gamma } \\right) \\right)",
+                                    "type": "interline_equation",
+                                    "image_path": "fc17daba551915b444155b637b9972b89541ce4691b2e2c14706d565e8c89847.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 24,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                213,
+                                462,
+                                397,
+                                490
+                            ],
+                            "spans": [],
+                            "index": 24
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        494,
+                        505,
+                        517
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                493,
+                                505,
+                                507
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        493,
+                                        171,
+                                        507
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with probability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        171,
+                                        494,
+                                        192,
+                                        505
+                                    ],
+                                    "score": 0.77,
+                                    "content": "1 - \\delta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        192,
+                                        493,
+                                        447,
+                                        507
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". In contrast, delayed Q-learning can only give an upper bound on",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        447,
+                                        496,
+                                        457,
+                                        505
+                                    ],
+                                    "score": 0.84,
+                                    "content": "\\epsilon _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        457,
+                                        493,
+                                        505,
+                                        507
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-suboptimal",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                504,
+                                235,
+                                519
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        504,
+                                        221,
+                                        519
+                                    ],
+                                    "score": 1.0,
+                                    "content": "steps after setting parameter",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        221,
+                                        507,
+                                        230,
+                                        516
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\epsilon _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        231,
+                                        504,
+                                        235,
+                                        519
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 25.5,
+                    "bbox_fs": [
+                        105,
+                        493,
+                        505,
+                        519
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        522,
+                        505,
+                        551
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                521,
+                                505,
+                                537
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        521,
+                                        159,
+                                        537
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Formally, let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        159,
+                                        523,
+                                        258,
+                                        536
+                                    ],
+                                    "score": 0.91,
+                                    "content": "X _ { k } = V ^ { \\ast } ( s _ { 1 } ) - V _ { 1 } ^ { k } ( s _ { 1 } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        258,
+                                        521,
+                                        320,
+                                        537
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be the regret of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        321,
+                                        524,
+                                        327,
+                                        533
+                                    ],
+                                    "score": 0.83,
+                                    "content": "k",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        327,
+                                        521,
+                                        407,
+                                        537
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-th episode. For any",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        407,
+                                        524,
+                                        415,
+                                        533
+                                    ],
+                                    "score": 0.81,
+                                    "content": "T",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        416,
+                                        521,
+                                        432,
+                                        537
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", set",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        433,
+                                        522,
+                                        487,
+                                        536
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\epsilon = \\sqrt { S A / T }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        488,
+                                        521,
+                                        505,
+                                        537
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                534,
+                                360,
+                                554
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        535,
+                                        189,
+                                        549
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\epsilon _ { 2 } = \\tilde { \\mathcal { O } } ( \\epsilon _ { 1 } / ( 1 - \\gamma ) )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        189,
+                                        534,
+                                        209,
+                                        554
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        209,
+                                        536,
+                                        293,
+                                        551
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\begin{array} { r } { M = \\lceil \\log _ { 2 } \\frac { 1 } { \\epsilon _ { 2 } ( 1 - \\gamma ) } \\rceil } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        293,
+                                        534,
+                                        360,
+                                        554
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". It follows that,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 27.5,
+                    "bbox_fs": [
+                        105,
+                        521,
+                        505,
+                        554
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        191,
+                        556,
+                        420,
+                        648
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                191,
+                                556,
+                                420,
+                                648
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        191,
+                                        556,
+                                        420,
+                                        648
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { r l r } {  { \\operatorname { R e g r e t } ( T ) \\le T \\epsilon _ { 2 } + \\sum _ { i = 1 } ^ { M } ( | k : \\{ X _ { k } \\ge \\epsilon _ { 2 } \\cdot 2 ^ { i - 1 } \\} | ) \\epsilon _ { 2 } \\cdot 2 ^ { i } } } \\\\ & { } & \\\\ & { } & { \\le \\tilde { \\mathcal { O } } ( T \\epsilon _ { 2 } + \\sum _ { i = 1 } ^ { M } \\frac { S A \\ln 1 / \\delta } { \\epsilon _ { 2 } \\cdot 2 ^ { i - 2 } } ) } \\\\ & { } & { \\le \\tilde { \\mathcal { O } } ( \\sqrt { S A T } \\ln 1 / \\delta ) } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "1d7fa9ef3cc29e1e3ac2d0a868dec889d151fa6dfb8e0d2bbd8979285d9e7f25.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 31.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                191,
+                                556,
+                                420,
+                                571.3333333333334
+                            ],
+                            "spans": [],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                191,
+                                571.3333333333334,
+                                420,
+                                586.6666666666667
+                            ],
+                            "spans": [],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                191,
+                                586.6666666666667,
+                                420,
+                                602.0000000000001
+                            ],
+                            "spans": [],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                191,
+                                602.0000000000001,
+                                420,
+                                617.3333333333335
+                            ],
+                            "spans": [],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                191,
+                                617.3333333333335,
+                                420,
+                                632.6666666666669
+                            ],
+                            "spans": [],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                191,
+                                632.6666666666669,
+                                420,
+                                648.0000000000002
+                            ],
+                            "spans": [],
+                            "index": 34
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        652,
+                        504,
+                        677
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                650,
+                                505,
+                                666
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        650,
+                                        171,
+                                        666
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with probability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        171,
+                                        653,
+                                        194,
+                                        663
+                                    ],
+                                    "score": 0.71,
+                                    "content": "1 - \\delta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        194,
+                                        650,
+                                        250,
+                                        666
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Note that the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        250,
+                                        651,
+                                        260,
+                                        663
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\tilde { \\mathcal { O } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        260,
+                                        650,
+                                        353,
+                                        666
+                                    ],
+                                    "score": 1.0,
+                                    "content": "notation hides the poly",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        353,
+                                        653,
+                                        438,
+                                        666
+                                    ],
+                                    "score": 0.87,
+                                    "content": "( 1 / ( 1 - \\gamma ) , \\log { 1 / \\epsilon _ { 1 } } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        438,
+                                        650,
+                                        505,
+                                        666
+                                    ],
+                                    "score": 1.0,
+                                    "content": "which is, by our",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                663,
+                                267,
+                                677
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        663,
+                                        169,
+                                        677
+                                    ],
+                                    "score": 1.0,
+                                    "content": "reduction, poly",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        169,
+                                        664,
+                                        262,
+                                        676
+                                    ],
+                                    "score": 0.9,
+                                    "content": "( H , \\log T , \\log S , \\log A )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        263,
+                                        663,
+                                        267,
+                                        677
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 35.5,
+                    "bbox_fs": [
+                        105,
+                        650,
+                        505,
+                        677
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        106,
+                        689,
+                        319,
+                        700
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                689,
+                                319,
+                                702
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        689,
+                                        319,
+                                        702
+                                    ],
+                                    "score": 1.0,
+                                    "content": "C.1 CONNECTION BETWEEN VALUE FUNCTIONS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 37
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        708,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                707,
+                                505,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        707,
+                                        275,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Recall that our MDP mapping from",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        275,
+                                        709,
+                                        454,
+                                        722
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\begin{array} { r c l } { \\mathcal { M } } & { = } & { ( S , A , H , r _ { h } ( s , a ) , p _ { h } ( s ^ { \\prime } \\mathrm { ~  ~ \\chi ~ } | \\mathrm { ~  ~ \\chi ~ } s , a ) ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        455,
+                                        707,
+                                        473,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        474,
+                                        708,
+                                        505,
+                                        721
+                                    ],
+                                    "score": 0.8,
+                                    "content": "\\begin{array} { r l } { \\bar { \\mathcal { M } } } & { { } = } \\end{array}",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                719,
+                                279,
+                                734
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        720,
+                                        221,
+                                        732
+                                    ],
+                                    "score": 0.9,
+                                    "content": "( \\bar { S } , \\bar { A } , \\gamma , \\bar { r } ( \\bar { s } , \\bar { a } ) , \\bar { p } ( \\bar { s } ^ { \\prime } \\mid \\bar { s } , \\bar { a } ) )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        222,
+                                        719,
+                                        279,
+                                        734
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is defined as,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 38.5,
+                    "bbox_fs": [
+                        105,
+                        707,
+                        505,
+                        734
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        131,
+                        81,
+                        508,
+                        148
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                131,
+                                79,
+                                228,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        131,
+                                        79,
+                                        141,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "•",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        142,
+                                        81,
+                                        224,
+                                        94
+                                    ],
+                                    "score": 0.81,
+                                    "content": "\\bar { S } = S \\times H , \\bar { A } = A",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        225,
+                                        79,
+                                        228,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": ";",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                131,
+                                97,
+                                211,
+                                109
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        131,
+                                        97,
+                                        142,
+                                        109
+                                    ],
+                                    "score": 1.0,
+                                    "content": "•",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        142,
+                                        97,
+                                        207,
+                                        109
+                                    ],
+                                    "score": 0.73,
+                                    "content": "\\gamma = ( 1 - 1 / H )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        207,
+                                        97,
+                                        211,
+                                        109
+                                    ],
+                                    "score": 1.0,
+                                    "content": ";",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                131,
+                                111,
+                                507,
+                                125
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        131,
+                                        111,
+                                        184,
+                                        125
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• for a state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        115,
+                                        190,
+                                        122
+                                    ],
+                                    "score": 0.76,
+                                    "content": "s",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        190,
+                                        111,
+                                        219,
+                                        125
+                                    ],
+                                    "score": 1.0,
+                                    "content": "at step",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        219,
+                                        113,
+                                        226,
+                                        122
+                                    ],
+                                    "score": 0.78,
+                                    "content": "h",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        226,
+                                        111,
+                                        242,
+                                        125
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        242,
+                                        113,
+                                        259,
+                                        124
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\bar { s } _ { s , h }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        259,
+                                        111,
+                                        429,
+                                        125
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be the corresponding state. For any action",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        429,
+                                        115,
+                                        436,
+                                        122
+                                    ],
+                                    "score": 0.75,
+                                    "content": "a",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        436,
+                                        111,
+                                        494,
+                                        125
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and next state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        494,
+                                        113,
+                                        502,
+                                        122
+                                    ],
+                                    "score": 0.85,
+                                    "content": "s ^ { \\prime }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        502,
+                                        111,
+                                        507,
+                                        125
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                140,
+                                122,
+                                509,
+                                138
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        140,
+                                        122,
+                                        170,
+                                        138
+                                    ],
+                                    "score": 1.0,
+                                    "content": "define",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        170,
+                                        123,
+                                        289,
+                                        136
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\bar { r } ( \\bar { s } _ { s , h } , a ) = \\gamma ^ { H - h + 1 } r _ { h } ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        290,
+                                        122,
+                                        308,
+                                        138
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        309,
+                                        124,
+                                        433,
+                                        136
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\bar { p } ( \\bar { s } _ { s ^ { \\prime } , h + 1 } \\mid \\bar { s } _ { s , h } , a ) = p _ { h } ( s , h )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        433,
+                                        122,
+                                        472,
+                                        138
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". And for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        473,
+                                        124,
+                                        502,
+                                        135
+                                    ],
+                                    "score": 0.89,
+                                    "content": "h = H",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        503,
+                                        122,
+                                        509,
+                                        138
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                140,
+                                134,
+                                464,
+                                149
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        140,
+                                        134,
+                                        156,
+                                        149
+                                    ],
+                                    "score": 1.0,
+                                    "content": "set",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        156,
+                                        136,
+                                        214,
+                                        147
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\bar { r } ( \\bar { s } _ { s , h } , a ) = 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        214,
+                                        134,
+                                        232,
+                                        149
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        232,
+                                        136,
+                                        352,
+                                        147
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\bar { p } ( \\bar { s } _ { s ^ { \\prime } , 1 } \\mid \\bar { s } _ { s , h } , a ) = I [ s ^ { \\prime } = s _ { 1 } ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        352,
+                                        134,
+                                        449,
+                                        149
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for a fixed starting state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        450,
+                                        137,
+                                        459,
+                                        146
+                                    ],
+                                    "score": 0.84,
+                                    "content": "s _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        460,
+                                        134,
+                                        464,
+                                        149
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        155,
+                        507,
+                        190
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                155,
+                                506,
+                                170
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        155,
+                                        169,
+                                        170
+                                    ],
+                                    "score": 1.0,
+                                    "content": "For a trajectory",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        169,
+                                        156,
+                                        284,
+                                        169
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\left\\{ { \\left( { \\bar { s } } _ { s _ { 1 } , 1 } , { \\bar { a } } _ { 1 } \\right) } , { \\left( { \\bar { s } } _ { s _ { 2 } , 2 } , { \\bar { a } } _ { 2 } \\right) } , \\cdot \\cdot \\cdot \\right\\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        285,
+                                        155,
+                                        295,
+                                        170
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        295,
+                                        156,
+                                        308,
+                                        167
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\bar { \\mathcal { M } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        309,
+                                        155,
+                                        325,
+                                        170
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        325,
+                                        156,
+                                        420,
+                                        169
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\{ ( s _ { 1 } , a _ { 1 } ) , ( s _ { 2 } , a _ { 2 } ) , \\cdot \\cdot \\cdot \\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        420,
+                                        155,
+                                        506,
+                                        170
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be the corresponding",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                167,
+                                505,
+                                180
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        167,
+                                        157,
+                                        180
+                                    ],
+                                    "score": 1.0,
+                                    "content": "trajectory in",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        158,
+                                        168,
+                                        170,
+                                        177
+                                    ],
+                                    "score": 0.83,
+                                    "content": "\\mathcal { M }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        171,
+                                        167,
+                                        214,
+                                        180
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Note that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        214,
+                                        169,
+                                        226,
+                                        177
+                                    ],
+                                    "score": 0.84,
+                                    "content": "\\mathcal { M }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        227,
+                                        167,
+                                        355,
+                                        180
+                                    ],
+                                    "score": 1.0,
+                                    "content": "has a unique fixed starting state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        355,
+                                        170,
+                                        365,
+                                        179
+                                    ],
+                                    "score": 0.87,
+                                    "content": "s _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        366,
+                                        167,
+                                        441,
+                                        180
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", which means that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        441,
+                                        169,
+                                        490,
+                                        180
+                                    ],
+                                    "score": 0.9,
+                                    "content": "s _ { t H + 1 } = s _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        490,
+                                        167,
+                                        505,
+                                        180
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                178,
+                                480,
+                                191
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        179,
+                                        119,
+                                        191
+                                    ],
+                                    "score": 1.0,
+                                    "content": "all",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        119,
+                                        179,
+                                        142,
+                                        190
+                                    ],
+                                    "score": 0.89,
+                                    "content": "t \\geq 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        142,
+                                        179,
+                                        290,
+                                        191
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Denote the corresponding policy of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        290,
+                                        178,
+                                        300,
+                                        189
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\bar { \\pi } ^ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        301,
+                                        179,
+                                        312,
+                                        191
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        313,
+                                        178,
+                                        323,
+                                        189
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\pi ^ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        324,
+                                        179,
+                                        480,
+                                        191
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(may be non-stationary), then we have",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        111,
+                        194,
+                        514,
+                        245
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                111,
+                                194,
+                                514,
+                                245
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        194,
+                                        514,
+                                        245
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\begin{array} { r l } & { \\bar { \\gamma } ^ { \\pi ^ { t } } ( \\bar { s } _ { s _ { 1 } , 1 } ) = \\mathbb { E } \\left[ \\bar { r } ( \\bar { s } _ { s _ { 1 } , 1 } , \\bar { a } _ { 1 } ) + \\gamma \\bar { r } ( \\bar { s } _ { s _ { 2 } , 2 } , \\bar { a } _ { 2 } ) + \\cdot \\cdot \\cdot + \\gamma ^ { H - 1 } \\bar { r } ( \\bar { s } _ { s _ { H - 1 } , H - 1 } , \\bar { a } _ { H - 1 } ) + \\gamma ^ { H } \\bar { V } ^ { \\pi _ { t + H - 1 } } ( \\bar { s } _ { s _ { H + 1 } , 1 } ) \\right] } \\\\ & { \\phantom { \\frac { 1 } { 1 } } = \\gamma ^ { H } \\mathbb { E } \\left[ r _ { 1 } ( s _ { 1 } , a _ { 1 } ) + r _ { 2 } ( s _ { 2 } , a _ { 2 } ) + \\cdot \\cdot \\cdot + r _ { H - 1 } ( s _ { H - 1 } , a _ { H - 1 } ) + \\bar { V } ^ { \\pi _ { t + H } } ( \\bar { s } _ { s _ { H + 1 } , 1 } ) \\right] } \\\\ & { \\phantom { \\frac { 1 } { 1 } } = \\gamma ^ { H } V ^ { \\pi ^ { t } } ( s _ { 1 } ) + \\gamma ^ { H } \\bar { V } ^ { \\pi + H } ( \\bar { s } _ { s _ { 1 } , 1 } ) . } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "52704ae56896c370e8ec3e398577b25911ebb487e2237bb93613270924e4d24c.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                111,
+                                194,
+                                514,
+                                211.0
+                            ],
+                            "spans": [],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                111,
+                                211.0,
+                                514,
+                                228.0
+                            ],
+                            "spans": [],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                111,
+                                228.0,
+                                514,
+                                245.0
+                            ],
+                            "spans": [],
+                            "index": 10
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        249,
+                        505,
+                        284
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                100,
+                                245,
+                                510,
+                                270
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        100,
+                                        245,
+                                        217,
+                                        270
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Then for a stationary policy",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        217,
+                                        254,
+                                        224,
+                                        262
+                                    ],
+                                    "score": 0.8,
+                                    "content": "\\bar { \\pi }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        224,
+                                        245,
+                                        295,
+                                        270
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", we can conclude",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        249,
+                                        404,
+                                        267
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { r } { \\bar { V } ^ { \\bar { \\pi } } ( \\bar { s } _ { s _ { 1 } , 1 } ) = \\frac { \\gamma ^ { H } } { 1 - \\gamma ^ { H } } V ^ { \\pi } ( s _ { 1 } ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        404,
+                                        245,
+                                        510,
+                                        270
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Since the optimal policy",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                266,
+                                321,
+                                286
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        270,
+                                        118,
+                                        279
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\bar { \\pi } ^ { * }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        118,
+                                        266,
+                                        207,
+                                        286
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is stationary, we have",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        208,
+                                        266,
+                                        315,
+                                        284
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { r } { \\bar { V } ^ { \\ast } ( \\bar { s } _ { s _ { 1 } , 1 } ) = \\frac { \\gamma ^ { H } } { 1 - \\gamma ^ { H } } V ^ { \\ast } ( s _ { 1 } ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        315,
+                                        266,
+                                        321,
+                                        286
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "index": 11.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        287,
+                        322,
+                        299
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                286,
+                                322,
+                                301
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        286,
+                                        164,
+                                        301
+                                    ],
+                                    "score": 1.0,
+                                    "content": "By definition,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        164,
+                                        289,
+                                        171,
+                                        298
+                                    ],
+                                    "score": 0.79,
+                                    "content": "\\bar { \\pi }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        171,
+                                        286,
+                                        181,
+                                        301
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        182,
+                                        290,
+                                        187,
+                                        298
+                                    ],
+                                    "score": 0.73,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        187,
+                                        286,
+                                        270,
+                                        301
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimal at time step",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        270,
+                                        289,
+                                        275,
+                                        298
+                                    ],
+                                    "score": 0.74,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        276,
+                                        286,
+                                        322,
+                                        301
+                                    ],
+                                    "score": 1.0,
+                                    "content": "means that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        246,
+                        303,
+                        364,
+                        320
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                246,
+                                303,
+                                364,
+                                320
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        246,
+                                        303,
+                                        364,
+                                        320
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\begin{array} { r } { \\bar { V } ^ { \\bar { \\pi } ^ { t } } ( \\bar { s } _ { s _ { 1 } , 1 } ) \\geq \\bar { V } ^ { * } ( \\bar { s } _ { s _ { 1 } , 1 } ) - \\epsilon . } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "f086319de63ecc59068ffa365e9e62e72d387018083ec5144b0aa425136c465f.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                246,
+                                303,
+                                364,
+                                320
+                            ],
+                            "spans": [],
+                            "index": 14
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        324,
+                        164,
+                        335
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                322,
+                                165,
+                                336
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        322,
+                                        165,
+                                        336
+                                    ],
+                                    "score": 1.0,
+                                    "content": "It follows that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        177,
+                        336,
+                        432,
+                        353
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                177,
+                                336,
+                                432,
+                                353
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        177,
+                                        336,
+                                        432,
+                                        353
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\gamma ^ { H } V ^ { \\pi ^ { t } } ( s _ { 1 } ) + \\gamma ^ { H } \\bar { V } ^ { \\pi _ { t + H } } ( \\bar { s } _ { s _ { 1 } , 1 } ) = \\bar { V } ^ { \\bar { \\pi } } ( \\bar { s } _ { s _ { 1 } , 1 } ) \\geq \\bar { V } ^ { * } ( \\bar { s } _ { s _ { 1 } , 1 } ) - \\epsilon ,",
+                                    "type": "interline_equation",
+                                    "image_path": "5cce7a222551bc6274bbc52ffdb272aeca3dced98abbbc8f80d2fab7858deadf.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                177,
+                                336,
+                                432,
+                                353
+                            ],
+                            "spans": [],
+                            "index": 16
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        357,
+                        132,
+                        368
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                356,
+                                133,
+                                370
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        356,
+                                        133,
+                                        370
+                                    ],
+                                    "score": 1.0,
+                                    "content": "hence",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        111,
+                        371,
+                        504,
+                        387
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                111,
+                                371,
+                                504,
+                                387
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        371,
+                                        504,
+                                        387
+                                    ],
+                                    "score": 0.86,
+                                    "content": "^ { H } V ^ { \\pi ^ { \\varepsilon } } ( s _ { 1 } ) \\geq ( 1 - \\gamma ^ { H } ) \\bar { V } ^ { * } ( \\bar { s } _ { s _ { 1 } , 1 } ) + \\gamma ^ { H } ( \\bar { V } ^ { * } ( \\bar { s } _ { s _ { 1 } , 1 } ) - \\bar { V } ^ { \\pi _ { t + H } } ( \\bar { s } _ { s _ { 1 } , 1 } ) ) - \\epsilon \\geq ( 1 - \\gamma ^ { H } ) \\bar { V } ^ { * } ( \\bar { s } _ { s _ { 1 } , 1 } ) - \\epsilon .",
+                                    "type": "interline_equation",
+                                    "image_path": "a3a5a1e7d68659f678d45d1177dbe36c95439ce8dceba0366c8e7ffef18cce5d.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                111,
+                                371,
+                                504,
+                                387
+                            ],
+                            "spans": [],
+                            "index": 18
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        390,
+                        183,
+                        402
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                389,
+                                183,
+                                403
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        389,
+                                        183,
+                                        403
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Therefore we have",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 19
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        187,
+                        404,
+                        423,
+                        431
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                187,
+                                404,
+                                423,
+                                431
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        187,
+                                        404,
+                                        423,
+                                        431
+                                    ],
+                                    "score": 0.93,
+                                    "content": "{ V ^ { \\pi } } ^ { t } ( s _ { 1 } ) \\ge \\frac { 1 - \\gamma ^ { H } } { \\gamma ^ { H } } \\bar { V } ^ { * } ( \\bar { s } _ { s 1 , 1 } ) - \\epsilon / \\gamma ^ { H } = V ^ { * } ( s _ { 1 } ) - \\epsilon / \\gamma ^ { H } ,",
+                                    "type": "interline_equation",
+                                    "image_path": "1f1b44222a0c1087458d2ccf43ee9da0e84754c0602268ed6cbc91b7c6c5c549.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 20,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                187,
+                                404,
+                                423,
+                                431
+                            ],
+                            "spans": [],
+                            "index": 20
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        435,
+                        306,
+                        449
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                433,
+                                307,
+                                451
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        433,
+                                        178,
+                                        451
+                                    ],
+                                    "score": 1.0,
+                                    "content": "which means that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        178,
+                                        436,
+                                        189,
+                                        446
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\pi ^ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        190,
+                                        433,
+                                        212,
+                                        451
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is an",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        212,
+                                        435,
+                                        242,
+                                        448
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( \\epsilon / \\gamma ^ { H } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        243,
+                                        433,
+                                        307,
+                                        451
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimal policy.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 21
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        106,
+                        462,
+                        372,
+                        477
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                461,
+                                373,
+                                480
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        461,
+                                        373,
+                                        480
+                                    ],
+                                    "score": 1.0,
+                                    "content": "D A HARD INSTANCE FOR DELAYED Q-LEARNING",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 22
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        488,
+                        456,
+                        501
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                485,
+                                456,
+                                504
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        485,
+                                        456,
+                                        504
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In this section, we prove Theorem 2 regarding the performance of Delayed Q-learning.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 23
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        502,
+                        506,
+                        545
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                501,
+                                505,
+                                516
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        501,
+                                        353,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Theorem 2. There exists a family of MDPs with constant",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        354,
+                                        503,
+                                        362,
+                                        513
+                                    ],
+                                    "score": 0.78,
+                                    "content": "S",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        362,
+                                        501,
+                                        383,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        383,
+                                        504,
+                                        392,
+                                        513
+                                    ],
+                                    "score": 0.71,
+                                    "content": "A",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        392,
+                                        501,
+                                        505,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", in which with probability",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                514,
+                                505,
+                                533
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        517,
+                                        129,
+                                        528
+                                    ],
+                                    "score": 0.71,
+                                    "content": "1 - \\delta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        129,
+                                        515,
+                                        169,
+                                        532
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", Delayed",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        170,
+                                        518,
+                                        178,
+                                        529
+                                    ],
+                                    "score": 0.71,
+                                    "content": "Q",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        178,
+                                        515,
+                                        393,
+                                        532
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-learning incurs sample complexity of exploration of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        393,
+                                        514,
+                                        441,
+                                        533
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\Omega \\left( \\frac { \\epsilon ^ { - 3 } } { \\ln ( 1 / \\delta ) } \\right)",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        442,
+                                        516,
+                                        505,
+                                        530
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", assuming that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                531,
+                                169,
+                                545
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        532,
+                                        166,
+                                        545
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\ln ( 1 / \\delta ) < \\epsilon ^ { - 2 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        167,
+                                        531,
+                                        169,
+                                        544
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 25
+                },
+                {
+                    "type": "image",
+                    "bbox": [
+                        243,
+                        559,
+                        367,
+                        657
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                243,
+                                559,
+                                367,
+                                657
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        243,
+                                        559,
+                                        367,
+                                        657
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                243,
+                                                559,
+                                                367,
+                                                657
+                                            ],
+                                            "score": 0.96,
+                                            "type": "image",
+                                            "image_path": "d5ea7466679255528080a8e623d46ab5efe02c60983c67939e2c04d8974b3167.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 27.5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        243,
+                                        559,
+                                        367,
+                                        608.0
+                                    ],
+                                    "spans": [],
+                                    "index": 27
+                                },
+                                {
+                                    "bbox": [
+                                        243,
+                                        608.0,
+                                        367,
+                                        657.0
+                                    ],
+                                    "spans": [],
+                                    "index": 28
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                105,
+                                667,
+                                506,
+                                690
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        667,
+                                        506,
+                                        680
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                667,
+                                                506,
+                                                680
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 1: The MDP family. Actions are denoted by arrows. Actions with red color have reward 1,",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 29
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        678,
+                                        205,
+                                        691
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                678,
+                                                205,
+                                                691
+                                            ],
+                                            "score": 1.0,
+                                            "content": "and reward 0 otherwise.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 30
+                                }
+                            ],
+                            "index": 29.5
+                        }
+                    ],
+                    "index": 28.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        698,
+                        505,
+                        733
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                696,
+                                505,
+                                713
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        696,
+                                        175,
+                                        713
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Proof. For each",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        175,
+                                        698,
+                                        227,
+                                        711
+                                    ],
+                                    "score": 0.92,
+                                    "content": "0 < \\epsilon < \\frac { 1 } { 1 0 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        227,
+                                        696,
+                                        484,
+                                        713
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", consider the following MDP (see also Fig. 1): state space is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        484,
+                                        699,
+                                        505,
+                                        709
+                                    ],
+                                    "score": 0.86,
+                                    "content": "{ \\boldsymbol { s } } =",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                709,
+                                505,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        710,
+                                        140,
+                                        721
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\{ a , b , c \\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        141,
+                                        709,
+                                        213,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "while action set is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        214,
+                                        710,
+                                        261,
+                                        721
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\overset { \\vartriangle } { \\mathcal { A } } = \\{ \\ v { x } , \\ v { y } \\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        262,
+                                        709,
+                                        369,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "; transition probabilities are",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        370,
+                                        710,
+                                        450,
+                                        721
+                                    ],
+                                    "score": 0.73,
+                                    "content": "P ( b | a , y ) = 1 - 1 0 \\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        450,
+                                        709,
+                                        455,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        455,
+                                        710,
+                                        505,
+                                        722
+                                    ],
+                                    "score": 0.61,
+                                    "content": "P ( c | a , y ) =",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                720,
+                                446,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        720,
+                                        125,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "10\u000f,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        126,
+                                        721,
+                                        182,
+                                        732
+                                    ],
+                                    "score": 0.91,
+                                    "content": "P ( b | a , x ) = 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        183,
+                                        720,
+                                        186,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        186,
+                                        721,
+                                        289,
+                                        732
+                                    ],
+                                    "score": 0.88,
+                                    "content": "P ( a | b , \\cdot ) = P ( a | c , \\cdot ) = 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        720,
+                                        396,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Rewards are all 1, except",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        396,
+                                        721,
+                                        442,
+                                        732
+                                    ],
+                                    "score": 0.92,
+                                    "content": "R ( c , \\cdot ) = 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        442,
+                                        720,
+                                        446,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 32
+                }
+            ],
+            "page_idx": 16,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        26,
+                        294,
+                        38
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                25,
+                                294,
+                                39
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        25,
+                                        294,
+                                        39
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        310,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                312,
+                                765
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        312,
+                                        765
+                                    ],
+                                    "score": 1.0,
+                                    "content": "",
+                                    "type": "text",
+                                    "height": 15,
+                                    "width": 13
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "list",
+                    "bbox": [
+                        131,
+                        81,
+                        508,
+                        148
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                131,
+                                79,
+                                228,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        131,
+                                        79,
+                                        141,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "•",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        142,
+                                        81,
+                                        224,
+                                        94
+                                    ],
+                                    "score": 0.81,
+                                    "content": "\\bar { S } = S \\times H , \\bar { A } = A",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        225,
+                                        79,
+                                        228,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": ";",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0,
+                            "is_list_start_line": true,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                131,
+                                97,
+                                211,
+                                109
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        131,
+                                        97,
+                                        142,
+                                        109
+                                    ],
+                                    "score": 1.0,
+                                    "content": "•",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        142,
+                                        97,
+                                        207,
+                                        109
+                                    ],
+                                    "score": 0.73,
+                                    "content": "\\gamma = ( 1 - 1 / H )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        207,
+                                        97,
+                                        211,
+                                        109
+                                    ],
+                                    "score": 1.0,
+                                    "content": ";",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1,
+                            "is_list_start_line": true,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                131,
+                                111,
+                                507,
+                                125
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        131,
+                                        111,
+                                        184,
+                                        125
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• for a state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        115,
+                                        190,
+                                        122
+                                    ],
+                                    "score": 0.76,
+                                    "content": "s",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        190,
+                                        111,
+                                        219,
+                                        125
+                                    ],
+                                    "score": 1.0,
+                                    "content": "at step",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        219,
+                                        113,
+                                        226,
+                                        122
+                                    ],
+                                    "score": 0.78,
+                                    "content": "h",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        226,
+                                        111,
+                                        242,
+                                        125
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        242,
+                                        113,
+                                        259,
+                                        124
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\bar { s } _ { s , h }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        259,
+                                        111,
+                                        429,
+                                        125
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be the corresponding state. For any action",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        429,
+                                        115,
+                                        436,
+                                        122
+                                    ],
+                                    "score": 0.75,
+                                    "content": "a",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        436,
+                                        111,
+                                        494,
+                                        125
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and next state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        494,
+                                        113,
+                                        502,
+                                        122
+                                    ],
+                                    "score": 0.85,
+                                    "content": "s ^ { \\prime }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        502,
+                                        111,
+                                        507,
+                                        125
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                140,
+                                122,
+                                509,
+                                138
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        140,
+                                        122,
+                                        170,
+                                        138
+                                    ],
+                                    "score": 1.0,
+                                    "content": "define",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        170,
+                                        123,
+                                        289,
+                                        136
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\bar { r } ( \\bar { s } _ { s , h } , a ) = \\gamma ^ { H - h + 1 } r _ { h } ( s , a )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        290,
+                                        122,
+                                        308,
+                                        138
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        309,
+                                        124,
+                                        433,
+                                        136
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\bar { p } ( \\bar { s } _ { s ^ { \\prime } , h + 1 } \\mid \\bar { s } _ { s , h } , a ) = p _ { h } ( s , h )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        433,
+                                        122,
+                                        472,
+                                        138
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". And for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        473,
+                                        124,
+                                        502,
+                                        135
+                                    ],
+                                    "score": 0.89,
+                                    "content": "h = H",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        503,
+                                        122,
+                                        509,
+                                        138
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                140,
+                                134,
+                                464,
+                                149
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        140,
+                                        134,
+                                        156,
+                                        149
+                                    ],
+                                    "score": 1.0,
+                                    "content": "set",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        156,
+                                        136,
+                                        214,
+                                        147
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\bar { r } ( \\bar { s } _ { s , h } , a ) = 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        214,
+                                        134,
+                                        232,
+                                        149
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        232,
+                                        136,
+                                        352,
+                                        147
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\bar { p } ( \\bar { s } _ { s ^ { \\prime } , 1 } \\mid \\bar { s } _ { s , h } , a ) = I [ s ^ { \\prime } = s _ { 1 } ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        352,
+                                        134,
+                                        449,
+                                        149
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for a fixed starting state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        450,
+                                        137,
+                                        459,
+                                        146
+                                    ],
+                                    "score": 0.84,
+                                    "content": "s _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        460,
+                                        134,
+                                        464,
+                                        149
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4,
+                            "is_list_end_line": true
+                        }
+                    ],
+                    "index": 2,
+                    "bbox_fs": [
+                        131,
+                        79,
+                        509,
+                        149
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        155,
+                        507,
+                        190
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                155,
+                                506,
+                                170
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        155,
+                                        169,
+                                        170
+                                    ],
+                                    "score": 1.0,
+                                    "content": "For a trajectory",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        169,
+                                        156,
+                                        284,
+                                        169
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\left\\{ { \\left( { \\bar { s } } _ { s _ { 1 } , 1 } , { \\bar { a } } _ { 1 } \\right) } , { \\left( { \\bar { s } } _ { s _ { 2 } , 2 } , { \\bar { a } } _ { 2 } \\right) } , \\cdot \\cdot \\cdot \\right\\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        285,
+                                        155,
+                                        295,
+                                        170
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        295,
+                                        156,
+                                        308,
+                                        167
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\bar { \\mathcal { M } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        309,
+                                        155,
+                                        325,
+                                        170
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        325,
+                                        156,
+                                        420,
+                                        169
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\{ ( s _ { 1 } , a _ { 1 } ) , ( s _ { 2 } , a _ { 2 } ) , \\cdot \\cdot \\cdot \\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        420,
+                                        155,
+                                        506,
+                                        170
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be the corresponding",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                167,
+                                505,
+                                180
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        167,
+                                        157,
+                                        180
+                                    ],
+                                    "score": 1.0,
+                                    "content": "trajectory in",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        158,
+                                        168,
+                                        170,
+                                        177
+                                    ],
+                                    "score": 0.83,
+                                    "content": "\\mathcal { M }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        171,
+                                        167,
+                                        214,
+                                        180
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Note that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        214,
+                                        169,
+                                        226,
+                                        177
+                                    ],
+                                    "score": 0.84,
+                                    "content": "\\mathcal { M }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        227,
+                                        167,
+                                        355,
+                                        180
+                                    ],
+                                    "score": 1.0,
+                                    "content": "has a unique fixed starting state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        355,
+                                        170,
+                                        365,
+                                        179
+                                    ],
+                                    "score": 0.87,
+                                    "content": "s _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        366,
+                                        167,
+                                        441,
+                                        180
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", which means that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        441,
+                                        169,
+                                        490,
+                                        180
+                                    ],
+                                    "score": 0.9,
+                                    "content": "s _ { t H + 1 } = s _ { 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        490,
+                                        167,
+                                        505,
+                                        180
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                178,
+                                480,
+                                191
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        179,
+                                        119,
+                                        191
+                                    ],
+                                    "score": 1.0,
+                                    "content": "all",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        119,
+                                        179,
+                                        142,
+                                        190
+                                    ],
+                                    "score": 0.89,
+                                    "content": "t \\geq 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        142,
+                                        179,
+                                        290,
+                                        191
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Denote the corresponding policy of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        290,
+                                        178,
+                                        300,
+                                        189
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\bar { \\pi } ^ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        301,
+                                        179,
+                                        312,
+                                        191
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        313,
+                                        178,
+                                        323,
+                                        189
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\pi ^ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        324,
+                                        179,
+                                        480,
+                                        191
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(may be non-stationary), then we have",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 6,
+                    "bbox_fs": [
+                        105,
+                        155,
+                        506,
+                        191
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        111,
+                        194,
+                        514,
+                        245
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                111,
+                                194,
+                                514,
+                                245
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        194,
+                                        514,
+                                        245
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\begin{array} { r l } & { \\bar { \\gamma } ^ { \\pi ^ { t } } ( \\bar { s } _ { s _ { 1 } , 1 } ) = \\mathbb { E } \\left[ \\bar { r } ( \\bar { s } _ { s _ { 1 } , 1 } , \\bar { a } _ { 1 } ) + \\gamma \\bar { r } ( \\bar { s } _ { s _ { 2 } , 2 } , \\bar { a } _ { 2 } ) + \\cdot \\cdot \\cdot + \\gamma ^ { H - 1 } \\bar { r } ( \\bar { s } _ { s _ { H - 1 } , H - 1 } , \\bar { a } _ { H - 1 } ) + \\gamma ^ { H } \\bar { V } ^ { \\pi _ { t + H - 1 } } ( \\bar { s } _ { s _ { H + 1 } , 1 } ) \\right] } \\\\ & { \\phantom { \\frac { 1 } { 1 } } = \\gamma ^ { H } \\mathbb { E } \\left[ r _ { 1 } ( s _ { 1 } , a _ { 1 } ) + r _ { 2 } ( s _ { 2 } , a _ { 2 } ) + \\cdot \\cdot \\cdot + r _ { H - 1 } ( s _ { H - 1 } , a _ { H - 1 } ) + \\bar { V } ^ { \\pi _ { t + H } } ( \\bar { s } _ { s _ { H + 1 } , 1 } ) \\right] } \\\\ & { \\phantom { \\frac { 1 } { 1 } } = \\gamma ^ { H } V ^ { \\pi ^ { t } } ( s _ { 1 } ) + \\gamma ^ { H } \\bar { V } ^ { \\pi + H } ( \\bar { s } _ { s _ { 1 } , 1 } ) . } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "52704ae56896c370e8ec3e398577b25911ebb487e2237bb93613270924e4d24c.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                111,
+                                194,
+                                514,
+                                211.0
+                            ],
+                            "spans": [],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                111,
+                                211.0,
+                                514,
+                                228.0
+                            ],
+                            "spans": [],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                111,
+                                228.0,
+                                514,
+                                245.0
+                            ],
+                            "spans": [],
+                            "index": 10
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        249,
+                        505,
+                        284
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                100,
+                                245,
+                                510,
+                                270
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        100,
+                                        245,
+                                        217,
+                                        270
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Then for a stationary policy",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        217,
+                                        254,
+                                        224,
+                                        262
+                                    ],
+                                    "score": 0.8,
+                                    "content": "\\bar { \\pi }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        224,
+                                        245,
+                                        295,
+                                        270
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", we can conclude",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        249,
+                                        404,
+                                        267
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { r } { \\bar { V } ^ { \\bar { \\pi } } ( \\bar { s } _ { s _ { 1 } , 1 } ) = \\frac { \\gamma ^ { H } } { 1 - \\gamma ^ { H } } V ^ { \\pi } ( s _ { 1 } ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        404,
+                                        245,
+                                        510,
+                                        270
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Since the optimal policy",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                266,
+                                321,
+                                286
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        270,
+                                        118,
+                                        279
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\bar { \\pi } ^ { * }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        118,
+                                        266,
+                                        207,
+                                        286
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is stationary, we have",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        208,
+                                        266,
+                                        315,
+                                        284
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { r } { \\bar { V } ^ { \\ast } ( \\bar { s } _ { s _ { 1 } , 1 } ) = \\frac { \\gamma ^ { H } } { 1 - \\gamma ^ { H } } V ^ { \\ast } ( s _ { 1 } ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        315,
+                                        266,
+                                        321,
+                                        286
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "index": 11.5,
+                    "bbox_fs": [
+                        100,
+                        245,
+                        510,
+                        286
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        287,
+                        322,
+                        299
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                286,
+                                322,
+                                301
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        286,
+                                        164,
+                                        301
+                                    ],
+                                    "score": 1.0,
+                                    "content": "By definition,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        164,
+                                        289,
+                                        171,
+                                        298
+                                    ],
+                                    "score": 0.79,
+                                    "content": "\\bar { \\pi }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        171,
+                                        286,
+                                        181,
+                                        301
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        182,
+                                        290,
+                                        187,
+                                        298
+                                    ],
+                                    "score": 0.73,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        187,
+                                        286,
+                                        270,
+                                        301
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimal at time step",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        270,
+                                        289,
+                                        275,
+                                        298
+                                    ],
+                                    "score": 0.74,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        276,
+                                        286,
+                                        322,
+                                        301
+                                    ],
+                                    "score": 1.0,
+                                    "content": "means that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 13,
+                    "bbox_fs": [
+                        106,
+                        286,
+                        322,
+                        301
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        246,
+                        303,
+                        364,
+                        320
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                246,
+                                303,
+                                364,
+                                320
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        246,
+                                        303,
+                                        364,
+                                        320
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\begin{array} { r } { \\bar { V } ^ { \\bar { \\pi } ^ { t } } ( \\bar { s } _ { s _ { 1 } , 1 } ) \\geq \\bar { V } ^ { * } ( \\bar { s } _ { s _ { 1 } , 1 } ) - \\epsilon . } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "f086319de63ecc59068ffa365e9e62e72d387018083ec5144b0aa425136c465f.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                246,
+                                303,
+                                364,
+                                320
+                            ],
+                            "spans": [],
+                            "index": 14
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        324,
+                        164,
+                        335
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                322,
+                                165,
+                                336
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        322,
+                                        165,
+                                        336
+                                    ],
+                                    "score": 1.0,
+                                    "content": "It follows that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 15,
+                    "bbox_fs": [
+                        105,
+                        322,
+                        165,
+                        336
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        177,
+                        336,
+                        432,
+                        353
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                177,
+                                336,
+                                432,
+                                353
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        177,
+                                        336,
+                                        432,
+                                        353
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\gamma ^ { H } V ^ { \\pi ^ { t } } ( s _ { 1 } ) + \\gamma ^ { H } \\bar { V } ^ { \\pi _ { t + H } } ( \\bar { s } _ { s _ { 1 } , 1 } ) = \\bar { V } ^ { \\bar { \\pi } } ( \\bar { s } _ { s _ { 1 } , 1 } ) \\geq \\bar { V } ^ { * } ( \\bar { s } _ { s _ { 1 } , 1 } ) - \\epsilon ,",
+                                    "type": "interline_equation",
+                                    "image_path": "5cce7a222551bc6274bbc52ffdb272aeca3dced98abbbc8f80d2fab7858deadf.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                177,
+                                336,
+                                432,
+                                353
+                            ],
+                            "spans": [],
+                            "index": 16
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        357,
+                        132,
+                        368
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                356,
+                                133,
+                                370
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        356,
+                                        133,
+                                        370
+                                    ],
+                                    "score": 1.0,
+                                    "content": "hence",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 17,
+                    "bbox_fs": [
+                        105,
+                        356,
+                        133,
+                        370
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        111,
+                        371,
+                        504,
+                        387
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                111,
+                                371,
+                                504,
+                                387
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        371,
+                                        504,
+                                        387
+                                    ],
+                                    "score": 0.86,
+                                    "content": "^ { H } V ^ { \\pi ^ { \\varepsilon } } ( s _ { 1 } ) \\geq ( 1 - \\gamma ^ { H } ) \\bar { V } ^ { * } ( \\bar { s } _ { s _ { 1 } , 1 } ) + \\gamma ^ { H } ( \\bar { V } ^ { * } ( \\bar { s } _ { s _ { 1 } , 1 } ) - \\bar { V } ^ { \\pi _ { t + H } } ( \\bar { s } _ { s _ { 1 } , 1 } ) ) - \\epsilon \\geq ( 1 - \\gamma ^ { H } ) \\bar { V } ^ { * } ( \\bar { s } _ { s _ { 1 } , 1 } ) - \\epsilon .",
+                                    "type": "interline_equation",
+                                    "image_path": "a3a5a1e7d68659f678d45d1177dbe36c95439ce8dceba0366c8e7ffef18cce5d.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                111,
+                                371,
+                                504,
+                                387
+                            ],
+                            "spans": [],
+                            "index": 18
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        390,
+                        183,
+                        402
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                389,
+                                183,
+                                403
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        389,
+                                        183,
+                                        403
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Therefore we have",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 19,
+                    "bbox_fs": [
+                        105,
+                        389,
+                        183,
+                        403
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        187,
+                        404,
+                        423,
+                        431
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                187,
+                                404,
+                                423,
+                                431
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        187,
+                                        404,
+                                        423,
+                                        431
+                                    ],
+                                    "score": 0.93,
+                                    "content": "{ V ^ { \\pi } } ^ { t } ( s _ { 1 } ) \\ge \\frac { 1 - \\gamma ^ { H } } { \\gamma ^ { H } } \\bar { V } ^ { * } ( \\bar { s } _ { s 1 , 1 } ) - \\epsilon / \\gamma ^ { H } = V ^ { * } ( s _ { 1 } ) - \\epsilon / \\gamma ^ { H } ,",
+                                    "type": "interline_equation",
+                                    "image_path": "1f1b44222a0c1087458d2ccf43ee9da0e84754c0602268ed6cbc91b7c6c5c549.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 20,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                187,
+                                404,
+                                423,
+                                431
+                            ],
+                            "spans": [],
+                            "index": 20
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        435,
+                        306,
+                        449
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                433,
+                                307,
+                                451
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        433,
+                                        178,
+                                        451
+                                    ],
+                                    "score": 1.0,
+                                    "content": "which means that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        178,
+                                        436,
+                                        189,
+                                        446
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\pi ^ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        190,
+                                        433,
+                                        212,
+                                        451
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is an",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        212,
+                                        435,
+                                        242,
+                                        448
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( \\epsilon / \\gamma ^ { H } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        243,
+                                        433,
+                                        307,
+                                        451
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimal policy.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 21,
+                    "bbox_fs": [
+                        105,
+                        433,
+                        307,
+                        451
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        106,
+                        462,
+                        372,
+                        477
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                461,
+                                373,
+                                480
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        461,
+                                        373,
+                                        480
+                                    ],
+                                    "score": 1.0,
+                                    "content": "D A HARD INSTANCE FOR DELAYED Q-LEARNING",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 22
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        488,
+                        456,
+                        501
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                485,
+                                456,
+                                504
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        485,
+                                        456,
+                                        504
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In this section, we prove Theorem 2 regarding the performance of Delayed Q-learning.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 23,
+                    "bbox_fs": [
+                        105,
+                        485,
+                        456,
+                        504
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        502,
+                        506,
+                        545
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                501,
+                                505,
+                                516
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        501,
+                                        353,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Theorem 2. There exists a family of MDPs with constant",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        354,
+                                        503,
+                                        362,
+                                        513
+                                    ],
+                                    "score": 0.78,
+                                    "content": "S",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        362,
+                                        501,
+                                        383,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        383,
+                                        504,
+                                        392,
+                                        513
+                                    ],
+                                    "score": 0.71,
+                                    "content": "A",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        392,
+                                        501,
+                                        505,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", in which with probability",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                514,
+                                505,
+                                533
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        517,
+                                        129,
+                                        528
+                                    ],
+                                    "score": 0.71,
+                                    "content": "1 - \\delta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        129,
+                                        515,
+                                        169,
+                                        532
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", Delayed",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        170,
+                                        518,
+                                        178,
+                                        529
+                                    ],
+                                    "score": 0.71,
+                                    "content": "Q",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        178,
+                                        515,
+                                        393,
+                                        532
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-learning incurs sample complexity of exploration of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        393,
+                                        514,
+                                        441,
+                                        533
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\Omega \\left( \\frac { \\epsilon ^ { - 3 } } { \\ln ( 1 / \\delta ) } \\right)",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        442,
+                                        516,
+                                        505,
+                                        530
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", assuming that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                531,
+                                169,
+                                545
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        532,
+                                        166,
+                                        545
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\ln ( 1 / \\delta ) < \\epsilon ^ { - 2 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        167,
+                                        531,
+                                        169,
+                                        544
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 25,
+                    "bbox_fs": [
+                        105,
+                        501,
+                        505,
+                        545
+                    ]
+                },
+                {
+                    "type": "image",
+                    "bbox": [
+                        243,
+                        559,
+                        367,
+                        657
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                243,
+                                559,
+                                367,
+                                657
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        243,
+                                        559,
+                                        367,
+                                        657
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                243,
+                                                559,
+                                                367,
+                                                657
+                                            ],
+                                            "score": 0.96,
+                                            "type": "image",
+                                            "image_path": "d5ea7466679255528080a8e623d46ab5efe02c60983c67939e2c04d8974b3167.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 27.5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        243,
+                                        559,
+                                        367,
+                                        608.0
+                                    ],
+                                    "spans": [],
+                                    "index": 27
+                                },
+                                {
+                                    "bbox": [
+                                        243,
+                                        608.0,
+                                        367,
+                                        657.0
+                                    ],
+                                    "spans": [],
+                                    "index": 28
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                105,
+                                667,
+                                506,
+                                690
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        667,
+                                        506,
+                                        680
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                667,
+                                                506,
+                                                680
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 1: The MDP family. Actions are denoted by arrows. Actions with red color have reward 1,",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 29
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        678,
+                                        205,
+                                        691
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                678,
+                                                205,
+                                                691
+                                            ],
+                                            "score": 1.0,
+                                            "content": "and reward 0 otherwise.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 30
+                                }
+                            ],
+                            "index": 29.5
+                        }
+                    ],
+                    "index": 28.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        698,
+                        505,
+                        733
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                696,
+                                505,
+                                713
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        696,
+                                        175,
+                                        713
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Proof. For each",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        175,
+                                        698,
+                                        227,
+                                        711
+                                    ],
+                                    "score": 0.92,
+                                    "content": "0 < \\epsilon < \\frac { 1 } { 1 0 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        227,
+                                        696,
+                                        484,
+                                        713
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", consider the following MDP (see also Fig. 1): state space is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        484,
+                                        699,
+                                        505,
+                                        709
+                                    ],
+                                    "score": 0.86,
+                                    "content": "{ \\boldsymbol { s } } =",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                709,
+                                505,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        710,
+                                        140,
+                                        721
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\{ a , b , c \\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        141,
+                                        709,
+                                        213,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "while action set is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        214,
+                                        710,
+                                        261,
+                                        721
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\overset { \\vartriangle } { \\mathcal { A } } = \\{ \\ v { x } , \\ v { y } \\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        262,
+                                        709,
+                                        369,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "; transition probabilities are",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        370,
+                                        710,
+                                        450,
+                                        721
+                                    ],
+                                    "score": 0.73,
+                                    "content": "P ( b | a , y ) = 1 - 1 0 \\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        450,
+                                        709,
+                                        455,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        455,
+                                        710,
+                                        505,
+                                        722
+                                    ],
+                                    "score": 0.61,
+                                    "content": "P ( c | a , y ) =",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                720,
+                                446,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        720,
+                                        125,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "10\u000f,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        126,
+                                        721,
+                                        182,
+                                        732
+                                    ],
+                                    "score": 0.91,
+                                    "content": "P ( b | a , x ) = 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        183,
+                                        720,
+                                        186,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        186,
+                                        721,
+                                        289,
+                                        732
+                                    ],
+                                    "score": 0.88,
+                                    "content": "P ( a | b , \\cdot ) = P ( a | c , \\cdot ) = 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        720,
+                                        396,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Rewards are all 1, except",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        396,
+                                        721,
+                                        442,
+                                        732
+                                    ],
+                                    "score": 0.92,
+                                    "content": "R ( c , \\cdot ) = 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        442,
+                                        720,
+                                        446,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 32,
+                    "bbox_fs": [
+                        105,
+                        696,
+                        505,
+                        733
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        81,
+                        505,
+                        169
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                81,
+                                504,
+                                97
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        81,
+                                        409,
+                                        97
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Assume that Delayed Q-learning is called for this MDP starting from state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        410,
+                                        85,
+                                        416,
+                                        93
+                                    ],
+                                    "score": 0.72,
+                                    "content": "a",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        416,
+                                        81,
+                                        477,
+                                        97
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", with discount",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        477,
+                                        81,
+                                        504,
+                                        96
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\begin{array} { r } { \\gamma > \\frac { 1 } { 2 } } \\end{array}",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                95,
+                                505,
+                                109
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        96,
+                                        193,
+                                        109
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and precision set as",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        194,
+                                        99,
+                                        199,
+                                        106
+                                    ],
+                                    "score": 0.49,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        200,
+                                        96,
+                                        257,
+                                        109
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Denote the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        257,
+                                        97,
+                                        267,
+                                        108
+                                    ],
+                                    "score": 0.84,
+                                    "content": "Q",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        267,
+                                        96,
+                                        432,
+                                        109
+                                    ],
+                                    "score": 1.0,
+                                    "content": "value maintained by the algorithm by",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        432,
+                                        95,
+                                        441,
+                                        108
+                                    ],
+                                    "score": 0.86,
+                                    "content": "\\hat { Q }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        442,
+                                        96,
+                                        505,
+                                        109
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Without loss",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                108,
+                                506,
+                                122
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        108,
+                                        371,
+                                        122
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of generality, assume that the initial tie-breaking favors action",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        371,
+                                        111,
+                                        378,
+                                        121
+                                    ],
+                                    "score": 0.76,
+                                    "content": "y",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        379,
+                                        108,
+                                        453,
+                                        122
+                                    ],
+                                    "score": 1.0,
+                                    "content": "when comparing",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        453,
+                                        108,
+                                        485,
+                                        121
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\hat { Q } ( a , x )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        486,
+                                        108,
+                                        506,
+                                        122
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                120,
+                                506,
+                                135
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        120,
+                                        138,
+                                        133
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\hat { Q } ( a , y )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        138,
+                                        120,
+                                        225,
+                                        135
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". In that case, unless",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        225,
+                                        120,
+                                        257,
+                                        133
+                                    ],
+                                    "score": 0.95,
+                                    "content": "\\hat { Q } ( a , y )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        257,
+                                        120,
+                                        426,
+                                        135
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is updated, the agent will always choose",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        427,
+                                        123,
+                                        434,
+                                        133
+                                    ],
+                                    "score": 0.79,
+                                    "content": "y",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        434,
+                                        120,
+                                        467,
+                                        135
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        468,
+                                        124,
+                                        474,
+                                        132
+                                    ],
+                                    "score": 0.71,
+                                    "content": "a",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        474,
+                                        120,
+                                        506,
+                                        135
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Since",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                132,
+                                506,
+                                146
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        133,
+                                        232,
+                                        145
+                                    ],
+                                    "score": 0.91,
+                                    "content": "Q ( a , x ) - Q ( a , y ) = 1 0 \\epsilon \\gamma > \\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        232,
+                                        132,
+                                        332,
+                                        146
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for any policy, choosing",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        333,
+                                        135,
+                                        339,
+                                        144
+                                    ],
+                                    "score": 0.76,
+                                    "content": "y",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        340,
+                                        132,
+                                        371,
+                                        146
+                                    ],
+                                    "score": 1.0,
+                                    "content": "at state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        371,
+                                        135,
+                                        378,
+                                        143
+                                    ],
+                                    "score": 0.66,
+                                    "content": "a",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        378,
+                                        132,
+                                        506,
+                                        146
+                                    ],
+                                    "score": 1.0,
+                                    "content": "implies that the timestep is not",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                144,
+                                505,
+                                156
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        146,
+                                        112,
+                                        154
+                                    ],
+                                    "score": 0.59,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        112,
+                                        144,
+                                        505,
+                                        156
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimal. In other words, sample complexity for exploration is at least the number of times the agent",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                154,
+                                274,
+                                169
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        155,
+                                        129,
+                                        169
+                                    ],
+                                    "score": 1.0,
+                                    "content": "visits",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        130,
+                                        158,
+                                        136,
+                                        166
+                                    ],
+                                    "score": 0.73,
+                                    "content": "a",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        137,
+                                        155,
+                                        238,
+                                        169
+                                    ],
+                                    "score": 1.0,
+                                    "content": "before the first update of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        238,
+                                        154,
+                                        269,
+                                        168
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\hat { Q } ( a , y )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        270,
+                                        155,
+                                        274,
+                                        169
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        174,
+                        506,
+                        213
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                173,
+                                506,
+                                189
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        173,
+                                        259,
+                                        189
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In the Delayed Q-learning algorithm,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        259,
+                                        173,
+                                        286,
+                                        187
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\hat { Q } ( \\cdot , \\cdot )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        286,
+                                        173,
+                                        356,
+                                        189
+                                    ],
+                                    "score": 1.0,
+                                    "content": "are initialized to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        356,
+                                        175,
+                                        397,
+                                        187
+                                    ],
+                                    "score": 0.92,
+                                    "content": "1 / ( 1 - \\gamma )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        397,
+                                        173,
+                                        447,
+                                        189
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Therefore,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        447,
+                                        173,
+                                        479,
+                                        187
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\hat { Q } ( a , y )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        479,
+                                        173,
+                                        506,
+                                        189
+                                    ],
+                                    "score": 1.0,
+                                    "content": "could",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                186,
+                                505,
+                                201
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        186,
+                                        202,
+                                        201
+                                    ],
+                                    "score": 1.0,
+                                    "content": "only be updated if max",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        202,
+                                        187,
+                                        230,
+                                        200
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\hat { Q } ( c , \\cdot )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        231,
+                                        186,
+                                        385,
+                                        201
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is updated (and becomes smaller than",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        386,
+                                        188,
+                                        429,
+                                        200
+                                    ],
+                                    "score": 0.9,
+                                    "content": "1 / ( 1 - \\gamma ) )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        430,
+                                        186,
+                                        505,
+                                        201
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". According to the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                199,
+                                368,
+                                214
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        199,
+                                        243,
+                                        214
+                                    ],
+                                    "score": 1.0,
+                                    "content": "algorithm, this can only happen if",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        244,
+                                        202,
+                                        249,
+                                        210
+                                    ],
+                                    "score": 0.74,
+                                    "content": "c",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        250,
+                                        199,
+                                        288,
+                                        214
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is visited",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        199,
+                                        339,
+                                        213
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { r } { m = \\Omega \\left( \\frac { 1 } { \\epsilon ^ { 2 } } \\right) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        339,
+                                        199,
+                                        368,
+                                        214
+                                    ],
+                                    "score": 1.0,
+                                    "content": "times.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        217,
+                        505,
+                        274
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                217,
+                                505,
+                                229
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        217,
+                                        259,
+                                        229
+                                    ],
+                                    "score": 1.0,
+                                    "content": "However, each time the agent visits",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        259,
+                                        220,
+                                        266,
+                                        227
+                                    ],
+                                    "score": 0.74,
+                                    "content": "a",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        266,
+                                        217,
+                                        345,
+                                        229
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", there is less than",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        345,
+                                        218,
+                                        361,
+                                        227
+                                    ],
+                                    "score": 0.61,
+                                    "content": "1 0 \\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        361,
+                                        217,
+                                        475,
+                                        229
+                                    ],
+                                    "score": 1.0,
+                                    "content": "probability of transiting to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        476,
+                                        219,
+                                        482,
+                                        227
+                                    ],
+                                    "score": 0.57,
+                                    "content": "c",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        482,
+                                        217,
+                                        505,
+                                        229
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Let",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                227,
+                                506,
+                                242
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        228,
+                                        173,
+                                        240
+                                    ],
+                                    "score": 0.91,
+                                    "content": "t _ { 0 } = m / ( 1 0 \\epsilon C )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        174,
+                                        227,
+                                        205,
+                                        242
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        206,
+                                        227,
+                                        270,
+                                        241
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\begin{array} { r } { C ^ { ' } = 3 \\ln \\frac { 1 } { \\delta } + 1 } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        271,
+                                        227,
+                                        275,
+                                        242
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        276,
+                                        228,
+                                        282,
+                                        238
+                                    ],
+                                    "score": 0.55,
+                                    "content": "\\delta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        282,
+                                        227,
+                                        363,
+                                        242
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is chosen such that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        364,
+                                        228,
+                                        396,
+                                        239
+                                    ],
+                                    "score": 0.91,
+                                    "content": "C \\leq m",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        396,
+                                        227,
+                                        447,
+                                        242
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". In the first",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        447,
+                                        228,
+                                        461,
+                                        239
+                                    ],
+                                    "score": 0.89,
+                                    "content": "2 t _ { 0 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        461,
+                                        227,
+                                        506,
+                                        242
+                                    ],
+                                    "score": 1.0,
+                                    "content": "timesteps,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                239,
+                                505,
+                                251
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        241,
+                                        113,
+                                        249
+                                    ],
+                                    "score": 0.64,
+                                    "content": "a",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        114,
+                                        239,
+                                        174,
+                                        251
+                                    ],
+                                    "score": 1.0,
+                                    "content": "will be visited",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        174,
+                                        240,
+                                        184,
+                                        250
+                                    ],
+                                    "score": 0.87,
+                                    "content": "t _ { 0 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        239,
+                                        372,
+                                        251
+                                    ],
+                                    "score": 1.0,
+                                    "content": "times. By Chernoff’s bound, with probability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        372,
+                                        240,
+                                        395,
+                                        250
+                                    ],
+                                    "score": 0.87,
+                                    "content": "1 - \\delta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        396,
+                                        239,
+                                        420,
+                                        251
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        420,
+                                        241,
+                                        426,
+                                        249
+                                    ],
+                                    "score": 0.73,
+                                    "content": "c",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        426,
+                                        239,
+                                        505,
+                                        251
+                                    ],
+                                    "score": 1.0,
+                                    "content": "will be visited less",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                250,
+                                505,
+                                264
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        251,
+                                        126,
+                                        264
+                                    ],
+                                    "score": 1.0,
+                                    "content": "than",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        127,
+                                        253,
+                                        137,
+                                        262
+                                    ],
+                                    "score": 0.73,
+                                    "content": "m",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        137,
+                                        251,
+                                        219,
+                                        264
+                                    ],
+                                    "score": 1.0,
+                                    "content": "times. In that case,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        219,
+                                        250,
+                                        250,
+                                        263
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\hat { Q } ( a , y )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        251,
+                                        251,
+                                        378,
+                                        264
+                                    ],
+                                    "score": 1.0,
+                                    "content": "will not be updated in the first",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        379,
+                                        252,
+                                        393,
+                                        263
+                                    ],
+                                    "score": 0.89,
+                                    "content": "2 t _ { 0 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        393,
+                                        251,
+                                        505,
+                                        264
+                                    ],
+                                    "score": 1.0,
+                                    "content": "timesteps. Therefore, with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                262,
+                                357,
+                                276
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        262,
+                                        153,
+                                        276
+                                    ],
+                                    "score": 1.0,
+                                    "content": "probability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        263,
+                                        176,
+                                        273
+                                    ],
+                                    "score": 0.87,
+                                    "content": "1 - \\delta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        176,
+                                        262,
+                                        357,
+                                        276
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", sample complexity of exploration is at least",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        257,
+                        279,
+                        354,
+                        307
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                257,
+                                279,
+                                354,
+                                307
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        257,
+                                        279,
+                                        354,
+                                        307
+                                    ],
+                                    "score": 0.94,
+                                    "content": "t _ { 0 } = \\Omega \\left( { \\frac { 1 } { \\epsilon ^ { 3 } \\left( \\ln { 1 / \\delta } \\right) } } \\right) .",
+                                    "type": "interline_equation",
+                                    "image_path": "446057ad76737ed78dbeb6c14c391ec04ae8a21d0dea27c95bf135aaaf7cc43f.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                257,
+                                279,
+                                354,
+                                307
+                            ],
+                            "spans": [],
+                            "index": 15
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        312,
+                        380,
+                        326
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                308,
+                                378,
+                                328
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        308,
+                                        132,
+                                        328
+                                    ],
+                                    "score": 1.0,
+                                    "content": "When",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        132,
+                                        312,
+                                        192,
+                                        325
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\ln ( 1 / \\delta ) < \\epsilon ^ { - 2 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        192,
+                                        308,
+                                        270,
+                                        328
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", it can be seen that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        270,
+                                        311,
+                                        378,
+                                        326
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { r } { C = 3 \\ln \\frac { 1 } { \\delta } + 1 < \\frac { 4 } { \\epsilon ^ { 2 } } < m } \\end{array}",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 16
+                }
+            ],
+            "page_idx": 17,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        293,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                294,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        294,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        311,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                312,
+                                763
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        312,
+                                        763
+                                    ],
+                                    "score": 1.0,
+                                    "content": "18",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        494,
+                        313,
+                        505,
+                        324
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                496,
+                                315,
+                                505,
+                                324
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        496,
+                                        315,
+                                        505,
+                                        324
+                                    ],
+                                    "score": 0.998,
+                                    "content": "□",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        81,
+                        505,
+                        169
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                81,
+                                504,
+                                97
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        81,
+                                        409,
+                                        97
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Assume that Delayed Q-learning is called for this MDP starting from state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        410,
+                                        85,
+                                        416,
+                                        93
+                                    ],
+                                    "score": 0.72,
+                                    "content": "a",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        416,
+                                        81,
+                                        477,
+                                        97
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", with discount",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        477,
+                                        81,
+                                        504,
+                                        96
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\begin{array} { r } { \\gamma > \\frac { 1 } { 2 } } \\end{array}",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                95,
+                                505,
+                                109
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        96,
+                                        193,
+                                        109
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and precision set as",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        194,
+                                        99,
+                                        199,
+                                        106
+                                    ],
+                                    "score": 0.49,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        200,
+                                        96,
+                                        257,
+                                        109
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Denote the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        257,
+                                        97,
+                                        267,
+                                        108
+                                    ],
+                                    "score": 0.84,
+                                    "content": "Q",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        267,
+                                        96,
+                                        432,
+                                        109
+                                    ],
+                                    "score": 1.0,
+                                    "content": "value maintained by the algorithm by",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        432,
+                                        95,
+                                        441,
+                                        108
+                                    ],
+                                    "score": 0.86,
+                                    "content": "\\hat { Q }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        442,
+                                        96,
+                                        505,
+                                        109
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Without loss",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                108,
+                                506,
+                                122
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        108,
+                                        371,
+                                        122
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of generality, assume that the initial tie-breaking favors action",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        371,
+                                        111,
+                                        378,
+                                        121
+                                    ],
+                                    "score": 0.76,
+                                    "content": "y",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        379,
+                                        108,
+                                        453,
+                                        122
+                                    ],
+                                    "score": 1.0,
+                                    "content": "when comparing",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        453,
+                                        108,
+                                        485,
+                                        121
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\hat { Q } ( a , x )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        486,
+                                        108,
+                                        506,
+                                        122
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                120,
+                                506,
+                                135
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        120,
+                                        138,
+                                        133
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\hat { Q } ( a , y )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        138,
+                                        120,
+                                        225,
+                                        135
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". In that case, unless",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        225,
+                                        120,
+                                        257,
+                                        133
+                                    ],
+                                    "score": 0.95,
+                                    "content": "\\hat { Q } ( a , y )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        257,
+                                        120,
+                                        426,
+                                        135
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is updated, the agent will always choose",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        427,
+                                        123,
+                                        434,
+                                        133
+                                    ],
+                                    "score": 0.79,
+                                    "content": "y",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        434,
+                                        120,
+                                        467,
+                                        135
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        468,
+                                        124,
+                                        474,
+                                        132
+                                    ],
+                                    "score": 0.71,
+                                    "content": "a",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        474,
+                                        120,
+                                        506,
+                                        135
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Since",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                132,
+                                506,
+                                146
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        133,
+                                        232,
+                                        145
+                                    ],
+                                    "score": 0.91,
+                                    "content": "Q ( a , x ) - Q ( a , y ) = 1 0 \\epsilon \\gamma > \\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        232,
+                                        132,
+                                        332,
+                                        146
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for any policy, choosing",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        333,
+                                        135,
+                                        339,
+                                        144
+                                    ],
+                                    "score": 0.76,
+                                    "content": "y",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        340,
+                                        132,
+                                        371,
+                                        146
+                                    ],
+                                    "score": 1.0,
+                                    "content": "at state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        371,
+                                        135,
+                                        378,
+                                        143
+                                    ],
+                                    "score": 0.66,
+                                    "content": "a",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        378,
+                                        132,
+                                        506,
+                                        146
+                                    ],
+                                    "score": 1.0,
+                                    "content": "implies that the timestep is not",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                144,
+                                505,
+                                156
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        146,
+                                        112,
+                                        154
+                                    ],
+                                    "score": 0.59,
+                                    "content": "\\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        112,
+                                        144,
+                                        505,
+                                        156
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-optimal. In other words, sample complexity for exploration is at least the number of times the agent",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                154,
+                                274,
+                                169
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        155,
+                                        129,
+                                        169
+                                    ],
+                                    "score": 1.0,
+                                    "content": "visits",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        130,
+                                        158,
+                                        136,
+                                        166
+                                    ],
+                                    "score": 0.73,
+                                    "content": "a",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        137,
+                                        155,
+                                        238,
+                                        169
+                                    ],
+                                    "score": 1.0,
+                                    "content": "before the first update of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        238,
+                                        154,
+                                        269,
+                                        168
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\hat { Q } ( a , y )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        270,
+                                        155,
+                                        274,
+                                        169
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 3,
+                    "bbox_fs": [
+                        104,
+                        81,
+                        506,
+                        169
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        174,
+                        506,
+                        213
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                173,
+                                506,
+                                189
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        173,
+                                        259,
+                                        189
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In the Delayed Q-learning algorithm,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        259,
+                                        173,
+                                        286,
+                                        187
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\hat { Q } ( \\cdot , \\cdot )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        286,
+                                        173,
+                                        356,
+                                        189
+                                    ],
+                                    "score": 1.0,
+                                    "content": "are initialized to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        356,
+                                        175,
+                                        397,
+                                        187
+                                    ],
+                                    "score": 0.92,
+                                    "content": "1 / ( 1 - \\gamma )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        397,
+                                        173,
+                                        447,
+                                        189
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Therefore,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        447,
+                                        173,
+                                        479,
+                                        187
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\hat { Q } ( a , y )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        479,
+                                        173,
+                                        506,
+                                        189
+                                    ],
+                                    "score": 1.0,
+                                    "content": "could",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                186,
+                                505,
+                                201
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        186,
+                                        202,
+                                        201
+                                    ],
+                                    "score": 1.0,
+                                    "content": "only be updated if max",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        202,
+                                        187,
+                                        230,
+                                        200
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\hat { Q } ( c , \\cdot )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        231,
+                                        186,
+                                        385,
+                                        201
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is updated (and becomes smaller than",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        386,
+                                        188,
+                                        429,
+                                        200
+                                    ],
+                                    "score": 0.9,
+                                    "content": "1 / ( 1 - \\gamma ) )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        430,
+                                        186,
+                                        505,
+                                        201
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". According to the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                199,
+                                368,
+                                214
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        199,
+                                        243,
+                                        214
+                                    ],
+                                    "score": 1.0,
+                                    "content": "algorithm, this can only happen if",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        244,
+                                        202,
+                                        249,
+                                        210
+                                    ],
+                                    "score": 0.74,
+                                    "content": "c",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        250,
+                                        199,
+                                        288,
+                                        214
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is visited",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        199,
+                                        339,
+                                        213
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { r } { m = \\Omega \\left( \\frac { 1 } { \\epsilon ^ { 2 } } \\right) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        339,
+                                        199,
+                                        368,
+                                        214
+                                    ],
+                                    "score": 1.0,
+                                    "content": "times.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 8,
+                    "bbox_fs": [
+                        105,
+                        173,
+                        506,
+                        214
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        217,
+                        505,
+                        274
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                217,
+                                505,
+                                229
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        217,
+                                        259,
+                                        229
+                                    ],
+                                    "score": 1.0,
+                                    "content": "However, each time the agent visits",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        259,
+                                        220,
+                                        266,
+                                        227
+                                    ],
+                                    "score": 0.74,
+                                    "content": "a",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        266,
+                                        217,
+                                        345,
+                                        229
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", there is less than",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        345,
+                                        218,
+                                        361,
+                                        227
+                                    ],
+                                    "score": 0.61,
+                                    "content": "1 0 \\epsilon",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        361,
+                                        217,
+                                        475,
+                                        229
+                                    ],
+                                    "score": 1.0,
+                                    "content": "probability of transiting to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        476,
+                                        219,
+                                        482,
+                                        227
+                                    ],
+                                    "score": 0.57,
+                                    "content": "c",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        482,
+                                        217,
+                                        505,
+                                        229
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Let",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                227,
+                                506,
+                                242
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        228,
+                                        173,
+                                        240
+                                    ],
+                                    "score": 0.91,
+                                    "content": "t _ { 0 } = m / ( 1 0 \\epsilon C )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        174,
+                                        227,
+                                        205,
+                                        242
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        206,
+                                        227,
+                                        270,
+                                        241
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\begin{array} { r } { C ^ { ' } = 3 \\ln \\frac { 1 } { \\delta } + 1 } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        271,
+                                        227,
+                                        275,
+                                        242
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        276,
+                                        228,
+                                        282,
+                                        238
+                                    ],
+                                    "score": 0.55,
+                                    "content": "\\delta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        282,
+                                        227,
+                                        363,
+                                        242
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is chosen such that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        364,
+                                        228,
+                                        396,
+                                        239
+                                    ],
+                                    "score": 0.91,
+                                    "content": "C \\leq m",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        396,
+                                        227,
+                                        447,
+                                        242
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". In the first",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        447,
+                                        228,
+                                        461,
+                                        239
+                                    ],
+                                    "score": 0.89,
+                                    "content": "2 t _ { 0 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        461,
+                                        227,
+                                        506,
+                                        242
+                                    ],
+                                    "score": 1.0,
+                                    "content": "timesteps,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                239,
+                                505,
+                                251
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        241,
+                                        113,
+                                        249
+                                    ],
+                                    "score": 0.64,
+                                    "content": "a",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        114,
+                                        239,
+                                        174,
+                                        251
+                                    ],
+                                    "score": 1.0,
+                                    "content": "will be visited",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        174,
+                                        240,
+                                        184,
+                                        250
+                                    ],
+                                    "score": 0.87,
+                                    "content": "t _ { 0 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        239,
+                                        372,
+                                        251
+                                    ],
+                                    "score": 1.0,
+                                    "content": "times. By Chernoff’s bound, with probability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        372,
+                                        240,
+                                        395,
+                                        250
+                                    ],
+                                    "score": 0.87,
+                                    "content": "1 - \\delta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        396,
+                                        239,
+                                        420,
+                                        251
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", state",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        420,
+                                        241,
+                                        426,
+                                        249
+                                    ],
+                                    "score": 0.73,
+                                    "content": "c",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        426,
+                                        239,
+                                        505,
+                                        251
+                                    ],
+                                    "score": 1.0,
+                                    "content": "will be visited less",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                250,
+                                505,
+                                264
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        251,
+                                        126,
+                                        264
+                                    ],
+                                    "score": 1.0,
+                                    "content": "than",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        127,
+                                        253,
+                                        137,
+                                        262
+                                    ],
+                                    "score": 0.73,
+                                    "content": "m",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        137,
+                                        251,
+                                        219,
+                                        264
+                                    ],
+                                    "score": 1.0,
+                                    "content": "times. In that case,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        219,
+                                        250,
+                                        250,
+                                        263
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\hat { Q } ( a , y )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        251,
+                                        251,
+                                        378,
+                                        264
+                                    ],
+                                    "score": 1.0,
+                                    "content": "will not be updated in the first",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        379,
+                                        252,
+                                        393,
+                                        263
+                                    ],
+                                    "score": 0.89,
+                                    "content": "2 t _ { 0 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        393,
+                                        251,
+                                        505,
+                                        264
+                                    ],
+                                    "score": 1.0,
+                                    "content": "timesteps. Therefore, with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                262,
+                                357,
+                                276
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        262,
+                                        153,
+                                        276
+                                    ],
+                                    "score": 1.0,
+                                    "content": "probability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        263,
+                                        176,
+                                        273
+                                    ],
+                                    "score": 0.87,
+                                    "content": "1 - \\delta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        176,
+                                        262,
+                                        357,
+                                        276
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", sample complexity of exploration is at least",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 12,
+                    "bbox_fs": [
+                        105,
+                        217,
+                        506,
+                        276
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        257,
+                        279,
+                        354,
+                        307
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                257,
+                                279,
+                                354,
+                                307
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        257,
+                                        279,
+                                        354,
+                                        307
+                                    ],
+                                    "score": 0.94,
+                                    "content": "t _ { 0 } = \\Omega \\left( { \\frac { 1 } { \\epsilon ^ { 3 } \\left( \\ln { 1 / \\delta } \\right) } } \\right) .",
+                                    "type": "interline_equation",
+                                    "image_path": "446057ad76737ed78dbeb6c14c391ec04ae8a21d0dea27c95bf135aaaf7cc43f.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                257,
+                                279,
+                                354,
+                                307
+                            ],
+                            "spans": [],
+                            "index": 15
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        312,
+                        380,
+                        326
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                308,
+                                378,
+                                328
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        308,
+                                        132,
+                                        328
+                                    ],
+                                    "score": 1.0,
+                                    "content": "When",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        132,
+                                        312,
+                                        192,
+                                        325
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\ln ( 1 / \\delta ) < \\epsilon ^ { - 2 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        192,
+                                        308,
+                                        270,
+                                        328
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", it can be seen that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        270,
+                                        311,
+                                        378,
+                                        326
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { r } { C = 3 \\ln \\frac { 1 } { \\delta } + 1 < \\frac { 4 } { \\epsilon ^ { 2 } } < m } \\end{array}",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 16,
+                    "bbox_fs": [
+                        105,
+                        308,
+                        378,
+                        328
+                    ]
+                }
+            ]
+        }
+    ],
+    "_backend": "pipeline",
+    "_version_name": "2.2.2"
+}
\ No newline at end of file
diff --git a/parse/train/BkglSTNFDB/BkglSTNFDB_model.json b/parse/train/BkglSTNFDB/BkglSTNFDB_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..6261e34c6bea6e8b40b411592e29f8fca563307e
--- /dev/null
+++ b/parse/train/BkglSTNFDB/BkglSTNFDB_model.json
@@ -0,0 +1,32281 @@
+[
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    398,
+                    993,
+                    1304,
+                    993,
+                    1304,
+                    1321,
+                    398,
+                    1321
+                ],
+                "score": 0.981
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1466,
+                    1404,
+                    1466,
+                    1404,
+                    1712,
+                    297,
+                    1712
+                ],
+                "score": 0.979
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1727,
+                    1405,
+                    1727,
+                    1405,
+                    1972,
+                    298,
+                    1972
+                ],
+                "score": 0.975
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    314,
+                    545,
+                    1029,
+                    545,
+                    1029,
+                    668,
+                    314,
+                    668
+                ],
+                "score": 0.964
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    300,
+                    219,
+                    1400,
+                    219,
+                    1400,
+                    323,
+                    300,
+                    323
+                ],
+                "score": 0.963
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    313,
+                    715,
+                    1024,
+                    715,
+                    1024,
+                    838,
+                    313,
+                    838
+                ],
+                "score": 0.942
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    332,
+                    2006,
+                    730,
+                    2006,
+                    730,
+                    2034,
+                    332,
+                    2034
+                ],
+                "score": 0.914
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    302,
+                    1392,
+                    574,
+                    1392,
+                    574,
+                    1427,
+                    302,
+                    1427
+                ],
+                "score": 0.905
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    313,
+                    374,
+                    946,
+                    374,
+                    946,
+                    499,
+                    313,
+                    499
+                ],
+                "score": 0.871
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    299,
+                    75,
+                    817,
+                    75,
+                    817,
+                    105,
+                    299,
+                    105
+                ],
+                "score": 0.87
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    773,
+                    919,
+                    927,
+                    919,
+                    927,
+                    952,
+                    773,
+                    952
+                ],
+                "score": 0.836
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    840,
+                    2088,
+                    856,
+                    2088,
+                    856,
+                    2112,
+                    840,
+                    2112
+                ],
+                "score": 0.737
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    315,
+                    717,
+                    461,
+                    717,
+                    461,
+                    746,
+                    315,
+                    746
+                ],
+                "score": 0.162
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    759,
+                    1177,
+                    899,
+                    1177,
+                    899,
+                    1222,
+                    759,
+                    1222
+                ],
+                "score": 0.94,
+                "latex": "\\begin{array} { r } { \\tilde { O } \\big ( \\frac { S A } { \\epsilon ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\big ) } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    575,
+                    1218,
+                    715,
+                    1218,
+                    715,
+                    1263,
+                    575,
+                    1263
+                ],
+                "score": 0.93,
+                "latex": "\\begin{array} { r } { \\tilde { O } \\big ( \\frac { S A } { \\epsilon ^ { 4 } ( 1 - \\gamma ) ^ { 8 } } \\big ) } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    738,
+                    1820,
+                    764,
+                    1820,
+                    764,
+                    1850,
+                    738,
+                    1850
+                ],
+                "score": 0.82,
+                "latex": "Q"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1141,
+                    1260,
+                    1163,
+                    1260,
+                    1163,
+                    1288,
+                    1141,
+                    1288
+                ],
+                "score": 0.8,
+                "latex": "S"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    822,
+                    1564,
+                    838,
+                    1564,
+                    838,
+                    1587,
+                    822,
+                    1587
+                ],
+                "score": 0.75,
+                "latex": "r"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1007,
+                    1266,
+                    1022,
+                    1266,
+                    1022,
+                    1287,
+                    1007,
+                    1287
+                ],
+                "score": 0.73,
+                "latex": "\\epsilon"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1213,
+                    1260,
+                    1238,
+                    1260,
+                    1238,
+                    1287,
+                    1213,
+                    1287
+                ],
+                "score": 0.7,
+                "latex": "A"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    615,
+                    1565,
+                    632,
+                    1565,
+                    632,
+                    1586,
+                    615,
+                    1586
+                ],
+                "score": 0.7,
+                "latex": "a"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    1565,
+                    314,
+                    1565,
+                    314,
+                    1586,
+                    298,
+                    1586
+                ],
+                "score": 0.52,
+                "latex": "s"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    219.0,
+                    1405.0,
+                    219.0,
+                    1405.0,
+                    272.0,
+                    294.0,
+                    272.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    275.0,
+                    1142.0,
+                    275.0,
+                    1142.0,
+                    327.0,
+                    294.0,
+                    327.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    329.0,
+                    1998.0,
+                    733.0,
+                    1998.0,
+                    733.0,
+                    2040.0,
+                    329.0,
+                    2040.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1388.0,
+                    579.0,
+                    1388.0,
+                    579.0,
+                    1435.0,
+                    294.0,
+                    1435.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    73.0,
+                    817.0,
+                    73.0,
+                    817.0,
+                    108.0,
+                    295.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    768.0,
+                    915.0,
+                    934.0,
+                    915.0,
+                    934.0,
+                    958.0,
+                    768.0,
+                    958.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    839.0,
+                    2087.0,
+                    859.0,
+                    2087.0,
+                    859.0,
+                    2117.0,
+                    839.0,
+                    2117.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    310.0,
+                    709.0,
+                    465.0,
+                    709.0,
+                    465.0,
+                    754.0,
+                    310.0,
+                    754.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    993.0,
+                    1308.0,
+                    993.0,
+                    1308.0,
+                    1029.0,
+                    393.0,
+                    1029.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    1022.0,
+                    1305.0,
+                    1022.0,
+                    1305.0,
+                    1061.0,
+                    393.0,
+                    1061.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1055.0,
+                    1305.0,
+                    1055.0,
+                    1305.0,
+                    1090.0,
+                    394.0,
+                    1090.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1085.0,
+                    1305.0,
+                    1085.0,
+                    1305.0,
+                    1120.0,
+                    394.0,
+                    1120.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    395.0,
+                    1116.0,
+                    1304.0,
+                    1116.0,
+                    1304.0,
+                    1148.0,
+                    395.0,
+                    1148.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    1146.0,
+                    1305.0,
+                    1146.0,
+                    1305.0,
+                    1184.0,
+                    393.0,
+                    1184.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    388.0,
+                    1173.0,
+                    758.0,
+                    1173.0,
+                    758.0,
+                    1231.0,
+                    388.0,
+                    1231.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    900.0,
+                    1173.0,
+                    1311.0,
+                    1173.0,
+                    1311.0,
+                    1231.0,
+                    900.0,
+                    1231.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    380.0,
+                    1202.0,
+                    574.0,
+                    1202.0,
+                    574.0,
+                    1279.0,
+                    380.0,
+                    1279.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    716.0,
+                    1202.0,
+                    1318.0,
+                    1202.0,
+                    1318.0,
+                    1279.0,
+                    716.0,
+                    1279.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    1258.0,
+                    1006.0,
+                    1258.0,
+                    1006.0,
+                    1295.0,
+                    393.0,
+                    1295.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1023.0,
+                    1258.0,
+                    1140.0,
+                    1258.0,
+                    1140.0,
+                    1295.0,
+                    1023.0,
+                    1295.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1164.0,
+                    1258.0,
+                    1212.0,
+                    1258.0,
+                    1212.0,
+                    1295.0,
+                    1164.0,
+                    1295.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1239.0,
+                    1258.0,
+                    1305.0,
+                    1258.0,
+                    1305.0,
+                    1295.0,
+                    1239.0,
+                    1295.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1290.0,
+                    619.0,
+                    1290.0,
+                    619.0,
+                    1323.0,
+                    394.0,
+                    1323.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1468.0,
+                    1404.0,
+                    1468.0,
+                    1404.0,
+                    1501.0,
+                    295.0,
+                    1501.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1498.0,
+                    1404.0,
+                    1498.0,
+                    1404.0,
+                    1531.0,
+                    295.0,
+                    1531.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1528.0,
+                    1406.0,
+                    1528.0,
+                    1406.0,
+                    1563.0,
+                    292.0,
+                    1563.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1559.0,
+                    297.0,
+                    1559.0,
+                    297.0,
+                    1593.0,
+                    294.0,
+                    1593.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    315.0,
+                    1559.0,
+                    614.0,
+                    1559.0,
+                    614.0,
+                    1593.0,
+                    315.0,
+                    1593.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    633.0,
+                    1559.0,
+                    821.0,
+                    1559.0,
+                    821.0,
+                    1593.0,
+                    633.0,
+                    1593.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    839.0,
+                    1559.0,
+                    1407.0,
+                    1559.0,
+                    1407.0,
+                    1593.0,
+                    839.0,
+                    1593.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1590.0,
+                    1406.0,
+                    1590.0,
+                    1406.0,
+                    1624.0,
+                    294.0,
+                    1624.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1620.0,
+                    1406.0,
+                    1620.0,
+                    1406.0,
+                    1654.0,
+                    295.0,
+                    1654.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1650.0,
+                    1407.0,
+                    1650.0,
+                    1407.0,
+                    1686.0,
+                    292.0,
+                    1686.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1682.0,
+                    1044.0,
+                    1682.0,
+                    1044.0,
+                    1715.0,
+                    295.0,
+                    1715.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1724.0,
+                    1406.0,
+                    1724.0,
+                    1406.0,
+                    1764.0,
+                    292.0,
+                    1764.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1758.0,
+                    1405.0,
+                    1758.0,
+                    1405.0,
+                    1792.0,
+                    295.0,
+                    1792.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1790.0,
+                    1405.0,
+                    1790.0,
+                    1405.0,
+                    1823.0,
+                    293.0,
+                    1823.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1817.0,
+                    737.0,
+                    1817.0,
+                    737.0,
+                    1853.0,
+                    293.0,
+                    1853.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    765.0,
+                    1817.0,
+                    1405.0,
+                    1817.0,
+                    1405.0,
+                    1853.0,
+                    765.0,
+                    1853.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1849.0,
+                    1405.0,
+                    1849.0,
+                    1405.0,
+                    1884.0,
+                    293.0,
+                    1884.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1876.0,
+                    1410.0,
+                    1876.0,
+                    1410.0,
+                    1915.0,
+                    292.0,
+                    1915.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1908.0,
+                    1409.0,
+                    1908.0,
+                    1409.0,
+                    1945.0,
+                    293.0,
+                    1945.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1937.0,
+                    411.0,
+                    1937.0,
+                    411.0,
+                    1976.0,
+                    293.0,
+                    1976.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    312.0,
+                    545.0,
+                    477.0,
+                    545.0,
+                    477.0,
+                    580.0,
+                    312.0,
+                    580.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    311.0,
+                    574.0,
+                    1031.0,
+                    574.0,
+                    1031.0,
+                    610.0,
+                    311.0,
+                    610.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    310.0,
+                    604.0,
+                    521.0,
+                    604.0,
+                    521.0,
+                    642.0,
+                    310.0,
+                    642.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    313.0,
+                    637.0,
+                    586.0,
+                    637.0,
+                    586.0,
+                    672.0,
+                    313.0,
+                    672.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    310.0,
+                    710.0,
+                    465.0,
+                    710.0,
+                    465.0,
+                    751.0,
+                    310.0,
+                    751.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    312.0,
+                    745.0,
+                    1023.0,
+                    745.0,
+                    1023.0,
+                    778.0,
+                    312.0,
+                    778.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    311.0,
+                    772.0,
+                    798.0,
+                    772.0,
+                    798.0,
+                    811.0,
+                    311.0,
+                    811.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    311.0,
+                    807.0,
+                    670.0,
+                    807.0,
+                    670.0,
+                    841.0,
+                    311.0,
+                    841.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    312.0,
+                    373.0,
+                    675.0,
+                    373.0,
+                    675.0,
+                    411.0,
+                    312.0,
+                    411.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    310.0,
+                    404.0,
+                    890.0,
+                    404.0,
+                    890.0,
+                    443.0,
+                    310.0,
+                    443.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    311.0,
+                    436.0,
+                    545.0,
+                    436.0,
+                    545.0,
+                    471.0,
+                    311.0,
+                    471.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    314.0,
+                    467.0,
+                    948.0,
+                    467.0,
+                    948.0,
+                    503.0,
+                    314.0,
+                    503.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 0,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1490,
+                    1404,
+                    1490,
+                    1404,
+                    1645,
+                    298,
+                    1645
+                ],
+                "score": 0.979
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1113,
+                    1404,
+                    1113,
+                    1404,
+                    1328,
+                    298,
+                    1328
+                ],
+                "score": 0.978
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    935,
+                    1404,
+                    935,
+                    1404,
+                    1098,
+                    298,
+                    1098
+                ],
+                "score": 0.978
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    428,
+                    1405,
+                    428,
+                    1405,
+                    614,
+                    298,
+                    614
+                ],
+                "score": 0.977
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    229,
+                    1404,
+                    229,
+                    1404,
+                    415,
+                    298,
+                    415
+                ],
+                "score": 0.976
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1343,
+                    1403,
+                    1343,
+                    1403,
+                    1476,
+                    299,
+                    1476
+                ],
+                "score": 0.976
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    766,
+                    1404,
+                    766,
+                    1404,
+                    920,
+                    299,
+                    920
+                ],
+                "score": 0.976
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    629,
+                    1404,
+                    629,
+                    1404,
+                    752,
+                    299,
+                    752
+                ],
+                "score": 0.976
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1659,
+                    1403,
+                    1659,
+                    1403,
+                    1813,
+                    299,
+                    1813
+                ],
+                "score": 0.974
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1971,
+                    1402,
+                    1971,
+                    1402,
+                    2035,
+                    297,
+                    2035
+                ],
+                "score": 0.942
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    300,
+                    76,
+                    816,
+                    76,
+                    816,
+                    104,
+                    300,
+                    104
+                ],
+                "score": 0.892
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    300,
+                    1886,
+                    551,
+                    1886,
+                    551,
+                    1921,
+                    300,
+                    1921
+                ],
+                "score": 0.884
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2088,
+                    858,
+                    2088,
+                    858,
+                    2112,
+                    841,
+                    2112
+                ],
+                "score": 0.7
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2088,
+                    859,
+                    2088,
+                    859,
+                    2112,
+                    841,
+                    2112
+                ],
+                "score": 0.176
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    606,
+                    2002,
+                    711,
+                    2002,
+                    711,
+                    2036,
+                    606,
+                    2036
+                ],
+                "score": 0.94,
+                "latex": "p ( s ^ { \\prime } | s , a )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    599,
+                    969,
+                    739,
+                    969,
+                    739,
+                    1012,
+                    599,
+                    1012
+                ],
+                "score": 0.94,
+                "latex": "\\begin{array} { r } { \\tilde { \\mathcal { O } } \\big ( \\frac { S A } { \\epsilon ^ { 4 } ( 1 - \\gamma ) ^ { 8 } } \\big ) } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    868,
+                    1376,
+                    1009,
+                    1376,
+                    1009,
+                    1419,
+                    868,
+                    1419
+                ],
+                "score": 0.93,
+                "latex": "\\begin{array} { r } { \\tilde { \\mathcal { O } } \\big ( \\frac { S A } { \\epsilon ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\big ) } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    644,
+                    1234,
+                    739,
+                    1234,
+                    739,
+                    1270,
+                    644,
+                    1270
+                ],
+                "score": 0.92,
+                "latex": "\\Omega ( 1 / \\epsilon ^ { 3 } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1191,
+                    720,
+                    1306,
+                    720,
+                    1306,
+                    754,
+                    1191,
+                    754
+                ],
+                "score": 0.92,
+                "latex": "1 / ( 1 - \\gamma )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1013,
+                    1973,
+                    1166,
+                    1973,
+                    1166,
+                    2005,
+                    1013,
+                    2005
+                ],
+                "score": 0.91,
+                "latex": "\\langle S , \\mathcal { A } , p , r , \\gamma \\rangle"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    989,
+                    2005,
+                    1190,
+                    2005,
+                    1190,
+                    2036,
+                    989,
+                    2036
+                ],
+                "score": 0.9,
+                "latex": "r : S \\times \\mathcal { A }  [ 0 , 1 ]"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1117,
+                    1114,
+                    1160,
+                    1114,
+                    1160,
+                    1148,
+                    1117,
+                    1148
+                ],
+                "score": 0.86,
+                "latex": "1 / \\epsilon"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1253,
+                    1974,
+                    1275,
+                    1974,
+                    1275,
+                    2000,
+                    1253,
+                    2000
+                ],
+                "score": 0.81,
+                "latex": "s"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    371,
+                    2004,
+                    395,
+                    2004,
+                    395,
+                    2030,
+                    371,
+                    2030
+                ],
+                "score": 0.8,
+                "latex": "\\mathcal { A }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1258,
+                    664,
+                    1278,
+                    664,
+                    1278,
+                    692,
+                    1258,
+                    692
+                ],
+                "score": 0.8,
+                "latex": "\\gamma"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    323,
+                    1445,
+                    344,
+                    1445,
+                    344,
+                    1473,
+                    323,
+                    1473
+                ],
+                "score": 0.72,
+                "latex": "S"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    395,
+                    1446,
+                    419,
+                    1446,
+                    419,
+                    1472,
+                    395,
+                    1472
+                ],
+                "score": 0.68,
+                "latex": "A"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    1451,
+                    312,
+                    1451,
+                    312,
+                    1472,
+                    298,
+                    1472
+                ],
+                "score": 0.41,
+                "latex": "\\epsilon"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    73.0,
+                    817.0,
+                    73.0,
+                    817.0,
+                    108.0,
+                    296.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1883.0,
+                    556.0,
+                    1883.0,
+                    556.0,
+                    1927.0,
+                    292.0,
+                    1927.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    839.0,
+                    2085.0,
+                    862.0,
+                    2085.0,
+                    862.0,
+                    2120.0,
+                    839.0,
+                    2120.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    838.0,
+                    2085.0,
+                    862.0,
+                    2085.0,
+                    862.0,
+                    2120.0,
+                    838.0,
+                    2120.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1490.0,
+                    1405.0,
+                    1490.0,
+                    1405.0,
+                    1528.0,
+                    296.0,
+                    1528.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1520.0,
+                    1402.0,
+                    1520.0,
+                    1402.0,
+                    1557.0,
+                    294.0,
+                    1557.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1550.0,
+                    1406.0,
+                    1550.0,
+                    1406.0,
+                    1590.0,
+                    293.0,
+                    1590.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1583.0,
+                    1404.0,
+                    1583.0,
+                    1404.0,
+                    1617.0,
+                    296.0,
+                    1617.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1611.0,
+                    1195.0,
+                    1611.0,
+                    1195.0,
+                    1650.0,
+                    292.0,
+                    1650.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1113.0,
+                    1116.0,
+                    1113.0,
+                    1116.0,
+                    1152.0,
+                    293.0,
+                    1152.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1161.0,
+                    1113.0,
+                    1405.0,
+                    1113.0,
+                    1405.0,
+                    1152.0,
+                    1161.0,
+                    1152.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1143.0,
+                    1404.0,
+                    1143.0,
+                    1404.0,
+                    1180.0,
+                    293.0,
+                    1180.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1177.0,
+                    1404.0,
+                    1177.0,
+                    1404.0,
+                    1208.0,
+                    296.0,
+                    1208.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1203.0,
+                    1404.0,
+                    1203.0,
+                    1404.0,
+                    1241.0,
+                    293.0,
+                    1241.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1236.0,
+                    643.0,
+                    1236.0,
+                    643.0,
+                    1271.0,
+                    294.0,
+                    1271.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    740.0,
+                    1236.0,
+                    1405.0,
+                    1236.0,
+                    1405.0,
+                    1271.0,
+                    740.0,
+                    1271.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1266.0,
+                    1404.0,
+                    1266.0,
+                    1404.0,
+                    1300.0,
+                    294.0,
+                    1300.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1297.0,
+                    1240.0,
+                    1297.0,
+                    1240.0,
+                    1331.0,
+                    293.0,
+                    1331.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    935.0,
+                    1404.0,
+                    935.0,
+                    1404.0,
+                    972.0,
+                    294.0,
+                    972.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    287.0,
+                    964.0,
+                    598.0,
+                    964.0,
+                    598.0,
+                    1019.0,
+                    287.0,
+                    1019.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    740.0,
+                    964.0,
+                    1411.0,
+                    964.0,
+                    1411.0,
+                    1019.0,
+                    740.0,
+                    1019.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1006.0,
+                    1405.0,
+                    1006.0,
+                    1405.0,
+                    1042.0,
+                    293.0,
+                    1042.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1038.0,
+                    1406.0,
+                    1038.0,
+                    1406.0,
+                    1071.0,
+                    294.0,
+                    1071.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1067.0,
+                    698.0,
+                    1067.0,
+                    698.0,
+                    1100.0,
+                    296.0,
+                    1100.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    428.0,
+                    1405.0,
+                    428.0,
+                    1405.0,
+                    464.0,
+                    295.0,
+                    464.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    460.0,
+                    1406.0,
+                    460.0,
+                    1406.0,
+                    494.0,
+                    291.0,
+                    494.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    488.0,
+                    1405.0,
+                    488.0,
+                    1405.0,
+                    525.0,
+                    293.0,
+                    525.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    521.0,
+                    1405.0,
+                    521.0,
+                    1405.0,
+                    557.0,
+                    295.0,
+                    557.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    546.0,
+                    1410.0,
+                    546.0,
+                    1410.0,
+                    591.0,
+                    291.0,
+                    591.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    580.0,
+                    1162.0,
+                    580.0,
+                    1162.0,
+                    619.0,
+                    293.0,
+                    619.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    229.0,
+                    1403.0,
+                    229.0,
+                    1403.0,
+                    263.0,
+                    295.0,
+                    263.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    258.0,
+                    1408.0,
+                    258.0,
+                    1408.0,
+                    298.0,
+                    293.0,
+                    298.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    293.0,
+                    1405.0,
+                    293.0,
+                    1405.0,
+                    325.0,
+                    296.0,
+                    325.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    322.0,
+                    1406.0,
+                    322.0,
+                    1406.0,
+                    354.0,
+                    294.0,
+                    354.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    351.0,
+                    1405.0,
+                    351.0,
+                    1405.0,
+                    387.0,
+                    294.0,
+                    387.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    383.0,
+                    566.0,
+                    383.0,
+                    566.0,
+                    419.0,
+                    294.0,
+                    419.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1343.0,
+                    1404.0,
+                    1343.0,
+                    1404.0,
+                    1380.0,
+                    293.0,
+                    1380.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1375.0,
+                    867.0,
+                    1375.0,
+                    867.0,
+                    1418.0,
+                    294.0,
+                    1418.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1010.0,
+                    1375.0,
+                    1410.0,
+                    1375.0,
+                    1410.0,
+                    1418.0,
+                    1010.0,
+                    1418.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1413.0,
+                    1403.0,
+                    1413.0,
+                    1403.0,
+                    1448.0,
+                    294.0,
+                    1448.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1443.0,
+                    297.0,
+                    1443.0,
+                    297.0,
+                    1481.0,
+                    294.0,
+                    1481.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    313.0,
+                    1443.0,
+                    322.0,
+                    1443.0,
+                    322.0,
+                    1481.0,
+                    313.0,
+                    1481.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    345.0,
+                    1443.0,
+                    394.0,
+                    1443.0,
+                    394.0,
+                    1481.0,
+                    345.0,
+                    1481.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    420.0,
+                    1443.0,
+                    711.0,
+                    1443.0,
+                    711.0,
+                    1481.0,
+                    420.0,
+                    1481.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    764.0,
+                    1409.0,
+                    764.0,
+                    1409.0,
+                    805.0,
+                    294.0,
+                    805.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    798.0,
+                    1406.0,
+                    798.0,
+                    1406.0,
+                    831.0,
+                    295.0,
+                    831.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    826.0,
+                    1406.0,
+                    826.0,
+                    1406.0,
+                    864.0,
+                    294.0,
+                    864.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    858.0,
+                    1406.0,
+                    858.0,
+                    1406.0,
+                    895.0,
+                    294.0,
+                    895.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    888.0,
+                    417.0,
+                    888.0,
+                    417.0,
+                    923.0,
+                    291.0,
+                    923.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    629.0,
+                    1409.0,
+                    629.0,
+                    1409.0,
+                    665.0,
+                    294.0,
+                    665.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    660.0,
+                    1257.0,
+                    660.0,
+                    1257.0,
+                    693.0,
+                    295.0,
+                    693.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1279.0,
+                    660.0,
+                    1404.0,
+                    660.0,
+                    1404.0,
+                    693.0,
+                    1279.0,
+                    693.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    691.0,
+                    1403.0,
+                    691.0,
+                    1403.0,
+                    723.0,
+                    294.0,
+                    723.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    718.0,
+                    1190.0,
+                    718.0,
+                    1190.0,
+                    757.0,
+                    293.0,
+                    757.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1307.0,
+                    718.0,
+                    1387.0,
+                    718.0,
+                    1387.0,
+                    757.0,
+                    1307.0,
+                    757.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1658.0,
+                    1405.0,
+                    1658.0,
+                    1405.0,
+                    1696.0,
+                    294.0,
+                    1696.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    1691.0,
+                    1405.0,
+                    1691.0,
+                    1405.0,
+                    1724.0,
+                    297.0,
+                    1724.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1720.0,
+                    1403.0,
+                    1720.0,
+                    1403.0,
+                    1753.0,
+                    295.0,
+                    1753.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1752.0,
+                    1405.0,
+                    1752.0,
+                    1405.0,
+                    1789.0,
+                    294.0,
+                    1789.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1784.0,
+                    443.0,
+                    1784.0,
+                    443.0,
+                    1814.0,
+                    295.0,
+                    1814.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1971.0,
+                    1012.0,
+                    1971.0,
+                    1012.0,
+                    2007.0,
+                    296.0,
+                    2007.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1167.0,
+                    1971.0,
+                    1252.0,
+                    1971.0,
+                    1252.0,
+                    2007.0,
+                    1167.0,
+                    2007.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1276.0,
+                    1971.0,
+                    1406.0,
+                    1971.0,
+                    1406.0,
+                    2007.0,
+                    1276.0,
+                    2007.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    2000.0,
+                    370.0,
+                    2000.0,
+                    370.0,
+                    2038.0,
+                    292.0,
+                    2038.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    396.0,
+                    2000.0,
+                    605.0,
+                    2000.0,
+                    605.0,
+                    2038.0,
+                    396.0,
+                    2038.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    712.0,
+                    2000.0,
+                    988.0,
+                    2000.0,
+                    988.0,
+                    2038.0,
+                    712.0,
+                    2038.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1191.0,
+                    2000.0,
+                    1405.0,
+                    2000.0,
+                    1405.0,
+                    2038.0,
+                    1191.0,
+                    2038.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 1,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    413,
+                    1405,
+                    413,
+                    1405,
+                    601,
+                    297,
+                    601
+                ],
+                "score": 0.979
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    712,
+                    1406,
+                    712,
+                    1406,
+                    806,
+                    297,
+                    806
+                ],
+                "score": 0.968
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1922,
+                    1404,
+                    1922,
+                    1404,
+                    2043,
+                    298,
+                    2043
+                ],
+                "score": 0.966
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    894,
+                    1403,
+                    894,
+                    1403,
+                    989,
+                    297,
+                    989
+                ],
+                "score": 0.964
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    307,
+                    1401,
+                    307,
+                    1401,
+                    402,
+                    299,
+                    402
+                ],
+                "score": 0.961
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    300,
+                    614,
+                    1399,
+                    614,
+                    1399,
+                    708,
+                    300,
+                    708
+                ],
+                "score": 0.952
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    293,
+                    228,
+                    1402,
+                    228,
+                    1402,
+                    294,
+                    293,
+                    294
+                ],
+                "score": 0.951
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    827,
+                    1401,
+                    827,
+                    1401,
+                    889,
+                    298,
+                    889
+                ],
+                "score": 0.944
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    299,
+                    1195,
+                    574,
+                    1195,
+                    574,
+                    1232,
+                    299,
+                    1232
+                ],
+                "score": 0.921
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1007,
+                    1011,
+                    1007,
+                    1011,
+                    1040,
+                    299,
+                    1040
+                ],
+                "score": 0.915
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    299,
+                    74,
+                    816,
+                    74,
+                    816,
+                    105,
+                    299,
+                    105
+                ],
+                "score": 0.914
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    286,
+                    1263,
+                    1322,
+                    1263,
+                    1322,
+                    1298,
+                    286,
+                    1298
+                ],
+                "score": 0.913
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    387,
+                    1045,
+                    1286,
+                    1045,
+                    1286,
+                    1117,
+                    387,
+                    1117
+                ],
+                "score": 0.91
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    288,
+                    1121,
+                    1370,
+                    1121,
+                    1370,
+                    1157,
+                    288,
+                    1157
+                ],
+                "score": 0.897
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    300,
+                    1396,
+                    777,
+                    1396,
+                    777,
+                    1429,
+                    300,
+                    1429
+                ],
+                "score": 0.885
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    298,
+                    1330,
+                    518,
+                    1330,
+                    518,
+                    1363,
+                    298,
+                    1363
+                ],
+                "score": 0.869
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2087,
+                    859,
+                    2087,
+                    859,
+                    2113,
+                    841,
+                    2113
+                ],
+                "score": 0.652
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2087,
+                    860,
+                    2087,
+                    860,
+                    2113,
+                    841,
+                    2113
+                ],
+                "score": 0.581
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    307,
+                    1435,
+                    1402,
+                    1435,
+                    1402,
+                    1893,
+                    307,
+                    1893
+                ],
+                "score": 0.47
+            },
+            {
+                "category_id": 5,
+                "poly": [
+                    307,
+                    1435,
+                    1402,
+                    1435,
+                    1402,
+                    1893,
+                    307,
+                    1893
+                ],
+                "score": 0.446,
+                "html": "<table><tr><td colspan=\"2\">Parameters: ∈, γ, δ E ,H← ln1/(1-2)∈1). In 1/q Define (k)= ln(SA(k + 1)(k + 2)/δ),αk = H· H+1 for t=1,2,.. do</td></tr><tr><td>5: Take action at ← arg maxa&#x27; Q(st, a&#x27;) Receive reward rt and transit to St+1 N(st,at)← N(st,at)+1</td><td></td></tr><tr><td>k←N(st,at),bk←1√ H(k) k</td><td> c2 is a constant and can be set to 4√2</td></tr><tr><td>V(St+1) ← maXa∈A Q(st+1,a)</td><td></td></tr><tr><td>Q(st,at) ←(1-ak)Q(st,at)+αk [r(st,at)+bk +γV(st+1)] 10:</td><td></td></tr><tr><td>Q(st,at) ← min(Q(st,at),Q(st,at))</td><td></td></tr></table>"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    470,
+                    1996,
+                    618,
+                    1996,
+                    618,
+                    2043,
+                    470,
+                    2043
+                ],
+                "score": 0.94,
+                "latex": "\\frac { \\ln { 1 } / ( ( 1 - \\gamma ) \\epsilon _ { 1 } ) } { \\ln { 1 } / \\gamma }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    648,
+                    1924,
+                    941,
+                    1924,
+                    941,
+                    1968,
+                    648,
+                    1968
+                ],
+                "score": 0.94,
+                "latex": "\\begin{array} { r } { R = \\lceil \\ln \\frac { 3 } { \\epsilon ( 1 - \\gamma ) } / ( 1 - \\gamma ) \\rceil } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    799,
+                    1995,
+                    1010,
+                    1995,
+                    1010,
+                    2042,
+                    799,
+                    2042
+                ],
+                "score": 0.93,
+                "latex": "H \\leq \\frac { \\ln 1 / ( ( 1 - \\gamma ) \\epsilon _ { 1 } ) } { 1 - \\gamma }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    360,
+                    1923,
+                    481,
+                    1923,
+                    481,
+                    1958,
+                    360,
+                    1958
+                ],
+                "score": 0.93,
+                "latex": "c _ { 2 } = 4 \\sqrt { 2 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    774,
+                    340,
+                    853,
+                    340,
+                    853,
+                    369,
+                    774,
+                    369
+                ],
+                "score": 0.93,
+                "latex": "s _ { t } \\in S"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1079,
+                    230,
+                    1171,
+                    230,
+                    1171,
+                    264,
+                    1079,
+                    264
+                ],
+                "score": 0.93,
+                "latex": "S = | S |"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    533,
+                    231,
+                    653,
+                    231,
+                    653,
+                    262,
+                    533,
+                    262
+                ],
+                "score": 0.93,
+                "latex": "0 \\leq \\gamma < 1"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1222,
+                    230,
+                    1320,
+                    230,
+                    1320,
+                    264,
+                    1222,
+                    264
+                ],
+                "score": 0.92,
+                "latex": "A = | { \\mathcal { A } } |"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1005,
+                    340,
+                    1088,
+                    340,
+                    1088,
+                    369,
+                    1005,
+                    369
+                ],
+                "score": 0.91,
+                "latex": "a _ { t } \\in \\mathcal A"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1158,
+                    477,
+                    1402,
+                    477,
+                    1402,
+                    509,
+                    1158,
+                    509
+                ],
+                "score": 0.91,
+                "latex": "V ^ { * } ( s ) = \\operatorname* { s u p } _ { \\pi } V ^ { \\pi } ( s )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    725,
+                    447,
+                    808,
+                    447,
+                    808,
+                    479,
+                    725,
+                    479
+                ],
+                "score": 0.91,
+                "latex": "V ^ { \\pi _ { t } } ( s )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    295,
+                    536,
+                    824,
+                    536,
+                    824,
+                    573,
+                    295,
+                    573
+                ],
+                "score": 0.91,
+                "latex": "\\begin{array} { r } { \\mathbb { E } [ \\sum _ { i = 2 } ^ { \\infty } \\gamma ^ { i - 1 } r ( s _ { i } , \\pi _ { t + i - 1 } ( s _ { i } ) ) | s _ { 1 } = \\stackrel { \\cdot } { s } , a _ { 1 } = \\stackrel { \\cdot } { a } ] } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1117,
+                    1963,
+                    1393,
+                    1963,
+                    1393,
+                    1999,
+                    1117,
+                    1999
+                ],
+                "score": 0.91,
+                "latex": "\\alpha _ { k } = ( H + 1 ) / ( H + k )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    663,
+                    374,
+                    716,
+                    374,
+                    716,
+                    402,
+                    663,
+                    402
+                ],
+                "score": 0.9,
+                "latex": "s _ { t + 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    773,
+                    564,
+                    773,
+                    564,
+                    807,
+                    298,
+                    807
+                ],
+                "score": 0.89,
+                "latex": "\\dot { V } ^ { \\pi _ { t } } \\left( s _ { t } \\right) \\dot { < } V ^ { * } \\left( s _ { t } \\right) - \\epsilon ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1209,
+                    540,
+                    1307,
+                    540,
+                    1307,
+                    570,
+                    1209,
+                    570
+                ],
+                "score": 0.89,
+                "latex": "Q ^ { * } ( s , a )"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    397,
+                    1043,
+                    1286,
+                    1043,
+                    1286,
+                    1120,
+                    397,
+                    1120
+                ],
+                "score": 0.89,
+                "latex": "\\left\\{ \\begin{array} { l l } { V ^ { \\pi _ { t } } ( s ) = Q ^ { \\pi _ { t } } \\left( s , \\pi _ { t } ( s ) \\right) } \\\\ { Q ^ { \\pi _ { t } } ( s , a ) : = \\left( r _ { t } + \\gamma \\mathbb { P } V ^ { \\pi _ { t + 1 } } \\right) ( s , a ) , } \\end{array} \\right. \\quad \\left\\{ \\begin{array} { l l } { V ^ { * } ( s ) = Q ^ { * } \\left( s , \\pi ^ { * } ( s ) \\right) } \\\\ { Q ^ { * } ( s , a ) : = \\left( r _ { t } + \\gamma \\mathbb { P } V ^ { * } \\right) ( s , a ) , } \\end{array} \\right."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    711,
+                    955,
+                    1009,
+                    955,
+                    1009,
+                    989,
+                    711,
+                    989
+                ],
+                "score": 0.89,
+                "latex": "( S , A , 1 / \\epsilon , 1 / \\delta , 1 / ( 1 - \\gamma ) )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1347,
+                    1689,
+                    1402,
+                    1689,
+                    1402,
+                    1725,
+                    1347,
+                    1725
+                ],
+                "score": 0.88,
+                "latex": "4 { \\sqrt { 2 } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    933,
+                    1123,
+                    1371,
+                    1123,
+                    1371,
+                    1158,
+                    933,
+                    1158
+                ],
+                "score": 0.87,
+                "latex": "\\left[ \\mathbb { P } V ^ { \\pi _ { t } } \\right] ( s , a ) : = \\mathbb { E } _ { s ^ { \\prime } \\sim p ( \\cdot \\vert s , a ) } V ^ { \\pi _ { t + 1 } } ( s ^ { \\prime } ) ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    451,
+                    1466,
+                    722,
+                    1466,
+                    722,
+                    1511,
+                    451,
+                    1511
+                ],
+                "score": 0.87,
+                "latex": "\\begin{array} { r } { Q ( s , a ) , \\hat { Q } ( s , a ) \\gets \\frac { 1 } { 1 - \\gamma } } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1153,
+                    509,
+                    1407,
+                    509,
+                    1407,
+                    540,
+                    1153,
+                    540
+                ],
+                "score": 0.86,
+                "latex": "Q ^ { \\pi _ { t } } ( s , a ) = r ( s , a ) +"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    888,
+                    421,
+                    918,
+                    421,
+                    918,
+                    447,
+                    888,
+                    447
+                ],
+                "score": 0.86,
+                "latex": "\\pi _ { t }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    533,
+                    314,
+                    561,
+                    314,
+                    561,
+                    339,
+                    533,
+                    339
+                ],
+                "score": 0.86,
+                "latex": "s _ { 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    447,
+                    476,
+                    1002,
+                    476,
+                    1002,
+                    512,
+                    447,
+                    512
+                ],
+                "score": 0.85,
+                "latex": "\\begin{array} { r } { V ^ { \\pi _ { t } } ( s ) = \\mathbb { E } \\bigl [ \\sum _ { i = 1 } ^ { \\infty } \\gamma ^ { i - 1 } r ( s _ { i } , \\pi _ { t + i - 1 } ( s _ { i } ) ) | s _ { 1 } = s \\bigr ] } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1326,
+                    343,
+                    1351,
+                    343,
+                    1351,
+                    369,
+                    1326,
+                    369
+                ],
+                "score": 0.85,
+                "latex": "r _ { t }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1295,
+                    956,
+                    1358,
+                    956,
+                    1358,
+                    985,
+                    1295,
+                    985
+                ],
+                "score": 0.85,
+                "latex": "1 - \\delta"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    633,
+                    572,
+                    665,
+                    572,
+                    665,
+                    596,
+                    633,
+                    596
+                ],
+                "score": 0.84,
+                "latex": "\\pi ^ { * }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    842,
+                    748,
+                    871,
+                    748,
+                    871,
+                    774,
+                    842,
+                    774
+                ],
+                "score": 0.84,
+                "latex": "\\pi _ { t }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    563,
+                    1622,
+                    589,
+                    1622,
+                    589,
+                    1647,
+                    563,
+                    1647
+                ],
+                "score": 0.82,
+                "latex": "r _ { t }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1288,
+                    452,
+                    1316,
+                    452,
+                    1316,
+                    476,
+                    1288,
+                    476
+                ],
+                "score": 0.82,
+                "latex": "\\pi _ { t }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    745,
+                    1624,
+                    798,
+                    1624,
+                    798,
+                    1650,
+                    745,
+                    1650
+                ],
+                "score": 0.8,
+                "latex": "s _ { t + 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1181,
+                    1928,
+                    1214,
+                    1928,
+                    1214,
+                    1955,
+                    1181,
+                    1955
+                ],
+                "score": 0.8,
+                "latex": "M"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1333,
+                    749,
+                    1358,
+                    749,
+                    1358,
+                    774,
+                    1333,
+                    774
+                ],
+                "score": 0.8,
+                "latex": "s _ { t }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    2002,
+                    326,
+                    2002,
+                    326,
+                    2030,
+                    298,
+                    2030
+                ],
+                "score": 0.79,
+                "latex": "H"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    426,
+                    1515,
+                    930,
+                    1515,
+                    930,
+                    1555,
+                    426,
+                    1555
+                ],
+                "score": 0.78,
+                "latex": "\\begin{array} { r } { \\iota ( k ) = \\ln ( S A ( k + 1 ) ( k + 2 ) / \\delta ) , \\alpha _ { k } = \\frac { H + 1 } { H + k } , } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    451,
+                    1964,
+                    752,
+                    1964,
+                    752,
+                    1998,
+                    451,
+                    1998
+                ],
+                "score": 0.75,
+                "latex": "{ \\cal { \\left( M = 0 \\left( \\ln 1 / ( 1 - \\gamma ) \\epsilon \\right) \\right) } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    520,
+                    1582,
+                    814,
+                    1582,
+                    814,
+                    1619,
+                    520,
+                    1619
+                ],
+                "score": 0.73,
+                "latex": "a _ { t } \\gets \\arg \\operatorname* { m a x } _ { a ^ { \\prime } } \\hat { Q } ( s _ { t } , a ^ { \\prime } )"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    432,
+                    1462,
+                    1332,
+                    1462,
+                    1332,
+                    1562,
+                    432,
+                    1562
+                ],
+                "score": 0.69,
+                "latex": "\\begin{array} { r l } & { \\textnormal { \\texttt { e } } Q ( s , a ) , \\hat { Q } ( s , a ) \\gets \\frac { 1 } { 1 - \\gamma } , N ( s , a ) \\gets 0 , \\epsilon _ { 1 } \\gets \\frac { \\epsilon } { 2 4 R M \\ln \\frac { 1 } { 1 - \\gamma } } , H \\gets \\frac { \\ln 1 / ( ( 1 - \\gamma ) \\epsilon _ { 1 } ) } { \\ln 1 / \\gamma } . } \\\\ & { \\cdot ( k ) = \\ln ( S A ( k + 1 ) ( k + 2 ) / \\delta ) , \\alpha _ { k } = \\frac { H + 1 } { H + k } . } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    957,
+                    748,
+                    971,
+                    748,
+                    971,
+                    771,
+                    957,
+                    771
+                ],
+                "score": 0.68,
+                "latex": "t"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    621,
+                    894,
+                    684,
+                    894,
+                    684,
+                    924,
+                    621,
+                    924
+                ],
+                "score": 0.67,
+                "latex": "\\mathcal { A L G }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    628,
+                    927,
+                    653,
+                    927,
+                    653,
+                    957,
+                    628,
+                    957
+                ],
+                "score": 0.67,
+                "latex": "i f ,"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    386,
+                    1553,
+                    548,
+                    1553,
+                    548,
+                    1583,
+                    386,
+                    1583
+                ],
+                "score": 0.66,
+                "latex": "t = 1 , 2 , \\dots \\mathbf { d o }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    819,
+                    926,
+                    834,
+                    926,
+                    834,
+                    952,
+                    819,
+                    952
+                ],
+                "score": 0.65,
+                "latex": "\\delta"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    980,
+                    1700,
+                    1007,
+                    1700,
+                    1007,
+                    1724,
+                    980,
+                    1724
+                ],
+                "score": 0.65,
+                "latex": "c _ { 2 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1168,
+                    542,
+                    1196,
+                    542,
+                    1196,
+                    569,
+                    1168,
+                    569
+                ],
+                "score": 0.64,
+                "latex": "\\pi _ { t }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    607,
+                    449,
+                    621,
+                    449,
+                    621,
+                    474,
+                    607,
+                    474
+                ],
+                "score": 0.62,
+                "latex": "t"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1138,
+                    925,
+                    1200,
+                    925,
+                    1200,
+                    955,
+                    1138,
+                    955
+                ],
+                "score": 0.61,
+                "latex": "\\mathcal { A L G }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1057,
+                    712,
+                    1119,
+                    712,
+                    1119,
+                    743,
+                    1057,
+                    743
+                ],
+                "score": 0.56,
+                "latex": "\\mathcal { A L G }"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    382,
+                    1640,
+                    1142,
+                    1640,
+                    1142,
+                    1863,
+                    382,
+                    1863
+                ],
+                "score": 0.48,
+                "latex": "\\begin{array} { r l r } & { N ( s _ { t } , a _ { t } ) \\gets N ( s _ { t } , a _ { t } ) + 1 } & \\\\ & { N ( s _ { t } , a _ { t } ) \\gets N ( s _ { t } , a _ { t } ) + 1 } & \\\\ & { k \\gets N ( s _ { t } , a _ { t } ) , b _ { k } \\gets \\frac { c _ { 2 } } { 1 - \\gamma } \\sqrt { \\frac { H ( k ) } { k } } } & \\\\ & { \\hat { V } ( s _ { t + 1 } ) \\gets \\operatorname* { m a x } _ { a \\in A } \\hat { Q } ( s _ { t + 1 } , a ) } & \\\\ & { Q ( s _ { t } , a _ { t } ) \\gets ( 1 - \\alpha _ { k } ) Q ( s _ { t } , a _ { t } ) + \\alpha _ { k } \\left[ r ( s _ { t } , a _ { t } ) + b _ { k } + \\gamma \\hat { V } ( s _ { t + 1 } ) \\right] } \\\\ & { \\hat { Q } ( s _ { t } , a _ { t } ) \\gets \\operatorname* { m i n } ( \\hat { Q } ( s _ { t } , a _ { t } ) , Q ( s _ { t } , a _ { t } ) ) } & \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1040,
+                    750,
+                    1055,
+                    750,
+                    1055,
+                    771,
+                    1040,
+                    771
+                ],
+                "score": 0.47,
+                "latex": "\\epsilon"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    709,
+                    1582,
+                    812,
+                    1582,
+                    812,
+                    1619,
+                    709,
+                    1619
+                ],
+                "score": 0.42,
+                "latex": "\\hat { Q } ( s _ { t } , a ^ { \\prime } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    385,
+                    1647,
+                    695,
+                    1647,
+                    695,
+                    1682,
+                    385,
+                    1682
+                ],
+                "score": 0.34,
+                "latex": "N ( s _ { t } , a _ { t } ) \\gets N ( s _ { t } , a _ { t } ) + 1"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    457,
+                    1964,
+                    551,
+                    1964,
+                    551,
+                    1994,
+                    457,
+                    1994
+                ],
+                "score": 0.28,
+                "latex": "M = \\mathcal { O }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    976,
+                    678,
+                    1001,
+                    678,
+                    1001,
+                    705,
+                    976,
+                    705
+                ],
+                "score": 0.28,
+                "latex": "\\&"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    898,
+                    539,
+                    923,
+                    539,
+                    923,
+                    569,
+                    898,
+                    569
+                ],
+                "score": 0.26,
+                "latex": "\\mathrm { Q }"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1191.0,
+                    575.0,
+                    1191.0,
+                    575.0,
+                    1238.0,
+                    291.0,
+                    1238.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    72.0,
+                    817.0,
+                    72.0,
+                    817.0,
+                    108.0,
+                    295.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1394.0,
+                    781.0,
+                    1394.0,
+                    781.0,
+                    1436.0,
+                    294.0,
+                    1436.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1329.0,
+                    521.0,
+                    1329.0,
+                    521.0,
+                    1365.0,
+                    294.0,
+                    1365.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    838.0,
+                    2085.0,
+                    862.0,
+                    2085.0,
+                    862.0,
+                    2119.0,
+                    838.0,
+                    2119.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    837.0,
+                    2085.0,
+                    862.0,
+                    2085.0,
+                    862.0,
+                    2119.0,
+                    837.0,
+                    2119.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    411.0,
+                    887.0,
+                    411.0,
+                    887.0,
+                    453.0,
+                    292.0,
+                    453.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    919.0,
+                    411.0,
+                    1406.0,
+                    411.0,
+                    1406.0,
+                    453.0,
+                    919.0,
+                    453.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    443.0,
+                    606.0,
+                    443.0,
+                    606.0,
+                    483.0,
+                    294.0,
+                    483.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    622.0,
+                    443.0,
+                    724.0,
+                    443.0,
+                    724.0,
+                    483.0,
+                    622.0,
+                    483.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    809.0,
+                    443.0,
+                    1287.0,
+                    443.0,
+                    1287.0,
+                    483.0,
+                    809.0,
+                    483.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1317.0,
+                    443.0,
+                    1407.0,
+                    443.0,
+                    1407.0,
+                    483.0,
+                    1317.0,
+                    483.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    286.0,
+                    463.0,
+                    446.0,
+                    463.0,
+                    446.0,
+                    524.0,
+                    286.0,
+                    524.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1003.0,
+                    463.0,
+                    1157.0,
+                    463.0,
+                    1157.0,
+                    524.0,
+                    1003.0,
+                    524.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1403.0,
+                    463.0,
+                    1415.0,
+                    463.0,
+                    1415.0,
+                    524.0,
+                    1403.0,
+                    524.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    290.0,
+                    503.0,
+                    1152.0,
+                    503.0,
+                    1152.0,
+                    544.0,
+                    290.0,
+                    544.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1408.0,
+                    503.0,
+                    1411.0,
+                    503.0,
+                    1411.0,
+                    544.0,
+                    1408.0,
+                    544.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    283.0,
+                    520.0,
+                    294.0,
+                    520.0,
+                    294.0,
+                    588.0,
+                    283.0,
+                    588.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    825.0,
+                    520.0,
+                    897.0,
+                    520.0,
+                    897.0,
+                    588.0,
+                    825.0,
+                    588.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    924.0,
+                    520.0,
+                    1167.0,
+                    520.0,
+                    1167.0,
+                    588.0,
+                    924.0,
+                    588.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1197.0,
+                    520.0,
+                    1208.0,
+                    520.0,
+                    1208.0,
+                    588.0,
+                    1197.0,
+                    588.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1308.0,
+                    520.0,
+                    1416.0,
+                    520.0,
+                    1416.0,
+                    588.0,
+                    1308.0,
+                    588.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    567.0,
+                    632.0,
+                    567.0,
+                    632.0,
+                    603.0,
+                    295.0,
+                    603.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    666.0,
+                    567.0,
+                    677.0,
+                    567.0,
+                    677.0,
+                    603.0,
+                    666.0,
+                    603.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    710.0,
+                    1056.0,
+                    710.0,
+                    1056.0,
+                    748.0,
+                    294.0,
+                    748.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1120.0,
+                    710.0,
+                    1406.0,
+                    710.0,
+                    1406.0,
+                    748.0,
+                    1120.0,
+                    748.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    742.0,
+                    841.0,
+                    742.0,
+                    841.0,
+                    781.0,
+                    292.0,
+                    781.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    872.0,
+                    742.0,
+                    956.0,
+                    742.0,
+                    956.0,
+                    781.0,
+                    872.0,
+                    781.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    972.0,
+                    742.0,
+                    1039.0,
+                    742.0,
+                    1039.0,
+                    781.0,
+                    972.0,
+                    781.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1056.0,
+                    742.0,
+                    1332.0,
+                    742.0,
+                    1332.0,
+                    781.0,
+                    1056.0,
+                    781.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1359.0,
+                    742.0,
+                    1409.0,
+                    742.0,
+                    1409.0,
+                    781.0,
+                    1359.0,
+                    781.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    769.0,
+                    297.0,
+                    769.0,
+                    297.0,
+                    811.0,
+                    294.0,
+                    811.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    565.0,
+                    769.0,
+                    575.0,
+                    769.0,
+                    575.0,
+                    811.0,
+                    565.0,
+                    811.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1918.0,
+                    359.0,
+                    1918.0,
+                    359.0,
+                    1974.0,
+                    291.0,
+                    1974.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    482.0,
+                    1918.0,
+                    647.0,
+                    1918.0,
+                    647.0,
+                    1974.0,
+                    482.0,
+                    1974.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    942.0,
+                    1918.0,
+                    1180.0,
+                    1918.0,
+                    1180.0,
+                    1974.0,
+                    942.0,
+                    1974.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1215.0,
+                    1918.0,
+                    1410.0,
+                    1918.0,
+                    1410.0,
+                    1974.0,
+                    1215.0,
+                    1974.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1959.0,
+                    450.0,
+                    1959.0,
+                    450.0,
+                    1999.0,
+                    293.0,
+                    1999.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    753.0,
+                    1959.0,
+                    1116.0,
+                    1959.0,
+                    1116.0,
+                    1999.0,
+                    753.0,
+                    1999.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1394.0,
+                    1959.0,
+                    1404.0,
+                    1959.0,
+                    1404.0,
+                    1999.0,
+                    1394.0,
+                    1999.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    327.0,
+                    1984.0,
+                    469.0,
+                    1984.0,
+                    469.0,
+                    2050.0,
+                    327.0,
+                    2050.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    619.0,
+                    1984.0,
+                    798.0,
+                    1984.0,
+                    798.0,
+                    2050.0,
+                    619.0,
+                    2050.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1011.0,
+                    1984.0,
+                    1018.0,
+                    1984.0,
+                    1018.0,
+                    2050.0,
+                    1011.0,
+                    2050.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    892.0,
+                    620.0,
+                    892.0,
+                    620.0,
+                    931.0,
+                    294.0,
+                    931.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    685.0,
+                    892.0,
+                    1404.0,
+                    892.0,
+                    1404.0,
+                    931.0,
+                    685.0,
+                    931.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    923.0,
+                    627.0,
+                    923.0,
+                    627.0,
+                    960.0,
+                    292.0,
+                    960.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    654.0,
+                    923.0,
+                    818.0,
+                    923.0,
+                    818.0,
+                    960.0,
+                    654.0,
+                    960.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    835.0,
+                    923.0,
+                    1137.0,
+                    923.0,
+                    1137.0,
+                    960.0,
+                    835.0,
+                    960.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1201.0,
+                    923.0,
+                    1404.0,
+                    923.0,
+                    1404.0,
+                    960.0,
+                    1201.0,
+                    960.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    955.0,
+                    710.0,
+                    955.0,
+                    710.0,
+                    993.0,
+                    292.0,
+                    993.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1010.0,
+                    955.0,
+                    1294.0,
+                    955.0,
+                    1294.0,
+                    993.0,
+                    1010.0,
+                    993.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1359.0,
+                    955.0,
+                    1370.0,
+                    955.0,
+                    1370.0,
+                    993.0,
+                    1359.0,
+                    993.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    306.0,
+                    532.0,
+                    306.0,
+                    532.0,
+                    345.0,
+                    293.0,
+                    345.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    562.0,
+                    306.0,
+                    1406.0,
+                    306.0,
+                    1406.0,
+                    345.0,
+                    562.0,
+                    345.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    337.0,
+                    773.0,
+                    337.0,
+                    773.0,
+                    372.0,
+                    295.0,
+                    372.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    854.0,
+                    337.0,
+                    1004.0,
+                    337.0,
+                    1004.0,
+                    372.0,
+                    854.0,
+                    372.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1089.0,
+                    337.0,
+                    1325.0,
+                    337.0,
+                    1325.0,
+                    372.0,
+                    1089.0,
+                    372.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1352.0,
+                    337.0,
+                    1403.0,
+                    337.0,
+                    1403.0,
+                    372.0,
+                    1352.0,
+                    372.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    365.0,
+                    662.0,
+                    365.0,
+                    662.0,
+                    408.0,
+                    293.0,
+                    408.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    717.0,
+                    365.0,
+                    730.0,
+                    365.0,
+                    730.0,
+                    408.0,
+                    717.0,
+                    408.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    611.0,
+                    1404.0,
+                    611.0,
+                    1404.0,
+                    653.0,
+                    294.0,
+                    653.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    645.0,
+                    1403.0,
+                    645.0,
+                    1403.0,
+                    679.0,
+                    296.0,
+                    679.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    677.0,
+                    975.0,
+                    677.0,
+                    975.0,
+                    711.0,
+                    296.0,
+                    711.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1002.0,
+                    677.0,
+                    1187.0,
+                    677.0,
+                    1187.0,
+                    711.0,
+                    1002.0,
+                    711.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    229.0,
+                    532.0,
+                    229.0,
+                    532.0,
+                    265.0,
+                    295.0,
+                    265.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    654.0,
+                    229.0,
+                    1078.0,
+                    229.0,
+                    1078.0,
+                    265.0,
+                    654.0,
+                    265.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1172.0,
+                    229.0,
+                    1221.0,
+                    229.0,
+                    1221.0,
+                    265.0,
+                    1172.0,
+                    265.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1321.0,
+                    229.0,
+                    1404.0,
+                    229.0,
+                    1404.0,
+                    265.0,
+                    1321.0,
+                    265.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    258.0,
+                    966.0,
+                    258.0,
+                    966.0,
+                    297.0,
+                    293.0,
+                    297.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    823.0,
+                    1405.0,
+                    823.0,
+                    1405.0,
+                    866.0,
+                    293.0,
+                    866.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    855.0,
+                    942.0,
+                    855.0,
+                    942.0,
+                    891.0,
+                    296.0,
+                    891.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1003.0,
+                    1014.0,
+                    1003.0,
+                    1014.0,
+                    1047.0,
+                    293.0,
+                    1047.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1260.0,
+                    1324.0,
+                    1260.0,
+                    1324.0,
+                    1303.0,
+                    292.0,
+                    1303.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1112.0,
+                    932.0,
+                    1112.0,
+                    932.0,
+                    1165.0,
+                    291.0,
+                    1165.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1372.0,
+                    1112.0,
+                    1377.0,
+                    1112.0,
+                    1377.0,
+                    1165.0,
+                    1372.0,
+                    1165.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    343.0,
+                    1431.0,
+                    561.0,
+                    1431.0,
+                    561.0,
+                    1467.0,
+                    343.0,
+                    1467.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    339.0,
+                    1463.0,
+                    431.0,
+                    1463.0,
+                    431.0,
+                    1510.0,
+                    339.0,
+                    1510.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    341.0,
+                    1508.0,
+                    425.0,
+                    1508.0,
+                    425.0,
+                    1558.0,
+                    341.0,
+                    1558.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    342.0,
+                    1549.0,
+                    385.0,
+                    1549.0,
+                    385.0,
+                    1584.0,
+                    342.0,
+                    1584.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    549.0,
+                    1549.0,
+                    552.0,
+                    1549.0,
+                    552.0,
+                    1584.0,
+                    549.0,
+                    1584.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    307.0,
+                    1584.0,
+                    342.0,
+                    1584.0,
+                    342.0,
+                    1620.0,
+                    307.0,
+                    1620.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    381.0,
+                    1583.0,
+                    519.0,
+                    1583.0,
+                    519.0,
+                    1622.0,
+                    381.0,
+                    1622.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    377.0,
+                    1680.0,
+                    381.0,
+                    1680.0,
+                    381.0,
+                    1740.0,
+                    377.0,
+                    1740.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1143.0,
+                    1691.0,
+                    1346.0,
+                    1691.0,
+                    1346.0,
+                    1725.0,
+                    1143.0,
+                    1725.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    298.0,
+                    1777.0,
+                    340.0,
+                    1777.0,
+                    340.0,
+                    1811.0,
+                    298.0,
+                    1811.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    340.0,
+                    1851.0,
+                    439.0,
+                    1851.0,
+                    439.0,
+                    1888.0,
+                    340.0,
+                    1888.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1080.25,
+                    1452.5,
+                    1338.25,
+                    1452.5,
+                    1338.25,
+                    1504.0,
+                    1080.25,
+                    1504.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    952.75,
+                    1480.5,
+                    1093.75,
+                    1480.5,
+                    1093.75,
+                    1517.5,
+                    952.75,
+                    1517.5
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    381.75,
+                    1613.0,
+                    801.75,
+                    1613.0,
+                    801.75,
+                    1652.0,
+                    381.75,
+                    1652.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 2,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1498,
+                    1404,
+                    1498,
+                    1404,
+                    1806,
+                    297,
+                    1806
+                ],
+                "score": 0.983
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1130,
+                    1404,
+                    1130,
+                    1404,
+                    1346,
+                    298,
+                    1346
+                ],
+                "score": 0.982
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    929,
+                    1406,
+                    929,
+                    1406,
+                    1115,
+                    297,
+                    1115
+                ],
+                "score": 0.98
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1819,
+                    1404,
+                    1819,
+                    1404,
+                    2035,
+                    297,
+                    2035
+                ],
+                "score": 0.98
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    228,
+                    1405,
+                    228,
+                    1405,
+                    426,
+                    297,
+                    426
+                ],
+                "score": 0.979
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1360,
+                    1404,
+                    1360,
+                    1404,
+                    1485,
+                    297,
+                    1485
+                ],
+                "score": 0.976
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    577,
+                    1409,
+                    577,
+                    1409,
+                    670,
+                    298,
+                    670
+                ],
+                "score": 0.97
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    738,
+                    678,
+                    959,
+                    678,
+                    959,
+                    768,
+                    738,
+                    768
+                ],
+                "score": 0.954
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    853,
+                    1405,
+                    853,
+                    1405,
+                    917,
+                    297,
+                    917
+                ],
+                "score": 0.947
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    531,
+                    1117,
+                    531,
+                    1117,
+                    566,
+                    298,
+                    566
+                ],
+                "score": 0.93
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    788,
+                    1042,
+                    788,
+                    1042,
+                    826,
+                    297,
+                    826
+                ],
+                "score": 0.92
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    299,
+                    75,
+                    816,
+                    75,
+                    816,
+                    105,
+                    299,
+                    105
+                ],
+                "score": 0.907
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    297,
+                    470,
+                    851,
+                    470,
+                    851,
+                    504,
+                    297,
+                    504
+                ],
+                "score": 0.867
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    840,
+                    2089,
+                    857,
+                    2089,
+                    857,
+                    2111,
+                    840,
+                    2111
+                ],
+                "score": 0.784
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    346,
+                    358,
+                    441,
+                    358,
+                    441,
+                    395,
+                    346,
+                    395
+                ],
+                "score": 0.93,
+                "latex": "\\hat { Q } _ { t } ( s , a )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    394,
+                    265,
+                    480,
+                    265,
+                    480,
+                    298,
+                    394,
+                    298
+                ],
+                "score": 0.93,
+                "latex": "Q ( s , a )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1275,
+                    1160,
+                    1361,
+                    1160,
+                    1361,
+                    1195,
+                    1275,
+                    1195
+                ],
+                "score": 0.92,
+                "latex": "o ( T ^ { - 1 } )"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    738,
+                    674,
+                    959,
+                    674,
+                    959,
+                    768,
+                    738,
+                    768
+                ],
+                "score": 0.92,
+                "latex": "\\tilde { \\mathcal { O } } \\left( \\frac { S A \\ln { 1 / \\delta } } { \\epsilon ^ { 2 } \\left( 1 - \\gamma \\right) ^ { 7 } } \\right) ,"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    764,
+                    1422,
+                    1028,
+                    1422,
+                    1028,
+                    1455,
+                    764,
+                    1455
+                ],
+                "score": 0.92,
+                "latex": "V ^ { \\ast } ( s _ { t } ) - V ^ { \\pi _ { t } } ( s _ { t } ) \\leq \\epsilon"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    745,
+                    296,
+                    852,
+                    296,
+                    852,
+                    329,
+                    745,
+                    329
+                ],
+                "score": 0.92,
+                "latex": "\\tau ( s , a , k )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    891,
+                    1881,
+                    1144,
+                    1881,
+                    1144,
+                    1914,
+                    891,
+                    1914
+                ],
+                "score": 0.92,
+                "latex": "V ^ { \\ast } ( s _ { t ^ { \\prime } } ) - Q ^ { \\ast } ( s _ { t ^ { \\prime } } , a _ { t ^ { \\prime } } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1223,
+                    295,
+                    1403,
+                    295,
+                    1403,
+                    328,
+                    1223,
+                    328
+                ],
+                "score": 0.91,
+                "latex": "( s _ { t } , a _ { t } ) = ( s , a )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    467,
+                    1973,
+                    698,
+                    1973,
+                    698,
+                    2006,
+                    467,
+                    2006
+                ],
+                "score": 0.91,
+                "latex": "V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    789,
+                    362,
+                    851,
+                    362,
+                    851,
+                    395,
+                    789,
+                    395
+                ],
+                "score": 0.91,
+                "latex": "( s , a )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    580,
+                    1914,
+                    681,
+                    1914,
+                    681,
+                    1944,
+                    580,
+                    1944
+                ],
+                "score": 0.91,
+                "latex": "[ t , t + R ]"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    296,
+                    296,
+                    358,
+                    296,
+                    358,
+                    328,
+                    296,
+                    328
+                ],
+                "score": 0.91,
+                "latex": "( s , a )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1210,
+                    992,
+                    1397,
+                    992,
+                    1397,
+                    1026,
+                    1210,
+                    1026
+                ],
+                "score": 0.91,
+                "latex": "( V ^ { * } - V ^ { \\pi } ) ( s _ { 1 } ) )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1100,
+                    1561,
+                    1167,
+                    1561,
+                    1167,
+                    1590,
+                    1100,
+                    1590
+                ],
+                "score": 0.91,
+                "latex": "h + 1"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    559,
+                    1882,
+                    812,
+                    1882,
+                    812,
+                    1915,
+                    559,
+                    1915
+                ],
+                "score": 0.91,
+                "latex": "V ^ { * } ( s _ { t } ) - V ^ { \\pi _ { t } } ( s _ { t } ) \\leq \\epsilon"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    775,
+                    791,
+                    942,
+                    791,
+                    942,
+                    825,
+                    775,
+                    825
+                ],
+                "score": 0.9,
+                "latex": "1 / \\epsilon , 1 / ( 1 - \\gamma )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1117,
+                    327,
+                    1291,
+                    327,
+                    1291,
+                    360,
+                    1117,
+                    360
+                ],
+                "score": 0.89,
+                "latex": "\\tau ( s , a , k ) = \\infty"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    659,
+                    357,
+                    685,
+                    357,
+                    685,
+                    395,
+                    659,
+                    395
+                ],
+                "score": 0.87,
+                "latex": "\\hat { Q }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1063,
+                    1657,
+                    1089,
+                    1657,
+                    1089,
+                    1682,
+                    1063,
+                    1682
+                ],
+                "score": 0.86,
+                "latex": "s _ { t }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    846,
+                    260,
+                    932,
+                    260,
+                    932,
+                    298,
+                    846,
+                    298
+                ],
+                "score": 0.86,
+                "latex": "\\hat { Q } ( s , a )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    897,
+                    614,
+                    925,
+                    614,
+                    925,
+                    640,
+                    897,
+                    640
+                ],
+                "score": 0.86,
+                "latex": "\\pi _ { t }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1153,
+                    1197,
+                    1181,
+                    1197,
+                    1181,
+                    1223,
+                    1153,
+                    1223
+                ],
+                "score": 0.85,
+                "latex": "s _ { 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    944,
+                    264,
+                    1040,
+                    264,
+                    1040,
+                    299,
+                    944,
+                    299
+                ],
+                "score": 0.85,
+                "latex": "N _ { t } ( s , a )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    487,
+                    1854,
+                    515,
+                    1854,
+                    515,
+                    1881,
+                    487,
+                    1881
+                ],
+                "score": 0.85,
+                "latex": "\\pi _ { t }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    824,
+                    1166,
+                    853,
+                    1166,
+                    853,
+                    1192,
+                    824,
+                    1192
+                ],
+                "score": 0.85,
+                "latex": "s _ { 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    588,
+                    1625,
+                    614,
+                    1625,
+                    614,
+                    1652,
+                    588,
+                    1652
+                ],
+                "score": 0.85,
+                "latex": "s _ { t }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1217,
+                    1165,
+                    1245,
+                    1165,
+                    1245,
+                    1193,
+                    1217,
+                    1193
+                ],
+                "score": 0.85,
+                "latex": "s _ { 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    581,
+                    362,
+                    607,
+                    362,
+                    607,
+                    395,
+                    581,
+                    395
+                ],
+                "score": 0.85,
+                "latex": "Q"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1064,
+                    1227,
+                    1093,
+                    1227,
+                    1093,
+                    1253,
+                    1064,
+                    1253
+                ],
+                "score": 0.85,
+                "latex": "s _ { 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    803,
+                    1625,
+                    830,
+                    1625,
+                    830,
+                    1652,
+                    803,
+                    1652
+                ],
+                "score": 0.84,
+                "latex": "a _ { t }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    675,
+                    1425,
+                    701,
+                    1425,
+                    701,
+                    1452,
+                    675,
+                    1452
+                ],
+                "score": 0.84,
+                "latex": "s _ { t }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1375,
+                    369,
+                    1400,
+                    369,
+                    1400,
+                    393,
+                    1375,
+                    393
+                ],
+                "score": 0.84,
+                "latex": "s _ { t }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1307,
+                    328,
+                    1403,
+                    328,
+                    1403,
+                    360,
+                    1307,
+                    360
+                ],
+                "score": 0.84,
+                "latex": "Q _ { t } ( s , a )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1119,
+                    996,
+                    1148,
+                    996,
+                    1148,
+                    1023,
+                    1119,
+                    1023
+                ],
+                "score": 0.83,
+                "latex": "s _ { 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    358,
+                    1911,
+                    379,
+                    1911,
+                    379,
+                    1939,
+                    358,
+                    1939
+                ],
+                "score": 0.83,
+                "latex": "t ^ { \\prime }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    1686,
+                    324,
+                    1686,
+                    324,
+                    1713,
+                    298,
+                    1713
+                ],
+                "score": 0.83,
+                "latex": "a _ { t }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1140,
+                    614,
+                    1167,
+                    614,
+                    1167,
+                    640,
+                    1140,
+                    640
+                ],
+                "score": 0.82,
+                "latex": "s _ { t . }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    380,
+                    328,
+                    399,
+                    328,
+                    399,
+                    354,
+                    380,
+                    354
+                ],
+                "score": 0.82,
+                "latex": "k"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    997,
+                    1562,
+                    1016,
+                    1562,
+                    1016,
+                    1588,
+                    997,
+                    1588
+                ],
+                "score": 0.81,
+                "latex": "k"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    619,
+                    1225,
+                    643,
+                    1225,
+                    643,
+                    1250,
+                    619,
+                    1250
+                ],
+                "score": 0.81,
+                "latex": "T"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    933,
+                    1856,
+                    957,
+                    1856,
+                    957,
+                    1881,
+                    933,
+                    1881
+                ],
+                "score": 0.81,
+                "latex": "s _ { t }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    297,
+                    1562,
+                    316,
+                    1562,
+                    316,
+                    1588,
+                    297,
+                    1588
+                ],
+                "score": 0.8,
+                "latex": "k"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    684,
+                    1854,
+                    697,
+                    1854,
+                    697,
+                    1878,
+                    684,
+                    1878
+                ],
+                "score": 0.8,
+                "latex": "t"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    420,
+                    1562,
+                    441,
+                    1562,
+                    441,
+                    1588,
+                    420,
+                    1588
+                ],
+                "score": 0.79,
+                "latex": "h"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    371,
+                    787,
+                    398,
+                    787,
+                    398,
+                    820,
+                    371,
+                    820
+                ],
+                "score": 0.79,
+                "latex": "\\tilde { \\mathcal { O } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    349,
+                    994,
+                    373,
+                    994,
+                    373,
+                    1020,
+                    349,
+                    1020
+                ],
+                "score": 0.79,
+                "latex": "T"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    927,
+                    1915,
+                    951,
+                    1915,
+                    951,
+                    1939,
+                    927,
+                    1939
+                ],
+                "score": 0.78,
+                "latex": "R"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    540,
+                    581,
+                    606,
+                    581,
+                    606,
+                    609,
+                    540,
+                    609
+                ],
+                "score": 0.77,
+                "latex": "\\epsilon > 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    995,
+                    791,
+                    1037,
+                    791,
+                    1037,
+                    820,
+                    995,
+                    820
+                ],
+                "score": 0.77,
+                "latex": "S A"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    921,
+                    1194,
+                    946,
+                    1194,
+                    946,
+                    1220,
+                    921,
+                    1220
+                ],
+                "score": 0.76,
+                "latex": "T"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1042,
+                    580,
+                    1107,
+                    580,
+                    1107,
+                    609,
+                    1042,
+                    609
+                ],
+                "score": 0.76,
+                "latex": "1 - \\delta"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    353,
+                    1623,
+                    368,
+                    1623,
+                    368,
+                    1649,
+                    353,
+                    1649
+                ],
+                "score": 0.75,
+                "latex": "t"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    727,
+                    1857,
+                    740,
+                    1857,
+                    740,
+                    1878,
+                    727,
+                    1878
+                ],
+                "score": 0.75,
+                "latex": "\\epsilon"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1100,
+                    299,
+                    1114,
+                    299,
+                    1114,
+                    324,
+                    1100,
+                    324
+                ],
+                "score": 0.75,
+                "latex": "t"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1133,
+                    1624,
+                    1147,
+                    1624,
+                    1147,
+                    1648,
+                    1133,
+                    1648
+                ],
+                "score": 0.74,
+                "latex": "t"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    438,
+                    1715,
+                    452,
+                    1715,
+                    452,
+                    1741,
+                    438,
+                    1741
+                ],
+                "score": 0.74,
+                "latex": "t"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    547,
+                    1425,
+                    561,
+                    1425,
+                    561,
+                    1449,
+                    547,
+                    1449
+                ],
+                "score": 0.72,
+                "latex": "t"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    1428,
+                    312,
+                    1428,
+                    312,
+                    1449,
+                    298,
+                    1449
+                ],
+                "score": 0.67,
+                "latex": "\\epsilon"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    683,
+                    1685,
+                    697,
+                    1685,
+                    697,
+                    1709,
+                    683,
+                    1709
+                ],
+                "score": 0.64,
+                "latex": "t"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    616,
+                    579,
+                    844,
+                    579,
+                    844,
+                    613,
+                    616,
+                    613
+                ],
+                "score": 0.6,
+                "latex": "\\delta > 0 , 1 / 2 < \\gamma < 1"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    998,
+                    617,
+                    1012,
+                    617,
+                    1012,
+                    637,
+                    998,
+                    637
+                ],
+                "score": 0.55,
+                "latex": "\\epsilon"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    719,
+                    298,
+                    734,
+                    298,
+                    734,
+                    325,
+                    719,
+                    325
+                ],
+                "score": 0.48,
+                "latex": "t"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    73.0,
+                    817.0,
+                    73.0,
+                    817.0,
+                    108.0,
+                    295.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    467.0,
+                    854.0,
+                    467.0,
+                    854.0,
+                    509.0,
+                    292.0,
+                    509.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    838.0,
+                    2086.0,
+                    862.0,
+                    2086.0,
+                    862.0,
+                    2118.0,
+                    838.0,
+                    2118.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1496.0,
+                    1405.0,
+                    1496.0,
+                    1405.0,
+                    1533.0,
+                    294.0,
+                    1533.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1527.0,
+                    1404.0,
+                    1527.0,
+                    1404.0,
+                    1564.0,
+                    292.0,
+                    1564.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1558.0,
+                    296.0,
+                    1558.0,
+                    296.0,
+                    1596.0,
+                    292.0,
+                    1596.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    317.0,
+                    1558.0,
+                    419.0,
+                    1558.0,
+                    419.0,
+                    1596.0,
+                    317.0,
+                    1596.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    442.0,
+                    1558.0,
+                    996.0,
+                    1558.0,
+                    996.0,
+                    1596.0,
+                    442.0,
+                    1596.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1017.0,
+                    1558.0,
+                    1099.0,
+                    1558.0,
+                    1099.0,
+                    1596.0,
+                    1017.0,
+                    1596.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1168.0,
+                    1558.0,
+                    1404.0,
+                    1558.0,
+                    1404.0,
+                    1596.0,
+                    1168.0,
+                    1596.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1590.0,
+                    1406.0,
+                    1590.0,
+                    1406.0,
+                    1625.0,
+                    294.0,
+                    1625.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1619.0,
+                    352.0,
+                    1619.0,
+                    352.0,
+                    1656.0,
+                    294.0,
+                    1656.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    369.0,
+                    1619.0,
+                    587.0,
+                    1619.0,
+                    587.0,
+                    1656.0,
+                    369.0,
+                    1656.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    615.0,
+                    1619.0,
+                    802.0,
+                    1619.0,
+                    802.0,
+                    1656.0,
+                    615.0,
+                    1656.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    831.0,
+                    1619.0,
+                    1132.0,
+                    1619.0,
+                    1132.0,
+                    1656.0,
+                    831.0,
+                    1656.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1148.0,
+                    1619.0,
+                    1406.0,
+                    1619.0,
+                    1406.0,
+                    1656.0,
+                    1148.0,
+                    1656.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1652.0,
+                    1062.0,
+                    1652.0,
+                    1062.0,
+                    1686.0,
+                    292.0,
+                    1686.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1090.0,
+                    1652.0,
+                    1406.0,
+                    1652.0,
+                    1406.0,
+                    1686.0,
+                    1090.0,
+                    1686.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1680.0,
+                    297.0,
+                    1680.0,
+                    297.0,
+                    1717.0,
+                    291.0,
+                    1717.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    325.0,
+                    1680.0,
+                    682.0,
+                    1680.0,
+                    682.0,
+                    1717.0,
+                    325.0,
+                    1717.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    698.0,
+                    1680.0,
+                    1407.0,
+                    1680.0,
+                    1407.0,
+                    1717.0,
+                    698.0,
+                    1717.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1712.0,
+                    437.0,
+                    1712.0,
+                    437.0,
+                    1748.0,
+                    294.0,
+                    1748.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    453.0,
+                    1712.0,
+                    1407.0,
+                    1712.0,
+                    1407.0,
+                    1748.0,
+                    453.0,
+                    1748.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1743.0,
+                    1406.0,
+                    1743.0,
+                    1406.0,
+                    1778.0,
+                    294.0,
+                    1778.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1770.0,
+                    599.0,
+                    1770.0,
+                    599.0,
+                    1812.0,
+                    294.0,
+                    1812.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1131.0,
+                    1408.0,
+                    1131.0,
+                    1408.0,
+                    1165.0,
+                    294.0,
+                    1165.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    289.0,
+                    1158.0,
+                    823.0,
+                    1158.0,
+                    823.0,
+                    1198.0,
+                    289.0,
+                    1198.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    854.0,
+                    1158.0,
+                    1216.0,
+                    1158.0,
+                    1216.0,
+                    1198.0,
+                    854.0,
+                    1198.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1246.0,
+                    1158.0,
+                    1274.0,
+                    1158.0,
+                    1274.0,
+                    1198.0,
+                    1246.0,
+                    1198.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1362.0,
+                    1158.0,
+                    1406.0,
+                    1158.0,
+                    1406.0,
+                    1198.0,
+                    1362.0,
+                    1198.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1191.0,
+                    920.0,
+                    1191.0,
+                    920.0,
+                    1228.0,
+                    293.0,
+                    1228.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    947.0,
+                    1191.0,
+                    1152.0,
+                    1191.0,
+                    1152.0,
+                    1228.0,
+                    947.0,
+                    1228.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1182.0,
+                    1191.0,
+                    1405.0,
+                    1191.0,
+                    1405.0,
+                    1228.0,
+                    1182.0,
+                    1228.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1223.0,
+                    618.0,
+                    1223.0,
+                    618.0,
+                    1258.0,
+                    294.0,
+                    1258.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    644.0,
+                    1223.0,
+                    1063.0,
+                    1223.0,
+                    1063.0,
+                    1258.0,
+                    644.0,
+                    1258.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1094.0,
+                    1223.0,
+                    1406.0,
+                    1223.0,
+                    1406.0,
+                    1258.0,
+                    1094.0,
+                    1258.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1249.0,
+                    1405.0,
+                    1249.0,
+                    1405.0,
+                    1290.0,
+                    292.0,
+                    1290.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1282.0,
+                    1405.0,
+                    1282.0,
+                    1405.0,
+                    1319.0,
+                    293.0,
+                    1319.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1313.0,
+                    679.0,
+                    1313.0,
+                    679.0,
+                    1352.0,
+                    294.0,
+                    1352.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    929.0,
+                    1404.0,
+                    929.0,
+                    1404.0,
+                    966.0,
+                    294.0,
+                    966.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    961.0,
+                    1404.0,
+                    961.0,
+                    1404.0,
+                    996.0,
+                    294.0,
+                    996.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    985.0,
+                    348.0,
+                    985.0,
+                    348.0,
+                    1031.0,
+                    291.0,
+                    1031.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    374.0,
+                    985.0,
+                    1118.0,
+                    985.0,
+                    1118.0,
+                    1031.0,
+                    374.0,
+                    1031.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1149.0,
+                    985.0,
+                    1209.0,
+                    985.0,
+                    1209.0,
+                    1031.0,
+                    1149.0,
+                    1031.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1398.0,
+                    985.0,
+                    1408.0,
+                    985.0,
+                    1408.0,
+                    1031.0,
+                    1398.0,
+                    1031.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1022.0,
+                    1406.0,
+                    1022.0,
+                    1406.0,
+                    1059.0,
+                    292.0,
+                    1059.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1054.0,
+                    1406.0,
+                    1054.0,
+                    1406.0,
+                    1088.0,
+                    292.0,
+                    1088.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1086.0,
+                    379.0,
+                    1086.0,
+                    379.0,
+                    1119.0,
+                    294.0,
+                    1119.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1820.0,
+                    1406.0,
+                    1820.0,
+                    1406.0,
+                    1854.0,
+                    295.0,
+                    1854.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1850.0,
+                    486.0,
+                    1850.0,
+                    486.0,
+                    1885.0,
+                    295.0,
+                    1885.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    516.0,
+                    1850.0,
+                    683.0,
+                    1850.0,
+                    683.0,
+                    1885.0,
+                    516.0,
+                    1885.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    698.0,
+                    1850.0,
+                    726.0,
+                    1850.0,
+                    726.0,
+                    1885.0,
+                    698.0,
+                    1885.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    741.0,
+                    1850.0,
+                    932.0,
+                    1850.0,
+                    932.0,
+                    1885.0,
+                    741.0,
+                    1885.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    958.0,
+                    1850.0,
+                    1407.0,
+                    1850.0,
+                    1407.0,
+                    1885.0,
+                    958.0,
+                    1885.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1878.0,
+                    558.0,
+                    1878.0,
+                    558.0,
+                    1918.0,
+                    292.0,
+                    1918.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    813.0,
+                    1878.0,
+                    890.0,
+                    1878.0,
+                    890.0,
+                    1918.0,
+                    813.0,
+                    1918.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1145.0,
+                    1878.0,
+                    1406.0,
+                    1878.0,
+                    1406.0,
+                    1918.0,
+                    1145.0,
+                    1918.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1911.0,
+                    357.0,
+                    1911.0,
+                    357.0,
+                    1946.0,
+                    295.0,
+                    1946.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    380.0,
+                    1911.0,
+                    579.0,
+                    1911.0,
+                    579.0,
+                    1946.0,
+                    380.0,
+                    1946.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    682.0,
+                    1911.0,
+                    926.0,
+                    1911.0,
+                    926.0,
+                    1946.0,
+                    682.0,
+                    1946.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    952.0,
+                    1911.0,
+                    1405.0,
+                    1911.0,
+                    1405.0,
+                    1946.0,
+                    952.0,
+                    1946.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1942.0,
+                    1406.0,
+                    1942.0,
+                    1406.0,
+                    1976.0,
+                    295.0,
+                    1976.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1969.0,
+                    466.0,
+                    1969.0,
+                    466.0,
+                    2008.0,
+                    292.0,
+                    2008.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    699.0,
+                    1969.0,
+                    1407.0,
+                    1969.0,
+                    1407.0,
+                    2008.0,
+                    699.0,
+                    2008.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    2000.0,
+                    1250.0,
+                    2000.0,
+                    1250.0,
+                    2037.0,
+                    294.0,
+                    2037.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    227.0,
+                    1406.0,
+                    227.0,
+                    1406.0,
+                    264.0,
+                    296.0,
+                    264.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    263.0,
+                    393.0,
+                    263.0,
+                    393.0,
+                    300.0,
+                    295.0,
+                    300.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    481.0,
+                    263.0,
+                    845.0,
+                    263.0,
+                    845.0,
+                    300.0,
+                    481.0,
+                    300.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    933.0,
+                    263.0,
+                    943.0,
+                    263.0,
+                    943.0,
+                    300.0,
+                    933.0,
+                    300.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1041.0,
+                    263.0,
+                    1406.0,
+                    263.0,
+                    1406.0,
+                    300.0,
+                    1041.0,
+                    300.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    359.0,
+                    295.0,
+                    718.0,
+                    295.0,
+                    718.0,
+                    332.0,
+                    359.0,
+                    332.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    735.0,
+                    295.0,
+                    744.0,
+                    295.0,
+                    744.0,
+                    332.0,
+                    735.0,
+                    332.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    853.0,
+                    295.0,
+                    1099.0,
+                    295.0,
+                    1099.0,
+                    332.0,
+                    853.0,
+                    332.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1115.0,
+                    295.0,
+                    1222.0,
+                    295.0,
+                    1222.0,
+                    332.0,
+                    1115.0,
+                    332.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    322.0,
+                    379.0,
+                    322.0,
+                    379.0,
+                    363.0,
+                    292.0,
+                    363.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    400.0,
+                    322.0,
+                    1116.0,
+                    322.0,
+                    1116.0,
+                    363.0,
+                    400.0,
+                    363.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1292.0,
+                    322.0,
+                    1306.0,
+                    322.0,
+                    1306.0,
+                    363.0,
+                    1292.0,
+                    363.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1404.0,
+                    322.0,
+                    1407.0,
+                    322.0,
+                    1407.0,
+                    363.0,
+                    1404.0,
+                    363.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    356.0,
+                    345.0,
+                    356.0,
+                    345.0,
+                    402.0,
+                    292.0,
+                    402.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    442.0,
+                    356.0,
+                    580.0,
+                    356.0,
+                    580.0,
+                    402.0,
+                    442.0,
+                    402.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    608.0,
+                    356.0,
+                    658.0,
+                    356.0,
+                    658.0,
+                    402.0,
+                    608.0,
+                    402.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    686.0,
+                    356.0,
+                    788.0,
+                    356.0,
+                    788.0,
+                    402.0,
+                    686.0,
+                    402.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    852.0,
+                    356.0,
+                    1374.0,
+                    356.0,
+                    1374.0,
+                    402.0,
+                    852.0,
+                    402.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1401.0,
+                    356.0,
+                    1407.0,
+                    356.0,
+                    1407.0,
+                    402.0,
+                    1401.0,
+                    402.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    387.0,
+                    442.0,
+                    387.0,
+                    442.0,
+                    432.0,
+                    293.0,
+                    432.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1358.0,
+                    1405.0,
+                    1358.0,
+                    1405.0,
+                    1396.0,
+                    292.0,
+                    1396.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1387.0,
+                    1405.0,
+                    1387.0,
+                    1405.0,
+                    1430.0,
+                    292.0,
+                    1430.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1421.0,
+                    297.0,
+                    1421.0,
+                    297.0,
+                    1458.0,
+                    294.0,
+                    1458.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    313.0,
+                    1421.0,
+                    546.0,
+                    1421.0,
+                    546.0,
+                    1458.0,
+                    313.0,
+                    1458.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    562.0,
+                    1421.0,
+                    674.0,
+                    1421.0,
+                    674.0,
+                    1458.0,
+                    562.0,
+                    1458.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    702.0,
+                    1421.0,
+                    763.0,
+                    1421.0,
+                    763.0,
+                    1458.0,
+                    702.0,
+                    1458.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1029.0,
+                    1421.0,
+                    1406.0,
+                    1421.0,
+                    1406.0,
+                    1458.0,
+                    1029.0,
+                    1458.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1451.0,
+                    1038.0,
+                    1451.0,
+                    1038.0,
+                    1489.0,
+                    292.0,
+                    1489.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    574.0,
+                    539.0,
+                    574.0,
+                    539.0,
+                    616.0,
+                    294.0,
+                    616.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    607.0,
+                    574.0,
+                    615.0,
+                    574.0,
+                    615.0,
+                    616.0,
+                    607.0,
+                    616.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    845.0,
+                    574.0,
+                    1041.0,
+                    574.0,
+                    1041.0,
+                    616.0,
+                    845.0,
+                    616.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1108.0,
+                    574.0,
+                    1409.0,
+                    574.0,
+                    1409.0,
+                    616.0,
+                    1108.0,
+                    616.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    610.0,
+                    896.0,
+                    610.0,
+                    896.0,
+                    644.0,
+                    296.0,
+                    644.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    926.0,
+                    610.0,
+                    997.0,
+                    610.0,
+                    997.0,
+                    644.0,
+                    926.0,
+                    644.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1013.0,
+                    610.0,
+                    1139.0,
+                    610.0,
+                    1139.0,
+                    644.0,
+                    1013.0,
+                    644.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1168.0,
+                    610.0,
+                    1406.0,
+                    610.0,
+                    1406.0,
+                    644.0,
+                    1168.0,
+                    644.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    640.0,
+                    360.0,
+                    640.0,
+                    360.0,
+                    673.0,
+                    292.0,
+                    673.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    853.0,
+                    1408.0,
+                    853.0,
+                    1408.0,
+                    889.0,
+                    295.0,
+                    889.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    884.0,
+                    1408.0,
+                    884.0,
+                    1408.0,
+                    920.0,
+                    295.0,
+                    920.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    528.0,
+                    1119.0,
+                    528.0,
+                    1119.0,
+                    572.0,
+                    295.0,
+                    572.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    785.0,
+                    370.0,
+                    785.0,
+                    370.0,
+                    830.0,
+                    295.0,
+                    830.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    399.0,
+                    785.0,
+                    774.0,
+                    785.0,
+                    774.0,
+                    830.0,
+                    399.0,
+                    830.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    943.0,
+                    785.0,
+                    994.0,
+                    785.0,
+                    994.0,
+                    830.0,
+                    943.0,
+                    830.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1038.0,
+                    785.0,
+                    1047.0,
+                    785.0,
+                    1047.0,
+                    830.0,
+                    1038.0,
+                    830.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 3,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    464,
+                    1406,
+                    464,
+                    1406,
+                    564,
+                    298,
+                    564
+                ],
+                "score": 0.969
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    228,
+                    1405,
+                    228,
+                    1405,
+                    324,
+                    297,
+                    324
+                ],
+                "score": 0.968
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    402,
+                    1718,
+                    1297,
+                    1718,
+                    1297,
+                    1909,
+                    402,
+                    1909
+                ],
+                "score": 0.968
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    350,
+                    579,
+                    1349,
+                    579,
+                    1349,
+                    1028,
+                    350,
+                    1028
+                ],
+                "score": 0.967
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    300,
+                    1616,
+                    1404,
+                    1616,
+                    1404,
+                    1703,
+                    300,
+                    1703
+                ],
+                "score": 0.967
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    565,
+                    1207,
+                    1131,
+                    1207,
+                    1131,
+                    1303,
+                    565,
+                    1303
+                ],
+                "score": 0.954
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1114,
+                    1399,
+                    1114,
+                    1399,
+                    1191,
+                    297,
+                    1191
+                ],
+                "score": 0.949
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1516,
+                    1404,
+                    1516,
+                    1404,
+                    1581,
+                    297,
+                    1581
+                ],
+                "score": 0.939
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1378,
+                    1088,
+                    1378,
+                    1088,
+                    1437,
+                    297,
+                    1437
+                ],
+                "score": 0.933
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    764,
+                    1456,
+                    934,
+                    1456,
+                    934,
+                    1504,
+                    764,
+                    1504
+                ],
+                "score": 0.93
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    1046,
+                    1298,
+                    1046,
+                    1298,
+                    1095,
+                    295,
+                    1095
+                ],
+                "score": 0.925
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    1332,
+                    1202,
+                    1332,
+                    1202,
+                    1369,
+                    295,
+                    1369
+                ],
+                "score": 0.925
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    74,
+                    817,
+                    74,
+                    817,
+                    106,
+                    298,
+                    106
+                ],
+                "score": 0.916
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    297,
+                    360,
+                    886,
+                    360,
+                    886,
+                    393,
+                    297,
+                    393
+                ],
+                "score": 0.909
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    416,
+                    1344,
+                    416,
+                    1344,
+                    453,
+                    295,
+                    453
+                ],
+                "score": 0.903
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1364,
+                    1467,
+                    1401,
+                    1467,
+                    1401,
+                    1499,
+                    1364,
+                    1499
+                ],
+                "score": 0.882
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    289,
+                    1924,
+                    1285,
+                    1924,
+                    1285,
+                    1974,
+                    289,
+                    1974
+                ],
+                "score": 0.881
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1364,
+                    942,
+                    1402,
+                    942,
+                    1402,
+                    973,
+                    1364,
+                    973
+                ],
+                "score": 0.866
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1364,
+                    1239,
+                    1401,
+                    1239,
+                    1401,
+                    1270,
+                    1364,
+                    1270
+                ],
+                "score": 0.864
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    1374,
+                    1999,
+                    1404,
+                    1999,
+                    1404,
+                    2028,
+                    1374,
+                    2028
+                ],
+                "score": 0.779
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    840,
+                    2087,
+                    860,
+                    2087,
+                    860,
+                    2113,
+                    840,
+                    2113
+                ],
+                "score": 0.742
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    285,
+                    1986,
+                    1324,
+                    1986,
+                    1324,
+                    2044,
+                    285,
+                    2044
+                ],
+                "score": 0.529
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    285,
+                    1986,
+                    1324,
+                    1986,
+                    1324,
+                    2044,
+                    285,
+                    2044
+                ],
+                "score": 0.502
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    840,
+                    2087,
+                    860,
+                    2087,
+                    860,
+                    2113,
+                    840,
+                    2113
+                ],
+                "score": 0.142
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    703,
+                    527,
+                    933,
+                    527,
+                    933,
+                    561,
+                    703,
+                    561
+                ],
+                "score": 0.94,
+                "latex": "V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } )"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    346,
+                    582,
+                    1348,
+                    582,
+                    1348,
+                    1034,
+                    346,
+                    1034
+                ],
+                "score": 0.94,
+                "latex": "\\begin{array} { r l } & { \\quad V ^ { * } ( s _ { t } ) - V ^ { \\pi } ( s _ { t } ) } \\\\ & { = V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) + Q ^ { * } ( s _ { t } , a _ { t } ) - V ^ { \\pi } ( s _ { t } ) } \\\\ & { = V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) + \\gamma \\mathbb { P } ( V ^ { * } - V ^ { \\pi } ) ( s _ { t } , \\pi _ { t } ( s _ { t } ) ) } \\\\ & { = V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) + \\gamma \\sum _ { s + 1 } ^ { \\infty } p ( s _ { t + 1 } | s _ { t } , \\pi _ { t } ( s _ { t } ) ) \\cdot [ V ^ { * } ( s _ { t + 1 } ) - Q ^ { * } ( s _ { t + 1 } , a _ { t + 1 } ) ] + } \\\\ & { \\quad \\Big . \\Big . \\Big . \\Big . \\Big . \\Big . } \\\\ & { \\quad \\quad \\Big .  \\gamma _ { s + 1 , s ^ { * } + 2 } \\mathrm { ~ } p ( s _ { t + 2 } | s _ { t + 1 } , \\pi _ { t + 1 } ( s _ { t + 1 } ) ) \\cdot p ( s _ { t + 1 } | s _ { t } , \\pi _ { t } ( s _ { t } ) ) \\big [ V ^ { * } ( s _ { t + 2 } ) - Q ^ { * } ( s _ { t + 2 } , a _ { t + 2 } ) \\Big ] } \\\\ & { \\quad \\quad \\cdot \\dots } \\\\ & { \\le \\epsilon _ { 2 } + \\displaystyle \\sum _ { s ^ { \\prime } = s ^ { \\prime } } p ( t r a _ { t } ) \\cdot [ \\frac { n - 1 } { \\lambda _ { 2 } } \\gamma ^ { 2 } \\Delta _ { t + 2 } ] , } \\\\ & { \\quad \\quad \\pi _ { s \\lambda ^ { ( 2 ) } ( L ) } ^ { R , a } } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    738,
+                    1046,
+                    847,
+                    1046,
+                    847,
+                    1096,
+                    738,
+                    1096
+                ],
+                "score": 0.94,
+                "latex": "\\frac { \\gamma ^ { R } } { 1 - \\gamma } \\leq \\epsilon _ { 2 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    863,
+                    1924,
+                    1125,
+                    1924,
+                    1125,
+                    1975,
+                    863,
+                    1975
+                ],
+                "score": 0.93,
+                "latex": "\\begin{array} { r } { \\sum _ { i = 1 } ^ { \\infty } \\frac { \\gamma ^ { i - 1 } } { i } = \\frac { 1 } { \\gamma } \\ln \\frac { 1 } { 1 - \\gamma } } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1124,
+                    1115,
+                    1292,
+                    1115,
+                    1292,
+                    1157,
+                    1124,
+                    1157
+                ],
+                "score": 0.93,
+                "latex": "\\left( \\Delta _ { t ^ { \\prime } } \\right) _ { t \\leq t ^ { \\prime } < t + R }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1269,
+                    1616,
+                    1404,
+                    1616,
+                    1404,
+                    1660,
+                    1269,
+                    1660
+                ],
+                "score": 0.93,
+                "latex": "E [ X _ { t } ^ { ( i ) } ] \\ \\leq"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    564,
+                    1206,
+                    1134,
+                    1206,
+                    1134,
+                    1303,
+                    564,
+                    1303
+                ],
+                "score": 0.93,
+                "latex": "V ^ { \\ast } ( s _ { t } ) - V ^ { \\pi _ { t } } ( s _ { t } ) \\leq \\epsilon _ { 2 } + E _ { t r a j } \\left[ \\sum _ { i = 1 } ^ { R } \\gamma ^ { i - 1 } X _ { t } ^ { ( i ) } \\right] ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    297,
+                    525,
+                    602,
+                    525,
+                    602,
+                    568,
+                    297,
+                    568
+                ],
+                "score": 0.93,
+                "latex": "\\begin{array} { r } { R : = \\lceil \\ln \\frac { 1 } { \\epsilon _ { 2 } ( 1 - \\gamma ) } / ( 1 - \\gamma ) \\rceil } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    1656,
+                    458,
+                    1656,
+                    458,
+                    1702,
+                    298,
+                    1702
+                ],
+                "score": 0.93,
+                "latex": "E [ X _ { t } ^ { ( 2 ^ { \\lfloor \\log _ { 2 } i \\rfloor } ) } ]"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    502,
+                    1617,
+                    557,
+                    1617,
+                    557,
+                    1659,
+                    502,
+                    1659
+                ],
+                "score": 0.93,
+                "latex": "X _ { t } ^ { ( i ) }"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    401,
+                    1716,
+                    1296,
+                    1716,
+                    1296,
+                    1911,
+                    401,
+                    1911
+                ],
+                "score": 0.93,
+                "latex": "\\begin{array} { r l } & { E \\left[ \\displaystyle \\sum _ { i = 1 } ^ { R } \\gamma ^ { i - 1 } X _ { t } ^ { ( i ) } \\right] = \\displaystyle \\sum _ { i = 1 } ^ { R } \\gamma ^ { i - 1 } E [ X _ { t } ^ { ( i ) } ] \\leq \\displaystyle \\sum _ { i = 1 } ^ { R } \\gamma ^ { i - 1 } E [ X _ { t } ^ { ( 2 ^ { \\lfloor \\log _ { 2 } i \\rfloor } ) } ] } \\\\ & { \\leq \\displaystyle \\sum _ { i = 1 } ^ { R } \\gamma ^ { i - 1 } 2 ^ { - \\lfloor \\log _ { 2 } i \\rfloor - 2 } \\epsilon _ { 2 } \\left( \\ln \\frac { 1 } { 1 - \\gamma } \\right) ^ { - 1 } \\leq \\displaystyle \\sum _ { i = 1 } ^ { R } \\frac { \\gamma ^ { i - 1 } } { i } \\epsilon _ { 2 } \\left( \\ln \\frac { 1 } { 1 - \\gamma } \\right) ^ { - 1 } \\leq 2 \\epsilon _ { 2 } , } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    586,
+                    1153,
+                    753,
+                    1153,
+                    753,
+                    1192,
+                    586,
+                    1192
+                ],
+                "score": 0.93,
+                "latex": "\\left( \\Delta _ { t ^ { \\prime } } \\right) _ { t \\leq t ^ { \\prime } < t + R }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    500,
+                    1376,
+                    783,
+                    1376,
+                    783,
+                    1438,
+                    500,
+                    1438
+                ],
+                "score": 0.92,
+                "latex": "\\begin{array} { r } { \\xi _ { i } : = \\frac { 1 } { 2 ^ { i + 2 } } \\epsilon _ { 2 } \\left( \\ln \\frac { 1 } { 1 - \\gamma } \\right) ^ { - 1 } } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1093,
+                    1334,
+                    1195,
+                    1334,
+                    1195,
+                    1368,
+                    1093,
+                    1368
+                ],
+                "score": 0.92,
+                "latex": "\\epsilon _ { 2 } = \\epsilon / 3"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1235,
+                    499,
+                    1316,
+                    499,
+                    1316,
+                    528,
+                    1235,
+                    528
+                ],
+                "score": 0.91,
+                "latex": "\\epsilon _ { 2 } > 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    732,
+                    1667,
+                    881,
+                    1667,
+                    881,
+                    1702,
+                    732,
+                    1702
+                ],
+                "score": 0.91,
+                "latex": "1 / 2 < \\gamma < 1"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1291,
+                    1516,
+                    1404,
+                    1516,
+                    1404,
+                    1551,
+                    1291,
+                    1551
+                ],
+                "score": 0.91,
+                "latex": "V ^ { \\ast } ( s _ { t } ) -"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    1548,
+                    438,
+                    1548,
+                    438,
+                    1581,
+                    298,
+                    1581
+                ],
+                "score": 0.91,
+                "latex": "V ^ { \\pi _ { t } } ( s _ { t } ) \\leq \\epsilon"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1346,
+                    1110,
+                    1400,
+                    1110,
+                    1400,
+                    1151,
+                    1346,
+                    1151
+                ],
+                "score": 0.91,
+                "latex": "X _ { t } ^ { ( i ) }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1176,
+                    1933,
+                    1273,
+                    1933,
+                    1273,
+                    1969,
+                    1176,
+                    1969
+                ],
+                "score": 0.91,
+                "latex": "\\gamma > 1 / 2"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    763,
+                    1452,
+                    936,
+                    1452,
+                    936,
+                    1502,
+                    763,
+                    1502
+                ],
+                "score": 0.9,
+                "latex": "E [ X _ { t } ^ { ( 2 ^ { i } ) } ] \\leq \\xi _ { i } ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    880,
+                    1392,
+                    1077,
+                    1392,
+                    1077,
+                    1428,
+                    880,
+                    1428
+                ],
+                "score": 0.88,
+                "latex": "0 \\leq i \\leq \\lfloor \\log _ { 2 } R \\rfloor"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    972,
+                    528,
+                    1007,
+                    528,
+                    1007,
+                    558,
+                    972,
+                    558
+                ],
+                "score": 0.88,
+                "latex": "\\Delta _ { t }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    663,
+                    1987,
+                    1322,
+                    1987,
+                    1322,
+                    2045,
+                    663,
+                    2045
+                ],
+                "score": 0.87,
+                "latex": "\\begin{array} { r } { V ^ { \\ast } ( s _ { t } ) - V ^ { \\pi _ { t } } ( s _ { t } ) \\leq \\epsilon _ { 2 } + E \\left[ \\sum _ { i = 1 } ^ { R } \\gamma ^ { i - 1 } X _ { t } ^ { ( i ) } \\right] \\leq 3 \\epsilon _ { 2 } = \\epsilon . } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    840,
+                    1124,
+                    866,
+                    1124,
+                    866,
+                    1149,
+                    840,
+                    1149
+                ],
+                "score": 0.85,
+                "latex": "s _ { t }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    959,
+                    1523,
+                    988,
+                    1523,
+                    988,
+                    1548,
+                    959,
+                    1548
+                ],
+                "score": 0.85,
+                "latex": "\\pi _ { t }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    628,
+                    502,
+                    656,
+                    502,
+                    656,
+                    528,
+                    628,
+                    528
+                ],
+                "score": 0.85,
+                "latex": "\\pi _ { t }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1268,
+                    1059,
+                    1290,
+                    1059,
+                    1290,
+                    1084,
+                    1268,
+                    1084
+                ],
+                "score": 0.84,
+                "latex": "R"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    425,
+                    471,
+                    451,
+                    471,
+                    451,
+                    497,
+                    425,
+                    497
+                ],
+                "score": 0.83,
+                "latex": "s _ { t }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1213,
+                    1524,
+                    1239,
+                    1524,
+                    1239,
+                    1548,
+                    1213,
+                    1548
+                ],
+                "score": 0.83,
+                "latex": "s _ { t }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1150,
+                    473,
+                    1175,
+                    473,
+                    1175,
+                    497,
+                    1150,
+                    497
+                ],
+                "score": 0.83,
+                "latex": "s _ { t }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    665,
+                    1119,
+                    689,
+                    1119,
+                    689,
+                    1145,
+                    665,
+                    1145
+                ],
+                "score": 0.82,
+                "latex": "R"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    837,
+                    468,
+                    861,
+                    468,
+                    861,
+                    494,
+                    837,
+                    494
+                ],
+                "score": 0.8,
+                "latex": "R"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1009,
+                    1338,
+                    1023,
+                    1338,
+                    1023,
+                    1362,
+                    1009,
+                    1362
+                ],
+                "score": 0.77,
+                "latex": "t"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    734,
+                    1341,
+                    748,
+                    1341,
+                    748,
+                    1362,
+                    734,
+                    1362
+                ],
+                "score": 0.76,
+                "latex": "\\epsilon"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    962,
+                    500,
+                    975,
+                    500,
+                    975,
+                    525,
+                    962,
+                    525
+                ],
+                "score": 0.75,
+                "latex": "t"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    371,
+                    1156,
+                    384,
+                    1156,
+                    384,
+                    1181,
+                    371,
+                    1181
+                ],
+                "score": 0.74,
+                "latex": "i"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1094,
+                    1628,
+                    1108,
+                    1628,
+                    1108,
+                    1653,
+                    1094,
+                    1653
+                ],
+                "score": 0.73,
+                "latex": "i"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1014,
+                    503,
+                    1029,
+                    503,
+                    1029,
+                    524,
+                    1014,
+                    524
+                ],
+                "score": 0.72,
+                "latex": "\\epsilon"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1321,
+                    423,
+                    1334,
+                    423,
+                    1334,
+                    447,
+                    1321,
+                    447
+                ],
+                "score": 0.71,
+                "latex": "t"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    551,
+                    1520,
+                    566,
+                    1520,
+                    566,
+                    1545,
+                    551,
+                    1545
+                ],
+                "score": 0.7,
+                "latex": "^ { l }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1017,
+                    1524,
+                    1031,
+                    1524,
+                    1031,
+                    1545,
+                    1017,
+                    1545
+                ],
+                "score": 0.68,
+                "latex": "\\epsilon"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    354,
+                    903,
+                    816,
+                    903,
+                    816,
+                    1028,
+                    354,
+                    1028
+                ],
+                "score": 0.68,
+                "latex": "\\leq \\epsilon _ { 2 } + \\sum _ { \\stackrel { t r a j \\in \\epsilon } { \\mathrm { T R A J } ( R ) } } p ( t r a j ) \\cdot \\left[ \\sum _ { j = 0 } ^ { R - 1 } \\gamma ^ { j } \\Delta _ { t + j } \\right] ,"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    711,
+                    368,
+                    725,
+                    368,
+                    725,
+                    389,
+                    711,
+                    389
+                ],
+                "score": 0.67,
+                "latex": "\\epsilon"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    568,
+                    468,
+                    608,
+                    468,
+                    608,
+                    498,
+                    568,
+                    498
+                ],
+                "score": 0.66,
+                "latex": "( R )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1046,
+                    427,
+                    1059,
+                    427,
+                    1059,
+                    447,
+                    1046,
+                    447
+                ],
+                "score": 0.65,
+                "latex": "\\epsilon"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    268,
+                    312,
+                    268,
+                    312,
+                    289,
+                    298,
+                    289
+                ],
+                "score": 0.64,
+                "latex": "\\epsilon"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    822,
+                    1521,
+                    836,
+                    1521,
+                    836,
+                    1546,
+                    822,
+                    1546
+                ],
+                "score": 0.51,
+                "latex": "t"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    72.0,
+                    817.0,
+                    72.0,
+                    817.0,
+                    109.0,
+                    295.0,
+                    109.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    360.0,
+                    710.0,
+                    360.0,
+                    710.0,
+                    396.0,
+                    295.0,
+                    396.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    726.0,
+                    360.0,
+                    887.0,
+                    360.0,
+                    887.0,
+                    396.0,
+                    726.0,
+                    396.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1380.0,
+                    2004.0,
+                    1402.0,
+                    2004.0,
+                    1402.0,
+                    2027.0,
+                    1380.0,
+                    2027.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    839.0,
+                    2086.0,
+                    860.0,
+                    2086.0,
+                    860.0,
+                    2119.0,
+                    839.0,
+                    2119.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    839.0,
+                    2086.0,
+                    860.0,
+                    2086.0,
+                    860.0,
+                    2119.0,
+                    839.0,
+                    2119.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    461.0,
+                    424.0,
+                    461.0,
+                    424.0,
+                    504.0,
+                    292.0,
+                    504.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    452.0,
+                    461.0,
+                    567.0,
+                    461.0,
+                    567.0,
+                    504.0,
+                    452.0,
+                    504.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    609.0,
+                    461.0,
+                    836.0,
+                    461.0,
+                    836.0,
+                    504.0,
+                    609.0,
+                    504.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    862.0,
+                    461.0,
+                    1149.0,
+                    461.0,
+                    1149.0,
+                    504.0,
+                    862.0,
+                    504.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1176.0,
+                    461.0,
+                    1406.0,
+                    461.0,
+                    1406.0,
+                    504.0,
+                    1176.0,
+                    504.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    496.0,
+                    627.0,
+                    496.0,
+                    627.0,
+                    531.0,
+                    293.0,
+                    531.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    657.0,
+                    496.0,
+                    961.0,
+                    496.0,
+                    961.0,
+                    531.0,
+                    657.0,
+                    531.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    976.0,
+                    496.0,
+                    1013.0,
+                    496.0,
+                    1013.0,
+                    531.0,
+                    976.0,
+                    531.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1030.0,
+                    496.0,
+                    1234.0,
+                    496.0,
+                    1234.0,
+                    531.0,
+                    1030.0,
+                    531.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1317.0,
+                    496.0,
+                    1404.0,
+                    496.0,
+                    1404.0,
+                    531.0,
+                    1317.0,
+                    531.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    522.0,
+                    296.0,
+                    522.0,
+                    296.0,
+                    573.0,
+                    292.0,
+                    573.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    603.0,
+                    522.0,
+                    702.0,
+                    522.0,
+                    702.0,
+                    573.0,
+                    603.0,
+                    573.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    934.0,
+                    522.0,
+                    971.0,
+                    522.0,
+                    971.0,
+                    573.0,
+                    934.0,
+                    573.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1008.0,
+                    522.0,
+                    1129.0,
+                    522.0,
+                    1129.0,
+                    573.0,
+                    1008.0,
+                    573.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    229.0,
+                    1405.0,
+                    229.0,
+                    1405.0,
+                    264.0,
+                    295.0,
+                    264.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    313.0,
+                    261.0,
+                    1405.0,
+                    261.0,
+                    1405.0,
+                    296.0,
+                    313.0,
+                    296.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    291.0,
+                    465.0,
+                    291.0,
+                    465.0,
+                    323.0,
+                    295.0,
+                    323.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    288.0,
+                    1609.0,
+                    501.0,
+                    1609.0,
+                    501.0,
+                    1667.0,
+                    288.0,
+                    1667.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    558.0,
+                    1609.0,
+                    1093.0,
+                    1609.0,
+                    1093.0,
+                    1667.0,
+                    558.0,
+                    1667.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1109.0,
+                    1609.0,
+                    1268.0,
+                    1609.0,
+                    1268.0,
+                    1667.0,
+                    1109.0,
+                    1667.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1405.0,
+                    1609.0,
+                    1409.0,
+                    1609.0,
+                    1409.0,
+                    1667.0,
+                    1405.0,
+                    1667.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    275.0,
+                    1635.0,
+                    297.0,
+                    1635.0,
+                    297.0,
+                    1719.0,
+                    275.0,
+                    1719.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    459.0,
+                    1635.0,
+                    731.0,
+                    1635.0,
+                    731.0,
+                    1719.0,
+                    459.0,
+                    1719.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    882.0,
+                    1635.0,
+                    910.0,
+                    1635.0,
+                    910.0,
+                    1719.0,
+                    882.0,
+                    1719.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    288.0,
+                    1107.0,
+                    664.0,
+                    1107.0,
+                    664.0,
+                    1163.0,
+                    288.0,
+                    1163.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    690.0,
+                    1107.0,
+                    839.0,
+                    1107.0,
+                    839.0,
+                    1163.0,
+                    690.0,
+                    1163.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    867.0,
+                    1107.0,
+                    1123.0,
+                    1107.0,
+                    1123.0,
+                    1163.0,
+                    867.0,
+                    1163.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1293.0,
+                    1107.0,
+                    1345.0,
+                    1107.0,
+                    1345.0,
+                    1163.0,
+                    1293.0,
+                    1163.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1401.0,
+                    1107.0,
+                    1405.0,
+                    1107.0,
+                    1405.0,
+                    1163.0,
+                    1401.0,
+                    1163.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1148.0,
+                    370.0,
+                    1148.0,
+                    370.0,
+                    1197.0,
+                    292.0,
+                    1197.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    385.0,
+                    1148.0,
+                    585.0,
+                    1148.0,
+                    585.0,
+                    1197.0,
+                    385.0,
+                    1197.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    754.0,
+                    1148.0,
+                    1118.0,
+                    1148.0,
+                    1118.0,
+                    1197.0,
+                    754.0,
+                    1197.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1510.0,
+                    550.0,
+                    1510.0,
+                    550.0,
+                    1556.0,
+                    292.0,
+                    1556.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    567.0,
+                    1510.0,
+                    821.0,
+                    1510.0,
+                    821.0,
+                    1556.0,
+                    567.0,
+                    1556.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    837.0,
+                    1510.0,
+                    958.0,
+                    1510.0,
+                    958.0,
+                    1556.0,
+                    837.0,
+                    1556.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    989.0,
+                    1510.0,
+                    1016.0,
+                    1510.0,
+                    1016.0,
+                    1556.0,
+                    989.0,
+                    1556.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1032.0,
+                    1510.0,
+                    1212.0,
+                    1510.0,
+                    1212.0,
+                    1556.0,
+                    1032.0,
+                    1556.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1240.0,
+                    1510.0,
+                    1290.0,
+                    1510.0,
+                    1290.0,
+                    1556.0,
+                    1240.0,
+                    1556.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1539.0,
+                    297.0,
+                    1539.0,
+                    297.0,
+                    1588.0,
+                    293.0,
+                    1588.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    439.0,
+                    1539.0,
+                    454.0,
+                    1539.0,
+                    454.0,
+                    1588.0,
+                    439.0,
+                    1588.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    286.0,
+                    1373.0,
+                    499.0,
+                    1373.0,
+                    499.0,
+                    1440.0,
+                    286.0,
+                    1440.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    784.0,
+                    1373.0,
+                    879.0,
+                    1373.0,
+                    879.0,
+                    1440.0,
+                    784.0,
+                    1440.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1078.0,
+                    1373.0,
+                    1096.0,
+                    1373.0,
+                    1096.0,
+                    1440.0,
+                    1078.0,
+                    1440.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1026.0,
+                    737.0,
+                    1026.0,
+                    737.0,
+                    1115.0,
+                    292.0,
+                    1115.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    848.0,
+                    1026.0,
+                    1267.0,
+                    1026.0,
+                    1267.0,
+                    1115.0,
+                    848.0,
+                    1115.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1291.0,
+                    1026.0,
+                    1317.0,
+                    1026.0,
+                    1317.0,
+                    1115.0,
+                    1291.0,
+                    1115.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1329.0,
+                    733.0,
+                    1329.0,
+                    733.0,
+                    1374.0,
+                    292.0,
+                    1374.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    749.0,
+                    1329.0,
+                    1008.0,
+                    1329.0,
+                    1008.0,
+                    1374.0,
+                    749.0,
+                    1374.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1024.0,
+                    1329.0,
+                    1092.0,
+                    1329.0,
+                    1092.0,
+                    1374.0,
+                    1024.0,
+                    1374.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1196.0,
+                    1329.0,
+                    1207.0,
+                    1329.0,
+                    1207.0,
+                    1374.0,
+                    1196.0,
+                    1374.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    412.0,
+                    1045.0,
+                    412.0,
+                    1045.0,
+                    459.0,
+                    292.0,
+                    459.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1060.0,
+                    412.0,
+                    1320.0,
+                    412.0,
+                    1320.0,
+                    459.0,
+                    1060.0,
+                    459.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1335.0,
+                    412.0,
+                    1347.0,
+                    412.0,
+                    1347.0,
+                    459.0,
+                    1335.0,
+                    459.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    285.0,
+                    1914.0,
+                    862.0,
+                    1914.0,
+                    862.0,
+                    1988.0,
+                    285.0,
+                    1988.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1126.0,
+                    1914.0,
+                    1175.0,
+                    1914.0,
+                    1175.0,
+                    1988.0,
+                    1126.0,
+                    1988.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1274.0,
+                    1914.0,
+                    1293.0,
+                    1914.0,
+                    1293.0,
+                    1988.0,
+                    1274.0,
+                    1988.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    288.0,
+                    1979.0,
+                    662.0,
+                    1979.0,
+                    662.0,
+                    2048.0,
+                    288.0,
+                    2048.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1323.0,
+                    1979.0,
+                    1334.0,
+                    1979.0,
+                    1334.0,
+                    2048.0,
+                    1323.0,
+                    2048.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 4,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    855,
+                    1406,
+                    855,
+                    1406,
+                    1014,
+                    296,
+                    1014
+                ],
+                "score": 0.977
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1107,
+                    1406,
+                    1107,
+                    1406,
+                    1237,
+                    296,
+                    1237
+                ],
+                "score": 0.976
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    520,
+                    1340,
+                    1177,
+                    1340,
+                    1177,
+                    1425,
+                    520,
+                    1425
+                ],
+                "score": 0.95
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    291,
+                    449,
+                    1408,
+                    449,
+                    1408,
+                    519,
+                    291,
+                    519
+                ],
+                "score": 0.949
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    385,
+                    537,
+                    1310,
+                    537,
+                    1310,
+                    630,
+                    385,
+                    630
+                ],
+                "score": 0.949
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    272,
+                    1408,
+                    272,
+                    1408,
+                    373,
+                    295,
+                    373
+                ],
+                "score": 0.948
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    691,
+                    775,
+                    1007,
+                    775,
+                    1007,
+                    840,
+                    691,
+                    840
+                ],
+                "score": 0.947
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    356,
+                    1716,
+                    1339,
+                    1716,
+                    1339,
+                    1812,
+                    356,
+                    1812
+                ],
+                "score": 0.945
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    293,
+                    1241,
+                    1403,
+                    1241,
+                    1403,
+                    1318,
+                    293,
+                    1318
+                ],
+                "score": 0.945
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1444,
+                    690,
+                    1444,
+                    690,
+                    1480,
+                    299,
+                    1480
+                ],
+                "score": 0.924
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    298,
+                    1050,
+                    536,
+                    1050,
+                    536,
+                    1083,
+                    298,
+                    1083
+                ],
+                "score": 0.92
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    293,
+                    1546,
+                    1402,
+                    1546,
+                    1402,
+                    1616,
+                    293,
+                    1616
+                ],
+                "score": 0.919
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1847,
+                    805,
+                    1847,
+                    805,
+                    1892,
+                    298,
+                    1892
+                ],
+                "score": 0.919
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    73,
+                    817,
+                    73,
+                    817,
+                    106,
+                    298,
+                    106
+                ],
+                "score": 0.918
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    293,
+                    720,
+                    1404,
+                    720,
+                    1404,
+                    758,
+                    293,
+                    758
+                ],
+                "score": 0.918
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    378,
+                    973,
+                    378,
+                    973,
+                    413,
+                    295,
+                    413
+                ],
+                "score": 0.906
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    290,
+                    1914,
+                    1300,
+                    1914,
+                    1300,
+                    1951,
+                    290,
+                    1951
+                ],
+                "score": 0.903
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1503,
+                    1223,
+                    1503,
+                    1223,
+                    1538,
+                    297,
+                    1538
+                ],
+                "score": 0.903
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    227,
+                    939,
+                    227,
+                    939,
+                    264,
+                    297,
+                    264
+                ],
+                "score": 0.901
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    293,
+                    1624,
+                    1349,
+                    1624,
+                    1349,
+                    1662,
+                    293,
+                    1662
+                ],
+                "score": 0.881
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1365,
+                    793,
+                    1400,
+                    793,
+                    1400,
+                    824,
+                    1365,
+                    824
+                ],
+                "score": 0.879
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1364,
+                    1366,
+                    1401,
+                    1366,
+                    1401,
+                    1397,
+                    1364,
+                    1397
+                ],
+                "score": 0.846
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    839,
+                    2088,
+                    859,
+                    2088,
+                    859,
+                    2113,
+                    839,
+                    2113
+                ],
+                "score": 0.815
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    1374,
+                    648,
+                    1403,
+                    648,
+                    1403,
+                    678,
+                    1374,
+                    678
+                ],
+                "score": 0.812
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    296,
+                    1973,
+                    1411,
+                    1973,
+                    1411,
+                    2036,
+                    296,
+                    2036
+                ],
+                "score": 0.812
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    690,
+                    771,
+                    1010,
+                    771,
+                    1010,
+                    840,
+                    690,
+                    840
+                ],
+                "score": 0.93,
+                "latex": "\\eta _ { j } \\mathrm { P r } [ X _ { t } ^ { ( 2 ^ { i } ) } > \\eta _ { j - 1 } ] > \\frac { \\xi _ { i } } { M } ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    914,
+                    723,
+                    1110,
+                    723,
+                    1110,
+                    757,
+                    914,
+                    757
+                ],
+                "score": 0.93,
+                "latex": "0 \\leq i < \\lfloor \\log _ { 2 } R \\rfloor"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    387,
+                    533,
+                    1309,
+                    533,
+                    1309,
+                    632,
+                    387,
+                    632
+                ],
+                "score": 0.93,
+                "latex": "E \\left[ { X _ { t } ^ { ( 2 ^ { i } ) } } \\right] = \\int _ { 0 } ^ { 1 / ( 1 - \\gamma ) } \\operatorname* { P r } \\left[ { X _ { t } ^ { ( 2 ^ { i } ) } } > x \\right] d x \\le \\eta _ { 1 } + \\sum _ { j = 2 } ^ { M } \\eta _ { j } \\operatorname* { P r } [ { X _ { t } ^ { ( 2 ^ { i } ) } } > \\eta _ { j - 1 } ] \\le \\xi _ { i } ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    663,
+                    919,
+                    953,
+                    919,
+                    953,
+                    971,
+                    663,
+                    971
+                ],
+                "score": 0.93,
+                "latex": "\\begin{array} { r } { \\operatorname* { P r } [ X _ { t } ^ { ( 2 ^ { i } ) } > \\eta _ { j - 1 } ] > \\frac { \\xi _ { i } } { M \\eta _ { j } } } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1199,
+                    1972,
+                    1404,
+                    1972,
+                    1404,
+                    2008,
+                    1199,
+                    2008
+                ],
+                "score": 0.93,
+                "latex": "2 ^ { M / 2 - 1 } > ( M + 1 )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    661,
+                    485,
+                    794,
+                    485,
+                    794,
+                    517,
+                    661,
+                    517
+                ],
+                "score": 0.92,
+                "latex": "1 \\leq j \\leq M"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    297,
+                    967,
+                    454,
+                    967,
+                    454,
+                    1014,
+                    297,
+                    1014
+                ],
+                "score": 0.92,
+                "latex": "X _ { t } ^ { ( 2 ^ { i } ) } > \\eta _ { j - 1 }"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    355,
+                    1716,
+                    1342,
+                    1716,
+                    1342,
+                    1810,
+                    355,
+                    1810
+                ],
+                "score": 0.92,
+                "latex": "\\sum _ { t \\ge 1 } w _ { t } ( \\hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) \\le \\frac { C \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\frac { \\sqrt { w S A C \\ell ( C ) } } { ( 1 - \\gamma ) ^ { 2 . 5 } } + \\frac { w S A \\ln C } { ( 1 - \\gamma ) ^ { 3 } } \\ln \\frac { 1 } { ( 1 - \\gamma ) \\epsilon _ { 1 } } \\right) ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1001,
+                    857,
+                    1080,
+                    857,
+                    1080,
+                    890,
+                    1001,
+                    890
+                ],
+                "score": 0.92,
+                "latex": "( t , i , j )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    536,
+                    1170,
+                    720,
+                    1170,
+                    720,
+                    1208,
+                    536,
+                    1208
+                ],
+                "score": 0.92,
+                "latex": "( \\hat { Q } _ { t } - Q ^ { * } ) ( s , a )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    929,
+                    1973,
+                    1154,
+                    1973,
+                    1154,
+                    2009,
+                    929,
+                    2009
+                ],
+                "score": 0.92,
+                "latex": "\\xi _ { i } \\cdot 2 ^ { M / 2 } \\geq 1 / ( 1 - \\gamma )"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    519,
+                    1333,
+                    1176,
+                    1333,
+                    1176,
+                    1430,
+                    519,
+                    1430
+                ],
+                "score": 0.92,
+                "latex": "\\sum _ { t = 1 } ^ { t = \\infty } I \\left[ B _ { \\eta } ^ { ( t ) } \\right] \\leq \\frac { S A \\ln S A \\ln 1 / \\delta } { \\eta ^ { 2 } ( 1 - \\gamma ) ^ { 3 } } \\cdot p o l y l o g \\left( \\frac { 1 } { \\epsilon _ { 1 } } , \\frac { 1 } { 1 - \\gamma } \\right) ,"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    735,
+                    1626,
+                    825,
+                    1626,
+                    825,
+                    1661,
+                    735,
+                    1661
+                ],
+                "score": 0.92,
+                "latex": "( w _ { t } ) _ { t \\geq 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    458,
+                    1580,
+                    619,
+                    1580,
+                    619,
+                    1618,
+                    458,
+                    1618
+                ],
+                "score": 0.92,
+                "latex": "\\begin{array} { r } { \\sum _ { t \\geq 1 } w _ { t } \\leq C } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    936,
+                    888,
+                    993,
+                    888,
+                    993,
+                    921,
+                    936,
+                    921
+                ],
+                "score": 0.92,
+                "latex": "( i , j )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    591,
+                    1548,
+                    681,
+                    1548,
+                    681,
+                    1582,
+                    591,
+                    1582
+                ],
+                "score": 0.91,
+                "latex": "( w _ { t } ) _ { t \\geq 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    543,
+                    1626,
+                    618,
+                    1626,
+                    618,
+                    1660,
+                    543,
+                    1660
+                ],
+                "score": 0.91,
+                "latex": "( C , w )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1163,
+                    724,
+                    1295,
+                    724,
+                    1295,
+                    756,
+                    1163,
+                    756
+                ],
+                "score": 0.91,
+                "latex": "2 \\leq j \\leq M"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    712,
+                    1240,
+                    764,
+                    1240,
+                    764,
+                    1282,
+                    712,
+                    1282
+                ],
+                "score": 0.91,
+                "latex": "{ B } _ { \\eta } ^ { ( t ) }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    957,
+                    1247,
+                    1272,
+                    1247,
+                    1272,
+                    1288,
+                    957,
+                    1288
+                ],
+                "score": 0.91,
+                "latex": "\\begin{array} { r } { V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > \\frac { \\eta } { 1 - \\gamma } } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    992,
+                    452,
+                    1203,
+                    452,
+                    1203,
+                    487,
+                    992,
+                    487
+                ],
+                "score": 0.91,
+                "latex": "\\eta _ { M } > 1 / ( 1 - \\gamma )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    541,
+                    283,
+                    703,
+                    283,
+                    703,
+                    318,
+                    541,
+                    318
+                ],
+                "score": 0.91,
+                "latex": "L = \\lfloor \\log _ { 2 } R \\rfloor"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    371,
+                    1849,
+                    636,
+                    1849,
+                    636,
+                    1892,
+                    371,
+                    1892
+                ],
+                "score": 0.9,
+                "latex": "\\begin{array} { r } { \\ell ( C ) = \\iota ( C ) \\ln { \\frac { 1 } { ( 1 - \\gamma ) \\epsilon _ { 1 } } } } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1020,
+                    1626,
+                    1112,
+                    1626,
+                    1112,
+                    1660,
+                    1020,
+                    1660
+                ],
+                "score": 0.9,
+                "latex": "1 - \\delta / 2"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    726,
+                    1284,
+                    816,
+                    1284,
+                    816,
+                    1318,
+                    726,
+                    1318
+                ],
+                "score": 0.9,
+                "latex": "1 - \\delta / 2"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    849,
+                    1548,
+                    924,
+                    1548,
+                    924,
+                    1582,
+                    849,
+                    1582
+                ],
+                "score": 0.9,
+                "latex": "( C , w )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    297,
+                    1285,
+                    389,
+                    1285,
+                    389,
+                    1317,
+                    297,
+                    1317
+                ],
+                "score": 0.89,
+                "latex": "\\eta > 2 \\epsilon _ { 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    598,
+                    1249,
+                    667,
+                    1249,
+                    667,
+                    1281,
+                    598,
+                    1281
+                ],
+                "score": 0.89,
+                "latex": "\\eta > 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    348,
+                    1976,
+                    519,
+                    1976,
+                    519,
+                    2008,
+                    348,
+                    2008
+                ],
+                "score": 0.88,
+                "latex": "\\eta _ { M } > 1 / ( 1 - \\gamma )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    334,
+                    1580,
+                    396,
+                    1580,
+                    396,
+                    1611,
+                    334,
+                    1611
+                ],
+                "score": 0.88,
+                "latex": "t \\geq 1"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    761,
+                    272,
+                    1158,
+                    272,
+                    1158,
+                    329,
+                    761,
+                    329
+                ],
+                "score": 0.87,
+                "latex": "\\begin{array} { r } { M = \\operatorname* { m a x } \\left\\{ \\lceil 2 \\log _ { 2 } \\frac { 1 } { \\xi _ { L } ( 1 - \\gamma ) } \\rceil , 1 0 \\right\\} } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    371,
+                    1446,
+                    411,
+                    1446,
+                    411,
+                    1480,
+                    371,
+                    1480
+                ],
+                "score": 0.87,
+                "latex": "I [ \\cdot ]"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1222,
+                    277,
+                    1397,
+                    277,
+                    1397,
+                    321,
+                    1222,
+                    321
+                ],
+                "score": 0.87,
+                "latex": "\\begin{array} { r } { \\eta _ { j } = \\frac { \\xi _ { i } } { M } \\cdot 2 ^ { j - 1 } } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    652,
+                    729,
+                    678,
+                    729,
+                    678,
+                    754,
+                    652,
+                    754
+                ],
+                "score": 0.85,
+                "latex": "\\epsilon _ { 2 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    760,
+                    455,
+                    793,
+                    455,
+                    793,
+                    481,
+                    760,
+                    481
+                ],
+                "score": 0.83,
+                "latex": "M"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    577,
+                    232,
+                    612,
+                    232,
+                    612,
+                    262,
+                    577,
+                    262
+                ],
+                "score": 0.82,
+                "latex": "i , t"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1081,
+                    1549,
+                    1187,
+                    1549,
+                    1187,
+                    1580,
+                    1081,
+                    1580
+                ],
+                "score": 0.82,
+                "latex": "C , w > 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    468,
+                    2007,
+                    498,
+                    2007,
+                    498,
+                    2030,
+                    468,
+                    2030
+                ],
+                "score": 0.8,
+                "latex": "M"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1200,
+                    1549,
+                    1361,
+                    1549,
+                    1361,
+                    1581,
+                    1200,
+                    1581
+                ],
+                "score": 0.79,
+                "latex": "i f 0 \\le w _ { t } \\le w"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    568,
+                    728,
+                    581,
+                    728,
+                    581,
+                    751,
+                    568,
+                    751
+                ],
+                "score": 0.79,
+                "latex": "t"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    389,
+                    325,
+                    823,
+                    325,
+                    823,
+                    373,
+                    389,
+                    373
+                ],
+                "score": 0.75,
+                "latex": "\\begin{array} { r } { \\because j \\le M , \\eta _ { j } \\operatorname* { P r } [ X _ { t } ^ { ( 2 ^ { i } ) } > \\eta _ { j - 1 } ] \\le \\frac { \\xi _ { i } } { M } , } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    539,
+                    933,
+                    553,
+                    933,
+                    553,
+                    957,
+                    539,
+                    957
+                ],
+                "score": 0.74,
+                "latex": "t"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1110,
+                    982,
+                    1123,
+                    982,
+                    1123,
+                    1006,
+                    1110,
+                    1006
+                ],
+                "score": 0.74,
+                "latex": "t"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    378,
+                    334,
+                    510,
+                    334,
+                    510,
+                    370,
+                    378,
+                    370
+                ],
+                "score": 0.63,
+                "latex": "2 \\leq j \\leq M"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    533,
+                    1251,
+                    547,
+                    1251,
+                    547,
+                    1276,
+                    533,
+                    1276
+                ],
+                "score": 0.25,
+                "latex": "t"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1046.0,
+                    538.0,
+                    1046.0,
+                    538.0,
+                    1087.0,
+                    293.0,
+                    1087.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    72.0,
+                    817.0,
+                    72.0,
+                    817.0,
+                    108.0,
+                    295.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    840.0,
+                    2087.0,
+                    861.0,
+                    2087.0,
+                    861.0,
+                    2117.0,
+                    840.0,
+                    2117.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1376.0,
+                    651.0,
+                    1404.0,
+                    651.0,
+                    1404.0,
+                    682.0,
+                    1376.0,
+                    682.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    331.0,
+                    1965.0,
+                    347.0,
+                    1965.0,
+                    347.0,
+                    2013.0,
+                    331.0,
+                    2013.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    520.0,
+                    1965.0,
+                    928.0,
+                    1965.0,
+                    928.0,
+                    2013.0,
+                    520.0,
+                    2013.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1155.0,
+                    1965.0,
+                    1198.0,
+                    1965.0,
+                    1198.0,
+                    2013.0,
+                    1155.0,
+                    2013.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1405.0,
+                    1965.0,
+                    1409.0,
+                    1965.0,
+                    1409.0,
+                    2013.0,
+                    1405.0,
+                    2013.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    2003.0,
+                    467.0,
+                    2003.0,
+                    467.0,
+                    2036.0,
+                    297.0,
+                    2036.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    499.0,
+                    2003.0,
+                    511.0,
+                    2003.0,
+                    511.0,
+                    2036.0,
+                    499.0,
+                    2036.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    855.0,
+                    1000.0,
+                    855.0,
+                    1000.0,
+                    893.0,
+                    294.0,
+                    893.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1081.0,
+                    855.0,
+                    1408.0,
+                    855.0,
+                    1408.0,
+                    893.0,
+                    1081.0,
+                    893.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    886.0,
+                    935.0,
+                    886.0,
+                    935.0,
+                    924.0,
+                    294.0,
+                    924.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    994.0,
+                    886.0,
+                    1404.0,
+                    886.0,
+                    1404.0,
+                    924.0,
+                    994.0,
+                    924.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    283.0,
+                    919.0,
+                    538.0,
+                    919.0,
+                    538.0,
+                    976.0,
+                    283.0,
+                    976.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    554.0,
+                    919.0,
+                    662.0,
+                    919.0,
+                    662.0,
+                    976.0,
+                    554.0,
+                    976.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    954.0,
+                    919.0,
+                    1405.0,
+                    919.0,
+                    1405.0,
+                    976.0,
+                    954.0,
+                    976.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    455.0,
+                    971.0,
+                    1109.0,
+                    971.0,
+                    1109.0,
+                    1018.0,
+                    455.0,
+                    1018.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1124.0,
+                    971.0,
+                    1138.0,
+                    971.0,
+                    1138.0,
+                    1018.0,
+                    1124.0,
+                    1018.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    288.0,
+                    966.0,
+                    378.0,
+                    966.0,
+                    378.0,
+                    1018.0,
+                    288.0,
+                    1018.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1105.0,
+                    1409.0,
+                    1105.0,
+                    1409.0,
+                    1146.0,
+                    293.0,
+                    1146.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1140.0,
+                    1404.0,
+                    1140.0,
+                    1404.0,
+                    1173.0,
+                    295.0,
+                    1173.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1172.0,
+                    535.0,
+                    1172.0,
+                    535.0,
+                    1209.0,
+                    294.0,
+                    1209.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    721.0,
+                    1172.0,
+                    1406.0,
+                    1172.0,
+                    1406.0,
+                    1209.0,
+                    721.0,
+                    1209.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1204.0,
+                    680.0,
+                    1204.0,
+                    680.0,
+                    1238.0,
+                    294.0,
+                    1238.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    451.0,
+                    759.0,
+                    451.0,
+                    759.0,
+                    488.0,
+                    296.0,
+                    488.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    794.0,
+                    451.0,
+                    991.0,
+                    451.0,
+                    991.0,
+                    488.0,
+                    794.0,
+                    488.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1204.0,
+                    451.0,
+                    1407.0,
+                    451.0,
+                    1407.0,
+                    488.0,
+                    1204.0,
+                    488.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    483.0,
+                    660.0,
+                    483.0,
+                    660.0,
+                    518.0,
+                    293.0,
+                    518.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    795.0,
+                    483.0,
+                    806.0,
+                    483.0,
+                    806.0,
+                    518.0,
+                    795.0,
+                    518.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    288.0,
+                    265.0,
+                    540.0,
+                    265.0,
+                    540.0,
+                    335.0,
+                    288.0,
+                    335.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    704.0,
+                    265.0,
+                    760.0,
+                    265.0,
+                    760.0,
+                    335.0,
+                    704.0,
+                    335.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1159.0,
+                    265.0,
+                    1221.0,
+                    265.0,
+                    1221.0,
+                    335.0,
+                    1159.0,
+                    335.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1398.0,
+                    265.0,
+                    1410.0,
+                    265.0,
+                    1410.0,
+                    335.0,
+                    1398.0,
+                    335.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    290.0,
+                    320.0,
+                    377.0,
+                    320.0,
+                    377.0,
+                    380.0,
+                    290.0,
+                    380.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    824.0,
+                    320.0,
+                    835.0,
+                    320.0,
+                    835.0,
+                    380.0,
+                    824.0,
+                    380.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    289.0,
+                    1231.0,
+                    532.0,
+                    1231.0,
+                    532.0,
+                    1293.0,
+                    289.0,
+                    1293.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    548.0,
+                    1231.0,
+                    597.0,
+                    1231.0,
+                    597.0,
+                    1293.0,
+                    548.0,
+                    1293.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    668.0,
+                    1231.0,
+                    711.0,
+                    1231.0,
+                    711.0,
+                    1293.0,
+                    668.0,
+                    1293.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    765.0,
+                    1231.0,
+                    956.0,
+                    1231.0,
+                    956.0,
+                    1293.0,
+                    765.0,
+                    1293.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1273.0,
+                    1231.0,
+                    1411.0,
+                    1231.0,
+                    1411.0,
+                    1293.0,
+                    1273.0,
+                    1293.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1281.0,
+                    296.0,
+                    1281.0,
+                    296.0,
+                    1321.0,
+                    292.0,
+                    1321.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    390.0,
+                    1281.0,
+                    725.0,
+                    1281.0,
+                    725.0,
+                    1321.0,
+                    390.0,
+                    1321.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    817.0,
+                    1281.0,
+                    829.0,
+                    1281.0,
+                    829.0,
+                    1321.0,
+                    817.0,
+                    1321.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    1445.0,
+                    370.0,
+                    1445.0,
+                    370.0,
+                    1482.0,
+                    297.0,
+                    1482.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    412.0,
+                    1445.0,
+                    692.0,
+                    1445.0,
+                    692.0,
+                    1482.0,
+                    412.0,
+                    1482.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1541.0,
+                    590.0,
+                    1541.0,
+                    590.0,
+                    1588.0,
+                    291.0,
+                    1588.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    682.0,
+                    1541.0,
+                    848.0,
+                    1541.0,
+                    848.0,
+                    1588.0,
+                    682.0,
+                    1588.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    925.0,
+                    1541.0,
+                    1080.0,
+                    1541.0,
+                    1080.0,
+                    1588.0,
+                    925.0,
+                    1588.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1188.0,
+                    1541.0,
+                    1199.0,
+                    1541.0,
+                    1199.0,
+                    1588.0,
+                    1188.0,
+                    1588.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1362.0,
+                    1541.0,
+                    1407.0,
+                    1541.0,
+                    1407.0,
+                    1588.0,
+                    1362.0,
+                    1588.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1576.0,
+                    333.0,
+                    1576.0,
+                    333.0,
+                    1618.0,
+                    293.0,
+                    1618.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    397.0,
+                    1576.0,
+                    457.0,
+                    1576.0,
+                    457.0,
+                    1618.0,
+                    397.0,
+                    1618.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    620.0,
+                    1576.0,
+                    631.0,
+                    1576.0,
+                    631.0,
+                    1618.0,
+                    620.0,
+                    1618.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    284.0,
+                    1824.0,
+                    370.0,
+                    1824.0,
+                    370.0,
+                    1911.0,
+                    284.0,
+                    1911.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    637.0,
+                    1824.0,
+                    821.0,
+                    1824.0,
+                    821.0,
+                    1911.0,
+                    637.0,
+                    1911.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    717.0,
+                    567.0,
+                    717.0,
+                    567.0,
+                    761.0,
+                    293.0,
+                    761.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    582.0,
+                    717.0,
+                    651.0,
+                    717.0,
+                    651.0,
+                    761.0,
+                    582.0,
+                    761.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    679.0,
+                    717.0,
+                    913.0,
+                    717.0,
+                    913.0,
+                    761.0,
+                    679.0,
+                    761.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1111.0,
+                    717.0,
+                    1162.0,
+                    717.0,
+                    1162.0,
+                    761.0,
+                    1111.0,
+                    761.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1296.0,
+                    717.0,
+                    1406.0,
+                    717.0,
+                    1406.0,
+                    761.0,
+                    1296.0,
+                    761.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    298.0,
+                    378.0,
+                    971.0,
+                    378.0,
+                    971.0,
+                    414.0,
+                    298.0,
+                    414.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1912.0,
+                    1301.0,
+                    1912.0,
+                    1301.0,
+                    1955.0,
+                    292.0,
+                    1955.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1502.0,
+                    1224.0,
+                    1502.0,
+                    1224.0,
+                    1543.0,
+                    292.0,
+                    1543.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    221.0,
+                    576.0,
+                    221.0,
+                    576.0,
+                    272.0,
+                    292.0,
+                    272.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    613.0,
+                    221.0,
+                    942.0,
+                    221.0,
+                    942.0,
+                    272.0,
+                    613.0,
+                    272.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1620.0,
+                    542.0,
+                    1620.0,
+                    542.0,
+                    1666.0,
+                    291.0,
+                    1666.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    619.0,
+                    1620.0,
+                    734.0,
+                    1620.0,
+                    734.0,
+                    1666.0,
+                    619.0,
+                    1666.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    826.0,
+                    1620.0,
+                    1019.0,
+                    1620.0,
+                    1019.0,
+                    1666.0,
+                    826.0,
+                    1666.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1113.0,
+                    1620.0,
+                    1352.0,
+                    1620.0,
+                    1352.0,
+                    1666.0,
+                    1113.0,
+                    1666.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 5,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    294,
+                    1128,
+                    1407,
+                    1128,
+                    1407,
+                    1315,
+                    294,
+                    1315
+                ],
+                "score": 0.977
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    348,
+                    1407,
+                    348,
+                    1407,
+                    516,
+                    295,
+                    516
+                ],
+                "score": 0.975
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    615,
+                    1404,
+                    615,
+                    1404,
+                    733,
+                    296,
+                    733
+                ],
+                "score": 0.975
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    1444,
+                    1407,
+                    1444,
+                    1407,
+                    1657,
+                    295,
+                    1657
+                ],
+                "score": 0.974
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    317,
+                    1669,
+                    1403,
+                    1669,
+                    1403,
+                    2033,
+                    317,
+                    2033
+                ],
+                "score": 0.96
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    228,
+                    1405,
+                    228,
+                    1405,
+                    299,
+                    295,
+                    299
+                ],
+                "score": 0.951
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    602,
+                    1323,
+                    1095,
+                    1323,
+                    1095,
+                    1390,
+                    602,
+                    1390
+                ],
+                "score": 0.948
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    408,
+                    521,
+                    1286,
+                    521,
+                    1286,
+                    607,
+                    408,
+                    607
+                ],
+                "score": 0.945
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    582,
+                    306,
+                    1119,
+                    306,
+                    1119,
+                    346,
+                    582,
+                    346
+                ],
+                "score": 0.931
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1397,
+                    1077,
+                    1397,
+                    1077,
+                    1434,
+                    298,
+                    1434
+                ],
+                "score": 0.925
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    73,
+                    817,
+                    73,
+                    817,
+                    106,
+                    298,
+                    106
+                ],
+                "score": 0.923
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    821,
+                    985,
+                    821,
+                    985,
+                    857,
+                    296,
+                    857
+                ],
+                "score": 0.922
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    299,
+                    765,
+                    651,
+                    765,
+                    651,
+                    797,
+                    299,
+                    797
+                ],
+                "score": 0.92
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1061,
+                    811,
+                    1061,
+                    811,
+                    1114,
+                    297,
+                    1114
+                ],
+                "score": 0.919
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1365,
+                    997,
+                    1401,
+                    997,
+                    1401,
+                    1028,
+                    1365,
+                    1028
+                ],
+                "score": 0.877
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    888,
+                    634,
+                    888,
+                    634,
+                    921,
+                    298,
+                    921
+                ],
+                "score": 0.873
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1365,
+                    1339,
+                    1401,
+                    1339,
+                    1401,
+                    1369,
+                    1365,
+                    1369
+                ],
+                "score": 0.863
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2086,
+                    858,
+                    2086,
+                    858,
+                    2112,
+                    841,
+                    2112
+                ],
+                "score": 0.773
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1174,
+                    1975,
+                    1403,
+                    1975,
+                    1403,
+                    2009,
+                    1174,
+                    2009
+                ],
+                "score": 0.588
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    696,
+                    977,
+                    1000,
+                    977,
+                    1000,
+                    1053,
+                    696,
+                    1053
+                ],
+                "score": 0.549
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    931,
+                    1249,
+                    931,
+                    1249,
+                    1053,
+                    298,
+                    1053
+                ],
+                "score": 0.228
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    298,
+                    931,
+                    1249,
+                    931,
+                    1249,
+                    1053,
+                    298,
+                    1053
+                ],
+                "score": 0.114
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    521,
+                    647,
+                    644,
+                    647,
+                    644,
+                    701,
+                    521,
+                    701
+                ],
+                "score": 0.93,
+                "latex": "\\tilde { \\mathcal { O } } \\left( \\sqrt { | J | } \\right)"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    885,
+                    1232,
+                    1222,
+                    1232,
+                    1222,
+                    1289,
+                    885,
+                    1289
+                ],
+                "score": 0.93,
+                "latex": "\\begin{array} { r } { T = \\mathcal { O } \\left( \\frac { C } { 2 ^ { i } } \\cdot \\frac { M \\eta _ { j } } { \\xi _ { i } } \\ln ( R M L ) \\right) } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    342,
+                    1128,
+                    596,
+                    1128,
+                    596,
+                    1173,
+                    342,
+                    1173
+                ],
+                "score": 0.93,
+                "latex": "A _ { t } = I [ X _ { t } ^ { ( 2 ^ { i } ) } \\geq \\eta _ { j - 1 } ]"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    604,
+                    1318,
+                    1094,
+                    1318,
+                    1094,
+                    1392,
+                    604,
+                    1392
+                ],
+                "score": 0.93,
+                "latex": "\\operatorname* { P r } \\left[ X _ { k + t R } ^ { ( 2 ^ { i } ) } \\geq \\eta _ { j - 1 } \\right] = \\mathbb { E } [ A _ { k + t R } ] > \\frac { \\xi _ { i } } { M \\eta _ { j } } ,"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    408,
+                    518,
+                    1291,
+                    518,
+                    1291,
+                    611,
+                    408,
+                    611
+                ],
+                "score": 0.93,
+                "latex": "| J | \\eta ( 1 - \\gamma ) ^ { - 1 } \\leq \\frac { C \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\frac { \\sqrt { S A | J | \\ell ( | J | ) } } { ( 1 - \\gamma ) ^ { 2 . 5 } } + \\frac { w S A \\ln | J | } { ( 1 - \\gamma ) ^ { 3 } } \\ln \\frac { 1 } { ( 1 - \\gamma ) \\epsilon _ { 1 } } \\right) ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    767,
+                    261,
+                    872,
+                    261,
+                    872,
+                    298,
+                    767,
+                    298
+                ],
+                "score": 0.93,
+                "latex": "\\hat { Q } _ { t } \\geq Q ^ { * }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    394,
+                    1397,
+                    611,
+                    1397,
+                    611,
+                    1436,
+                    394,
+                    1436
+                ],
+                "score": 0.93,
+                "latex": "\\textstyle \\sum _ { t } A _ { k + t R } \\geq C / 2 ^ { i }"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    315,
+                    1678,
+                    1424,
+                    1678,
+                    1424,
+                    2039,
+                    315,
+                    2039
+                ],
+                "score": 0.93,
+                "latex": "\\begin{array} { r l r } {  { \\sum _ { t = 1 } ^ { \\ell - 1 } I [ V ^ { * } ( s _ { t } ) - V ^ { \\pi _ { t } } ( s _ { t } ) > \\epsilon ] } } \\\\ & { \\leq \\sum _ { t = 1 } ^ { \\infty } \\sum _ { i = 0 } ^ { L } \\sum _ { j = 2 } ^ { M } I [ \\eta _ { j } \\operatorname* { P r } [ X _ { t } ^ { ( 2 ^ { i } ) } > \\eta _ { j - 1 } ] > \\frac { \\xi _ { i } } { M } ] = \\sum _ { i = 0 } ^ { L } \\sum _ { j = 2 } ^ { M } \\sum _ { t = 1 } ^ { \\infty } I [ \\operatorname* { P r } [ X _ { t } ^ { ( 2 ^ { i } ) } > \\eta _ { j - 1 } ] > \\frac { \\xi _ { i } } { \\eta _ { j } M } ] } \\\\ & { \\leq \\sum _ { i = 0 } ^ { L } \\sum _ { j = 2 } ^ { M } \\frac { S A M R \\ln 1 / \\delta \\ln S A } { \\eta _ { j } \\xi _ { i } \\cdot 2 ^ { i } ( 1 - \\gamma ) ^ { 5 } } \\tilde { P } \\leq \\sum _ { i = 0 } ^ { L } \\frac { S A \\cdot 2 ^ { i + 4 } \\ln S A \\ln 1 / \\delta } { \\epsilon _ { 2 } ^ { 2 } ( 1 - \\gamma ) ^ { 6 } } \\tilde { P } \\mathrm { ( B y ~ d e f i n i t i o n ~ o f } \\xi _ { i } \\mathrm { ~ a n d } \\eta _ { j } ) } \\\\ & { \\leq \\frac { S A R \\ln S A \\ln 1 / \\delta } { \\epsilon _ { 2 } ^ { 2 } ( 1 - \\gamma ) ^ { 6 } } \\tilde { P } \\leq \\frac { S A \\ln S A \\ln 1 / \\delta } { \\epsilon _ { 2 } ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\tilde { P } . } & { \\mathrm { ( B y ~ d e f i n i t i o n ~ o f } \\hbar ) } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1010,
+                    1139,
+                    1106,
+                    1139,
+                    1106,
+                    1173,
+                    1010,
+                    1173
+                ],
+                "score": 0.92,
+                "latex": "\\{ \\mathcal { F } _ { t } \\} _ { t \\ge 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    810,
+                    1571,
+                    969,
+                    1571,
+                    969,
+                    1605,
+                    810,
+                    1605
+                ],
+                "score": 0.92,
+                "latex": "1 - \\delta / ( 2 M L )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1136,
+                    448,
+                    1330,
+                    448,
+                    1330,
+                    486,
+                    1136,
+                    486
+                ],
+                "score": 0.92,
+                "latex": "( \\hat { Q } - Q ^ { * } ) ( s _ { t } , a _ { t } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1233,
+                    410,
+                    1397,
+                    410,
+                    1397,
+                    445,
+                    1233,
+                    445
+                ],
+                "score": 0.92,
+                "latex": "| J | \\bar { \\eta ( 1 - \\gamma ) } ^ { - 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    929,
+                    1509,
+                    1180,
+                    1509,
+                    1180,
+                    1545,
+                    929,
+                    1545
+                ],
+                "score": 0.92,
+                "latex": "\\textstyle \\sum _ { t = 0 } ^ { \\infty } A _ { k + t R } \\leq C / 2 ^ { i }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    829,
+                    1447,
+                    1135,
+                    1447,
+                    1135,
+                    1479,
+                    829,
+                    1479
+                ],
+                "score": 0.92,
+                "latex": "[ k + t R , k + t R + R - 1 ]"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1313,
+                    350,
+                    1395,
+                    350,
+                    1395,
+                    384,
+                    1313,
+                    384
+                ],
+                "score": 0.91,
+                "latex": "( | J | , 1 )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    635,
+                    383,
+                    817,
+                    383,
+                    817,
+                    414,
+                    635,
+                    414
+                ],
+                "score": 0.91,
+                "latex": "w _ { t } ~ = ~ I \\left[ t \\in J \\right]"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1309,
+                    657,
+                    1344,
+                    657,
+                    1344,
+                    691,
+                    1309,
+                    691
+                ],
+                "score": 0.91,
+                "latex": "| J |"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    563,
+                    1478,
+                    896,
+                    1478,
+                    896,
+                    1511,
+                    563,
+                    1511
+                ],
+                "score": 0.91,
+                "latex": "V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > ^ { \\mathsf { ^ { * } } } \\eta _ { j - 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    348,
+                    1511,
+                    648,
+                    1511,
+                    648,
+                    1544,
+                    348,
+                    1544
+                ],
+                "score": 0.9,
+                "latex": "[ k + t R , k + t R + R - 1 ]"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    551,
+                    1448,
+                    630,
+                    1448,
+                    630,
+                    1479,
+                    551,
+                    1479
+                ],
+                "score": 0.9,
+                "latex": "A _ { k + t R }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1266,
+                    1170,
+                    1397,
+                    1170,
+                    1397,
+                    1201,
+                    1266,
+                    1201
+                ],
+                "score": 0.9,
+                "latex": "0 \\leq k < R"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    1242,
+                    427,
+                    1242,
+                    427,
+                    1274,
+                    298,
+                    1274
+                ],
+                "score": 0.9,
+                "latex": "0 \\leq k < R"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    1572,
+                    425,
+                    1572,
+                    425,
+                    1602,
+                    298,
+                    1602
+                ],
+                "score": 0.9,
+                "latex": "0 \\leq k < R"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    696,
+                    976,
+                    1001,
+                    976,
+                    1001,
+                    1054,
+                    696,
+                    1054
+                ],
+                "score": 0.89,
+                "latex": "C = \\frac { S A \\ln S A \\ln 1 / \\delta } { \\eta _ { j - 1 } ^ { 2 } ( 1 - \\gamma ) ^ { 5 } } \\cdot \\tilde { P } ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    885,
+                    1398,
+                    1067,
+                    1398,
+                    1067,
+                    1433,
+                    885,
+                    1433
+                ],
+                "score": 0.89,
+                "latex": "1 - \\delta / ( 2 M R L )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    673,
+                    616,
+                    708,
+                    616,
+                    708,
+                    649,
+                    673,
+                    649
+                ],
+                "score": 0.89,
+                "latex": "| J |"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    923,
+                    261,
+                    1204,
+                    261,
+                    1204,
+                    299,
+                    923,
+                    299
+                ],
+                "score": 0.89,
+                "latex": "a _ { t } = \\arg \\operatorname* { m a x } _ { a } \\hat { Q } _ { t } ( s _ { t } , a )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    1200,
+                    690,
+                    1200,
+                    690,
+                    1235,
+                    298,
+                    1235
+                ],
+                "score": 0.88,
+                "latex": "\\{ \\dot { A } _ { k + t R } - E [ A _ { k + t R } \\ | \\ \\mathcal { F } _ { k + t R } ] \\} _ { t \\geq 0 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    884,
+                    1171,
+                    917,
+                    1171,
+                    917,
+                    1201,
+                    884,
+                    1201
+                ],
+                "score": 0.88,
+                "latex": "A _ { t }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    537,
+                    1170,
+                    798,
+                    1170,
+                    798,
+                    1203,
+                    537,
+                    1203
+                ],
+                "score": 0.88,
+                "latex": "\\bar { \\{ ( s _ { \\tau } , a _ { \\tau } ) : 1 \\leq \\tau \\leq t \\} }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1219,
+                    616,
+                    1255,
+                    616,
+                    1255,
+                    650,
+                    1219,
+                    650
+                ],
+                "score": 0.88,
+                "latex": "| J |"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    297,
+                    410,
+                    657,
+                    410,
+                    657,
+                    450,
+                    297,
+                    450
+                ],
+                "score": 0.87,
+                "latex": "\\begin{array} { r } { \\sum _ { t \\geq 1 } \\dot { w } _ { t } \\left[ \\bar { V } ^ { \\ast } ( s _ { t } ) - Q ^ { \\ast } ( s _ { t } , \\dot { a } _ { t } ) \\right] , } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    580,
+                    701,
+                    625,
+                    701,
+                    625,
+                    733,
+                    580,
+                    733
+                ],
+                "score": 0.87,
+                "latex": "1 / \\eta"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    358,
+                    1066,
+                    384,
+                    1066,
+                    384,
+                    1098,
+                    358,
+                    1098
+                ],
+                "score": 0.86,
+                "latex": "\\tilde { P }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1288,
+                    1888,
+                    1312,
+                    1888,
+                    1312,
+                    1918,
+                    1288,
+                    1918
+                ],
+                "score": 0.86,
+                "latex": "\\xi _ { i }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    532,
+                    934,
+                    1164,
+                    934,
+                    1164,
+                    971,
+                    532,
+                    971
+                ],
+                "score": 0.85,
+                "latex": "2 \\leq j \\leq M , \\sum _ { t = 1 } ^ { \\infty } I \\left[ V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > \\eta _ { j - 1 } \\right] \\leq C"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    296,
+                    1602,
+                    664,
+                    1602,
+                    664,
+                    1658,
+                    296,
+                    1658
+                ],
+                "score": 0.85,
+                "latex": "\\mathrm { P r } \\left[ X _ { t } ^ { ( 2 ^ { i } ) } \\geq \\eta _ { j - 1 } \\right] > \\xi _ { i } / ( M \\eta _ { j } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    562,
+                    349,
+                    1104,
+                    349,
+                    1104,
+                    384,
+                    562,
+                    384
+                ],
+                "score": 0.85,
+                "latex": "J = \\{ t : \\ V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > \\eta ( 1 - \\gamma ) ^ { - 1 } \\}"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    576,
+                    304,
+                    1113,
+                    304,
+                    1113,
+                    345,
+                    576,
+                    345
+                ],
+                "score": 0.83,
+                "latex": "V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) \\leq \\hat { Q } _ { t } ( s _ { t } , a _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    296,
+                    1476,
+                    323,
+                    1476,
+                    323,
+                    1506,
+                    296,
+                    1506
+                ],
+                "score": 0.83,
+                "latex": "2 ^ { i }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    815,
+                    1543,
+                    839,
+                    1543,
+                    839,
+                    1569,
+                    815,
+                    1569
+                ],
+                "score": 0.83,
+                "latex": "T"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1302,
+                    1479,
+                    1327,
+                    1479,
+                    1327,
+                    1505,
+                    1302,
+                    1505
+                ],
+                "score": 0.81,
+                "latex": "C"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1363,
+                    1890,
+                    1390,
+                    1890,
+                    1390,
+                    1921,
+                    1363,
+                    1921
+                ],
+                "score": 0.81,
+                "latex": "\\eta _ { j }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    948,
+                    1172,
+                    1015,
+                    1172,
+                    1015,
+                    1203,
+                    948,
+                    1203
+                ],
+                "score": 0.8,
+                "latex": "\\mathcal { F } _ { t + R }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1099,
+                    1546,
+                    1115,
+                    1546,
+                    1115,
+                    1573,
+                    1099,
+                    1573
+                ],
+                "score": 0.8,
+                "latex": "j"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1168,
+                    1572,
+                    1212,
+                    1572,
+                    1212,
+                    1600,
+                    1168,
+                    1600
+                ],
+                "score": 0.78,
+                "latex": "R T"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1028,
+                    1546,
+                    1042,
+                    1546,
+                    1042,
+                    1569,
+                    1028,
+                    1569
+                ],
+                "score": 0.75,
+                "latex": "i"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1367,
+                    1979,
+                    1391,
+                    1979,
+                    1391,
+                    2004,
+                    1367,
+                    2004
+                ],
+                "score": 0.71,
+                "latex": "R"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    677,
+                    1059,
+                    800,
+                    1059,
+                    800,
+                    1115,
+                    677,
+                    1115
+                ],
+                "score": 0.69,
+                "latex": "\\begin{array} { r } { \\left( \\frac { 1 } { \\epsilon _ { 1 } } , \\frac { 1 } { 1 - \\gamma } \\right) } \\end{array}"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    72.0,
+                    817.0,
+                    72.0,
+                    817.0,
+                    108.0,
+                    295.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    763.0,
+                    654.0,
+                    763.0,
+                    654.0,
+                    799.0,
+                    292.0,
+                    799.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    839.0,
+                    2086.0,
+                    860.0,
+                    2086.0,
+                    860.0,
+                    2119.0,
+                    839.0,
+                    2119.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    287.0,
+                    1120.0,
+                    341.0,
+                    1120.0,
+                    341.0,
+                    1186.0,
+                    287.0,
+                    1186.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    597.0,
+                    1120.0,
+                    1009.0,
+                    1120.0,
+                    1009.0,
+                    1186.0,
+                    597.0,
+                    1186.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1107.0,
+                    1120.0,
+                    1413.0,
+                    1120.0,
+                    1413.0,
+                    1186.0,
+                    1107.0,
+                    1186.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1165.0,
+                    536.0,
+                    1165.0,
+                    536.0,
+                    1207.0,
+                    292.0,
+                    1207.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    799.0,
+                    1165.0,
+                    883.0,
+                    1165.0,
+                    883.0,
+                    1207.0,
+                    799.0,
+                    1207.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    918.0,
+                    1165.0,
+                    947.0,
+                    1165.0,
+                    947.0,
+                    1207.0,
+                    918.0,
+                    1207.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1016.0,
+                    1165.0,
+                    1265.0,
+                    1165.0,
+                    1265.0,
+                    1207.0,
+                    1016.0,
+                    1207.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1398.0,
+                    1165.0,
+                    1409.0,
+                    1165.0,
+                    1409.0,
+                    1207.0,
+                    1398.0,
+                    1207.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1195.0,
+                    297.0,
+                    1195.0,
+                    297.0,
+                    1239.0,
+                    293.0,
+                    1239.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    691.0,
+                    1195.0,
+                    1408.0,
+                    1195.0,
+                    1408.0,
+                    1239.0,
+                    691.0,
+                    1239.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1231.0,
+                    297.0,
+                    1231.0,
+                    297.0,
+                    1286.0,
+                    292.0,
+                    1286.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    428.0,
+                    1231.0,
+                    884.0,
+                    1231.0,
+                    884.0,
+                    1286.0,
+                    428.0,
+                    1286.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1280.0,
+                    643.0,
+                    1280.0,
+                    643.0,
+                    1316.0,
+                    293.0,
+                    1316.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1024.0,
+                    1228.5,
+                    1410.0,
+                    1228.5,
+                    1410.0,
+                    1285.0,
+                    1024.0,
+                    1285.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    346.0,
+                    561.0,
+                    346.0,
+                    561.0,
+                    387.0,
+                    293.0,
+                    387.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1105.0,
+                    346.0,
+                    1312.0,
+                    346.0,
+                    1312.0,
+                    387.0,
+                    1105.0,
+                    387.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1396.0,
+                    346.0,
+                    1409.0,
+                    346.0,
+                    1409.0,
+                    387.0,
+                    1396.0,
+                    387.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    377.0,
+                    634.0,
+                    377.0,
+                    634.0,
+                    416.0,
+                    292.0,
+                    416.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    818.0,
+                    377.0,
+                    1408.0,
+                    377.0,
+                    1408.0,
+                    416.0,
+                    818.0,
+                    416.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    290.0,
+                    407.0,
+                    296.0,
+                    407.0,
+                    296.0,
+                    450.0,
+                    290.0,
+                    450.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    658.0,
+                    407.0,
+                    1232.0,
+                    407.0,
+                    1232.0,
+                    450.0,
+                    658.0,
+                    450.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1398.0,
+                    407.0,
+                    1408.0,
+                    407.0,
+                    1408.0,
+                    450.0,
+                    1398.0,
+                    450.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    450.0,
+                    1135.0,
+                    450.0,
+                    1135.0,
+                    487.0,
+                    294.0,
+                    487.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1331.0,
+                    450.0,
+                    1405.0,
+                    450.0,
+                    1405.0,
+                    487.0,
+                    1331.0,
+                    487.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    290.0,
+                    485.0,
+                    380.0,
+                    485.0,
+                    380.0,
+                    519.0,
+                    290.0,
+                    519.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    614.0,
+                    672.0,
+                    614.0,
+                    672.0,
+                    652.0,
+                    295.0,
+                    652.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    709.0,
+                    614.0,
+                    1218.0,
+                    614.0,
+                    1218.0,
+                    652.0,
+                    709.0,
+                    652.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1256.0,
+                    614.0,
+                    1404.0,
+                    614.0,
+                    1404.0,
+                    652.0,
+                    1256.0,
+                    652.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    648.0,
+                    520.0,
+                    648.0,
+                    520.0,
+                    700.0,
+                    291.0,
+                    700.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    645.0,
+                    648.0,
+                    1308.0,
+                    648.0,
+                    1308.0,
+                    700.0,
+                    645.0,
+                    700.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1345.0,
+                    648.0,
+                    1407.0,
+                    648.0,
+                    1407.0,
+                    700.0,
+                    1345.0,
+                    700.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    699.0,
+                    579.0,
+                    699.0,
+                    579.0,
+                    738.0,
+                    296.0,
+                    738.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    626.0,
+                    699.0,
+                    635.0,
+                    699.0,
+                    635.0,
+                    738.0,
+                    626.0,
+                    738.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1443.0,
+                    550.0,
+                    1443.0,
+                    550.0,
+                    1484.0,
+                    293.0,
+                    1484.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    631.0,
+                    1443.0,
+                    828.0,
+                    1443.0,
+                    828.0,
+                    1484.0,
+                    631.0,
+                    1484.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1136.0,
+                    1443.0,
+                    1408.0,
+                    1443.0,
+                    1408.0,
+                    1484.0,
+                    1136.0,
+                    1484.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1471.0,
+                    295.0,
+                    1471.0,
+                    295.0,
+                    1516.0,
+                    291.0,
+                    1516.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    1471.0,
+                    562.0,
+                    1471.0,
+                    562.0,
+                    1516.0,
+                    324.0,
+                    1516.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    897.0,
+                    1471.0,
+                    1301.0,
+                    1471.0,
+                    1301.0,
+                    1516.0,
+                    897.0,
+                    1516.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1328.0,
+                    1471.0,
+                    1412.0,
+                    1471.0,
+                    1412.0,
+                    1516.0,
+                    1328.0,
+                    1516.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    284.0,
+                    1493.0,
+                    347.0,
+                    1493.0,
+                    347.0,
+                    1577.0,
+                    284.0,
+                    1577.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    649.0,
+                    1493.0,
+                    814.0,
+                    1493.0,
+                    814.0,
+                    1577.0,
+                    649.0,
+                    1577.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    840.0,
+                    1493.0,
+                    928.0,
+                    1493.0,
+                    928.0,
+                    1577.0,
+                    840.0,
+                    1577.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1181.0,
+                    1493.0,
+                    1417.0,
+                    1493.0,
+                    1417.0,
+                    1577.0,
+                    1181.0,
+                    1577.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1568.0,
+                    297.0,
+                    1568.0,
+                    297.0,
+                    1607.0,
+                    293.0,
+                    1607.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    426.0,
+                    1568.0,
+                    809.0,
+                    1568.0,
+                    809.0,
+                    1607.0,
+                    426.0,
+                    1607.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    970.0,
+                    1568.0,
+                    1167.0,
+                    1568.0,
+                    1167.0,
+                    1607.0,
+                    970.0,
+                    1607.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1213.0,
+                    1568.0,
+                    1407.0,
+                    1568.0,
+                    1407.0,
+                    1607.0,
+                    1213.0,
+                    1607.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    289.0,
+                    1598.0,
+                    295.0,
+                    1598.0,
+                    295.0,
+                    1659.0,
+                    289.0,
+                    1659.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    665.0,
+                    1598.0,
+                    1283.0,
+                    1598.0,
+                    1283.0,
+                    1659.0,
+                    665.0,
+                    1659.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    227.0,
+                    1405.0,
+                    227.0,
+                    1405.0,
+                    265.0,
+                    295.0,
+                    265.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    262.0,
+                    766.0,
+                    262.0,
+                    766.0,
+                    304.0,
+                    294.0,
+                    304.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    873.0,
+                    262.0,
+                    922.0,
+                    262.0,
+                    922.0,
+                    304.0,
+                    873.0,
+                    304.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1205.0,
+                    262.0,
+                    1216.0,
+                    262.0,
+                    1216.0,
+                    304.0,
+                    1205.0,
+                    304.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1392.0,
+                    393.0,
+                    1392.0,
+                    393.0,
+                    1441.0,
+                    291.0,
+                    1441.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    612.0,
+                    1392.0,
+                    884.0,
+                    1392.0,
+                    884.0,
+                    1441.0,
+                    612.0,
+                    1441.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1068.0,
+                    1392.0,
+                    1080.0,
+                    1392.0,
+                    1080.0,
+                    1441.0,
+                    1068.0,
+                    1441.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    820.0,
+                    988.0,
+                    820.0,
+                    988.0,
+                    859.0,
+                    294.0,
+                    859.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    283.0,
+                    1051.0,
+                    357.0,
+                    1051.0,
+                    357.0,
+                    1124.0,
+                    283.0,
+                    1124.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    385.0,
+                    1051.0,
+                    676.0,
+                    1051.0,
+                    676.0,
+                    1124.0,
+                    385.0,
+                    1124.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    801.0,
+                    1051.0,
+                    818.0,
+                    1051.0,
+                    818.0,
+                    1124.0,
+                    801.0,
+                    1124.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    887.0,
+                    633.0,
+                    887.0,
+                    633.0,
+                    926.0,
+                    296.0,
+                    926.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    926.0,
+                    531.0,
+                    926.0,
+                    531.0,
+                    977.0,
+                    293.0,
+                    977.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1165.0,
+                    926.0,
+                    1251.0,
+                    926.0,
+                    1251.0,
+                    977.0,
+                    1165.0,
+                    977.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    752.25,
+                    966.5,
+                    1008.25,
+                    966.5,
+                    1008.25,
+                    1026.5,
+                    752.25,
+                    1026.5
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 6,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1330,
+                    1406,
+                    1330,
+                    1406,
+                    1539,
+                    296,
+                    1539
+                ],
+                "score": 0.98
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    226,
+                    1405,
+                    226,
+                    1405,
+                    378,
+                    296,
+                    378
+                ],
+                "score": 0.978
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    947,
+                    1406,
+                    947,
+                    1406,
+                    1135,
+                    296,
+                    1135
+                ],
+                "score": 0.977
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1677,
+                    1405,
+                    1677,
+                    1405,
+                    1838,
+                    297,
+                    1838
+                ],
+                "score": 0.976
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    787,
+                    1406,
+                    787,
+                    1406,
+                    936,
+                    296,
+                    936
+                ],
+                "score": 0.976
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1852,
+                    1404,
+                    1852,
+                    1404,
+                    1954,
+                    298,
+                    1954
+                ],
+                "score": 0.976
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1142,
+                    1405,
+                    1142,
+                    1405,
+                    1260,
+                    296,
+                    1260
+                ],
+                "score": 0.966
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    631,
+                    1405,
+                    631,
+                    1405,
+                    695,
+                    298,
+                    695
+                ],
+                "score": 0.954
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    588,
+                    1968,
+                    1105,
+                    1968,
+                    1105,
+                    2047,
+                    588,
+                    2047
+                ],
+                "score": 0.954
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    741,
+                    391,
+                    956,
+                    391,
+                    956,
+                    469,
+                    741,
+                    469
+                ],
+                "score": 0.954
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    482,
+                    870,
+                    482,
+                    870,
+                    524,
+                    297,
+                    524
+                ],
+                "score": 0.932
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1283,
+                    1202,
+                    1283,
+                    1202,
+                    1319,
+                    297,
+                    1319
+                ],
+                "score": 0.925
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    298,
+                    561,
+                    531,
+                    561,
+                    531,
+                    598,
+                    298,
+                    598
+                ],
+                "score": 0.925
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    1630,
+                    1345,
+                    1630,
+                    1345,
+                    1665,
+                    295,
+                    1665
+                ],
+                "score": 0.92
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    74,
+                    817,
+                    74,
+                    817,
+                    105,
+                    298,
+                    105
+                ],
+                "score": 0.916
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    300,
+                    1575,
+                    755,
+                    1575,
+                    755,
+                    1606,
+                    300,
+                    1606
+                ],
+                "score": 0.911
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    299,
+                    732,
+                    836,
+                    732,
+                    836,
+                    763,
+                    299,
+                    763
+                ],
+                "score": 0.9
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    1374,
+                    486,
+                    1403,
+                    486,
+                    1403,
+                    515,
+                    1374,
+                    515
+                ],
+                "score": 0.839
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    840,
+                    2088,
+                    859,
+                    2088,
+                    859,
+                    2112,
+                    840,
+                    2112
+                ],
+                "score": 0.825
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    325,
+                    980,
+                    482,
+                    980,
+                    482,
+                    1034,
+                    325,
+                    1034
+                ],
+                "score": 0.95,
+                "latex": "\\begin{array} { r } { \\tilde { \\mathcal O } \\left( \\frac { S A } { \\epsilon ^ { 4 } ( 1 - \\gamma ) ^ { 8 } } \\right) } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    906,
+                    1393,
+                    1063,
+                    1393,
+                    1063,
+                    1448,
+                    906,
+                    1448
+                ],
+                "score": 0.94,
+                "latex": "\\begin{array} { r } { \\tilde { \\mathcal O } \\left( \\frac { S A } { \\epsilon ^ { 2 } ( 1 - \\gamma ) ^ { 6 } } \\right) } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1093,
+                    1174,
+                    1227,
+                    1174,
+                    1227,
+                    1229,
+                    1093,
+                    1229
+                ],
+                "score": 0.94,
+                "latex": "\\Omega \\left( \\frac { \\epsilon ^ { - 3 } } { \\ln ( 1 / \\delta ) } \\right)"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    588,
+                    1968,
+                    1109,
+                    1968,
+                    1109,
+                    2045,
+                    588,
+                    2045
+                ],
+                "score": 0.94,
+                "latex": "\\mathcal { O } \\left( \\frac { S A \\ln S A \\ln 1 / \\delta } { \\epsilon _ { 2 } ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\mathrm { p o l y l o g } \\left( \\frac { 1 } { \\epsilon _ { 1 } } , \\frac { 1 } { 1 - \\gamma } \\right) \\right) ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    847,
+                    1852,
+                    936,
+                    1852,
+                    936,
+                    1890,
+                    847,
+                    1890
+                ],
+                "score": 0.93,
+                "latex": "\\tilde { \\mathcal { O } } ( { \\sqrt { T } } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    961,
+                    1030,
+                    1046,
+                    1030,
+                    1046,
+                    1075,
+                    961,
+                    1075
+                ],
+                "score": 0.93,
+                "latex": "\\frac { 1 } { \\epsilon ^ { 2 } ( 1 - \\gamma ) }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1036,
+                    1887,
+                    1262,
+                    1887,
+                    1262,
+                    1925,
+                    1036,
+                    1925
+                ],
+                "score": 0.93,
+                "latex": "\\epsilon _ { 2 } > \\tilde { \\mathcal { O } } ( \\epsilon _ { 1 } / ( 1 - \\gamma ) )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1034,
+                    261,
+                    1240,
+                    261,
+                    1240,
+                    308,
+                    1034,
+                    308
+                ],
+                "score": 0.93,
+                "latex": "\\begin{array} { r } { \\epsilon _ { 1 } = \\frac { \\epsilon } { 2 4 R M \\ln \\frac { 1 } { 1 - \\gamma } } } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    457,
+                    821,
+                    685,
+                    821,
+                    685,
+                    874,
+                    457,
+                    874
+                ],
+                "score": 0.93,
+                "latex": "\\begin{array} { r } { \\Omega \\left( \\frac { S A } { \\epsilon ^ { 2 } ( 1 - \\gamma ) ^ { 3 } } \\ln { 1 / \\delta } \\right) } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    809,
+                    1504,
+                    904,
+                    1504,
+                    904,
+                    1539,
+                    809,
+                    1539
+                ],
+                "score": 0.93,
+                "latex": "\\Omega ( S ^ { 2 } A )"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    741,
+                    391,
+                    955,
+                    391,
+                    955,
+                    468,
+                    741,
+                    468
+                ],
+                "score": 0.93,
+                "latex": "\\tilde { \\mathcal { O } } \\left( \\frac { S A \\ln 1 / \\delta } { \\epsilon ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\right) ,"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    860,
+                    870,
+                    968,
+                    870,
+                    968,
+                    905,
+                    860,
+                    905
+                ],
+                "score": 0.93,
+                "latex": "1 / ( 1 - \\gamma )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1084,
+                    1476,
+                    1170,
+                    1476,
+                    1170,
+                    1509,
+                    1084,
+                    1509
+                ],
+                "score": 0.92,
+                "latex": "O ( S A )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    887,
+                    262,
+                    973,
+                    262,
+                    973,
+                    298,
+                    887,
+                    298
+                ],
+                "score": 0.92,
+                "latex": "\\epsilon _ { 2 } = \\textstyle { \\frac { \\epsilon } { 3 } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    419,
+                    303,
+                    741,
+                    303,
+                    741,
+                    345,
+                    419,
+                    345
+                ],
+                "score": 0.92,
+                "latex": "\\ln 1 / \\epsilon _ { 1 } = \\mathrm { p o l y } ( \\ln \\textstyle \\frac { 1 } { \\epsilon } , \\ln \\frac { 1 } { 1 - \\gamma } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    490,
+                    1445,
+                    576,
+                    1445,
+                    576,
+                    1479,
+                    490,
+                    1479
+                ],
+                "score": 0.91,
+                "latex": "( 1 - \\gamma )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    1709,
+                    392,
+                    1709,
+                    392,
+                    1749,
+                    298,
+                    1749
+                ],
+                "score": 0.91,
+                "latex": "\\tilde { \\mathcal { O } } \\left( \\epsilon ^ { - 2 } \\right)"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    739,
+                    1709,
+                    847,
+                    1709,
+                    847,
+                    1749,
+                    739,
+                    1749
+                ],
+                "score": 0.9,
+                "latex": "\\bar { \\mathcal { O } } \\left( T ^ { 1 / 2 } \\right)"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    644,
+                    344,
+                    871,
+                    344,
+                    871,
+                    379,
+                    644,
+                    379
+                ],
+                "score": 0.9,
+                "latex": "\\left( V ^ { * } - \\dot { V } ^ { \\pi } \\right) \\left( s _ { t } \\right) > \\epsilon"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    297,
+                    1224,
+                    464,
+                    1224,
+                    464,
+                    1261,
+                    297,
+                    1261
+                ],
+                "score": 0.89,
+                "latex": "\\ln ( 1 / \\delta ) < \\epsilon ^ { - 2 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1253,
+                    869,
+                    1403,
+                    869,
+                    1403,
+                    905,
+                    1253,
+                    905
+                ],
+                "score": 0.88,
+                "latex": "\\mathrm { { } } ^ { \\mathrm { { 3 } } A , 1 / ( 1 - \\gamma ) }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    296,
+                    1070,
+                    339,
+                    1070,
+                    339,
+                    1105,
+                    296,
+                    1105
+                ],
+                "score": 0.87,
+                "latex": "1 / \\epsilon"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    345,
+                    903,
+                    386,
+                    903,
+                    386,
+                    935,
+                    345,
+                    935
+                ],
+                "score": 0.87,
+                "latex": "1 / \\epsilon"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    806,
+                    226,
+                    831,
+                    226,
+                    831,
+                    258,
+                    806,
+                    258
+                ],
+                "score": 0.87,
+                "latex": "\\tilde { P }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    889,
+                    1892,
+                    952,
+                    1892,
+                    952,
+                    1921,
+                    889,
+                    1921
+                ],
+                "score": 0.86,
+                "latex": "1 - \\delta"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    733,
+                    265,
+                    760,
+                    265,
+                    760,
+                    292,
+                    733,
+                    292
+                ],
+                "score": 0.85,
+                "latex": "\\epsilon _ { 2 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    327,
+                    1926,
+                    354,
+                    1926,
+                    354,
+                    1953,
+                    327,
+                    1953
+                ],
+                "score": 0.85,
+                "latex": "\\epsilon _ { 2 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    813,
+                    267,
+                    840,
+                    267,
+                    840,
+                    292,
+                    813,
+                    292
+                ],
+                "score": 0.85,
+                "latex": "\\epsilon _ { 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1255,
+                    1862,
+                    1282,
+                    1862,
+                    1282,
+                    1887,
+                    1255,
+                    1887
+                ],
+                "score": 0.82,
+                "latex": "\\epsilon _ { 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    580,
+                    481,
+                    860,
+                    481,
+                    860,
+                    527,
+                    580,
+                    527
+                ],
+                "score": 0.79,
+                "latex": "\\begin{array} { r } { \\operatorname { p o l y } ( \\ln { \\frac { 1 } { \\epsilon } } , \\ln { \\frac { 1 } { 1 - \\gamma } } , \\ln S A ) } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1288,
+                    308,
+                    1352,
+                    308,
+                    1352,
+                    337,
+                    1288,
+                    337
+                ],
+                "score": 0.79,
+                "latex": "1 - \\delta"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    984,
+                    1145,
+                    1006,
+                    1145,
+                    1006,
+                    1171,
+                    984,
+                    1171
+                ],
+                "score": 0.77,
+                "latex": "S"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1066,
+                    1145,
+                    1089,
+                    1145,
+                    1089,
+                    1171,
+                    1066,
+                    1171
+                ],
+                "score": 0.71,
+                "latex": "A"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    295,
+                    1183,
+                    360,
+                    1183,
+                    360,
+                    1214,
+                    295,
+                    1214
+                ],
+                "score": 0.68,
+                "latex": "1 - \\delta"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    473,
+                    1185,
+                    496,
+                    1185,
+                    496,
+                    1215,
+                    473,
+                    1215
+                ],
+                "score": 0.66,
+                "latex": "Q"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    558.0,
+                    535.0,
+                    558.0,
+                    535.0,
+                    605.0,
+                    291.0,
+                    605.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    72.0,
+                    817.0,
+                    72.0,
+                    817.0,
+                    108.0,
+                    296.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1574.0,
+                    757.0,
+                    1574.0,
+                    757.0,
+                    1609.0,
+                    295.0,
+                    1609.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    731.0,
+                    838.0,
+                    731.0,
+                    838.0,
+                    767.0,
+                    295.0,
+                    767.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1378.0,
+                    490.0,
+                    1403.0,
+                    490.0,
+                    1403.0,
+                    516.0,
+                    1378.0,
+                    516.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    839.0,
+                    2085.0,
+                    861.0,
+                    2085.0,
+                    861.0,
+                    2116.0,
+                    839.0,
+                    2116.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1332.0,
+                    1404.0,
+                    1332.0,
+                    1404.0,
+                    1366.0,
+                    295.0,
+                    1366.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1362.0,
+                    1406.0,
+                    1362.0,
+                    1406.0,
+                    1396.0,
+                    294.0,
+                    1396.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1402.0,
+                    905.0,
+                    1402.0,
+                    905.0,
+                    1438.0,
+                    291.0,
+                    1438.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1064.0,
+                    1404.0,
+                    1404.0,
+                    1404.0,
+                    1404.0,
+                    1438.0,
+                    1064.0,
+                    1438.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1444.0,
+                    489.0,
+                    1444.0,
+                    489.0,
+                    1482.0,
+                    294.0,
+                    1482.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    577.0,
+                    1444.0,
+                    1407.0,
+                    1444.0,
+                    1407.0,
+                    1482.0,
+                    577.0,
+                    1482.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1476.0,
+                    1083.0,
+                    1476.0,
+                    1083.0,
+                    1509.0,
+                    294.0,
+                    1509.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1171.0,
+                    1476.0,
+                    1404.0,
+                    1476.0,
+                    1404.0,
+                    1509.0,
+                    1171.0,
+                    1509.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1506.0,
+                    808.0,
+                    1506.0,
+                    808.0,
+                    1540.0,
+                    296.0,
+                    1540.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    905.0,
+                    1506.0,
+                    1331.0,
+                    1506.0,
+                    1331.0,
+                    1540.0,
+                    905.0,
+                    1540.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    223.0,
+                    805.0,
+                    223.0,
+                    805.0,
+                    267.0,
+                    291.0,
+                    267.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    832.0,
+                    223.0,
+                    1406.0,
+                    223.0,
+                    1406.0,
+                    267.0,
+                    832.0,
+                    267.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1241.0,
+                    260.0,
+                    1404.0,
+                    260.0,
+                    1404.0,
+                    292.0,
+                    1241.0,
+                    292.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    290.0,
+                    299.0,
+                    418.0,
+                    299.0,
+                    418.0,
+                    353.0,
+                    290.0,
+                    353.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    742.0,
+                    299.0,
+                    1287.0,
+                    299.0,
+                    1287.0,
+                    353.0,
+                    742.0,
+                    353.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1353.0,
+                    299.0,
+                    1408.0,
+                    299.0,
+                    1408.0,
+                    353.0,
+                    1353.0,
+                    353.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    340.0,
+                    643.0,
+                    340.0,
+                    643.0,
+                    381.0,
+                    293.0,
+                    381.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    872.0,
+                    340.0,
+                    902.0,
+                    340.0,
+                    902.0,
+                    381.0,
+                    872.0,
+                    381.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    289.0,
+                    255.0,
+                    1208.0,
+                    255.0,
+                    1208.0,
+                    304.5,
+                    289.0,
+                    304.5
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1191.25,
+                    285.0,
+                    1229.25,
+                    285.0,
+                    1229.25,
+                    307.0,
+                    1191.25,
+                    307.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    945.0,
+                    1406.0,
+                    945.0,
+                    1406.0,
+                    986.0,
+                    291.0,
+                    986.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    290.0,
+                    978.0,
+                    324.0,
+                    978.0,
+                    324.0,
+                    1026.0,
+                    290.0,
+                    1026.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    484.0,
+                    987.0,
+                    1408.0,
+                    987.0,
+                    1408.0,
+                    1026.0,
+                    484.0,
+                    1026.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    286.0,
+                    1026.0,
+                    960.0,
+                    1026.0,
+                    960.0,
+                    1086.0,
+                    286.0,
+                    1086.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1047.0,
+                    1026.0,
+                    1412.0,
+                    1026.0,
+                    1412.0,
+                    1086.0,
+                    1047.0,
+                    1086.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    340.0,
+                    1071.0,
+                    1406.0,
+                    1071.0,
+                    1406.0,
+                    1107.0,
+                    340.0,
+                    1107.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1100.0,
+                    1025.0,
+                    1100.0,
+                    1025.0,
+                    1141.0,
+                    294.0,
+                    1141.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1676.0,
+                    1405.0,
+                    1676.0,
+                    1405.0,
+                    1717.0,
+                    292.0,
+                    1717.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1704.0,
+                    297.0,
+                    1704.0,
+                    297.0,
+                    1753.0,
+                    292.0,
+                    1753.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    1704.0,
+                    738.0,
+                    1704.0,
+                    738.0,
+                    1753.0,
+                    393.0,
+                    1753.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    848.0,
+                    1704.0,
+                    1408.0,
+                    1704.0,
+                    1408.0,
+                    1753.0,
+                    848.0,
+                    1753.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1745.0,
+                    1405.0,
+                    1745.0,
+                    1405.0,
+                    1779.0,
+                    295.0,
+                    1779.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1771.0,
+                    1408.0,
+                    1771.0,
+                    1408.0,
+                    1815.0,
+                    291.0,
+                    1815.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1804.0,
+                    445.0,
+                    1804.0,
+                    445.0,
+                    1843.0,
+                    294.0,
+                    1843.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    788.0,
+                    1404.0,
+                    788.0,
+                    1404.0,
+                    824.0,
+                    295.0,
+                    824.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    825.0,
+                    456.0,
+                    825.0,
+                    456.0,
+                    867.0,
+                    295.0,
+                    867.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    871.0,
+                    859.0,
+                    871.0,
+                    859.0,
+                    907.0,
+                    294.0,
+                    907.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    969.0,
+                    871.0,
+                    1252.0,
+                    871.0,
+                    1252.0,
+                    907.0,
+                    969.0,
+                    907.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    899.0,
+                    344.0,
+                    899.0,
+                    344.0,
+                    938.0,
+                    293.0,
+                    938.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    387.0,
+                    899.0,
+                    400.0,
+                    899.0,
+                    400.0,
+                    938.0,
+                    387.0,
+                    938.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    482.75,
+                    815.5,
+                    1411.75,
+                    815.5,
+                    1411.75,
+                    876.5,
+                    482.75,
+                    876.5
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1852.0,
+                    846.0,
+                    1852.0,
+                    846.0,
+                    1892.0,
+                    294.0,
+                    1892.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    937.0,
+                    1852.0,
+                    1254.0,
+                    1852.0,
+                    1254.0,
+                    1892.0,
+                    937.0,
+                    1892.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1283.0,
+                    1852.0,
+                    1404.0,
+                    1852.0,
+                    1404.0,
+                    1892.0,
+                    1283.0,
+                    1892.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1890.0,
+                    888.0,
+                    1890.0,
+                    888.0,
+                    1926.0,
+                    294.0,
+                    1926.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    953.0,
+                    1890.0,
+                    1035.0,
+                    1890.0,
+                    1035.0,
+                    1926.0,
+                    953.0,
+                    1926.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1263.0,
+                    1890.0,
+                    1405.0,
+                    1890.0,
+                    1405.0,
+                    1926.0,
+                    1263.0,
+                    1926.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1922.0,
+                    326.0,
+                    1922.0,
+                    326.0,
+                    1957.0,
+                    296.0,
+                    1957.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    1922.0,
+                    713.0,
+                    1922.0,
+                    713.0,
+                    1957.0,
+                    355.0,
+                    1957.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1138.0,
+                    983.0,
+                    1138.0,
+                    983.0,
+                    1179.0,
+                    294.0,
+                    1179.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1007.0,
+                    1138.0,
+                    1065.0,
+                    1138.0,
+                    1065.0,
+                    1179.0,
+                    1007.0,
+                    1179.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1090.0,
+                    1138.0,
+                    1403.0,
+                    1138.0,
+                    1403.0,
+                    1179.0,
+                    1090.0,
+                    1179.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1175.0,
+                    294.0,
+                    1175.0,
+                    294.0,
+                    1221.0,
+                    291.0,
+                    1221.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    361.0,
+                    1175.0,
+                    472.0,
+                    1175.0,
+                    472.0,
+                    1221.0,
+                    361.0,
+                    1221.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    497.0,
+                    1175.0,
+                    1092.0,
+                    1175.0,
+                    1092.0,
+                    1221.0,
+                    497.0,
+                    1221.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1233.0,
+                    1183.0,
+                    1403.0,
+                    1183.0,
+                    1403.0,
+                    1219.0,
+                    1233.0,
+                    1219.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1223.0,
+                    296.0,
+                    1223.0,
+                    296.0,
+                    1259.0,
+                    292.0,
+                    1259.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    465.0,
+                    1223.0,
+                    473.0,
+                    1223.0,
+                    473.0,
+                    1259.0,
+                    465.0,
+                    1259.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1140.0,
+                    1173.0,
+                    1203.0,
+                    1173.0,
+                    1203.0,
+                    1202.5,
+                    1140.0,
+                    1202.5
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    630.0,
+                    1406.0,
+                    630.0,
+                    1406.0,
+                    669.0,
+                    293.0,
+                    669.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    662.0,
+                    875.0,
+                    662.0,
+                    875.0,
+                    698.0,
+                    293.0,
+                    698.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    477.0,
+                    579.0,
+                    477.0,
+                    579.0,
+                    530.0,
+                    292.0,
+                    530.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    861.0,
+                    477.0,
+                    873.0,
+                    477.0,
+                    873.0,
+                    530.0,
+                    861.0,
+                    530.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1281.0,
+                    1204.0,
+                    1281.0,
+                    1204.0,
+                    1322.0,
+                    293.0,
+                    1322.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1627.0,
+                    1348.0,
+                    1627.0,
+                    1348.0,
+                    1672.0,
+                    292.0,
+                    1672.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 7,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    405,
+                    1405,
+                    405,
+                    1405,
+                    612,
+                    298,
+                    612
+                ],
+                "score": 0.98
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    723,
+                    1401,
+                    723,
+                    1401,
+                    818,
+                    299,
+                    818
+                ],
+                "score": 0.95
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    229,
+                    1402,
+                    229,
+                    1402,
+                    294,
+                    296,
+                    294
+                ],
+                "score": 0.947
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    300,
+                    1744,
+                    1405,
+                    1744,
+                    1405,
+                    1839,
+                    300,
+                    1839
+                ],
+                "score": 0.909
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1221,
+                    1402,
+                    1221,
+                    1402,
+                    1315,
+                    297,
+                    1315
+                ],
+                "score": 0.903
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    300,
+                    335,
+                    544,
+                    335,
+                    544,
+                    372,
+                    300,
+                    372
+                ],
+                "score": 0.898
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    300,
+                    75,
+                    816,
+                    75,
+                    816,
+                    105,
+                    300,
+                    105
+                ],
+                "score": 0.895
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    1333,
+                    1401,
+                    1333,
+                    1401,
+                    1397,
+                    295,
+                    1397
+                ],
+                "score": 0.894
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    293,
+                    1663,
+                    1402,
+                    1663,
+                    1402,
+                    1728,
+                    293,
+                    1728
+                ],
+                "score": 0.89
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    1416,
+                    1402,
+                    1416,
+                    1402,
+                    1481,
+                    295,
+                    1481
+                ],
+                "score": 0.89
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    914,
+                    1401,
+                    914,
+                    1401,
+                    977,
+                    299,
+                    977
+                ],
+                "score": 0.887
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1077,
+                    1406,
+                    1077,
+                    1406,
+                    1201,
+                    299,
+                    1201
+                ],
+                "score": 0.881
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1581,
+                    1404,
+                    1581,
+                    1404,
+                    1645,
+                    297,
+                    1645
+                ],
+                "score": 0.878
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    995,
+                    1402,
+                    995,
+                    1402,
+                    1059,
+                    296,
+                    1059
+                ],
+                "score": 0.87
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    300,
+                    656,
+                    674,
+                    656,
+                    674,
+                    691,
+                    300,
+                    691
+                ],
+                "score": 0.868
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1498,
+                    1401,
+                    1498,
+                    1401,
+                    1564,
+                    296,
+                    1564
+                ],
+                "score": 0.864
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    299,
+                    862,
+                    489,
+                    862,
+                    489,
+                    897,
+                    299,
+                    897
+                ],
+                "score": 0.824
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1971,
+                    1397,
+                    1971,
+                    1397,
+                    2035,
+                    297,
+                    2035
+                ],
+                "score": 0.811
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    840,
+                    2088,
+                    859,
+                    2088,
+                    859,
+                    2111,
+                    840,
+                    2111
+                ],
+                "score": 0.777
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1858,
+                    1402,
+                    1858,
+                    1402,
+                    1953,
+                    297,
+                    1953
+                ],
+                "score": 0.374
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1065,
+                    467,
+                    1206,
+                    467,
+                    1206,
+                    513,
+                    1065,
+                    513
+                ],
+                "score": 0.94,
+                "latex": "\\tilde { \\cal O } \\big ( { \\textstyle \\frac { S A } { \\epsilon ^ { 4 } ( 1 - \\gamma _ { _ { - } } ) ^ { 8 } } } \\big )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1059,
+                    538,
+                    1199,
+                    538,
+                    1199,
+                    582,
+                    1059,
+                    582
+                ],
+                "score": 0.94,
+                "latex": "\\begin{array} { r } { \\tilde { \\mathcal { O } } \\big ( \\frac { S A } { \\epsilon ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\big ) } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    774,
+                    578,
+                    889,
+                    578,
+                    889,
+                    613,
+                    774,
+                    613
+                ],
+                "score": 0.93,
+                "latex": "1 / ( 1 - \\gamma )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    615,
+                    267,
+                    642,
+                    267,
+                    642,
+                    292,
+                    615,
+                    292
+                ],
+                "score": 0.84,
+                "latex": "\\epsilon _ { 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1242,
+                    236,
+                    1268,
+                    236,
+                    1268,
+                    261,
+                    1242,
+                    261
+                ],
+                "score": 0.84,
+                "latex": "\\epsilon _ { 1 }"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    332.0,
+                    550.0,
+                    332.0,
+                    550.0,
+                    380.0,
+                    291.0,
+                    380.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    73.0,
+                    817.0,
+                    73.0,
+                    817.0,
+                    108.0,
+                    296.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    657.0,
+                    676.0,
+                    657.0,
+                    676.0,
+                    697.0,
+                    294.0,
+                    697.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    865.0,
+                    490.0,
+                    865.0,
+                    490.0,
+                    898.0,
+                    297.0,
+                    898.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    839.0,
+                    2087.0,
+                    861.0,
+                    2087.0,
+                    861.0,
+                    2117.0,
+                    839.0,
+                    2117.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    408.0,
+                    1405.0,
+                    408.0,
+                    1405.0,
+                    438.0,
+                    297.0,
+                    438.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    283.0,
+                    437.0,
+                    1064.0,
+                    437.0,
+                    1064.0,
+                    530.0,
+                    283.0,
+                    530.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1207.0,
+                    437.0,
+                    1406.0,
+                    437.0,
+                    1406.0,
+                    530.0,
+                    1207.0,
+                    530.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    506.0,
+                    1406.0,
+                    506.0,
+                    1406.0,
+                    543.0,
+                    295.0,
+                    543.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    285.0,
+                    523.0,
+                    1058.0,
+                    523.0,
+                    1058.0,
+                    596.0,
+                    285.0,
+                    596.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1200.0,
+                    523.0,
+                    1414.0,
+                    523.0,
+                    1414.0,
+                    596.0,
+                    1200.0,
+                    596.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    576.0,
+                    773.0,
+                    576.0,
+                    773.0,
+                    616.0,
+                    292.0,
+                    616.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    890.0,
+                    576.0,
+                    1165.0,
+                    576.0,
+                    1165.0,
+                    616.0,
+                    890.0,
+                    616.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    723.0,
+                    1405.0,
+                    723.0,
+                    1405.0,
+                    761.0,
+                    293.0,
+                    761.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    752.0,
+                    1406.0,
+                    752.0,
+                    1406.0,
+                    790.0,
+                    293.0,
+                    790.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    784.0,
+                    1181.0,
+                    784.0,
+                    1181.0,
+                    823.0,
+                    293.0,
+                    823.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    227.0,
+                    1241.0,
+                    227.0,
+                    1241.0,
+                    267.0,
+                    292.0,
+                    267.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1269.0,
+                    227.0,
+                    1404.0,
+                    227.0,
+                    1404.0,
+                    267.0,
+                    1269.0,
+                    267.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    259.0,
+                    614.0,
+                    259.0,
+                    614.0,
+                    299.0,
+                    295.0,
+                    299.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    643.0,
+                    259.0,
+                    653.0,
+                    259.0,
+                    653.0,
+                    299.0,
+                    643.0,
+                    299.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1744.0,
+                    1405.0,
+                    1744.0,
+                    1405.0,
+                    1782.0,
+                    296.0,
+                    1782.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1776.0,
+                    1404.0,
+                    1776.0,
+                    1404.0,
+                    1813.0,
+                    322.0,
+                    1813.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    1809.0,
+                    596.0,
+                    1809.0,
+                    596.0,
+                    1838.0,
+                    323.0,
+                    1838.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1221.0,
+                    1406.0,
+                    1221.0,
+                    1406.0,
+                    1258.0,
+                    296.0,
+                    1258.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1249.0,
+                    1408.0,
+                    1249.0,
+                    1408.0,
+                    1291.0,
+                    321.0,
+                    1291.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    1284.0,
+                    533.0,
+                    1284.0,
+                    533.0,
+                    1314.0,
+                    324.0,
+                    1314.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1329.0,
+                    1405.0,
+                    1329.0,
+                    1405.0,
+                    1373.0,
+                    293.0,
+                    1373.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1365.0,
+                    661.0,
+                    1365.0,
+                    661.0,
+                    1397.0,
+                    322.0,
+                    1397.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1659.0,
+                    1404.0,
+                    1659.0,
+                    1404.0,
+                    1701.0,
+                    295.0,
+                    1701.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    1693.0,
+                    992.0,
+                    1693.0,
+                    992.0,
+                    1728.0,
+                    320.0,
+                    1728.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    1416.0,
+                    1404.0,
+                    1416.0,
+                    1404.0,
+                    1452.0,
+                    297.0,
+                    1452.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1447.0,
+                    1184.0,
+                    1447.0,
+                    1184.0,
+                    1482.0,
+                    322.0,
+                    1482.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    909.0,
+                    1405.0,
+                    909.0,
+                    1405.0,
+                    953.0,
+                    293.0,
+                    953.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    944.0,
+                    1137.0,
+                    944.0,
+                    1137.0,
+                    979.0,
+                    323.0,
+                    979.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1076.0,
+                    1406.0,
+                    1076.0,
+                    1406.0,
+                    1113.0,
+                    294.0,
+                    1113.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    319.0,
+                    1109.0,
+                    1406.0,
+                    1109.0,
+                    1406.0,
+                    1142.0,
+                    319.0,
+                    1142.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1140.0,
+                    1406.0,
+                    1140.0,
+                    1406.0,
+                    1173.0,
+                    322.0,
+                    1173.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1171.0,
+                    640.0,
+                    1171.0,
+                    640.0,
+                    1203.0,
+                    322.0,
+                    1203.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1580.0,
+                    1408.0,
+                    1580.0,
+                    1408.0,
+                    1618.0,
+                    295.0,
+                    1618.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    326.0,
+                    1612.0,
+                    843.0,
+                    1612.0,
+                    843.0,
+                    1644.0,
+                    326.0,
+                    1644.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    991.0,
+                    1407.0,
+                    991.0,
+                    1407.0,
+                    1033.0,
+                    294.0,
+                    1033.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    1027.0,
+                    947.0,
+                    1027.0,
+                    947.0,
+                    1062.0,
+                    323.0,
+                    1062.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1499.0,
+                    1405.0,
+                    1499.0,
+                    1405.0,
+                    1535.0,
+                    296.0,
+                    1535.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    1530.0,
+                    1196.0,
+                    1530.0,
+                    1196.0,
+                    1562.0,
+                    324.0,
+                    1562.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1968.0,
+                    1403.0,
+                    1968.0,
+                    1403.0,
+                    2009.0,
+                    293.0,
+                    2009.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    2002.0,
+                    1377.0,
+                    2002.0,
+                    1377.0,
+                    2036.0,
+                    322.0,
+                    2036.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1857.0,
+                    1403.0,
+                    1857.0,
+                    1403.0,
+                    1896.0,
+                    296.0,
+                    1896.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    1890.0,
+                    1403.0,
+                    1890.0,
+                    1403.0,
+                    1924.0,
+                    324.0,
+                    1924.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1919.0,
+                    1236.0,
+                    1919.0,
+                    1236.0,
+                    1955.0,
+                    321.0,
+                    1955.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 8,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 8,
+                "poly": [
+                    390,
+                    1268,
+                    1310,
+                    1268,
+                    1310,
+                    1643,
+                    390,
+                    1643
+                ],
+                "score": 0.97
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    360,
+                    1777,
+                    1342,
+                    1777,
+                    1342,
+                    2035,
+                    360,
+                    2035
+                ],
+                "score": 0.967
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    520,
+                    996,
+                    1177,
+                    996,
+                    1177,
+                    1082,
+                    520,
+                    1082
+                ],
+                "score": 0.948
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    683,
+                    1405,
+                    683,
+                    1405,
+                    780,
+                    298,
+                    780
+                ],
+                "score": 0.945
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    292,
+                    899,
+                    1404,
+                    899,
+                    1404,
+                    977,
+                    292,
+                    977
+                ],
+                "score": 0.94
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    342,
+                    1404,
+                    342,
+                    1404,
+                    467,
+                    298,
+                    467
+                ],
+                "score": 0.933
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1098,
+                    690,
+                    1098,
+                    690,
+                    1133,
+                    298,
+                    1133
+                ],
+                "score": 0.922
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    301,
+                    228,
+                    1401,
+                    228,
+                    1401,
+                    324,
+                    301,
+                    324
+                ],
+                "score": 0.922
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1714,
+                    1355,
+                    1714,
+                    1355,
+                    1762,
+                    297,
+                    1762
+                ],
+                "score": 0.921
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    568,
+                    1406,
+                    568,
+                    1406,
+                    665,
+                    298,
+                    665
+                ],
+                "score": 0.913
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    299,
+                    75,
+                    817,
+                    75,
+                    817,
+                    105,
+                    299,
+                    105
+                ],
+                "score": 0.898
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1210,
+                    1196,
+                    1210,
+                    1196,
+                    1252,
+                    296,
+                    1252
+                ],
+                "score": 0.891
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1163,
+                    1198,
+                    1163,
+                    1198,
+                    1200,
+                    296,
+                    1200
+                ],
+                "score": 0.888
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    294,
+                    486,
+                    1399,
+                    486,
+                    1399,
+                    551,
+                    294,
+                    551
+                ],
+                "score": 0.871
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    835,
+                    2087,
+                    865,
+                    2087,
+                    865,
+                    2114,
+                    835,
+                    2114
+                ],
+                "score": 0.854
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1364,
+                    1022,
+                    1401,
+                    1022,
+                    1401,
+                    1053,
+                    1364,
+                    1053
+                ],
+                "score": 0.839
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    301,
+                    835,
+                    646,
+                    835,
+                    646,
+                    872,
+                    301,
+                    872
+                ],
+                "score": 0.562
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    301,
+                    835,
+                    646,
+                    835,
+                    646,
+                    872,
+                    301,
+                    872
+                ],
+                "score": 0.395
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    386,
+                    1272,
+                    1313,
+                    1272,
+                    1313,
+                    1645,
+                    386,
+                    1645
+                ],
+                "score": 0.95,
+                "latex": "\\begin{array} { r l } & { \\frac { \\eta | I | } { 1 - \\gamma } \\leq \\displaystyle \\sum _ { t \\in I } \\left( V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) \\right) \\leq \\displaystyle \\sum _ { t \\in I } \\left[ \\left( \\hat { Q } _ { t } - Q ^ { * } \\right) ( s _ { t } , a _ { t } ) \\right] } \\\\ & { \\qquad \\leq \\displaystyle \\frac { | I | \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\frac { 1 } { ( 1 - \\gamma ) ^ { 5 / 2 } } \\sqrt { S A | I | \\ell | ( I | ) } + \\frac { S A } { ( 1 - \\gamma ) ^ { 3 } } \\ln | I | \\ln \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\right) } \\\\ & { \\qquad \\leq \\displaystyle \\frac { | I | \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\ln \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\cdot \\left( \\frac { \\sqrt { S A | I | \\ln \\frac { S A | I | } { \\delta } } } { ( 1 - \\gamma ) ^ { 5 / 2 } } + \\frac { S A \\ln | I | } { ( 1 - \\gamma ) ^ { 3 } } \\right) \\right) } \\\\ & { \\qquad \\leq \\displaystyle \\frac { | I | \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\sqrt { \\ln \\frac { 1 } { \\delta } } \\ln \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\cdot \\left( \\frac { \\sqrt { S A | I | \\ln S A | I | } } { ( 1 - \\gamma ) ^ { 5 / 2 } } + \\frac { S A \\ln | I | } { ( 1 - \\gamma ) ^ { 3 } } \\right) \\right) } \\end{array}"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    356,
+                    1775,
+                    1344,
+                    1775,
+                    1344,
+                    2038,
+                    356,
+                    2038
+                ],
+                "score": 0.95,
+                "latex": "\\begin{array} { r l } & { \\frac { \\eta | I | } { 1 - \\gamma } = \\cfrac { k ^ { 2 } S A \\ln S A } { ( 1 - \\gamma ) ^ { 4 } \\eta } \\leq 2 \\cfrac { ( \\eta - \\epsilon _ { 1 } ) | I | } { 1 - \\gamma } } \\\\ & { \\qquad \\leq C _ { 1 } \\sqrt { \\ln \\frac { 1 } { \\delta } } \\ln \\cfrac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\left( \\cfrac { \\sqrt { S A | I | \\ln \\left( S A | I | \\right) } } { ( 1 - \\gamma ) ^ { 5 / 2 } } + \\cfrac { S A \\ln | I | } { ( 1 - \\gamma ) ^ { 3 } } \\right) } \\\\ & { \\qquad \\leq C _ { 1 } \\sqrt { \\ln \\frac { 1 } { \\delta } } \\ln \\cfrac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\left( \\cfrac { S A k } { \\eta ( 1 - \\gamma ) ^ { 4 } } \\sqrt { \\ln S A \\cdot ( \\ln S A + \\ln | I | ) } + \\cfrac { S A \\ln | I | } { ( 1 - \\gamma ) ^ { 3 } } \\right) . } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    447,
+                    1714,
+                    687,
+                    1714,
+                    687,
+                    1763,
+                    447,
+                    1763
+                ],
+                "score": 0.94,
+                "latex": "\\begin{array} { r } { | I | = \\frac { S A k ^ { 2 } } { \\eta ^ { 2 } ( 1 - \\gamma ) ^ { 3 } } \\ln S A } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    957,
+                    905,
+                    1272,
+                    905,
+                    1272,
+                    946,
+                    957,
+                    946
+                ],
+                "score": 0.93,
+                "latex": "\\begin{array} { r } { V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > \\frac { \\eta } { 1 - \\gamma } } \\end{array}"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    519,
+                    990,
+                    1176,
+                    990,
+                    1176,
+                    1086,
+                    519,
+                    1086
+                ],
+                "score": 0.92,
+                "latex": "\\sum _ { t = 1 } ^ { t = \\infty } I \\left[ B _ { \\eta } ^ { ( t ) } \\right] \\leq \\frac { S A \\ln S A \\ln 1 / \\delta } { \\eta ^ { 2 } ( 1 - \\gamma ) ^ { 3 } } \\cdot p o l y l o g \\left( \\frac { 1 } { \\epsilon _ { 1 } } , \\frac { 1 } { 1 - \\gamma } \\right) ,"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    341,
+                    1211,
+                    777,
+                    1211,
+                    777,
+                    1254,
+                    341,
+                    1254
+                ],
+                "score": 0.92,
+                "latex": "\\begin{array} { r } { I = \\{ t \\colon V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > \\frac { \\eta } { 1 - \\gamma } \\} } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    599,
+                    907,
+                    667,
+                    907,
+                    667,
+                    939,
+                    599,
+                    939
+                ],
+                "score": 0.92,
+                "latex": "\\eta > 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    712,
+                    899,
+                    764,
+                    899,
+                    764,
+                    940,
+                    712,
+                    940
+                ],
+                "score": 0.92,
+                "latex": "B _ { \\eta } ^ { ( t ) }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    453,
+                    1168,
+                    522,
+                    1168,
+                    522,
+                    1199,
+                    453,
+                    1199
+                ],
+                "score": 0.91,
+                "latex": "\\eta > 1"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1121,
+                    1168,
+                    1189,
+                    1168,
+                    1189,
+                    1199,
+                    1121,
+                    1199
+                ],
+                "score": 0.91,
+                "latex": "\\eta \\leq 1"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    726,
+                    943,
+                    817,
+                    943,
+                    817,
+                    977,
+                    726,
+                    977
+                ],
+                "score": 0.9,
+                "latex": "1 - \\delta / 2"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    944,
+                    388,
+                    944,
+                    388,
+                    976,
+                    298,
+                    976
+                ],
+                "score": 0.9,
+                "latex": "\\eta > 2 \\epsilon _ { 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    802,
+                    1722,
+                    871,
+                    1722,
+                    871,
+                    1750,
+                    802,
+                    1750
+                ],
+                "score": 0.9,
+                "latex": "k > 1"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1312,
+                    1723,
+                    1345,
+                    1723,
+                    1345,
+                    1753,
+                    1312,
+                    1753
+                ],
+                "score": 0.88,
+                "latex": "C _ { 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    371,
+                    1099,
+                    411,
+                    1099,
+                    411,
+                    1133,
+                    371,
+                    1133
+                ],
+                "score": 0.87,
+                "latex": "I [ \\cdot ]"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1124,
+                    1214,
+                    1187,
+                    1214,
+                    1187,
+                    1243,
+                    1124,
+                    1243
+                ],
+                "score": 0.84,
+                "latex": "1 - \\delta"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    73.0,
+                    817.0,
+                    73.0,
+                    817.0,
+                    108.0,
+                    295.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    831.0,
+                    2085.0,
+                    869.0,
+                    2085.0,
+                    869.0,
+                    2123.0,
+                    831.0,
+                    2123.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    833.0,
+                    649.0,
+                    833.0,
+                    649.0,
+                    877.0,
+                    295.0,
+                    877.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    685.0,
+                    1402.0,
+                    685.0,
+                    1402.0,
+                    719.0,
+                    295.0,
+                    719.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    712.0,
+                    1405.0,
+                    712.0,
+                    1405.0,
+                    754.0,
+                    321.0,
+                    754.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    746.0,
+                    706.0,
+                    746.0,
+                    706.0,
+                    781.0,
+                    322.0,
+                    781.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    290.0,
+                    892.0,
+                    598.0,
+                    892.0,
+                    598.0,
+                    951.0,
+                    290.0,
+                    951.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    668.0,
+                    892.0,
+                    711.0,
+                    892.0,
+                    711.0,
+                    951.0,
+                    668.0,
+                    951.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    765.0,
+                    892.0,
+                    956.0,
+                    892.0,
+                    956.0,
+                    951.0,
+                    765.0,
+                    951.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1273.0,
+                    892.0,
+                    1411.0,
+                    892.0,
+                    1411.0,
+                    951.0,
+                    1273.0,
+                    951.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    941.0,
+                    297.0,
+                    941.0,
+                    297.0,
+                    981.0,
+                    292.0,
+                    981.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    389.0,
+                    941.0,
+                    725.0,
+                    941.0,
+                    725.0,
+                    981.0,
+                    389.0,
+                    981.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    818.0,
+                    941.0,
+                    826.0,
+                    941.0,
+                    826.0,
+                    981.0,
+                    818.0,
+                    981.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    345.0,
+                    1405.0,
+                    345.0,
+                    1405.0,
+                    378.0,
+                    296.0,
+                    378.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    374.0,
+                    1404.0,
+                    374.0,
+                    1404.0,
+                    407.0,
+                    322.0,
+                    407.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    317.0,
+                    403.0,
+                    1405.0,
+                    403.0,
+                    1405.0,
+                    443.0,
+                    317.0,
+                    443.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    436.0,
+                    563.0,
+                    436.0,
+                    563.0,
+                    469.0,
+                    321.0,
+                    469.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1098.0,
+                    370.0,
+                    1098.0,
+                    370.0,
+                    1134.0,
+                    296.0,
+                    1134.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    412.0,
+                    1098.0,
+                    693.0,
+                    1098.0,
+                    693.0,
+                    1134.0,
+                    412.0,
+                    1134.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    227.0,
+                    1406.0,
+                    227.0,
+                    1406.0,
+                    269.0,
+                    295.0,
+                    269.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    325.0,
+                    264.0,
+                    1404.0,
+                    264.0,
+                    1404.0,
+                    294.0,
+                    325.0,
+                    294.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    288.0,
+                    1039.0,
+                    288.0,
+                    1039.0,
+                    329.0,
+                    320.0,
+                    329.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1712.0,
+                    446.0,
+                    1712.0,
+                    446.0,
+                    1764.0,
+                    295.0,
+                    1764.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    688.0,
+                    1712.0,
+                    801.0,
+                    1712.0,
+                    801.0,
+                    1764.0,
+                    688.0,
+                    1764.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    872.0,
+                    1712.0,
+                    1311.0,
+                    1712.0,
+                    1311.0,
+                    1764.0,
+                    872.0,
+                    1764.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1346.0,
+                    1712.0,
+                    1357.0,
+                    1712.0,
+                    1357.0,
+                    1764.0,
+                    1346.0,
+                    1764.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    571.0,
+                    1408.0,
+                    571.0,
+                    1408.0,
+                    605.0,
+                    296.0,
+                    605.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    603.0,
+                    1404.0,
+                    603.0,
+                    1404.0,
+                    637.0,
+                    324.0,
+                    637.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    631.0,
+                    730.0,
+                    631.0,
+                    730.0,
+                    666.0,
+                    323.0,
+                    666.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1205.0,
+                    340.0,
+                    1205.0,
+                    340.0,
+                    1258.0,
+                    292.0,
+                    1258.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    778.0,
+                    1205.0,
+                    1123.0,
+                    1205.0,
+                    1123.0,
+                    1258.0,
+                    778.0,
+                    1258.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1188.0,
+                    1205.0,
+                    1202.0,
+                    1205.0,
+                    1202.0,
+                    1258.0,
+                    1188.0,
+                    1258.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1163.0,
+                    452.0,
+                    1163.0,
+                    452.0,
+                    1203.0,
+                    294.0,
+                    1203.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    523.0,
+                    1163.0,
+                    1120.0,
+                    1163.0,
+                    1120.0,
+                    1203.0,
+                    523.0,
+                    1203.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1190.0,
+                    1163.0,
+                    1201.0,
+                    1163.0,
+                    1201.0,
+                    1203.0,
+                    1190.0,
+                    1203.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    298.0,
+                    489.0,
+                    1403.0,
+                    489.0,
+                    1403.0,
+                    521.0,
+                    298.0,
+                    521.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    519.0,
+                    1392.0,
+                    519.0,
+                    1392.0,
+                    552.0,
+                    322.0,
+                    552.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    833.0,
+                    649.0,
+                    833.0,
+                    649.0,
+                    877.0,
+                    295.0,
+                    877.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 9,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 8,
+                "poly": [
+                    417,
+                    272,
+                    1279,
+                    272,
+                    1279,
+                    603,
+                    417,
+                    603
+                ],
+                "score": 0.968
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    581,
+                    788,
+                    1114,
+                    788,
+                    1114,
+                    871,
+                    581,
+                    871
+                ],
+                "score": 0.959
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    356,
+                    1483,
+                    1341,
+                    1483,
+                    1341,
+                    1579,
+                    356,
+                    1579
+                ],
+                "score": 0.95
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    534,
+                    934,
+                    1159,
+                    934,
+                    1159,
+                    1004,
+                    534,
+                    1004
+                ],
+                "score": 0.944
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    696,
+                    1818,
+                    1002,
+                    1818,
+                    1002,
+                    1864,
+                    696,
+                    1864
+                ],
+                "score": 0.943
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    699,
+                    1713,
+                    998,
+                    1713,
+                    998,
+                    1758,
+                    699,
+                    1758
+                ],
+                "score": 0.941
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    744,
+                    688,
+                    951,
+                    688,
+                    951,
+                    728,
+                    744,
+                    728
+                ],
+                "score": 0.938
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1017,
+                    603,
+                    1017,
+                    603,
+                    1049,
+                    297,
+                    1049
+                ],
+                "score": 0.936
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    294,
+                    619,
+                    843,
+                    619,
+                    843,
+                    672,
+                    294,
+                    672
+                ],
+                "score": 0.932
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    884,
+                    906,
+                    884,
+                    906,
+                    919,
+                    297,
+                    919
+                ],
+                "score": 0.929
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    740,
+                    561,
+                    740,
+                    561,
+                    774,
+                    297,
+                    774
+                ],
+                "score": 0.928
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1769,
+                    770,
+                    1769,
+                    770,
+                    1802,
+                    297,
+                    1802
+                ],
+                "score": 0.926
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1890,
+                    1167,
+                    1890,
+                    1167,
+                    1927,
+                    296,
+                    1927
+                ],
+                "score": 0.922
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1612,
+                    804,
+                    1612,
+                    804,
+                    1657,
+                    298,
+                    1657
+                ],
+                "score": 0.919
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    297,
+                    73,
+                    817,
+                    73,
+                    817,
+                    106,
+                    297,
+                    106
+                ],
+                "score": 0.918
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    287,
+                    1393,
+                    1347,
+                    1393,
+                    1347,
+                    1432,
+                    287,
+                    1432
+                ],
+                "score": 0.916
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    229,
+                    411,
+                    229,
+                    411,
+                    262,
+                    296,
+                    262
+                ],
+                "score": 0.915
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    300,
+                    1325,
+                    648,
+                    1325,
+                    648,
+                    1362,
+                    300,
+                    1362
+                ],
+                "score": 0.913
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1663,
+                    1059,
+                    1663,
+                    1059,
+                    1697,
+                    296,
+                    1697
+                ],
+                "score": 0.91
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    293,
+                    1959,
+                    992,
+                    1959,
+                    992,
+                    1995,
+                    293,
+                    1995
+                ],
+                "score": 0.905
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1351,
+                    950,
+                    1401,
+                    950,
+                    1401,
+                    982,
+                    1351,
+                    982
+                ],
+                "score": 0.893
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1351,
+                    1165,
+                    1401,
+                    1165,
+                    1401,
+                    1197,
+                    1351,
+                    1197
+                ],
+                "score": 0.887
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1351,
+                    1087,
+                    1401,
+                    1087,
+                    1401,
+                    1119,
+                    1351,
+                    1119
+                ],
+                "score": 0.885
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    835,
+                    2087,
+                    862,
+                    2087,
+                    862,
+                    2114,
+                    835,
+                    2114
+                ],
+                "score": 0.849
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1364,
+                    693,
+                    1402,
+                    693,
+                    1402,
+                    724,
+                    1364,
+                    724
+                ],
+                "score": 0.847
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    1373,
+                    1892,
+                    1404,
+                    1892,
+                    1404,
+                    1923,
+                    1373,
+                    1923
+                ],
+                "score": 0.845
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    2001,
+                    849,
+                    2001,
+                    849,
+                    2036,
+                    298,
+                    2036
+                ],
+                "score": 0.843
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    585,
+                    1066,
+                    863,
+                    1066,
+                    863,
+                    1140,
+                    585,
+                    1140
+                ],
+                "score": 0.836
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    624,
+                    1144,
+                    1111,
+                    1144,
+                    1111,
+                    1221,
+                    624,
+                    1221
+                ],
+                "score": 0.82
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    1374,
+                    1249,
+                    1404,
+                    1249,
+                    1404,
+                    1279,
+                    1374,
+                    1279
+                ],
+                "score": 0.817
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    585,
+                    1065,
+                    1113,
+                    1065,
+                    1113,
+                    1221,
+                    585,
+                    1221
+                ],
+                "score": 0.118
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    418,
+                    271,
+                    1281,
+                    271,
+                    1281,
+                    604,
+                    418,
+                    604
+                ],
+                "score": 0.95,
+                "latex": "\\begin{array} { r l } & { k ^ { 2 } \\ln ( S A ) \\le C _ { 1 } \\sqrt { \\ln \\displaystyle \\frac { 1 } { \\delta } } \\ln \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\left( k \\left( \\ln S A + \\ln | I | \\right) + \\eta ( 1 - \\gamma ) \\ln | I | \\right) } \\\\ & { \\qquad \\le k C _ { 1 } \\sqrt { \\ln \\displaystyle \\frac { 1 } { \\delta } } \\ln \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\cdot \\left( \\ln S A + 2 \\ln | I | \\right) } \\\\ & { \\qquad \\le k C _ { 1 } \\sqrt { \\ln \\displaystyle \\frac { 1 } { \\delta } } \\ln \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\cdot \\left( 3 \\ln S A + 4 \\ln k + 6 \\ln \\frac { 1 } { \\eta ( 1 - \\gamma ) } \\right) } \\\\ & { \\qquad \\le 6 k C _ { 1 } \\sqrt { \\ln \\displaystyle \\frac { 1 } { \\delta } } \\ln ^ { 2 } \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\left( \\ln S A + \\ln \\epsilon k \\right) . } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    342,
+                    618,
+                    765,
+                    618,
+                    765,
+                    675,
+                    342,
+                    675
+                ],
+                "score": 0.94,
+                "latex": "\\begin{array} { r } { C ^ { \\prime } = \\operatorname* { m a x } \\lbrace 2 , 6 C _ { 1 } \\sqrt { \\ln \\frac { 1 } { \\delta } } \\ln ^ { 2 } \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\rbrace } \\end{array}"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    584,
+                    1063,
+                    1115,
+                    1063,
+                    1115,
+                    1223,
+                    584,
+                    1223
+                ],
+                "score": 0.93,
+                "latex": "\\begin{array} { r l r } {  { \\vert I \\vert = \\frac { S A k ^ { 2 } } { \\eta ^ { 2 } ( 1 - \\gamma ) ^ { 3 } } \\ln S A } } \\\\ & { \\leq \\frac { S A \\ln S A } { \\eta ^ { 2 } ( 1 - \\gamma ) ^ { 5 } } \\cdot \\ln \\frac { 1 } { \\delta } \\cdot \\mathcal { O } ( \\ln ^ { 8 } \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } ) . } \\end{array}"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    356,
+                    1484,
+                    1340,
+                    1484,
+                    1340,
+                    1579,
+                    356,
+                    1579
+                ],
+                "score": 0.93,
+                "latex": "\\sum _ { t \\ge 1 } w _ { t } ( \\hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) \\le \\frac { C \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\frac { \\sqrt { w S A C \\ell ( C ) } } { ( 1 - \\gamma ) ^ { 2 . 5 } } + \\frac { w S A \\ln C } { ( 1 - \\gamma ) ^ { 3 } } \\ln \\frac { 1 } { ( 1 - \\gamma ) \\epsilon _ { 1 } } \\right) ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    586,
+                    1769,
+                    662,
+                    1769,
+                    662,
+                    1802,
+                    586,
+                    1802
+                ],
+                "score": 0.92,
+                "latex": "p ^ { \\prime } \\leq p"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    372,
+                    1613,
+                    636,
+                    1613,
+                    636,
+                    1658,
+                    372,
+                    1658
+                ],
+                "score": 0.92,
+                "latex": "\\begin{array} { r } { \\ell ( C ) = \\iota ( C ) \\ln { \\frac { 1 } { ( 1 - \\gamma ) \\epsilon _ { 1 } } } } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    324,
+                    742,
+                    496,
+                    742,
+                    496,
+                    773,
+                    324,
+                    773
+                ],
+                "score": 0.91,
+                "latex": "k \\geq 1 0 C ^ { \\prime } \\ln C ^ { \\prime }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    543,
+                    1396,
+                    619,
+                    1396,
+                    619,
+                    1430,
+                    543,
+                    1430
+                ],
+                "score": 0.91,
+                "latex": "( C , w )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    735,
+                    1396,
+                    825,
+                    1396,
+                    825,
+                    1431,
+                    735,
+                    1431
+                ],
+                "score": 0.91,
+                "latex": "( w _ { t } ) _ { t \\geq 1 }"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    696,
+                    1816,
+                    1002,
+                    1816,
+                    1002,
+                    1861,
+                    696,
+                    1861
+                ],
+                "score": 0.91,
+                "latex": "{ \\hat { Q } } _ { p + 1 } ( s , a ) \\geq Q _ { p ^ { \\prime } + 1 } ( s , a ) ."
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    699,
+                    1711,
+                    998,
+                    1711,
+                    998,
+                    1756,
+                    699,
+                    1756
+                ],
+                "score": 0.91,
+                "latex": "\\hat { Q } _ { p + 1 } ( s , a ) \\leq Q _ { p + 1 } ( s , a ) ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    818,
+                    885,
+                    903,
+                    885,
+                    903,
+                    917,
+                    818,
+                    917
+                ],
+                "score": 0.91,
+                "latex": "C ^ { \\prime } \\geq 2"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    537,
+                    930,
+                    1161,
+                    930,
+                    1161,
+                    1004,
+                    537,
+                    1004
+                ],
+                "score": 0.9,
+                "latex": "k \\leq 1 0 C ^ { \\prime } \\ln C ^ { \\prime } \\leq 3 6 0 C _ { 1 } ^ { 2 } \\operatorname* { m a x } \\{ \\ln ^ { 4 } { \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } } , 2 0 \\ln 2 \\} ."
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    582,
+                    786,
+                    1114,
+                    786,
+                    1114,
+                    875,
+                    582,
+                    875
+                ],
+                "score": 0.9,
+                "latex": "\\begin{array} { c } { k - C ^ { \\prime } \\left( 2 + \\ln k \\right) \\geq 8 C ^ { \\prime } \\ln C ^ { \\prime } - ( 2 + \\ln 1 0 ) C ^ { \\prime } } \\\\ { \\geq 4 C ^ { \\prime } \\left( 2 \\ln C ^ { \\prime } - 4 \\right) \\geq 0 , } \\end{array}"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    745,
+                    686,
+                    954,
+                    686,
+                    954,
+                    728,
+                    745,
+                    728
+                ],
+                "score": 0.89,
+                "latex": "k \\leq C ^ { \\prime } ( 2 + \\ln k ) ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1020,
+                    1396,
+                    1111,
+                    1396,
+                    1111,
+                    1430,
+                    1020,
+                    1430
+                ],
+                "score": 0.89,
+                "latex": "1 - \\delta / 2"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    805,
+                    2002,
+                    835,
+                    2002,
+                    835,
+                    2036,
+                    805,
+                    2036
+                ],
+                "score": 0.86,
+                "latex": "\\alpha _ { t } ^ { i }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    427,
+                    1776,
+                    444,
+                    1776,
+                    444,
+                    1802,
+                    427,
+                    1802
+                ],
+                "score": 0.54,
+                "latex": "p"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    72.0,
+                    818.0,
+                    72.0,
+                    818.0,
+                    108.0,
+                    296.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1323.0,
+                    649.0,
+                    1323.0,
+                    649.0,
+                    1367.0,
+                    293.0,
+                    1367.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    831.0,
+                    2085.0,
+                    867.0,
+                    2085.0,
+                    867.0,
+                    2124.0,
+                    831.0,
+                    2124.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1379.0,
+                    1898.0,
+                    1402.0,
+                    1898.0,
+                    1402.0,
+                    1921.0,
+                    1379.0,
+                    1921.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1378.0,
+                    1254.0,
+                    1403.0,
+                    1254.0,
+                    1403.0,
+                    1282.0,
+                    1378.0,
+                    1282.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1012.0,
+                    605.0,
+                    1012.0,
+                    605.0,
+                    1054.0,
+                    294.0,
+                    1054.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    280.0,
+                    612.0,
+                    341.0,
+                    612.0,
+                    341.0,
+                    686.0,
+                    280.0,
+                    686.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    766.0,
+                    612.0,
+                    854.0,
+                    612.0,
+                    854.0,
+                    686.0,
+                    766.0,
+                    686.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    883.0,
+                    817.0,
+                    883.0,
+                    817.0,
+                    923.0,
+                    294.0,
+                    923.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    904.0,
+                    883.0,
+                    908.0,
+                    883.0,
+                    908.0,
+                    923.0,
+                    904.0,
+                    923.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    738.0,
+                    323.0,
+                    738.0,
+                    323.0,
+                    778.0,
+                    294.0,
+                    778.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    497.0,
+                    738.0,
+                    563.0,
+                    738.0,
+                    563.0,
+                    778.0,
+                    497.0,
+                    778.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1766.0,
+                    426.0,
+                    1766.0,
+                    426.0,
+                    1805.0,
+                    292.0,
+                    1805.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    445.0,
+                    1766.0,
+                    585.0,
+                    1766.0,
+                    585.0,
+                    1805.0,
+                    445.0,
+                    1805.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    663.0,
+                    1766.0,
+                    774.0,
+                    1766.0,
+                    774.0,
+                    1805.0,
+                    663.0,
+                    1805.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1889.0,
+                    1169.0,
+                    1889.0,
+                    1169.0,
+                    1930.0,
+                    295.0,
+                    1930.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    284.0,
+                    1603.0,
+                    371.0,
+                    1603.0,
+                    371.0,
+                    1672.0,
+                    284.0,
+                    1672.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    637.0,
+                    1603.0,
+                    819.0,
+                    1603.0,
+                    819.0,
+                    1672.0,
+                    637.0,
+                    1672.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1393.0,
+                    542.0,
+                    1393.0,
+                    542.0,
+                    1434.0,
+                    294.0,
+                    1434.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    620.0,
+                    1393.0,
+                    734.0,
+                    1393.0,
+                    734.0,
+                    1434.0,
+                    620.0,
+                    1434.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    826.0,
+                    1393.0,
+                    1019.0,
+                    1393.0,
+                    1019.0,
+                    1434.0,
+                    826.0,
+                    1434.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1112.0,
+                    1393.0,
+                    1350.0,
+                    1393.0,
+                    1350.0,
+                    1434.0,
+                    1112.0,
+                    1434.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    229.0,
+                    412.0,
+                    229.0,
+                    412.0,
+                    263.0,
+                    296.0,
+                    263.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1659.0,
+                    1061.0,
+                    1659.0,
+                    1061.0,
+                    1704.0,
+                    293.0,
+                    1704.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1956.0,
+                    994.0,
+                    1956.0,
+                    994.0,
+                    2000.0,
+                    293.0,
+                    2000.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1998.0,
+                    804.0,
+                    1998.0,
+                    804.0,
+                    2042.0,
+                    295.0,
+                    2042.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    836.0,
+                    1998.0,
+                    855.0,
+                    1998.0,
+                    855.0,
+                    2042.0,
+                    836.0,
+                    2042.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 10,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 8,
+                "poly": [
+                    587,
+                    1518,
+                    1108,
+                    1518,
+                    1108,
+                    1609,
+                    587,
+                    1609
+                ],
+                "score": 0.958
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    497,
+                    546,
+                    1200,
+                    546,
+                    1200,
+                    638,
+                    497,
+                    638
+                ],
+                "score": 0.954
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    610,
+                    723,
+                    1087,
+                    723,
+                    1087,
+                    813,
+                    610,
+                    813
+                ],
+                "score": 0.953
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    863,
+                    1404,
+                    863,
+                    1404,
+                    927,
+                    297,
+                    927
+                ],
+                "score": 0.949
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    433,
+                    1086,
+                    1265,
+                    1086,
+                    1265,
+                    1166,
+                    433,
+                    1166
+                ],
+                "score": 0.949
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    344,
+                    939,
+                    1354,
+                    939,
+                    1354,
+                    1032,
+                    344,
+                    1032
+                ],
+                "score": 0.945
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    473,
+                    1270,
+                    1224,
+                    1270,
+                    1224,
+                    1356,
+                    473,
+                    1356
+                ],
+                "score": 0.942
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    390,
+                    1808,
+                    1307,
+                    1808,
+                    1307,
+                    1894,
+                    390,
+                    1894
+                ],
+                "score": 0.934
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1759,
+                    690,
+                    1759,
+                    690,
+                    1794,
+                    297,
+                    1794
+                ],
+                "score": 0.934
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    294,
+                    1615,
+                    1270,
+                    1615,
+                    1270,
+                    1649,
+                    294,
+                    1649
+                ],
+                "score": 0.932
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    1043,
+                    1226,
+                    1043,
+                    1226,
+                    1078,
+                    295,
+                    1078
+                ],
+                "score": 0.931
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1903,
+                    697,
+                    1903,
+                    697,
+                    1938,
+                    299,
+                    1938
+                ],
+                "score": 0.928
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    294,
+                    1219,
+                    1126,
+                    1219,
+                    1126,
+                    1257,
+                    294,
+                    1257
+                ],
+                "score": 0.927
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    298,
+                    1952,
+                    1536,
+                    1952,
+                    1536,
+                    2039,
+                    298,
+                    2039
+                ],
+                "score": 0.926
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    648,
+                    1167,
+                    648,
+                    1167,
+                    683,
+                    297,
+                    683
+                ],
+                "score": 0.923
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    817,
+                    850,
+                    817,
+                    850,
+                    851,
+                    296,
+                    851
+                ],
+                "score": 0.923
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    500,
+                    505,
+                    500,
+                    505,
+                    534,
+                    296,
+                    534
+                ],
+                "score": 0.917
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    297,
+                    73,
+                    817,
+                    73,
+                    817,
+                    106,
+                    297,
+                    106
+                ],
+                "score": 0.913
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1485,
+                    504,
+                    1485,
+                    504,
+                    1518,
+                    297,
+                    1518
+                ],
+                "score": 0.911
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1351,
+                    1295,
+                    1401,
+                    1295,
+                    1401,
+                    1328,
+                    1351,
+                    1328
+                ],
+                "score": 0.881
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1351,
+                    1369,
+                    1402,
+                    1369,
+                    1402,
+                    1401,
+                    1351,
+                    1401
+                ],
+                "score": 0.879
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    696,
+                    490,
+                    696,
+                    490,
+                    728,
+                    297,
+                    728
+                ],
+                "score": 0.872
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1417,
+                    1073,
+                    1417,
+                    1073,
+                    1458,
+                    299,
+                    1458
+                ],
+                "score": 0.866
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    506,
+                    1664,
+                    1189,
+                    1664,
+                    1189,
+                    1750,
+                    506,
+                    1750
+                ],
+                "score": 0.842
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    1374,
+                    1174,
+                    1403,
+                    1174,
+                    1403,
+                    1202,
+                    1374,
+                    1202
+                ],
+                "score": 0.813
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    360,
+                    296,
+                    1041,
+                    296,
+                    1041,
+                    343,
+                    360,
+                    343
+                ],
+                "score": 0.796
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    360,
+                    357,
+                    819,
+                    357,
+                    819,
+                    397,
+                    360,
+                    397
+                ],
+                "score": 0.739
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    835,
+                    2087,
+                    864,
+                    2087,
+                    864,
+                    2114,
+                    835,
+                    2114
+                ],
+                "score": 0.72
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    361,
+                    222,
+                    982,
+                    222,
+                    982,
+                    282,
+                    361,
+                    282
+                ],
+                "score": 0.669
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    361,
+                    412,
+                    1400,
+                    412,
+                    1400,
+                    473,
+                    361,
+                    473
+                ],
+                "score": 0.49
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    361,
+                    412,
+                    1400,
+                    412,
+                    1400,
+                    473,
+                    361,
+                    473
+                ],
+                "score": 0.446
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    476,
+                    1363,
+                    729,
+                    1363,
+                    729,
+                    1406,
+                    476,
+                    1406
+                ],
+                "score": 0.446
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    835,
+                    2087,
+                    865,
+                    2087,
+                    865,
+                    2114,
+                    835,
+                    2114
+                ],
+                "score": 0.313
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    506,
+                    1664,
+                    1190,
+                    1664,
+                    1190,
+                    1750,
+                    506,
+                    1750
+                ],
+                "score": 0.197
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    609,
+                    721,
+                    1085,
+                    721,
+                    1085,
+                    815,
+                    609,
+                    815
+                ],
+                "score": 0.95,
+                "latex": "\\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\sqrt { \\frac { \\iota ( i ) } { i } } \\leq \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\sqrt { \\frac { \\iota ( t ) } { i } } \\leq 2 \\sqrt { \\frac { \\iota ( t ) } { t } } ,"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    508,
+                    1657,
+                    1192,
+                    1657,
+                    1192,
+                    1752,
+                    508,
+                    1752
+                ],
+                "score": 0.94,
+                "latex": "Q _ { p } ( s , a ) = \\alpha _ { t } ^ { 0 } \\frac { 1 } { 1 - \\gamma } + \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\left[ r ( s , a ) + b _ { i } + \\gamma \\hat { V } _ { t _ { i } } ( s _ { t _ { i } + 1 } ) \\right] ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    466,
+                    1043,
+                    618,
+                    1043,
+                    618,
+                    1078,
+                    466,
+                    1078
+                ],
+                "score": 0.94,
+                "latex": "f ( t ) = \\iota ( t ) / t"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    499,
+                    542,
+                    1200,
+                    542,
+                    1200,
+                    641,
+                    499,
+                    641
+                ],
+                "score": 0.94,
+                "latex": "\\alpha _ { t } = \\frac { H + 1 } { H + t } , \\quad \\alpha _ { t } ^ { 0 } = \\prod _ { j = 1 } ^ { t } ( 1 - \\alpha _ { j } ) , \\quad \\alpha _ { t } ^ { i } = \\alpha _ { i } \\prod _ { j = i + 1 } ^ { t } ( 1 - \\alpha _ { j } ) ."
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    433,
+                    1086,
+                    1264,
+                    1086,
+                    1264,
+                    1165,
+                    433,
+                    1165
+                ],
+                "score": 0.93,
+                "latex": "\\alpha _ { t } \\sqrt { \\frac { \\iota ( t ) } { t } } + ( 1 - \\alpha _ { t } ) \\sqrt { \\frac { \\iota ( t - 1 ) } { t - 1 } } \\geq \\alpha _ { t } \\sqrt { \\frac { \\iota ( t ) } { t } } + ( 1 - \\alpha _ { t } ) \\sqrt { \\frac { \\iota ( t ) } { t } } \\geq \\sqrt { \\frac { \\iota ( t ) } { t } } ."
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    591,
+                    1512,
+                    1108,
+                    1512,
+                    1108,
+                    1611,
+                    591,
+                    1611
+                ],
+                "score": 0.93,
+                "latex": "\\alpha _ { t } ^ { 0 } = \\prod _ { j = 1 } ^ { t } ( 1 - \\alpha _ { j } ) , \\quad \\alpha _ { t } ^ { i } = \\alpha _ { i } \\prod _ { j = i + 1 } ^ { t } ( 1 - \\alpha _ { j } ) ."
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    341,
+                    938,
+                    1353,
+                    938,
+                    1353,
+                    1034,
+                    341,
+                    1034
+                ],
+                "score": 0.93,
+                "latex": "\\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\sqrt { \\frac { \\iota ( i ) } { i } } = \\alpha _ { t } \\sqrt { \\frac { \\iota ( t ) } { t } } + ( 1 - \\alpha _ { t } ) \\sum _ { i = 1 } ^ { t - 1 } \\alpha _ { t - 1 } ^ { i } \\sqrt { \\frac { \\iota ( i ) } { i } } \\geq \\alpha _ { t } \\sqrt { \\frac { \\iota ( t ) } { t } } + ( 1 - \\alpha _ { t } ) \\sqrt { \\frac { \\iota ( t - 1 ) } { t - 1 } } ."
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    391,
+                    1802,
+                    1308,
+                    1802,
+                    1308,
+                    1896,
+                    391,
+                    1896
+                ],
+                "score": 0.93,
+                "latex": "Q ^ { * } ( s , a ) = r ( s , a ) + \\gamma \\mathbb { P } V ^ { * } ( s , a ) = \\alpha _ { t } ^ { 0 } Q ^ { * } ( s , a ) + \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\left[ r ( s , a ) + \\gamma \\mathbb { P } V ^ { * } ( s , a ) \\right] ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    357,
+                    893,
+                    575,
+                    893,
+                    575,
+                    931,
+                    357,
+                    931
+                ],
+                "score": 0.93,
+                "latex": "\\alpha _ { t } ^ { i } = ( 1 - \\alpha _ { t } ) \\dot { \\alpha _ { t - 1 } ^ { i } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    979,
+                    1046,
+                    1117,
+                    1046,
+                    1117,
+                    1077,
+                    979,
+                    1077
+                ],
+                "score": 0.92,
+                "latex": "t \\geq 1 , c \\geq 1"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    882,
+                    1223,
+                    950,
+                    1223,
+                    950,
+                    1255,
+                    882,
+                    1255
+                ],
+                "score": 0.92,
+                "latex": "p \\geq 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1176,
+                    1615,
+                    1261,
+                    1615,
+                    1261,
+                    1649,
+                    1176,
+                    1649
+                ],
+                "score": 0.92,
+                "latex": "Q ( s , a )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1003,
+                    1223,
+                    1065,
+                    1223,
+                    1065,
+                    1256,
+                    1003,
+                    1256
+                ],
+                "score": 0.91,
+                "latex": "( s , a )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1080,
+                    864,
+                    1234,
+                    864,
+                    1234,
+                    898,
+                    1080,
+                    898
+                ],
+                "score": 0.91,
+                "latex": "t = 1 , \\alpha _ { t } ^ { t } = 1"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    473,
+                    1265,
+                    1222,
+                    1265,
+                    1222,
+                    1407,
+                    473,
+                    1407
+                ],
+                "score": 0.91,
+                "latex": "\\begin{array} { r l } & { 0 \\le ( Q _ { p } - Q ^ { * } ) ( s , a ) \\le \\displaystyle \\frac { \\alpha _ { t } ^ { 0 } } { 1 - \\gamma } + \\displaystyle \\sum _ { i = 1 } ^ { t } \\gamma \\alpha _ { t } ^ { i } ( { \\hat { V } } _ { t _ { i } } - V ^ { * } ) ( s _ { t _ { i } + 1 } ) + \\beta _ { t } , } \\\\ & { 0 \\le ( { \\hat { Q } } _ { p } - Q ^ { * } ) ( s , a ) , } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    704,
+                    1222,
+                    796,
+                    1222,
+                    796,
+                    1256,
+                    704,
+                    1256
+                ],
+                "score": 0.91,
+                "latex": "1 - \\delta / 2"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    619,
+                    895,
+                    777,
+                    895,
+                    777,
+                    925,
+                    619,
+                    925
+                ],
+                "score": 0.9,
+                "latex": "1 \\leq i \\leq t - 1"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    396,
+                    359,
+                    634,
+                    359,
+                    634,
+                    397,
+                    396,
+                    397
+                ],
+                "score": 0.9,
+                "latex": "\\textstyle \\sum _ { t = i } ^ { \\infty } \\alpha _ { t } ^ { i } = 1 + 1 / H"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    310,
+                    1946,
+                    1428,
+                    1946,
+                    1428,
+                    2040,
+                    310,
+                    2040
+                ],
+                "score": 0.9,
+                "latex": "Q _ { p } - Q ^ { * } ) ( s , a ) = \\alpha _ { t } ^ { 0 } ( \\frac { 1 } { 1 - \\gamma } - Q ^ { * } ( s , a ) ) + \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\left[ b _ { i } + \\gamma \\left( V _ { t _ { i } } - V ^ { * } \\right) \\left( s _ { t _ { i } + 1 } \\right) + \\gamma \\left( V ^ { * } \\left( s _ { t _ { i } + 1 } \\right) - \\mathbb { P } V ^ { * } \\right) \\right] ,"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    737,
+                    1416,
+                    1064,
+                    1416,
+                    1064,
+                    1457,
+                    737,
+                    1457
+                ],
+                "score": 0.89,
+                "latex": "\\beta _ { t } = c _ { 3 } \\sqrt { H \\iota ( t ) / ( ( 1 - \\gamma ) ^ { 2 } t ) }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    371,
+                    1420,
+                    684,
+                    1420,
+                    684,
+                    1456,
+                    371,
+                    1456
+                ],
+                "score": 0.89,
+                "latex": "t = N _ { p } ( s , a ) , t _ { i } = \\tau ( s , a , i )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    397,
+                    223,
+                    722,
+                    223,
+                    722,
+                    282,
+                    397,
+                    282
+                ],
+                "score": 0.89,
+                "latex": "\\begin{array} { r } { \\sqrt { \\frac { 1 } { t } } \\leq \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\sqrt { \\frac { 1 } { i } } \\leq 2 \\sqrt { \\frac { 1 } { t } } } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1291,
+                    865,
+                    1355,
+                    865,
+                    1355,
+                    895,
+                    1291,
+                    895
+                ],
+                "score": 0.88,
+                "latex": "t \\geq 2"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1254,
+                    431,
+                    1393,
+                    431,
+                    1393,
+                    463,
+                    1254,
+                    463
+                ],
+                "score": 0.88,
+                "latex": "t \\geq 1 , c \\geq 1"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    656,
+                    298,
+                    861,
+                    298,
+                    861,
+                    341,
+                    656,
+                    341
+                ],
+                "score": 0.87,
+                "latex": "\\begin{array} { r } { \\sum _ { i = 1 } ^ { t } ( \\alpha _ { t } ^ { i } ) ^ { 2 } \\le \\frac { 2 H } { t } } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    396,
+                    300,
+                    602,
+                    300,
+                    602,
+                    341,
+                    396,
+                    341
+                ],
+                "score": 0.84,
+                "latex": "\\begin{array} { r } { \\operatorname* { m a x } _ { i \\in [ t ] } \\alpha _ { t } ^ { i } \\leq \\frac { 2 H } { t } } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    749,
+                    362,
+                    812,
+                    362,
+                    812,
+                    394,
+                    749,
+                    394
+                ],
+                "score": 0.83,
+                "latex": "i \\geq 1"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    787,
+                    868,
+                    801,
+                    868,
+                    801,
+                    892,
+                    787,
+                    892
+                ],
+                "score": 0.7,
+                "latex": "t"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    396,
+                    413,
+                    792,
+                    413,
+                    792,
+                    473,
+                    396,
+                    473
+                ],
+                "score": 0.7,
+                "latex": "\\begin{array} { r } { \\sqrt { \\frac { \\iota ( t ) } { t } } \\leq \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\sqrt { \\frac { \\iota ( i ) } { i } } \\leq 2 \\sqrt { \\frac { \\iota ( t ) } { t } } } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    969,
+                    304,
+                    1034,
+                    304,
+                    1034,
+                    337,
+                    969,
+                    337
+                ],
+                "score": 0.68,
+                "latex": "t \\geq 1"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    866,
+                    427,
+                    1141,
+                    427,
+                    1141,
+                    466,
+                    866,
+                    466
+                ],
+                "score": 0.63,
+                "latex": "\\iota ( t ) = \\ln ( c ( t + 1 ) ( t + 2 ) )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    831,
+                    235,
+                    971,
+                    235,
+                    971,
+                    272,
+                    831,
+                    272
+                ],
+                "score": 0.58,
+                "latex": "t \\geq 1 , c > 0"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    72.0,
+                    818.0,
+                    72.0,
+                    818.0,
+                    108.0,
+                    296.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1377.0,
+                    1177.0,
+                    1403.0,
+                    1177.0,
+                    1403.0,
+                    1205.0,
+                    1377.0,
+                    1205.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    831.0,
+                    2085.0,
+                    869.0,
+                    2085.0,
+                    869.0,
+                    2124.0,
+                    831.0,
+                    2124.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    831.0,
+                    2085.0,
+                    868.0,
+                    2085.0,
+                    868.0,
+                    2124.0,
+                    831.0,
+                    2124.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    858.0,
+                    786.0,
+                    858.0,
+                    786.0,
+                    901.0,
+                    292.0,
+                    901.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    802.0,
+                    858.0,
+                    1079.0,
+                    858.0,
+                    1079.0,
+                    901.0,
+                    802.0,
+                    901.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1235.0,
+                    858.0,
+                    1290.0,
+                    858.0,
+                    1290.0,
+                    901.0,
+                    1235.0,
+                    901.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1356.0,
+                    858.0,
+                    1405.0,
+                    858.0,
+                    1405.0,
+                    901.0,
+                    1356.0,
+                    901.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    891.0,
+                    356.0,
+                    891.0,
+                    356.0,
+                    931.0,
+                    294.0,
+                    931.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    576.0,
+                    891.0,
+                    618.0,
+                    891.0,
+                    618.0,
+                    931.0,
+                    576.0,
+                    931.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    778.0,
+                    891.0,
+                    952.0,
+                    891.0,
+                    952.0,
+                    931.0,
+                    778.0,
+                    931.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1756.0,
+                    693.0,
+                    1756.0,
+                    693.0,
+                    1799.0,
+                    294.0,
+                    1799.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1612.0,
+                    1175.0,
+                    1612.0,
+                    1175.0,
+                    1653.0,
+                    292.0,
+                    1653.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1262.0,
+                    1612.0,
+                    1273.0,
+                    1612.0,
+                    1273.0,
+                    1653.0,
+                    1262.0,
+                    1653.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1042.0,
+                    465.0,
+                    1042.0,
+                    465.0,
+                    1082.0,
+                    295.0,
+                    1082.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    619.0,
+                    1042.0,
+                    978.0,
+                    1042.0,
+                    978.0,
+                    1082.0,
+                    619.0,
+                    1082.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1118.0,
+                    1042.0,
+                    1227.0,
+                    1042.0,
+                    1227.0,
+                    1082.0,
+                    1118.0,
+                    1082.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1899.0,
+                    697.0,
+                    1899.0,
+                    697.0,
+                    1943.0,
+                    295.0,
+                    1943.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1218.0,
+                    703.0,
+                    1218.0,
+                    703.0,
+                    1262.0,
+                    295.0,
+                    1262.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    797.0,
+                    1218.0,
+                    881.0,
+                    1218.0,
+                    881.0,
+                    1262.0,
+                    797.0,
+                    1262.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    951.0,
+                    1218.0,
+                    1002.0,
+                    1218.0,
+                    1002.0,
+                    1262.0,
+                    951.0,
+                    1262.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1066.0,
+                    1218.0,
+                    1129.0,
+                    1218.0,
+                    1129.0,
+                    1262.0,
+                    1066.0,
+                    1262.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    639.0,
+                    1170.0,
+                    639.0,
+                    1170.0,
+                    694.0,
+                    291.0,
+                    694.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    812.0,
+                    854.0,
+                    812.0,
+                    854.0,
+                    857.0,
+                    294.0,
+                    857.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    499.0,
+                    507.0,
+                    499.0,
+                    507.0,
+                    536.0,
+                    296.0,
+                    536.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1483.0,
+                    508.0,
+                    1483.0,
+                    508.0,
+                    1520.0,
+                    293.0,
+                    1520.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    694.0,
+                    493.0,
+                    694.0,
+                    493.0,
+                    731.0,
+                    296.0,
+                    731.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1409.0,
+                    370.0,
+                    1409.0,
+                    370.0,
+                    1464.0,
+                    293.0,
+                    1464.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    685.0,
+                    1409.0,
+                    736.0,
+                    1409.0,
+                    736.0,
+                    1464.0,
+                    685.0,
+                    1464.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1065.0,
+                    1409.0,
+                    1075.0,
+                    1409.0,
+                    1075.0,
+                    1464.0,
+                    1065.0,
+                    1464.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    351.0,
+                    291.0,
+                    395.0,
+                    291.0,
+                    395.0,
+                    349.0,
+                    351.0,
+                    349.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    603.0,
+                    291.0,
+                    655.0,
+                    291.0,
+                    655.0,
+                    349.0,
+                    603.0,
+                    349.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    862.0,
+                    291.0,
+                    968.0,
+                    291.0,
+                    968.0,
+                    349.0,
+                    862.0,
+                    349.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1035.0,
+                    291.0,
+                    1050.0,
+                    291.0,
+                    1050.0,
+                    349.0,
+                    1035.0,
+                    349.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    354.0,
+                    350.0,
+                    395.0,
+                    350.0,
+                    395.0,
+                    405.0,
+                    354.0,
+                    405.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    635.0,
+                    350.0,
+                    748.0,
+                    350.0,
+                    748.0,
+                    405.0,
+                    635.0,
+                    405.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    813.0,
+                    350.0,
+                    826.0,
+                    350.0,
+                    826.0,
+                    405.0,
+                    813.0,
+                    405.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    217.0,
+                    396.0,
+                    217.0,
+                    396.0,
+                    286.0,
+                    355.0,
+                    286.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    723.0,
+                    217.0,
+                    830.0,
+                    217.0,
+                    830.0,
+                    286.0,
+                    723.0,
+                    286.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    972.0,
+                    217.0,
+                    990.0,
+                    217.0,
+                    990.0,
+                    286.0,
+                    972.0,
+                    286.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    347.0,
+                    404.0,
+                    395.0,
+                    404.0,
+                    395.0,
+                    487.0,
+                    347.0,
+                    487.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    793.0,
+                    404.0,
+                    865.0,
+                    404.0,
+                    865.0,
+                    487.0,
+                    793.0,
+                    487.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1142.0,
+                    404.0,
+                    1253.0,
+                    404.0,
+                    1253.0,
+                    487.0,
+                    1142.0,
+                    487.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1394.0,
+                    404.0,
+                    1417.0,
+                    404.0,
+                    1417.0,
+                    487.0,
+                    1394.0,
+                    487.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 11,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    386,
+                    1411,
+                    386,
+                    1411,
+                    484,
+                    295,
+                    484
+                ],
+                "score": 0.974
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    456,
+                    1675,
+                    1242,
+                    1675,
+                    1242,
+                    1861,
+                    456,
+                    1861
+                ],
+                "score": 0.974
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    417,
+                    1229,
+                    1406,
+                    1229,
+                    1406,
+                    1546,
+                    417,
+                    1546
+                ],
+                "score": 0.964
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    574,
+                    860,
+                    1127,
+                    860,
+                    1127,
+                    945,
+                    574,
+                    945
+                ],
+                "score": 0.961
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    576,
+                    324,
+                    1123,
+                    324,
+                    1123,
+                    380,
+                    576,
+                    380
+                ],
+                "score": 0.958
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    417,
+                    669,
+                    1281,
+                    669,
+                    1281,
+                    773,
+                    417,
+                    773
+                ],
+                "score": 0.957
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    228,
+                    1406,
+                    228,
+                    1406,
+                    322,
+                    297,
+                    322
+                ],
+                "score": 0.956
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    953,
+                    1401,
+                    953,
+                    1401,
+                    1018,
+                    297,
+                    1018
+                ],
+                "score": 0.951
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    1602,
+                    1403,
+                    1602,
+                    1403,
+                    1668,
+                    295,
+                    1668
+                ],
+                "score": 0.951
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    581,
+                    1096,
+                    1117,
+                    1096,
+                    1117,
+                    1186,
+                    581,
+                    1186
+                ],
+                "score": 0.95
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1915,
+                    1405,
+                    1915,
+                    1405,
+                    1992,
+                    296,
+                    1992
+                ],
+                "score": 0.95
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    509,
+                    491,
+                    1185,
+                    491,
+                    1185,
+                    584,
+                    509,
+                    584
+                ],
+                "score": 0.949
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    300,
+                    781,
+                    1408,
+                    781,
+                    1408,
+                    851,
+                    300,
+                    851
+                ],
+                "score": 0.943
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1190,
+                    574,
+                    1190,
+                    574,
+                    1224,
+                    297,
+                    1224
+                ],
+                "score": 0.929
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1866,
+                    1181,
+                    1866,
+                    1181,
+                    1902,
+                    296,
+                    1902
+                ],
+                "score": 0.925
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    73,
+                    817,
+                    73,
+                    817,
+                    106,
+                    298,
+                    106
+                ],
+                "score": 0.923
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    294,
+                    1552,
+                    955,
+                    1552,
+                    955,
+                    1592,
+                    294,
+                    1592
+                ],
+                "score": 0.909
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    587,
+                    1172,
+                    587,
+                    1172,
+                    623,
+                    297,
+                    623
+                ],
+                "score": 0.907
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1351,
+                    520,
+                    1401,
+                    520,
+                    1401,
+                    552,
+                    1351,
+                    552
+                ],
+                "score": 0.896
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1351,
+                    708,
+                    1400,
+                    708,
+                    1400,
+                    740,
+                    1351,
+                    740
+                ],
+                "score": 0.885
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1037,
+                    1163,
+                    1037,
+                    1163,
+                    1088,
+                    296,
+                    1088
+                ],
+                "score": 0.882
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    835,
+                    2087,
+                    864,
+                    2087,
+                    864,
+                    2113,
+                    835,
+                    2113
+                ],
+                "score": 0.872
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    1374,
+                    2004,
+                    1402,
+                    2004,
+                    1402,
+                    2031,
+                    1374,
+                    2031
+                ],
+                "score": 0.745
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    454,
+                    1671,
+                    1242,
+                    1671,
+                    1242,
+                    1865,
+                    454,
+                    1865
+                ],
+                "score": 0.94,
+                "latex": "\\begin{array} { c l } { ( Q _ { p } - Q ^ { * } ) ( s , a ) \\geq - \\gamma \\displaystyle \\left| \\displaystyle \\sum _ { i = 1 } ^ { t } \\Delta _ { i } \\right| + \\displaystyle \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\left[ \\gamma ( \\hat { V } _ { t _ { i } } - V ^ { * } ) ( x _ { t _ { i } + 1 } ) + b _ { i } \\right] } \\\\ { \\geq \\displaystyle \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } b _ { i } - \\gamma \\displaystyle \\left| \\displaystyle \\sum _ { i = 1 } ^ { t } \\Delta _ { i } \\right| \\geq 0 . } \\end{array}"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    509,
+                    488,
+                    1190,
+                    488,
+                    1190,
+                    585,
+                    509,
+                    585
+                ],
+                "score": 0.93,
+                "latex": "\\mathrm { P r } \\left[ \\left| \\sum _ { i = 1 } ^ { k } \\Delta _ { i } \\right| > \\eta \\right] \\leq 2 \\exp \\left\\{ - \\frac { \\eta ^ { 2 } } { 8 \\left( 1 - \\gamma \\right) ^ { - 2 } \\sum _ { i = 1 } ^ { k } ( \\alpha _ { k } ^ { i } ) ^ { 2 } } \\right\\} ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1106,
+                    1913,
+                    1205,
+                    1913,
+                    1205,
+                    1953,
+                    1106,
+                    1953
+                ],
+                "score": 0.93,
+                "latex": "\\hat { Q } _ { p } ( s , a )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    352,
+                    1954,
+                    458,
+                    1954,
+                    458,
+                    1991,
+                    352,
+                    1991
+                ],
+                "score": 0.93,
+                "latex": "Q _ { p ^ { \\prime } } ( s , a )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    297,
+                    261,
+                    454,
+                    261,
+                    454,
+                    295,
+                    297,
+                    295
+                ],
+                "score": 0.93,
+                "latex": "t _ { i } = \\tau ( s , a , i )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1032,
+                    954,
+                    1183,
+                    954,
+                    1183,
+                    989,
+                    1032,
+                    989
+                ],
+                "score": 0.93,
+                "latex": "t = N _ { p } ( s , a )"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    572,
+                    853,
+                    1124,
+                    853,
+                    1124,
+                    948,
+                    572,
+                    948
+                ],
+                "score": 0.93,
+                "latex": "1 - \\sum _ { s ^ { \\prime } \\in S , a ^ { \\prime } \\in A } \\sum _ { k = 1 } ^ { \\infty } \\frac { \\delta } { 2 S A ( k + 1 ) ( k + 2 ) } = 1 - \\frac { \\delta } { 2 } ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1252,
+                    231,
+                    1396,
+                    231,
+                    1396,
+                    265,
+                    1252,
+                    265
+                ],
+                "score": 0.93,
+                "latex": "t = N _ { p } ( s , a )"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    413,
+                    670,
+                    1282,
+                    670,
+                    1282,
+                    775,
+                    413,
+                    775
+                ],
+                "score": 0.93,
+                "latex": "\\left| \\sum _ { i = 1 } ^ { k } \\Delta _ { i } \\right| \\leq \\frac { 2 \\sqrt { 2 } } { 1 - \\gamma } \\cdot \\sqrt { \\sum _ { i = 1 } ^ { k } ( \\alpha _ { k } ^ { i } ) ^ { 2 } \\cdot \\ln \\frac { 2 ( k + 1 ) ( k + 2 ) S A } { \\delta } } \\leq \\frac { c _ { 2 } } { 1 - \\gamma } \\sqrt { \\frac { H \\iota ( k ) } { k } } ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    485,
+                    782,
+                    751,
+                    782,
+                    751,
+                    824,
+                    485,
+                    824
+                ],
+                "score": 0.93,
+                "latex": "\\begin{array} { r } { \\iota ( k ) = \\ln { \\frac { ( k + 1 ) ( k + 2 ) S A } { \\delta } } } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1107,
+                    1635,
+                    1182,
+                    1635,
+                    1182,
+                    1666,
+                    1107,
+                    1666
+                ],
+                "score": 0.93,
+                "latex": "p ^ { \\prime } = 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    297,
+                    417,
+                    463,
+                    417,
+                    463,
+                    450,
+                    297,
+                    450
+                ],
+                "score": 0.92,
+                "latex": "\\mathbb { E } \\left[ \\Delta _ { i } | F _ { i } \\right] = 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    1635,
+                    406,
+                    1635,
+                    406,
+                    1669,
+                    298,
+                    1669
+                ],
+                "score": 0.92,
+                "latex": "Q _ { p } \\geq Q ^ { * }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    486,
+                    1634,
+                    548,
+                    1634,
+                    548,
+                    1668,
+                    486,
+                    1668
+                ],
+                "score": 0.92,
+                "latex": "( s , a )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    599,
+                    1635,
+                    674,
+                    1635,
+                    674,
+                    1667,
+                    599,
+                    1667
+                ],
+                "score": 0.92,
+                "latex": "p \\leq p ^ { \\prime }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    809,
+                    1953,
+                    1181,
+                    1953,
+                    1181,
+                    1991,
+                    809,
+                    1991
+                ],
+                "score": 0.92,
+                "latex": "\\hat { Q } _ { p } ( s , a ) \\geq Q _ { p ^ { \\prime } } ( s , a ) \\geq Q ^ { * } ( s , a )"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    574,
+                    321,
+                    1124,
+                    321,
+                    1124,
+                    381,
+                    574,
+                    381
+                ],
+                "score": 0.92,
+                "latex": "\\Delta _ { i } = \\left( \\alpha _ { k } ^ { i } \\cdot I [ t _ { i } < \\infty ] \\cdot \\left( \\mathbb { P } V ^ { * } - \\mathbb { \\hat { P } } _ { t _ { i } } V ^ { * } \\right) ( s , a ) \\right)"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    567,
+                    1954,
+                    642,
+                    1954,
+                    642,
+                    1988,
+                    567,
+                    1988
+                ],
+                "score": 0.92,
+                "latex": "p ^ { \\prime } \\leq p"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    783,
+                    417,
+                    841,
+                    417,
+                    841,
+                    450,
+                    783,
+                    450
+                ],
+                "score": 0.92,
+                "latex": "F _ { i + 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    427,
+                    985,
+                    517,
+                    985,
+                    517,
+                    1019,
+                    427,
+                    1019
+                ],
+                "score": 0.91,
+                "latex": "1 - \\delta / 2"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    664,
+                    1867,
+                    738,
+                    1867,
+                    738,
+                    1899,
+                    664,
+                    1899
+                ],
+                "score": 0.91,
+                "latex": "p ^ { \\prime } + 1"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    781,
+                    1918,
+                    872,
+                    1918,
+                    872,
+                    1952,
+                    781,
+                    1952
+                ],
+                "score": 0.91,
+                "latex": "1 - \\delta / 2"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    856,
+                    589,
+                    1158,
+                    589,
+                    1158,
+                    622,
+                    856,
+                    622
+                ],
+                "score": 0.9,
+                "latex": "1 - \\delta / \\left[ S A ( k + 1 ) ( k + 2 ) \\right]"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1125,
+                    231,
+                    1196,
+                    231,
+                    1196,
+                    262,
+                    1125,
+                    262
+                ],
+                "score": 0.9,
+                "latex": "p \\in \\mathbb N"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    873,
+                    263,
+                    937,
+                    263,
+                    937,
+                    292,
+                    873,
+                    292
+                ],
+                "score": 0.9,
+                "latex": "t \\geq 1"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1257,
+                    414,
+                    1397,
+                    414,
+                    1397,
+                    457,
+                    1257,
+                    457
+                ],
+                "score": 0.9,
+                "latex": "\\begin{array} { r } { | \\Delta _ { i } | \\le \\frac { 2 } { 1 - \\gamma } } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    517,
+                    263,
+                    582,
+                    263,
+                    582,
+                    290,
+                    517,
+                    290
+                ],
+                "score": 0.9,
+                "latex": "t = 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1329,
+                    789,
+                    1397,
+                    789,
+                    1397,
+                    817,
+                    1329,
+                    817
+                ],
+                "score": 0.89,
+                "latex": "k > 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    420,
+                    453,
+                    454,
+                    453,
+                    454,
+                    482,
+                    420,
+                    482
+                ],
+                "score": 0.89,
+                "latex": "\\Delta _ { i }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    548,
+                    418,
+                    583,
+                    418,
+                    583,
+                    447,
+                    548,
+                    447
+                ],
+                "score": 0.89,
+                "latex": "\\Delta _ { i }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    925,
+                    232,
+                    993,
+                    232,
+                    993,
+                    260,
+                    925,
+                    260
+                ],
+                "score": 0.89,
+                "latex": "s \\in S"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    358,
+                    784,
+                    474,
+                    784,
+                    474,
+                    819,
+                    358,
+                    819
+                ],
+                "score": 0.89,
+                "latex": "c _ { 2 } = 4 \\sqrt { 2 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1003,
+                    232,
+                    1076,
+                    232,
+                    1076,
+                    260,
+                    1003,
+                    260
+                ],
+                "score": 0.88,
+                "latex": "a \\in A"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    937,
+                    388,
+                    1149,
+                    388,
+                    1149,
+                    419,
+                    937,
+                    419
+                ],
+                "score": 0.88,
+                "latex": "( s _ { 1 } , a _ { 1 } , . . . , s _ { t _ { i } } , a _ { t _ { i } } )"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    415,
+                    1228,
+                    1285,
+                    1228,
+                    1285,
+                    1418,
+                    415,
+                    1418
+                ],
+                "score": 0.88,
+                "latex": "\\begin{array} { r l } & { ( Q _ { p } - Q ^ { * } ) ( s , a ) \\leq \\displaystyle \\frac { \\alpha _ { t } ^ { 0 } } { 1 - \\gamma } + \\gamma \\left| \\displaystyle \\sum _ { i = 1 } ^ { t } \\Delta _ { i } \\right| + \\displaystyle \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\left[ \\gamma ( \\hat { V } _ { t _ { i } } - V ^ { * } ) ( x _ { t _ { i } + 1 } ) + b _ { i } \\right] } \\\\ & { \\qquad \\leq \\displaystyle \\frac { \\alpha _ { t } ^ { 0 } } { 1 - \\gamma } + \\displaystyle \\frac { 3 c _ { 2 } } { 1 - \\gamma } \\sqrt { \\frac { H \\iota ( t ) } { t } } + \\displaystyle \\sum _ { i = 1 } ^ { t } \\gamma \\alpha _ { t } ^ { i } ( \\hat { V } ^ { t _ { i } } - V ^ { * } ) ( x _ { t _ { i } + 1 } ) } \\end{array}"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    580,
+                    1093,
+                    1115,
+                    1093,
+                    1115,
+                    1187,
+                    580,
+                    1187
+                ],
+                "score": 0.86,
+                "latex": "\\frac { c _ { 2 } } { 1 - \\gamma } \\sqrt { \\frac { H \\iota ( k ) } { k } } \\leq \\sum _ { i = 1 } ^ { k } \\alpha _ { k } ^ { i } b _ { i } \\leq \\frac { 2 c _ { 2 } } { 1 - \\gamma } \\sqrt { \\frac { H \\iota ( k ) } { k } } ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    346,
+                    388,
+                    376,
+                    388,
+                    376,
+                    416,
+                    346,
+                    416
+                ],
+                "score": 0.86,
+                "latex": "F _ { i }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    407,
+                    1553,
+                    729,
+                    1553,
+                    729,
+                    1593,
+                    407,
+                    1593
+                ],
+                "score": 0.85,
+                "latex": "\\beta _ { t } = c _ { 3 } ( 1 - \\gamma ) ^ { - 1 } \\sqrt { H \\iota ( t ) / t }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    996,
+                    417,
+                    1242,
+                    417,
+                    1242,
+                    455,
+                    996,
+                    455
+                ],
+                "score": 0.85,
+                "latex": "\\textstyle 0 \\leq V ^ { \\ast } ( s , { \\bar { a } } ) \\leq { \\frac { 1 } { 1 - \\gamma } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1380,
+                    265,
+                    1398,
+                    265,
+                    1398,
+                    289,
+                    1380,
+                    289
+                ],
+                "score": 0.83,
+                "latex": "k"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    469,
+                    391,
+                    489,
+                    391,
+                    489,
+                    414,
+                    469,
+                    414
+                ],
+                "score": 0.81,
+                "latex": "\\sigma"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1043,
+                    790,
+                    1061,
+                    790,
+                    1061,
+                    816,
+                    1043,
+                    816
+                ],
+                "score": 0.81,
+                "latex": "k"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1155,
+                    1874,
+                    1171,
+                    1874,
+                    1171,
+                    1899,
+                    1155,
+                    1899
+                ],
+                "score": 0.79,
+                "latex": "p"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1317,
+                    962,
+                    1334,
+                    962,
+                    1334,
+                    987,
+                    1317,
+                    987
+                ],
+                "score": 0.77,
+                "latex": "p"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    951,
+                    1922,
+                    1024,
+                    1922,
+                    1024,
+                    1951,
+                    951,
+                    1951
+                ],
+                "score": 0.77,
+                "latex": "p , s , a"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    479,
+                    822,
+                    551,
+                    822,
+                    551,
+                    847,
+                    479,
+                    847
+                ],
+                "score": 0.77,
+                "latex": "a \\in A"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    444,
+                    596,
+                    461,
+                    596,
+                    461,
+                    621,
+                    444,
+                    621
+                ],
+                "score": 0.76,
+                "latex": "\\eta"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    400,
+                    821,
+                    469,
+                    821,
+                    469,
+                    848,
+                    400,
+                    848
+                ],
+                "score": 0.74,
+                "latex": "s \\in S"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    740,
+                    1552,
+                    948,
+                    1552,
+                    948,
+                    1590,
+                    740,
+                    1590
+                ],
+                "score": 0.73,
+                "latex": "c _ { 3 } = 3 c _ { 2 } = 1 2 { \\sqrt { 2 } } ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    801,
+                    237,
+                    819,
+                    237,
+                    819,
+                    258,
+                    801,
+                    258
+                ],
+                "score": 0.73,
+                "latex": "a"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    937,
+                    1033,
+                    1157,
+                    1033,
+                    1157,
+                    1089,
+                    937,
+                    1089
+                ],
+                "score": 0.68,
+                "latex": "\\begin{array} { r } { ( b _ { k } = \\frac { c _ { 2 } } { 1 - \\gamma } \\sqrt { \\frac { H \\iota ( k ) } { k } } ) } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    708,
+                    238,
+                    725,
+                    238,
+                    725,
+                    262,
+                    708,
+                    262
+                ],
+                "score": 0.6,
+                "latex": "p"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    736,
+                    238,
+                    753,
+                    238,
+                    753,
+                    259,
+                    736,
+                    259
+                ],
+                "score": 0.47,
+                "latex": "s"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    608,
+                    1453,
+                    1121,
+                    1453,
+                    1121,
+                    1546,
+                    608,
+                    1546
+                ],
+                "score": 0.38,
+                "latex": "\\leq \\frac { \\alpha _ { t } ^ { 0 } } { 1 - \\gamma } + \\sum _ { i = 1 } ^ { t } \\gamma \\alpha _ { t } ^ { i } ( { \\hat { V } } ^ { t _ { i } } - V ^ { * } ) ( x _ { t _ { i } + 1 } ) + \\beta _ { t } ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    399,
+                    820,
+                    551,
+                    820,
+                    551,
+                    849,
+                    399,
+                    849
+                ],
+                "score": 0.33,
+                "latex": "s \\in S , a \\in A"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    707,
+                    237,
+                    753,
+                    237,
+                    753,
+                    261,
+                    707,
+                    261
+                ],
+                "score": 0.31,
+                "latex": "p , s"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    72.0,
+                    817.0,
+                    72.0,
+                    817.0,
+                    108.0,
+                    295.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    831.0,
+                    2085.0,
+                    868.0,
+                    2085.0,
+                    868.0,
+                    2124.0,
+                    831.0,
+                    2124.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1381.0,
+                    2009.0,
+                    1401.0,
+                    2009.0,
+                    1401.0,
+                    2029.0,
+                    1381.0,
+                    2029.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    381.0,
+                    345.0,
+                    381.0,
+                    345.0,
+                    423.0,
+                    292.0,
+                    423.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    377.0,
+                    381.0,
+                    468.0,
+                    381.0,
+                    468.0,
+                    423.0,
+                    377.0,
+                    423.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    490.0,
+                    381.0,
+                    936.0,
+                    381.0,
+                    936.0,
+                    423.0,
+                    490.0,
+                    423.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1150.0,
+                    381.0,
+                    1408.0,
+                    381.0,
+                    1408.0,
+                    423.0,
+                    1150.0,
+                    423.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    287.0,
+                    401.0,
+                    296.0,
+                    401.0,
+                    296.0,
+                    465.0,
+                    287.0,
+                    465.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    464.0,
+                    401.0,
+                    547.0,
+                    401.0,
+                    547.0,
+                    465.0,
+                    464.0,
+                    465.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    584.0,
+                    401.0,
+                    782.0,
+                    401.0,
+                    782.0,
+                    465.0,
+                    584.0,
+                    465.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    842.0,
+                    401.0,
+                    995.0,
+                    401.0,
+                    995.0,
+                    465.0,
+                    842.0,
+                    465.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1243.0,
+                    401.0,
+                    1256.0,
+                    401.0,
+                    1256.0,
+                    465.0,
+                    1243.0,
+                    465.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1398.0,
+                    401.0,
+                    1410.0,
+                    401.0,
+                    1410.0,
+                    465.0,
+                    1398.0,
+                    465.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    446.0,
+                    419.0,
+                    446.0,
+                    419.0,
+                    488.0,
+                    293.0,
+                    488.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    455.0,
+                    446.0,
+                    1271.0,
+                    446.0,
+                    1271.0,
+                    488.0,
+                    455.0,
+                    488.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    225.0,
+                    706.0,
+                    225.0,
+                    706.0,
+                    267.0,
+                    292.0,
+                    267.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    754.0,
+                    225.0,
+                    800.0,
+                    225.0,
+                    800.0,
+                    267.0,
+                    754.0,
+                    267.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    820.0,
+                    225.0,
+                    924.0,
+                    225.0,
+                    924.0,
+                    267.0,
+                    820.0,
+                    267.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    994.0,
+                    225.0,
+                    1002.0,
+                    225.0,
+                    1002.0,
+                    267.0,
+                    994.0,
+                    267.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1077.0,
+                    225.0,
+                    1124.0,
+                    225.0,
+                    1124.0,
+                    267.0,
+                    1077.0,
+                    267.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1197.0,
+                    225.0,
+                    1251.0,
+                    225.0,
+                    1251.0,
+                    267.0,
+                    1197.0,
+                    267.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1397.0,
+                    225.0,
+                    1408.0,
+                    225.0,
+                    1408.0,
+                    267.0,
+                    1397.0,
+                    267.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    259.0,
+                    296.0,
+                    259.0,
+                    296.0,
+                    296.0,
+                    291.0,
+                    296.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    455.0,
+                    259.0,
+                    516.0,
+                    259.0,
+                    516.0,
+                    296.0,
+                    455.0,
+                    296.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    583.0,
+                    259.0,
+                    872.0,
+                    259.0,
+                    872.0,
+                    296.0,
+                    583.0,
+                    296.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    938.0,
+                    259.0,
+                    1379.0,
+                    259.0,
+                    1379.0,
+                    296.0,
+                    938.0,
+                    296.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1399.0,
+                    259.0,
+                    1411.0,
+                    259.0,
+                    1411.0,
+                    296.0,
+                    1399.0,
+                    296.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    288.0,
+                    381.0,
+                    288.0,
+                    381.0,
+                    325.0,
+                    292.0,
+                    325.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    949.0,
+                    1031.0,
+                    949.0,
+                    1031.0,
+                    989.0,
+                    293.0,
+                    989.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1184.0,
+                    949.0,
+                    1316.0,
+                    949.0,
+                    1316.0,
+                    989.0,
+                    1184.0,
+                    989.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1335.0,
+                    949.0,
+                    1403.0,
+                    949.0,
+                    1403.0,
+                    989.0,
+                    1335.0,
+                    989.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    986.0,
+                    426.0,
+                    986.0,
+                    426.0,
+                    1019.0,
+                    293.0,
+                    1019.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    518.0,
+                    986.0,
+                    613.0,
+                    986.0,
+                    613.0,
+                    1019.0,
+                    518.0,
+                    1019.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1600.0,
+                    1406.0,
+                    1600.0,
+                    1406.0,
+                    1638.0,
+                    293.0,
+                    1638.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1632.0,
+                    297.0,
+                    1632.0,
+                    297.0,
+                    1671.0,
+                    294.0,
+                    1671.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    407.0,
+                    1632.0,
+                    485.0,
+                    1632.0,
+                    485.0,
+                    1671.0,
+                    407.0,
+                    1671.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    549.0,
+                    1632.0,
+                    598.0,
+                    1632.0,
+                    598.0,
+                    1671.0,
+                    549.0,
+                    1671.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    675.0,
+                    1632.0,
+                    1106.0,
+                    1632.0,
+                    1106.0,
+                    1671.0,
+                    675.0,
+                    1671.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1183.0,
+                    1632.0,
+                    1260.0,
+                    1632.0,
+                    1260.0,
+                    1671.0,
+                    1183.0,
+                    1671.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1913.0,
+                    780.0,
+                    1913.0,
+                    780.0,
+                    1955.0,
+                    294.0,
+                    1955.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    873.0,
+                    1913.0,
+                    950.0,
+                    1913.0,
+                    950.0,
+                    1955.0,
+                    873.0,
+                    1955.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1025.0,
+                    1913.0,
+                    1105.0,
+                    1913.0,
+                    1105.0,
+                    1955.0,
+                    1025.0,
+                    1955.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1206.0,
+                    1913.0,
+                    1405.0,
+                    1913.0,
+                    1405.0,
+                    1955.0,
+                    1206.0,
+                    1955.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1952.0,
+                    351.0,
+                    1952.0,
+                    351.0,
+                    1995.0,
+                    295.0,
+                    1995.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    459.0,
+                    1952.0,
+                    566.0,
+                    1952.0,
+                    566.0,
+                    1995.0,
+                    459.0,
+                    1995.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    643.0,
+                    1952.0,
+                    808.0,
+                    1952.0,
+                    808.0,
+                    1995.0,
+                    643.0,
+                    1995.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1182.0,
+                    1952.0,
+                    1398.0,
+                    1952.0,
+                    1398.0,
+                    1995.0,
+                    1182.0,
+                    1995.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    289.0,
+                    769.0,
+                    357.0,
+                    769.0,
+                    357.0,
+                    831.0,
+                    289.0,
+                    831.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    475.0,
+                    769.0,
+                    484.0,
+                    769.0,
+                    484.0,
+                    831.0,
+                    475.0,
+                    831.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    752.0,
+                    769.0,
+                    1042.0,
+                    769.0,
+                    1042.0,
+                    831.0,
+                    752.0,
+                    831.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1062.0,
+                    769.0,
+                    1328.0,
+                    769.0,
+                    1328.0,
+                    831.0,
+                    1062.0,
+                    831.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1398.0,
+                    769.0,
+                    1414.0,
+                    769.0,
+                    1414.0,
+                    831.0,
+                    1398.0,
+                    831.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    815.0,
+                    398.0,
+                    815.0,
+                    398.0,
+                    855.0,
+                    295.0,
+                    855.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    552.0,
+                    815.0,
+                    912.0,
+                    815.0,
+                    912.0,
+                    855.0,
+                    552.0,
+                    855.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1187.0,
+                    576.0,
+                    1187.0,
+                    576.0,
+                    1229.0,
+                    293.0,
+                    1229.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1862.0,
+                    663.0,
+                    1862.0,
+                    663.0,
+                    1905.0,
+                    293.0,
+                    1905.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    739.0,
+                    1862.0,
+                    1154.0,
+                    1862.0,
+                    1154.0,
+                    1905.0,
+                    739.0,
+                    1905.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1172.0,
+                    1862.0,
+                    1182.0,
+                    1862.0,
+                    1182.0,
+                    1905.0,
+                    1172.0,
+                    1905.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1548.0,
+                    406.0,
+                    1548.0,
+                    406.0,
+                    1596.0,
+                    294.0,
+                    1596.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    730.0,
+                    1548.0,
+                    739.0,
+                    1548.0,
+                    739.0,
+                    1596.0,
+                    730.0,
+                    1596.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    949.0,
+                    1548.0,
+                    955.0,
+                    1548.0,
+                    955.0,
+                    1596.0,
+                    949.0,
+                    1596.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    584.0,
+                    443.0,
+                    584.0,
+                    443.0,
+                    627.0,
+                    295.0,
+                    627.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    462.0,
+                    584.0,
+                    855.0,
+                    584.0,
+                    855.0,
+                    627.0,
+                    462.0,
+                    627.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1159.0,
+                    584.0,
+                    1171.0,
+                    584.0,
+                    1171.0,
+                    627.0,
+                    1159.0,
+                    627.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1045.0,
+                    936.0,
+                    1045.0,
+                    936.0,
+                    1083.0,
+                    293.0,
+                    1083.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1158.0,
+                    1029.0,
+                    1164.0,
+                    1029.0,
+                    1164.0,
+                    1075.0,
+                    1158.0,
+                    1075.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1004.0,
+                    1062.0,
+                    1056.0,
+                    1062.0,
+                    1056.0,
+                    1084.5,
+                    1004.0,
+                    1084.5
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 12,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 8,
+                "poly": [
+                    444,
+                    376,
+                    1252,
+                    376,
+                    1252,
+                    629,
+                    444,
+                    629
+                ],
+                "score": 0.97
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    578,
+                    882,
+                    1120,
+                    882,
+                    1120,
+                    1081,
+                    578,
+                    1081
+                ],
+                "score": 0.964
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    551,
+                    1350,
+                    1145,
+                    1350,
+                    1145,
+                    1592,
+                    551,
+                    1592
+                ],
+                "score": 0.962
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    648,
+                    1663,
+                    1048,
+                    1663,
+                    1048,
+                    1813,
+                    648,
+                    1813
+                ],
+                "score": 0.962
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    716,
+                    716,
+                    983,
+                    716,
+                    983,
+                    804,
+                    716,
+                    804
+                ],
+                "score": 0.957
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    633,
+                    1896,
+                    1064,
+                    1896,
+                    1064,
+                    1983,
+                    633,
+                    1983
+                ],
+                "score": 0.954
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    291,
+                    227,
+                    1403,
+                    227,
+                    1403,
+                    298,
+                    291,
+                    298
+                ],
+                "score": 0.951
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1224,
+                    1406,
+                    1224,
+                    1406,
+                    1295,
+                    297,
+                    1295
+                ],
+                "score": 0.949
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    639,
+                    1403,
+                    639,
+                    1403,
+                    708,
+                    297,
+                    708
+                ],
+                "score": 0.949
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    1831,
+                    1400,
+                    1831,
+                    1400,
+                    1895,
+                    295,
+                    1895
+                ],
+                "score": 0.939
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    831,
+                    1063,
+                    831,
+                    1063,
+                    870,
+                    295,
+                    870
+                ],
+                "score": 0.935
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    329,
+                    870,
+                    329,
+                    870,
+                    364,
+                    296,
+                    364
+                ],
+                "score": 0.927
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1308,
+                    804,
+                    1308,
+                    804,
+                    1340,
+                    297,
+                    1340
+                ],
+                "score": 0.922
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1642,
+                    377,
+                    1642,
+                    377,
+                    1674,
+                    296,
+                    1674
+                ],
+                "score": 0.921
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    73,
+                    817,
+                    73,
+                    817,
+                    106,
+                    298,
+                    106
+                ],
+                "score": 0.921
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    704,
+                    1174,
+                    1085,
+                    1174,
+                    1085,
+                    1215,
+                    704,
+                    1215
+                ],
+                "score": 0.897
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1351,
+                    739,
+                    1401,
+                    739,
+                    1401,
+                    771,
+                    1351,
+                    771
+                ],
+                "score": 0.896
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1351,
+                    1181,
+                    1400,
+                    1181,
+                    1400,
+                    1212,
+                    1351,
+                    1212
+                ],
+                "score": 0.896
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1351,
+                    563,
+                    1401,
+                    563,
+                    1401,
+                    595,
+                    1351,
+                    595
+                ],
+                "score": 0.893
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1351,
+                    1499,
+                    1401,
+                    1499,
+                    1401,
+                    1531,
+                    1351,
+                    1531
+                ],
+                "score": 0.888
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1351,
+                    1019,
+                    1401,
+                    1019,
+                    1401,
+                    1051,
+                    1351,
+                    1051
+                ],
+                "score": 0.886
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1351,
+                    1597,
+                    1401,
+                    1597,
+                    1401,
+                    1629,
+                    1351,
+                    1629
+                ],
+                "score": 0.885
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    702,
+                    1090,
+                    1113,
+                    1090,
+                    1113,
+                    1165,
+                    702,
+                    1165
+                ],
+                "score": 0.885
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1351,
+                    1103,
+                    1400,
+                    1103,
+                    1400,
+                    1135,
+                    1351,
+                    1135
+                ],
+                "score": 0.879
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    835,
+                    2088,
+                    864,
+                    2088,
+                    864,
+                    2113,
+                    835,
+                    2113
+                ],
+                "score": 0.879
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    328,
+                    2002,
+                    1096,
+                    2002,
+                    1096,
+                    2036,
+                    328,
+                    2036
+                ],
+                "score": 0.731
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    328,
+                    2002,
+                    1096,
+                    2002,
+                    1096,
+                    2036,
+                    328,
+                    2036
+                ],
+                "score": 0.159
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    457,
+                    262,
+                    532,
+                    262,
+                    532,
+                    295,
+                    457,
+                    295
+                ],
+                "score": 0.95,
+                "latex": "( C , w )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    424,
+                    331,
+                    602,
+                    331,
+                    602,
+                    365,
+                    424,
+                    365
+                ],
+                "score": 0.95,
+                "latex": "n _ { t } = N _ { t } ( s _ { t } , a _ { t } )"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    577,
+                    881,
+                    1119,
+                    881,
+                    1119,
+                    1217,
+                    577,
+                    1217
+                ],
+                "score": 0.94,
+                "latex": "\\begin{array} { l } { \\displaystyle \\sum _ { t \\geq 1 } w _ { t } \\beta _ { n _ { t } } = \\sum _ { s , o } ^ { u ( s , o ) } w _ { \\tau ( s , a , i ) } \\beta _ { i } } \\\\ { \\displaystyle \\qquad \\leq \\sum _ { s , a } ( 1 - \\gamma ) ^ { - 1 } c _ { 3 } \\sum _ { i = 1 } ^ { C _ { s , a } / w } \\sqrt { \\frac { H \\iota ( i ) } { i } } w } \\\\ { \\displaystyle \\qquad \\leq 2 \\sum _ { s , a } ( 1 - \\gamma ) ^ { - 1 } c _ { 3 } \\sqrt { \\iota ( C ) H C _ { s , a } w } } \\\\ { \\displaystyle \\qquad \\leq 2 c _ { 3 } ( 1 - \\gamma ) ^ { - 1 } \\sqrt { w S A H C \\iota ( C ) } . } \\end{array}"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    632,
+                    1889,
+                    1066,
+                    1889,
+                    1066,
+                    1985,
+                    632,
+                    1985
+                ],
+                "score": 0.94,
+                "latex": "w _ { t ^ { \\prime } + 1 } ^ { \\prime } \\leq w \\sum _ { j = n _ { t ^ { \\prime } } } ^ { \\infty } \\alpha _ { j } ^ { n _ { t ^ { \\prime } } } = ( 1 + 1 / H ) w ."
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    439,
+                    374,
+                    1253,
+                    374,
+                    1253,
+                    630,
+                    439,
+                    630
+                ],
+                "score": 0.94,
+                "latex": "\\begin{array} { r l } {  { \\sum _ { t \\geq 1 } w _ { t } ( \\hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) } } \\\\ & { \\leq \\sum _ { t \\geq 1 } w _ { t } ( Q _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) } \\\\ & { \\leq \\sum _ { t \\geq 1 } w _ { t } [ \\cfrac { \\alpha _ { n _ { t } } ^ { 0 } } { 1 - \\gamma } + \\beta _ { n _ { t } } + \\gamma \\sum _ { i = 1 } ^ { n _ { t } } \\alpha _ { n _ { t } } ^ { i } ( \\hat { V } _ { \\tau ( s _ { t } , a _ { t } , i ) } - V ^ { * } ) ( s _ { \\tau ( s _ { t } , a _ { t } , i ) + 1 } ) ] } \\end{array}"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    649,
+                    1662,
+                    1049,
+                    1662,
+                    1049,
+                    1810,
+                    649,
+                    1810
+                ],
+                "score": 0.94,
+                "latex": "w _ { t ^ { \\prime } + 1 } ^ { \\prime } = \\left( \\sum _ { \\stackrel { t = t ^ { \\prime } + 1 } { ( s _ { t } , a _ { t } ) = ( s _ { t } ^ { \\prime } , a _ { t } ^ { \\prime } ) } } ^ { \\infty } \\alpha _ { n _ { t } } ^ { n _ { t ^ { \\prime } } } w _ { t } \\right) ."
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    713,
+                    713,
+                    984,
+                    713,
+                    984,
+                    806,
+                    713,
+                    806
+                ],
+                "score": 0.93,
+                "latex": "\\sum _ { t \\geq 1 } w _ { t } \\frac { \\alpha _ { n _ { t } } ^ { 0 } } { 1 - \\gamma } \\leq \\frac { S A w } { 1 - \\gamma } ."
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    550,
+                    1348,
+                    1150,
+                    1348,
+                    1150,
+                    1593,
+                    550,
+                    1593
+                ],
+                "score": 0.93,
+                "latex": "\\begin{array} { c } { { \\displaystyle \\sum _ { t \\ge 1 } w _ { t } \\sum _ { i = 1 } ^ { n _ { t } } \\alpha _ { n _ { t } } ^ { i } \\left( \\hat { V } _ { \\tau ( s _ { t } , a _ { t } , i ) } - V ^ { * } \\right) \\left( s _ { \\tau ( s _ { t } , a _ { t } , i ) + 1 } \\right) } } \\\\ { { \\displaystyle \\le \\sum _ { t ^ { \\prime } \\ge 1 } \\left( \\hat { V } _ { t ^ { \\prime } } - V ^ { * } \\right) \\left( s _ { t ^ { \\prime } + 1 } \\right) \\left( \\sum _ { t = t ^ { \\prime } + 1 } ^ { \\infty } \\alpha _ { n _ { t } } ^ { n _ { t ^ { \\prime } } } w _ { t } \\right) . } } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    606,
+                    834,
+                    874,
+                    834,
+                    874,
+                    869,
+                    606,
+                    869
+                ],
+                "score": 0.93,
+                "latex": "u ( s , a ) = \\operatorname* { s u p } _ { t } N _ { t } ( s , a )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    823,
+                    640,
+                    1007,
+                    640,
+                    1007,
+                    679,
+                    823,
+                    679
+                ],
+                "score": 0.93,
+                "latex": "\\alpha _ { n _ { t } } ^ { 0 } = \\mathbb { I } [ n _ { t } = 0 ]"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    460,
+                    1834,
+                    520,
+                    1834,
+                    520,
+                    1870,
+                    460,
+                    1870
+                ],
+                "score": 0.92,
+                "latex": "w _ { t + 1 } ^ { \\prime }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1168,
+                    261,
+                    1330,
+                    261,
+                    1330,
+                    300,
+                    1168,
+                    300
+                ],
+                "score": 0.92,
+                "latex": "\\textstyle \\sum _ { t \\geq 1 } w _ { t } \\leq C"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    828,
+                    263,
+                    969,
+                    263,
+                    969,
+                    293,
+                    828,
+                    293
+                ],
+                "score": 0.92,
+                "latex": "0 \\leq w _ { t } \\leq w"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    975,
+                    231,
+                    1051,
+                    231,
+                    1051,
+                    263,
+                    975,
+                    263
+                ],
+                "score": 0.92,
+                "latex": "( C , w )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    686,
+                    262,
+                    793,
+                    262,
+                    793,
+                    294,
+                    686,
+                    294
+                ],
+                "score": 0.92,
+                "latex": "C , w > 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    572,
+                    1832,
+                    742,
+                    1832,
+                    742,
+                    1871,
+                    572,
+                    1871
+                ],
+                "score": 0.92,
+                "latex": "\\textstyle ( C , ( 1 + { \\frac { 1 } { H } } ) w )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1312,
+                    230,
+                    1403,
+                    230,
+                    1403,
+                    265,
+                    1312,
+                    265
+                ],
+                "score": 0.91,
+                "latex": "( w _ { t } ) _ { t \\geq 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    379,
+                    1225,
+                    706,
+                    1225,
+                    706,
+                    1265,
+                    379,
+                    1265
+                ],
+                "score": 0.91,
+                "latex": "\\begin{array} { r } { C _ { s , a } = \\sum _ { t \\geq 1 , ( s _ { t } , a _ { t } ) = ( s , a ) } w _ { t } } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    1260,
+                    377,
+                    1260,
+                    377,
+                    1295,
+                    298,
+                    1295
+                ],
+                "score": 0.9,
+                "latex": "\\iota ( x ) / x"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1046,
+                    263,
+                    1110,
+                    263,
+                    1110,
+                    292,
+                    1046,
+                    292
+                ],
+                "score": 0.89,
+                "latex": "t \\geq 1"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    651,
+                    2006,
+                    709,
+                    2006,
+                    709,
+                    2035,
+                    651,
+                    2035
+                ],
+                "score": 0.89,
+                "latex": "( s , a )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    333,
+                    2003,
+                    416,
+                    2003,
+                    416,
+                    2035,
+                    333,
+                    2035
+                ],
+                "score": 0.89,
+                "latex": "^ 2 u ( s , a )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    1865,
+                    369,
+                    1865,
+                    369,
+                    1897,
+                    298,
+                    1897
+                ],
+                "score": 0.88,
+                "latex": "t ^ { \\prime } \\geq 0"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    72.0,
+                    817.0,
+                    72.0,
+                    817.0,
+                    108.0,
+                    295.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    831.0,
+                    2085.0,
+                    869.0,
+                    2085.0,
+                    869.0,
+                    2123.0,
+                    831.0,
+                    2123.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    417.0,
+                    2001.0,
+                    650.0,
+                    2001.0,
+                    650.0,
+                    2038.0,
+                    417.0,
+                    2038.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    710.0,
+                    2001.0,
+                    1097.0,
+                    2001.0,
+                    1097.0,
+                    2038.0,
+                    710.0,
+                    2038.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    221.0,
+                    974.0,
+                    221.0,
+                    974.0,
+                    272.0,
+                    292.0,
+                    272.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1052.0,
+                    221.0,
+                    1311.0,
+                    221.0,
+                    1311.0,
+                    272.0,
+                    1052.0,
+                    272.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    258.0,
+                    456.0,
+                    258.0,
+                    456.0,
+                    300.0,
+                    293.0,
+                    300.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    533.0,
+                    258.0,
+                    685.0,
+                    258.0,
+                    685.0,
+                    300.0,
+                    533.0,
+                    300.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    794.0,
+                    258.0,
+                    827.0,
+                    258.0,
+                    827.0,
+                    300.0,
+                    794.0,
+                    300.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    970.0,
+                    258.0,
+                    1045.0,
+                    258.0,
+                    1045.0,
+                    300.0,
+                    970.0,
+                    300.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1111.0,
+                    258.0,
+                    1167.0,
+                    258.0,
+                    1167.0,
+                    300.0,
+                    1111.0,
+                    300.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1331.0,
+                    258.0,
+                    1342.0,
+                    258.0,
+                    1342.0,
+                    300.0,
+                    1331.0,
+                    300.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    289.0,
+                    1213.0,
+                    378.0,
+                    1213.0,
+                    378.0,
+                    1274.0,
+                    289.0,
+                    1274.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    707.0,
+                    1213.0,
+                    1409.0,
+                    1213.0,
+                    1409.0,
+                    1274.0,
+                    707.0,
+                    1274.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    378.0,
+                    1255.0,
+                    1251.0,
+                    1255.0,
+                    1251.0,
+                    1300.0,
+                    378.0,
+                    1300.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    635.0,
+                    822.0,
+                    635.0,
+                    822.0,
+                    684.0,
+                    291.0,
+                    684.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1008.0,
+                    635.0,
+                    1409.0,
+                    635.0,
+                    1409.0,
+                    684.0,
+                    1008.0,
+                    684.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    668.0,
+                    473.0,
+                    668.0,
+                    473.0,
+                    711.0,
+                    293.0,
+                    711.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    289.0,
+                    1825.0,
+                    459.0,
+                    1825.0,
+                    459.0,
+                    1876.0,
+                    289.0,
+                    1876.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    521.0,
+                    1825.0,
+                    571.0,
+                    1825.0,
+                    571.0,
+                    1876.0,
+                    521.0,
+                    1876.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    743.0,
+                    1825.0,
+                    1407.0,
+                    1825.0,
+                    1407.0,
+                    1876.0,
+                    743.0,
+                    1876.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    290.0,
+                    1857.0,
+                    297.0,
+                    1857.0,
+                    297.0,
+                    1904.0,
+                    290.0,
+                    1904.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    370.0,
+                    1857.0,
+                    385.0,
+                    1857.0,
+                    385.0,
+                    1904.0,
+                    370.0,
+                    1904.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    831.0,
+                    605.0,
+                    831.0,
+                    605.0,
+                    872.0,
+                    294.0,
+                    872.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    875.0,
+                    831.0,
+                    1064.0,
+                    831.0,
+                    1064.0,
+                    872.0,
+                    875.0,
+                    872.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    329.0,
+                    423.0,
+                    329.0,
+                    423.0,
+                    369.0,
+                    295.0,
+                    369.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    603.0,
+                    329.0,
+                    869.0,
+                    329.0,
+                    869.0,
+                    369.0,
+                    603.0,
+                    369.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1305.0,
+                    805.0,
+                    1305.0,
+                    805.0,
+                    1343.0,
+                    294.0,
+                    1343.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1638.0,
+                    379.0,
+                    1638.0,
+                    379.0,
+                    1679.0,
+                    294.0,
+                    1679.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    417.0,
+                    2001.0,
+                    650.0,
+                    2001.0,
+                    650.0,
+                    2038.0,
+                    417.0,
+                    2038.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    710.0,
+                    2001.0,
+                    1097.0,
+                    2001.0,
+                    1097.0,
+                    2038.0,
+                    710.0,
+                    2038.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 13,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1267,
+                    1410,
+                    1267,
+                    1410,
+                    1440,
+                    296,
+                    1440
+                ],
+                "score": 0.977
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    301,
+                    750,
+                    1398,
+                    750,
+                    1398,
+                    853,
+                    301,
+                    853
+                ],
+                "score": 0.972
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    349,
+                    1454,
+                    1353,
+                    1454,
+                    1353,
+                    1714,
+                    349,
+                    1714
+                ],
+                "score": 0.969
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1760,
+                    1406,
+                    1760,
+                    1406,
+                    1849,
+                    297,
+                    1849
+                ],
+                "score": 0.967
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    330,
+                    1087,
+                    1323,
+                    1087,
+                    1323,
+                    1256,
+                    330,
+                    1256
+                ],
+                "score": 0.967
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    410,
+                    871,
+                    1285,
+                    871,
+                    1285,
+                    974,
+                    410,
+                    974
+                ],
+                "score": 0.96
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    480,
+                    308,
+                    1219,
+                    308,
+                    1219,
+                    467,
+                    480,
+                    467
+                ],
+                "score": 0.956
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    290,
+                    225,
+                    1405,
+                    225,
+                    1405,
+                    297,
+                    290,
+                    297
+                ],
+                "score": 0.942
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    317,
+                    1896,
+                    1334,
+                    1896,
+                    1334,
+                    1989,
+                    317,
+                    1989
+                ],
+                "score": 0.936
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1001,
+                    804,
+                    1001,
+                    804,
+                    1036,
+                    297,
+                    1036
+                ],
+                "score": 0.931
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    481,
+                    474,
+                    1186,
+                    474,
+                    1186,
+                    558,
+                    481,
+                    558
+                ],
+                "score": 0.923
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    297,
+                    73,
+                    817,
+                    73,
+                    817,
+                    106,
+                    297,
+                    106
+                ],
+                "score": 0.92
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    480,
+                    655,
+                    1168,
+                    655,
+                    1168,
+                    737,
+                    480,
+                    737
+                ],
+                "score": 0.905
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1351,
+                    584,
+                    1400,
+                    584,
+                    1400,
+                    615,
+                    1351,
+                    615
+                ],
+                "score": 0.883
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1351,
+                    674,
+                    1401,
+                    674,
+                    1401,
+                    706,
+                    1351,
+                    706
+                ],
+                "score": 0.882
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1351,
+                    494,
+                    1401,
+                    494,
+                    1401,
+                    525,
+                    1351,
+                    525
+                ],
+                "score": 0.878
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1350,
+                    402,
+                    1401,
+                    402,
+                    1401,
+                    434,
+                    1350,
+                    434
+                ],
+                "score": 0.875
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1352,
+                    1192,
+                    1401,
+                    1192,
+                    1401,
+                    1224,
+                    1352,
+                    1224
+                ],
+                "score": 0.869
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    835,
+                    2087,
+                    864,
+                    2087,
+                    864,
+                    2113,
+                    835,
+                    2113
+                ],
+                "score": 0.863
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    481,
+                    566,
+                    1100,
+                    566,
+                    1100,
+                    646,
+                    481,
+                    646
+                ],
+                "score": 0.853
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1353,
+                    1926,
+                    1400,
+                    1926,
+                    1400,
+                    1956,
+                    1353,
+                    1956
+                ],
+                "score": 0.84
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    1374,
+                    2004,
+                    1402,
+                    2004,
+                    1402,
+                    2032,
+                    1374,
+                    2032
+                ],
+                "score": 0.804
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    471,
+                    308,
+                    1219,
+                    308,
+                    1219,
+                    743,
+                    471,
+                    743
+                ],
+                "score": 0.95,
+                "latex": "\\begin{array} { r l } & { \\quad \\underset { t \\geq 1 } { \\sum \\sigma } u _ { t + 1 } ^ { \\prime } \\left( \\hat { V } _ { t } - V ^ { * } \\right) \\left( s _ { t + 1 } \\right) } \\\\ & { = \\underset { t \\geq 1 } { \\sum \\sigma } u _ { t + 1 } ^ { \\prime } \\left( \\hat { V } _ { t + 1 } - V ^ { * } \\right) \\left( s _ { t + 1 } \\right) + \\underset { t \\geq 1 } { \\sum \\sigma } u _ { t + 1 } ^ { \\prime } \\left( \\hat { V } _ { t } - \\hat { V } _ { t + 1 } \\right) \\left( s _ { t + 1 } \\right) } \\\\ & { \\quad \\leq \\underset { t \\geq 1 } { \\sum \\sigma } u _ { t + 1 } ^ { \\prime } \\left( \\hat { V } _ { t + 1 } - V ^ { * } \\right) \\left( s _ { t + 1 } \\right) + \\underset { t \\geq 1 } { \\sum \\sigma } u _ { t + 1 } ^ { \\prime } \\left( 2 \\alpha _ { n _ { t } + 1 } \\frac { 1 } { 1 - \\gamma } \\right) } \\\\ & { \\quad \\leq \\underset { t \\geq 1 } { \\sum \\sigma } w _ { t + 1 } ^ { \\prime } \\left( \\hat { V } _ { t + 1 } - V ^ { * } \\right) \\left( s _ { t + 1 } \\right) + \\mathcal { O } \\left( \\frac { w S A H } { 1 - \\gamma } \\ln { C } \\right) } \\\\ & { \\quad \\leq \\underset { t \\geq 1 } { \\sum \\sigma } w _ { t + 1 } ^ { \\prime } \\left( \\hat { Q } _ { t + 1 } - Q ^ { * } \\right) \\left( s _ { t + 1 } , a _ { t + 1 } \\right) + \\mathcal { O } \\left( \\frac { w S A H } { 1 - \\gamma } \\ln { C } \\right) } \\end{array}"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    349,
+                    1450,
+                    1353,
+                    1450,
+                    1353,
+                    1714,
+                    349,
+                    1714
+                ],
+                "score": 0.94,
+                "latex": "\\begin{array} { r l } & { \\displaystyle \\sum _ { t \\geq 1 } w _ { t } ( \\hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) } \\\\ & { \\leq 2 c _ { 3 } \\frac { \\sqrt { w ^ { ( H ) } S A H C \\iota ( C ) } } { ( 1 - \\gamma ) ^ { 2 } } + \\mathcal { O } \\left( \\frac { w ^ { ( H ) } S A H } { ( 1 - \\gamma ) ^ { 2 } } \\ln C \\right) + \\gamma ^ { H } \\displaystyle \\sum _ { t \\geq 1 } w _ { t } ^ { ( H ) } \\left( \\hat { Q } _ { t } - Q ^ { * } \\right) ( s _ { t } , a _ { t } ) } \\\\ & { \\leq 2 c _ { 3 } \\frac { \\sqrt { w ^ { ( H ) } S A H C \\iota ( C ) } } { ( 1 - \\gamma ) ^ { 2 } } + \\mathcal { O } \\left( \\frac { w ^ { ( H ) } S A H } { ( 1 - \\gamma ) ^ { 2 } } \\ln C \\right) + \\gamma ^ { H } \\frac { C } { 1 - \\gamma } . } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1009,
+                    1369,
+                    1128,
+                    1369,
+                    1128,
+                    1412,
+                    1009,
+                    1412
+                ],
+                "score": 0.94,
+                "latex": "\\{ w _ { t } ^ { ( k ) } \\} _ { t \\ge 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    379,
+                    1761,
+                    778,
+                    1761,
+                    778,
+                    1810,
+                    379,
+                    1810
+                ],
+                "score": 0.94,
+                "latex": "\\begin{array} { r } { H = \\frac { \\ln 1 / ( ( 1 - \\gamma ) \\epsilon _ { 1 } ) } { \\ln 1 / \\gamma } \\leq \\frac { \\ln 1 / ( ( 1 - \\gamma ) \\epsilon _ { 1 } ) } { 1 - \\gamma } , } \\end{array}"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    315,
+                    1895,
+                    1339,
+                    1895,
+                    1339,
+                    1989,
+                    315,
+                    1989
+                ],
+                "score": 0.93,
+                "latex": "\\sum _ { t \\geq 1 } w _ { t } ( \\hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) \\leq \\frac { C \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\frac { \\sqrt { w S A C \\ell ( C ) } } { ( 1 - \\gamma ) ^ { 2 . 5 } } + \\frac { w S A } { ( 1 - \\gamma ) ^ { 3 } } \\ln C \\ln \\frac { 1 } { ( 1 - \\gamma ) \\epsilon _ { 1 } } \\right) ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    803,
+                    1331,
+                    921,
+                    1331,
+                    921,
+                    1373,
+                    803,
+                    1373
+                ],
+                "score": 0.93,
+                "latex": "\\{ w _ { t } ^ { ( k ) } \\} _ { t \\ge 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    597,
+                    228,
+                    943,
+                    228,
+                    943,
+                    269,
+                    597,
+                    269
+                ],
+                "score": 0.93,
+                "latex": "\\begin{array} { r } { \\sum _ { t ^ { \\prime } \\geq 1 } w _ { t ^ { \\prime } + 1 } ^ { \\prime } \\leq \\sum _ { t \\geq 1 } w _ { t } \\leq C . } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    573,
+                    1372,
+                    751,
+                    1372,
+                    751,
+                    1411,
+                    573,
+                    1411
+                ],
+                "score": 0.93,
+                "latex": "w \\cdot \\left( 1 + 1 / H \\right) ^ { k }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    606,
+                    1330,
+                    724,
+                    1330,
+                    724,
+                    1372,
+                    606,
+                    1372
+                ],
+                "score": 0.93,
+                "latex": "\\{ \\bar { w _ { t } ^ { ( 0 ) } } \\} _ { t \\ge 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    347,
+                    1807,
+                    515,
+                    1807,
+                    515,
+                    1851,
+                    347,
+                    1851
+                ],
+                "score": 0.92,
+                "latex": "\\gamma ^ { H } \\frac { C } { 1 - \\gamma } \\leq C \\epsilon _ { 1 }"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    412,
+                    866,
+                    1286,
+                    866,
+                    1286,
+                    975,
+                    412,
+                    975
+                ],
+                "score": 0.92,
+                "latex": "\\sum _ { t \\geq 1 } w _ { t + 1 } ^ { \\prime } \\alpha _ { n _ { t } + 1 } \\leq \\sum _ { s , a } \\sum _ { n = 1 } ^ { C _ { s , a } ^ { \\prime } / w ^ { \\prime } } w ^ { \\prime } \\frac { H } { n } \\leq \\sum _ { s , a } H w ^ { \\prime } \\ln ( C _ { s , a } ^ { \\prime } / w ) \\leq 2 S A H w \\ln C ."
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    326,
+                    1083,
+                    1326,
+                    1083,
+                    1326,
+                    1260,
+                    326,
+                    1260
+                ],
+                "score": 0.92,
+                "latex": "\\begin{array} { r l } & { \\displaystyle \\sum _ { t \\geq 1 } w _ { t } ( \\hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) } \\\\ & { \\leq 2 c _ { 3 } \\frac { \\sqrt { w S A H C \\iota ( C ) } } { 1 - \\gamma } + \\mathcal { O } \\left( \\frac { w S A H } { 1 - \\gamma } \\ln C \\right) + \\gamma \\displaystyle \\sum _ { t \\geq 1 } w _ { t + 1 } ^ { \\prime } \\left( \\hat { Q } _ { t + 1 } - Q ^ { * } \\right) ( s _ { t + 1 } , a _ { t + 1 } ) . } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    951,
+                    1765,
+                    1344,
+                    1765,
+                    1344,
+                    1804,
+                    951,
+                    1804
+                ],
+                "score": 0.92,
+                "latex": "w ^ { ( H ) } = ( 1 + 1 / H ) ^ { H } w ^ { ( 0 ) } \\leq e w ^ { ( 0 ) }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1179,
+                    1373,
+                    1285,
+                    1373,
+                    1285,
+                    1411,
+                    1179,
+                    1411
+                ],
+                "score": 0.91,
+                "latex": "( C , w ^ { ( k ) } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1315,
+                    782,
+                    1404,
+                    782,
+                    1404,
+                    820,
+                    1315,
+                    820
+                ],
+                "score": 0.91,
+                "latex": "C _ { s , a } ^ { \\prime } ="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    336,
+                    224,
+                    492,
+                    224,
+                    492,
+                    269,
+                    336,
+                    269
+                ],
+                "score": 0.91,
+                "latex": "\\textstyle \\sum _ { j = 0 } ^ { i } \\alpha _ { i } ^ { j } = 1"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    401,
+                    782,
+                    771,
+                    782,
+                    771,
+                    816,
+                    401,
+                    816
+                ],
+                "score": 0.91,
+                "latex": "\\dot { \\alpha } _ { t } = ( H + 1 ) / ( H + t ) \\overset { \\cdot } { \\leq } H / t"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    481,
+                    1373,
+                    534,
+                    1373,
+                    534,
+                    1406,
+                    481,
+                    1406
+                ],
+                "score": 0.9,
+                "latex": "w ^ { ( k ) }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    629,
+                    1807,
+                    980,
+                    1807,
+                    980,
+                    1845,
+                    629,
+                    1845
+                ],
+                "score": 0.9,
+                "latex": "\\ell ( C ) = \\iota ( C ) \\ln ( ( 1 - \\gamma ) ^ { - 1 } \\epsilon _ { 1 } ^ { - 1 } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    297,
+                    816,
+                    537,
+                    816,
+                    537,
+                    857,
+                    297,
+                    857
+                ],
+                "score": 0.85,
+                "latex": "\\scriptstyle \\sum _ { t \\geq 1 , ( s _ { t } , a _ { t } = s , a } w _ { t + 1 } ^ { \\prime }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    550,
+                    817,
+                    761,
+                    817,
+                    761,
+                    851,
+                    550,
+                    851
+                ],
+                "score": 0.83,
+                "latex": "w ^ { \\prime } = w ( 1 + 1 / H )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    598,
+                    1411,
+                    626,
+                    1411,
+                    626,
+                    1435,
+                    598,
+                    1435
+                ],
+                "score": 0.81,
+                "latex": "H"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    337,
+                    1378,
+                    356,
+                    1378,
+                    356,
+                    1405,
+                    337,
+                    1405
+                ],
+                "score": 0.81,
+                "latex": "k"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    72.0,
+                    818.0,
+                    72.0,
+                    818.0,
+                    108.0,
+                    296.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    831.0,
+                    2085.0,
+                    868.0,
+                    2085.0,
+                    868.0,
+                    2124.0,
+                    831.0,
+                    2124.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1380.0,
+                    2009.0,
+                    1401.0,
+                    2009.0,
+                    1401.0,
+                    2030.0,
+                    1380.0,
+                    2030.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1265.0,
+                    1406.0,
+                    1265.0,
+                    1406.0,
+                    1304.0,
+                    294.0,
+                    1304.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1300.0,
+                    1406.0,
+                    1300.0,
+                    1406.0,
+                    1334.0,
+                    294.0,
+                    1334.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    285.0,
+                    1322.0,
+                    605.0,
+                    1322.0,
+                    605.0,
+                    1383.0,
+                    285.0,
+                    1383.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    725.0,
+                    1322.0,
+                    802.0,
+                    1322.0,
+                    802.0,
+                    1383.0,
+                    725.0,
+                    1383.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    922.0,
+                    1322.0,
+                    1413.0,
+                    1322.0,
+                    1413.0,
+                    1383.0,
+                    922.0,
+                    1383.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    289.0,
+                    1366.0,
+                    336.0,
+                    1366.0,
+                    336.0,
+                    1419.0,
+                    289.0,
+                    1419.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    357.0,
+                    1366.0,
+                    480.0,
+                    1366.0,
+                    480.0,
+                    1419.0,
+                    357.0,
+                    1419.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    535.0,
+                    1366.0,
+                    572.0,
+                    1366.0,
+                    572.0,
+                    1419.0,
+                    535.0,
+                    1419.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    752.0,
+                    1366.0,
+                    1008.0,
+                    1366.0,
+                    1008.0,
+                    1419.0,
+                    752.0,
+                    1419.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1129.0,
+                    1366.0,
+                    1178.0,
+                    1366.0,
+                    1178.0,
+                    1419.0,
+                    1129.0,
+                    1419.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1286.0,
+                    1366.0,
+                    1413.0,
+                    1366.0,
+                    1413.0,
+                    1419.0,
+                    1286.0,
+                    1419.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1406.0,
+                    597.0,
+                    1406.0,
+                    597.0,
+                    1441.0,
+                    294.0,
+                    1441.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    627.0,
+                    1406.0,
+                    772.0,
+                    1406.0,
+                    772.0,
+                    1441.0,
+                    627.0,
+                    1441.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    751.0,
+                    1402.0,
+                    751.0,
+                    1402.0,
+                    786.0,
+                    297.0,
+                    786.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    771.0,
+                    400.0,
+                    771.0,
+                    400.0,
+                    827.0,
+                    291.0,
+                    827.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    772.0,
+                    771.0,
+                    1314.0,
+                    771.0,
+                    1314.0,
+                    827.0,
+                    772.0,
+                    827.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    813.0,
+                    296.0,
+                    813.0,
+                    296.0,
+                    861.0,
+                    291.0,
+                    861.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    538.0,
+                    813.0,
+                    549.0,
+                    813.0,
+                    549.0,
+                    861.0,
+                    538.0,
+                    861.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    762.0,
+                    813.0,
+                    842.0,
+                    813.0,
+                    842.0,
+                    861.0,
+                    762.0,
+                    861.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    285.0,
+                    1748.0,
+                    378.0,
+                    1748.0,
+                    378.0,
+                    1814.0,
+                    285.0,
+                    1814.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    779.0,
+                    1748.0,
+                    950.0,
+                    1748.0,
+                    950.0,
+                    1814.0,
+                    779.0,
+                    1814.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1345.0,
+                    1748.0,
+                    1412.0,
+                    1748.0,
+                    1412.0,
+                    1814.0,
+                    1345.0,
+                    1814.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    516.0,
+                    1804.0,
+                    628.0,
+                    1804.0,
+                    628.0,
+                    1849.0,
+                    516.0,
+                    1849.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    981.0,
+                    1804.0,
+                    1117.0,
+                    1804.0,
+                    1117.0,
+                    1849.0,
+                    981.0,
+                    1849.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    284.0,
+                    1796.0,
+                    442.0,
+                    1796.0,
+                    442.0,
+                    1856.0,
+                    284.0,
+                    1856.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    282.0,
+                    206.0,
+                    335.0,
+                    206.0,
+                    335.0,
+                    283.0,
+                    282.0,
+                    283.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    493.0,
+                    206.0,
+                    596.0,
+                    206.0,
+                    596.0,
+                    283.0,
+                    493.0,
+                    283.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    944.0,
+                    206.0,
+                    1416.0,
+                    206.0,
+                    1416.0,
+                    283.0,
+                    944.0,
+                    283.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    258.0,
+                    405.0,
+                    258.0,
+                    405.0,
+                    303.0,
+                    291.0,
+                    303.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    996.0,
+                    807.0,
+                    996.0,
+                    807.0,
+                    1043.0,
+                    293.0,
+                    1043.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 14,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    648,
+                    1406,
+                    648,
+                    1406,
+                    826,
+                    296,
+                    826
+                ],
+                "score": 0.977
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    293,
+                    1406,
+                    293,
+                    1406,
+                    419,
+                    298,
+                    419
+                ],
+                "score": 0.976
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1176,
+                    1406,
+                    1176,
+                    1406,
+                    1274,
+                    297,
+                    1274
+                ],
+                "score": 0.974
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    841,
+                    1407,
+                    841,
+                    1407,
+                    993,
+                    297,
+                    993
+                ],
+                "score": 0.974
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    534,
+                    1548,
+                    1163,
+                    1548,
+                    1163,
+                    1798,
+                    534,
+                    1798
+                ],
+                "score": 0.969
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    582,
+                    1052,
+                    1113,
+                    1052,
+                    1113,
+                    1150,
+                    582,
+                    1150
+                ],
+                "score": 0.961
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    365,
+                    439,
+                    1404,
+                    439,
+                    1404,
+                    629,
+                    365,
+                    629
+                ],
+                "score": 0.957
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    594,
+                    1286,
+                    1101,
+                    1286,
+                    1101,
+                    1365,
+                    594,
+                    1365
+                ],
+                "score": 0.956
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    1812,
+                    1402,
+                    1812,
+                    1402,
+                    1882,
+                    295,
+                    1882
+                ],
+                "score": 0.954
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    294,
+                    1451,
+                    1405,
+                    1451,
+                    1405,
+                    1533,
+                    294,
+                    1533
+                ],
+                "score": 0.952
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1373,
+                    1403,
+                    1373,
+                    1403,
+                    1438,
+                    298,
+                    1438
+                ],
+                "score": 0.95
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1968,
+                    1403,
+                    1968,
+                    1403,
+                    2036,
+                    297,
+                    2036
+                ],
+                "score": 0.929
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1004,
+                    977,
+                    1004,
+                    977,
+                    1038,
+                    297,
+                    1038
+                ],
+                "score": 0.916
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    297,
+                    1915,
+                    887,
+                    1915,
+                    887,
+                    1947,
+                    297,
+                    1947
+                ],
+                "score": 0.911
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    74,
+                    817,
+                    74,
+                    817,
+                    106,
+                    298,
+                    106
+                ],
+                "score": 0.909
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    300,
+                    226,
+                    822,
+                    226,
+                    822,
+                    262,
+                    300,
+                    262
+                ],
+                "score": 0.901
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    835,
+                    2088,
+                    864,
+                    2088,
+                    864,
+                    2113,
+                    835,
+                    2113
+                ],
+                "score": 0.86
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    531,
+                    1545,
+                    1167,
+                    1545,
+                    1167,
+                    1800,
+                    531,
+                    1800
+                ],
+                "score": 0.94,
+                "latex": "\\begin{array} { r l r } {  { \\operatorname { R e g r e t } ( T ) \\le T \\epsilon _ { 2 } + \\sum _ { i = 1 } ^ { M } ( | k : \\{ X _ { k } \\ge \\epsilon _ { 2 } \\cdot 2 ^ { i - 1 } \\} | ) \\epsilon _ { 2 } \\cdot 2 ^ { i } } } \\\\ & { } & \\\\ & { } & { \\le \\tilde { \\mathcal { O } } ( T \\epsilon _ { 2 } + \\sum _ { i = 1 } ^ { M } \\frac { S A \\ln 1 / \\delta } { \\epsilon _ { 2 } \\cdot 2 ^ { i - 2 } } ) } \\\\ & { } & { \\le \\tilde { \\mathcal { O } } ( \\sqrt { S A T } \\ln 1 / \\delta ) } \\end{array}"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    594,
+                    1285,
+                    1105,
+                    1285,
+                    1105,
+                    1363,
+                    594,
+                    1363
+                ],
+                "score": 0.94,
+                "latex": "\\mathcal { O } \\left( \\frac { S A \\ln S A \\ln 1 / \\delta } { \\epsilon _ { 2 } ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\mathrm { p o l y l o g } \\left( \\frac { 1 } { \\epsilon _ { 1 } } , \\frac { 1 } { 1 - \\gamma } \\right) \\right)"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    583,
+                    1049,
+                    1114,
+                    1049,
+                    1114,
+                    1151,
+                    583,
+                    1151
+                ],
+                "score": 0.94,
+                "latex": "\\mathrm { R e g r e t } ( T ) = \\sum _ { k = 1 } ^ { T / H } \\left[ V ^ { * } ( s _ { 1 } ) - V _ { 1 } ^ { k } ( s _ { 1 } ) \\right] \\propto T ^ { 1 / 2 } ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    439,
+                    684,
+                    736,
+                    684,
+                    736,
+                    732,
+                    439,
+                    732
+                ],
+                "score": 0.94,
+                "latex": "\\begin{array} { r } { \\bar { V } ^ { \\ast } ( \\bar { s } _ { s _ { 1 } , 1 } ) = \\frac { \\gamma ^ { H } } { 1 - \\gamma ^ { H } } V _ { 1 } ^ { \\ast } ( s _ { 1 } ) } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    888,
+                    840,
+                    1012,
+                    840,
+                    1012,
+                    883,
+                    888,
+                    883
+                ],
+                "score": 0.94,
+                "latex": "\\tilde { \\mathcal O } \\big ( \\frac { 3 S A H ^ { 9 } } { \\epsilon ^ { 2 } } \\big )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1008,
+                    954,
+                    1102,
+                    954,
+                    1102,
+                    995,
+                    1008,
+                    995
+                ],
+                "score": 0.94,
+                "latex": "\\tilde { \\mathcal { O } } \\left( \\epsilon ^ { - 2 } \\right)"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1203,
+                    1451,
+                    1355,
+                    1451,
+                    1355,
+                    1490,
+                    1203,
+                    1490
+                ],
+                "score": 0.94,
+                "latex": "\\epsilon = \\sqrt { S A / T }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    975,
+                    1207,
+                    1217,
+                    1207,
+                    1217,
+                    1246,
+                    975,
+                    1246
+                ],
+                "score": 0.93,
+                "latex": "\\epsilon _ { 2 } > \\tilde { \\mathcal { O } } ( \\epsilon _ { 1 } / ( 1 - \\gamma ) )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    465,
+                    881,
+                    589,
+                    881,
+                    589,
+                    924,
+                    465,
+                    924
+                ],
+                "score": 0.93,
+                "latex": "\\tilde { \\mathcal O } \\big ( { \\textstyle { \\frac { 3 S A H ^ { 8 } } { \\epsilon ^ { 2 } } } } \\big )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1174,
+                    692,
+                    1361,
+                    692,
+                    1361,
+                    728,
+                    1174,
+                    728
+                ],
+                "score": 0.93,
+                "latex": "\\pi _ { h } ( s ) = \\bar { \\pi } ( \\bar { s } _ { s , h } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    830,
+                    922,
+                    988,
+                    922,
+                    988,
+                    957,
+                    830,
+                    957
+                ],
+                "score": 0.93,
+                "latex": "0 \\leq t < T / H"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    1487,
+                    526,
+                    1487,
+                    526,
+                    1527,
+                    298,
+                    1527
+                ],
+                "score": 0.93,
+                "latex": "\\epsilon _ { 2 } = \\tilde { \\mathcal { O } } ( \\epsilon _ { 1 } / ( 1 - \\gamma ) )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    401,
+                    790,
+                    714,
+                    790,
+                    714,
+                    826,
+                    401,
+                    826
+                ],
+                "score": 0.93,
+                "latex": "\\gamma ^ { H } = ( 1 - \\dot { 1 } / H ) ^ { \\tilde { H } } = \\mathcal { O } ( \\dot { 1 } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    738,
+                    593,
+                    1068,
+                    593,
+                    1068,
+                    625,
+                    738,
+                    625
+                ],
+                "score": 0.92,
+                "latex": "\\bar { p } ( \\bar { s } _ { s ^ { \\prime } , 1 } \\mid \\bar { s } _ { s , h } , a ) = I [ s ^ { \\prime } = s _ { 1 } ]"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    765,
+                    1970,
+                    1263,
+                    1970,
+                    1263,
+                    2007,
+                    765,
+                    2007
+                ],
+                "score": 0.91,
+                "latex": "\\begin{array} { r c l } { \\mathcal { M } } & { = } & { ( S , A , H , r _ { h } ( s , a ) , p _ { h } ( s ^ { \\prime } \\mathrm { ~  ~ \\chi ~ } | \\mathrm { ~  ~ \\chi ~ } s , a ) ) } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    583,
+                    1489,
+                    815,
+                    1489,
+                    815,
+                    1533,
+                    583,
+                    1533
+                ],
+                "score": 0.91,
+                "latex": "\\begin{array} { r } { M = \\lceil \\log _ { 2 } \\frac { 1 } { \\epsilon _ { 2 } ( 1 - \\gamma ) } \\rceil } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    528,
+                    593,
+                    687,
+                    593,
+                    687,
+                    625,
+                    528,
+                    625
+                ],
+                "score": 0.91,
+                "latex": "\\bar { r } ( \\bar { s } _ { s , h } , a ) = 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1241,
+                    958,
+                    1332,
+                    958,
+                    1332,
+                    990,
+                    1241,
+                    990
+                ],
+                "score": 0.91,
+                "latex": "S , A , H"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    692,
+                    761,
+                    776,
+                    761,
+                    776,
+                    796,
+                    692,
+                    796
+                ],
+                "score": 0.91,
+                "latex": "( \\epsilon / \\gamma ^ { H } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    831,
+                    650,
+                    869,
+                    650,
+                    869,
+                    687,
+                    831,
+                    687
+                ],
+                "score": 0.91,
+                "latex": "V _ { h } ^ { k }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    443,
+                    1453,
+                    717,
+                    1453,
+                    717,
+                    1489,
+                    443,
+                    1489
+                ],
+                "score": 0.91,
+                "latex": "X _ { k } = V ^ { \\ast } ( s _ { 1 } ) - V _ { 1 } ^ { k } ( s _ { 1 } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    898,
+                    559,
+                    1296,
+                    559,
+                    1296,
+                    593,
+                    898,
+                    593
+                ],
+                "score": 0.91,
+                "latex": "\\bar { p } ( \\bar { s } _ { s ^ { \\prime } , h + 1 } \\mid \\bar { s } _ { s , h } , a ) = p _ { h } ( s ^ { \\prime } \\mid s , h )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    511,
+                    559,
+                    844,
+                    559,
+                    844,
+                    593,
+                    511,
+                    593
+                ],
+                "score": 0.91,
+                "latex": "\\bar { r } ( \\bar { s } _ { s , h } , a ) = \\gamma ^ { H - h + 1 } r _ { h } ( s , a )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    868,
+                    326,
+                    1293,
+                    326,
+                    1293,
+                    359,
+                    868,
+                    359
+                ],
+                "score": 0.91,
+                "latex": "\\mathcal { M } = ( S , A , H , r _ { h } ( s _ { \\perp } a ) , p _ { h } ( s ^ { \\prime } \\mid s , a ) )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    296,
+                    2000,
+                    616,
+                    2000,
+                    616,
+                    2036,
+                    296,
+                    2036
+                ],
+                "score": 0.9,
+                "latex": "( \\bar { S } , \\bar { A } , \\gamma , \\bar { r } ( \\bar { s } , \\bar { a } ) , \\bar { p } ( \\bar { s } ^ { \\prime } \\mid \\bar { s } , \\bar { a } ) )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    471,
+                    1847,
+                    730,
+                    1847,
+                    730,
+                    1879,
+                    471,
+                    1879
+                ],
+                "score": 0.9,
+                "latex": "( H , \\log T , \\log S , \\log A )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    709,
+                    921,
+                    785,
+                    921,
+                    785,
+                    952,
+                    709,
+                    952
+                ],
+                "score": 0.9,
+                "latex": "\\pi ^ { t H + 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    341,
+                    650,
+                    370,
+                    650,
+                    370,
+                    683,
+                    341,
+                    683
+                ],
+                "score": 0.88,
+                "latex": "\\bar { V } _ { t }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    393,
+                    849,
+                    462,
+                    849,
+                    462,
+                    877,
+                    393,
+                    877
+                ],
+                "score": 0.88,
+                "latex": "\\epsilon > 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    397,
+                    592,
+                    478,
+                    592,
+                    478,
+                    620,
+                    397,
+                    620
+                ],
+                "score": 0.88,
+                "latex": "h = H"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    684,
+                    530,
+                    731,
+                    530,
+                    731,
+                    559,
+                    684,
+                    559
+                ],
+                "score": 0.88,
+                "latex": "\\bar { s } _ { s , h }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1012,
+                    359,
+                    1402,
+                    359,
+                    1402,
+                    390,
+                    1012,
+                    390
+                ],
+                "score": 0.88,
+                "latex": "\\mathcal { M } = ( S , A , \\gamma , \\bar { r } ( \\bar { s } , \\bar { a } ) , \\bar { p } ( \\bar { s } ^ { \\prime } \\mid \\bar { s } , \\bar { a } ) )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    982,
+                    1814,
+                    1218,
+                    1814,
+                    1218,
+                    1850,
+                    982,
+                    1850
+                ],
+                "score": 0.87,
+                "latex": "( 1 / ( 1 - \\gamma ) , \\log { 1 / \\epsilon _ { 1 } } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    644,
+                    650,
+                    679,
+                    650,
+                    679,
+                    681,
+                    644,
+                    681
+                ],
+                "score": 0.87,
+                "latex": "\\bar { \\mathcal { M } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    833,
+                    730,
+                    869,
+                    730,
+                    869,
+                    761,
+                    833,
+                    761
+                ],
+                "score": 0.86,
+                "latex": "\\bar { \\mathcal { M } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    697,
+                    1811,
+                    723,
+                    1811,
+                    723,
+                    1843,
+                    697,
+                    1843
+                ],
+                "score": 0.85,
+                "latex": "\\tilde { \\mathcal { O } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    616,
+                    1411,
+                    641,
+                    1411,
+                    641,
+                    1435,
+                    616,
+                    1435
+                ],
+                "score": 0.85,
+                "latex": "\\epsilon _ { 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    425,
+                    730,
+                    460,
+                    730,
+                    460,
+                    760,
+                    425,
+                    760
+                ],
+                "score": 0.85,
+                "latex": "\\bar { \\mathcal { M } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    1247,
+                    324,
+                    1247,
+                    324,
+                    1273,
+                    298,
+                    1273
+                ],
+                "score": 0.85,
+                "latex": "\\epsilon _ { 2 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    809,
+                    844,
+                    841,
+                    844,
+                    841,
+                    876,
+                    809,
+                    876
+                ],
+                "score": 0.85,
+                "latex": "\\bar { M }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1345,
+                    853,
+                    1373,
+                    853,
+                    1373,
+                    878,
+                    1345,
+                    878
+                ],
+                "score": 0.85,
+                "latex": "s _ { 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1244,
+                    1379,
+                    1270,
+                    1379,
+                    1270,
+                    1404,
+                    1244,
+                    1404
+                ],
+                "score": 0.84,
+                "latex": "\\epsilon _ { 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1341,
+                    597,
+                    1369,
+                    597,
+                    1369,
+                    622,
+                    1341,
+                    622
+                ],
+                "score": 0.84,
+                "latex": "s _ { 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    397,
+                    560,
+                    420,
+                    560,
+                    420,
+                    588,
+                    397,
+                    588
+                ],
+                "score": 0.84,
+                "latex": "s ^ { \\prime }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    892,
+                    1457,
+                    910,
+                    1457,
+                    910,
+                    1483,
+                    892,
+                    1483
+                ],
+                "score": 0.83,
+                "latex": "k"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    838,
+                    1007,
+                    866,
+                    1007,
+                    866,
+                    1033,
+                    838,
+                    1033
+                ],
+                "score": 0.83,
+                "latex": "K"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1001,
+                    764,
+                    1037,
+                    764,
+                    1037,
+                    791,
+                    1001,
+                    791
+                ],
+                "score": 0.83,
+                "latex": "\\mathcal { M }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    617,
+                    528,
+                    636,
+                    528,
+                    636,
+                    555,
+                    617,
+                    555
+                ],
+                "score": 0.83,
+                "latex": "h"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1109,
+                    654,
+                    1145,
+                    654,
+                    1145,
+                    681,
+                    1109,
+                    681
+                ],
+                "score": 0.82,
+                "latex": "\\mathcal { M }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    427,
+                    761,
+                    462,
+                    761,
+                    462,
+                    790,
+                    427,
+                    790
+                ],
+                "score": 0.82,
+                "latex": "\\bar { \\mathcal { M } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1132,
+                    1457,
+                    1155,
+                    1457,
+                    1155,
+                    1483,
+                    1132,
+                    1483
+                ],
+                "score": 0.81,
+                "latex": "T"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1317,
+                    1968,
+                    1403,
+                    1968,
+                    1403,
+                    2005,
+                    1317,
+                    2005
+                ],
+                "score": 0.8,
+                "latex": "\\begin{array} { r l } { \\bar { \\mathcal { M } } } & { { } = } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    1217,
+                    323,
+                    1217,
+                    323,
+                    1242,
+                    298,
+                    1242
+                ],
+                "score": 0.79,
+                "latex": "\\epsilon _ { 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1373,
+                    327,
+                    1401,
+                    327,
+                    1401,
+                    354,
+                    1373,
+                    354
+                ],
+                "score": 0.79,
+                "latex": "H"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    372,
+                    766,
+                    393,
+                    766,
+                    393,
+                    790,
+                    372,
+                    790
+                ],
+                "score": 0.79,
+                "latex": "\\bar { \\pi }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    747,
+                    733,
+                    782,
+                    733,
+                    782,
+                    760,
+                    747,
+                    760
+                ],
+                "score": 0.78,
+                "latex": "\\mathcal { M }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    372,
+                    735,
+                    393,
+                    735,
+                    393,
+                    761,
+                    372,
+                    761
+                ],
+                "score": 0.78,
+                "latex": "\\bar { \\pi }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1268,
+                    654,
+                    1286,
+                    654,
+                    1286,
+                    680,
+                    1268,
+                    680
+                ],
+                "score": 0.78,
+                "latex": "k"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    477,
+                    1374,
+                    535,
+                    1374,
+                    535,
+                    1403,
+                    477,
+                    1403
+                ],
+                "score": 0.77,
+                "latex": "1 - \\delta"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1220,
+                    534,
+                    1238,
+                    534,
+                    1238,
+                    554,
+                    1220,
+                    554
+                ],
+                "score": 0.77,
+                "latex": "a"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    766,
+                    655,
+                    781,
+                    655,
+                    781,
+                    680,
+                    766,
+                    680
+                ],
+                "score": 0.76,
+                "latex": "t"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1349,
+                    654,
+                    1368,
+                    654,
+                    1368,
+                    680,
+                    1349,
+                    680
+                ],
+                "score": 0.76,
+                "latex": "h"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    517,
+                    534,
+                    533,
+                    534,
+                    533,
+                    554,
+                    517,
+                    554
+                ],
+                "score": 0.76,
+                "latex": "s"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    948,
+                    767,
+                    969,
+                    767,
+                    969,
+                    790,
+                    948,
+                    790
+                ],
+                "score": 0.75,
+                "latex": "\\pi"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    806,
+                    887,
+                    850,
+                    887,
+                    850,
+                    921,
+                    806,
+                    921
+                ],
+                "score": 0.72,
+                "latex": "1 / 3"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    477,
+                    1816,
+                    539,
+                    1816,
+                    539,
+                    1844,
+                    477,
+                    1844
+                ],
+                "score": 0.71,
+                "latex": "1 - \\delta"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    396,
+                    483,
+                    575,
+                    483,
+                    575,
+                    520,
+                    396,
+                    520
+                ],
+                "score": 0.71,
+                "latex": "\\gamma = ( 1 - 1 / H )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1031,
+                    894,
+                    1045,
+                    894,
+                    1045,
+                    915,
+                    1031,
+                    915
+                ],
+                "score": 0.71,
+                "latex": "\\epsilon"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1294,
+                    739,
+                    1308,
+                    739,
+                    1308,
+                    760,
+                    1294,
+                    760
+                ],
+                "score": 0.68,
+                "latex": "\\epsilon"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    371,
+                    965,
+                    384,
+                    965,
+                    384,
+                    986,
+                    371,
+                    986
+                ],
+                "score": 0.65,
+                "latex": "\\epsilon"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1271,
+                    922,
+                    1316,
+                    922,
+                    1316,
+                    957,
+                    1271,
+                    957
+                ],
+                "score": 0.44,
+                "latex": "2 / 3"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    392,
+                    440,
+                    626,
+                    440,
+                    626,
+                    477,
+                    392,
+                    477
+                ],
+                "score": 0.42,
+                "latex": "\\bar { S } = S \\times H , \\bar { A } = A ;"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    366,
+                    438,
+                    630,
+                    438,
+                    630,
+                    522,
+                    366,
+                    522
+                ],
+                "score": 0.37,
+                "latex": "\\begin{array} { l } { { \\bullet \\ { \\bar { S } } = S \\times H , { \\bar { A } } = A ; } } \\\\ { { \\bullet \\ \\gamma = ( 1 - 1 / H ) ; } } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    395,
+                    440,
+                    625,
+                    440,
+                    625,
+                    477,
+                    395,
+                    477
+                ],
+                "score": 0.3,
+                "latex": "\\bar { S } = S \\times H , \\bar { A } = A ;"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    1915.0,
+                    887.0,
+                    1915.0,
+                    887.0,
+                    1950.0,
+                    297.0,
+                    1950.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    72.0,
+                    817.0,
+                    72.0,
+                    817.0,
+                    109.0,
+                    295.0,
+                    109.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    224.0,
+                    827.0,
+                    224.0,
+                    827.0,
+                    266.0,
+                    294.0,
+                    266.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    831.0,
+                    2085.0,
+                    869.0,
+                    2085.0,
+                    869.0,
+                    2124.0,
+                    831.0,
+                    2124.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    649.0,
+                    340.0,
+                    649.0,
+                    340.0,
+                    687.0,
+                    294.0,
+                    687.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    371.0,
+                    649.0,
+                    643.0,
+                    649.0,
+                    643.0,
+                    687.0,
+                    371.0,
+                    687.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    680.0,
+                    649.0,
+                    765.0,
+                    649.0,
+                    765.0,
+                    687.0,
+                    680.0,
+                    687.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    782.0,
+                    649.0,
+                    830.0,
+                    649.0,
+                    830.0,
+                    687.0,
+                    782.0,
+                    687.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    870.0,
+                    649.0,
+                    1108.0,
+                    649.0,
+                    1108.0,
+                    687.0,
+                    870.0,
+                    687.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1146.0,
+                    649.0,
+                    1267.0,
+                    649.0,
+                    1267.0,
+                    687.0,
+                    1146.0,
+                    687.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1287.0,
+                    649.0,
+                    1348.0,
+                    649.0,
+                    1348.0,
+                    687.0,
+                    1287.0,
+                    687.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1369.0,
+                    649.0,
+                    1407.0,
+                    649.0,
+                    1407.0,
+                    687.0,
+                    1369.0,
+                    687.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    290.0,
+                    682.0,
+                    438.0,
+                    682.0,
+                    438.0,
+                    737.0,
+                    290.0,
+                    737.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    737.0,
+                    682.0,
+                    1173.0,
+                    682.0,
+                    1173.0,
+                    737.0,
+                    737.0,
+                    737.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1362.0,
+                    682.0,
+                    1409.0,
+                    682.0,
+                    1409.0,
+                    737.0,
+                    1362.0,
+                    737.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    730.0,
+                    371.0,
+                    730.0,
+                    371.0,
+                    767.0,
+                    294.0,
+                    767.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    730.0,
+                    424.0,
+                    730.0,
+                    424.0,
+                    767.0,
+                    394.0,
+                    767.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    461.0,
+                    730.0,
+                    746.0,
+                    730.0,
+                    746.0,
+                    767.0,
+                    461.0,
+                    767.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    783.0,
+                    730.0,
+                    832.0,
+                    730.0,
+                    832.0,
+                    767.0,
+                    783.0,
+                    767.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    870.0,
+                    730.0,
+                    1293.0,
+                    730.0,
+                    1293.0,
+                    767.0,
+                    870.0,
+                    767.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1309.0,
+                    730.0,
+                    1406.0,
+                    730.0,
+                    1406.0,
+                    767.0,
+                    1309.0,
+                    767.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    759.0,
+                    371.0,
+                    759.0,
+                    371.0,
+                    798.0,
+                    294.0,
+                    798.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    759.0,
+                    426.0,
+                    759.0,
+                    426.0,
+                    798.0,
+                    394.0,
+                    798.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    463.0,
+                    759.0,
+                    691.0,
+                    759.0,
+                    691.0,
+                    798.0,
+                    463.0,
+                    798.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    777.0,
+                    759.0,
+                    947.0,
+                    759.0,
+                    947.0,
+                    798.0,
+                    777.0,
+                    798.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    970.0,
+                    759.0,
+                    1000.0,
+                    759.0,
+                    1000.0,
+                    798.0,
+                    970.0,
+                    798.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1038.0,
+                    759.0,
+                    1407.0,
+                    759.0,
+                    1407.0,
+                    798.0,
+                    1038.0,
+                    798.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    788.0,
+                    400.0,
+                    788.0,
+                    400.0,
+                    829.0,
+                    294.0,
+                    829.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    715.0,
+                    788.0,
+                    871.0,
+                    788.0,
+                    871.0,
+                    829.0,
+                    715.0,
+                    829.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    294.0,
+                    1404.0,
+                    294.0,
+                    1404.0,
+                    328.0,
+                    292.0,
+                    328.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    324.0,
+                    867.0,
+                    324.0,
+                    867.0,
+                    361.0,
+                    295.0,
+                    361.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1294.0,
+                    324.0,
+                    1372.0,
+                    324.0,
+                    1372.0,
+                    361.0,
+                    1294.0,
+                    361.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    355.0,
+                    1011.0,
+                    355.0,
+                    1011.0,
+                    391.0,
+                    292.0,
+                    391.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1403.0,
+                    355.0,
+                    1406.0,
+                    355.0,
+                    1406.0,
+                    391.0,
+                    1403.0,
+                    391.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    384.0,
+                    450.0,
+                    384.0,
+                    450.0,
+                    422.0,
+                    291.0,
+                    422.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1173.0,
+                    1404.0,
+                    1173.0,
+                    1404.0,
+                    1215.0,
+                    292.0,
+                    1215.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1209.0,
+                    297.0,
+                    1209.0,
+                    297.0,
+                    1247.0,
+                    294.0,
+                    1247.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    1209.0,
+                    974.0,
+                    1209.0,
+                    974.0,
+                    1247.0,
+                    324.0,
+                    1247.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1218.0,
+                    1209.0,
+                    1406.0,
+                    1209.0,
+                    1406.0,
+                    1247.0,
+                    1218.0,
+                    1247.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1241.0,
+                    297.0,
+                    1241.0,
+                    297.0,
+                    1278.0,
+                    294.0,
+                    1278.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    325.0,
+                    1241.0,
+                    684.0,
+                    1241.0,
+                    684.0,
+                    1278.0,
+                    325.0,
+                    1278.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    289.0,
+                    833.0,
+                    392.0,
+                    833.0,
+                    392.0,
+                    931.0,
+                    289.0,
+                    931.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    590.0,
+                    833.0,
+                    805.0,
+                    833.0,
+                    805.0,
+                    931.0,
+                    590.0,
+                    931.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    851.0,
+                    833.0,
+                    887.0,
+                    833.0,
+                    887.0,
+                    931.0,
+                    851.0,
+                    931.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1013.0,
+                    833.0,
+                    1030.0,
+                    833.0,
+                    1030.0,
+                    931.0,
+                    1013.0,
+                    931.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1046.0,
+                    833.0,
+                    1344.0,
+                    833.0,
+                    1344.0,
+                    931.0,
+                    1046.0,
+                    931.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1374.0,
+                    833.0,
+                    1410.0,
+                    833.0,
+                    1410.0,
+                    931.0,
+                    1374.0,
+                    931.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    914.0,
+                    708.0,
+                    914.0,
+                    708.0,
+                    963.0,
+                    292.0,
+                    963.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    786.0,
+                    914.0,
+                    829.0,
+                    914.0,
+                    829.0,
+                    963.0,
+                    786.0,
+                    963.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    989.0,
+                    914.0,
+                    1270.0,
+                    914.0,
+                    1270.0,
+                    963.0,
+                    989.0,
+                    963.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1317.0,
+                    914.0,
+                    1408.0,
+                    914.0,
+                    1408.0,
+                    963.0,
+                    1317.0,
+                    963.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    954.0,
+                    370.0,
+                    954.0,
+                    370.0,
+                    998.0,
+                    292.0,
+                    998.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    385.0,
+                    954.0,
+                    1007.0,
+                    954.0,
+                    1007.0,
+                    998.0,
+                    385.0,
+                    998.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1103.0,
+                    954.0,
+                    1240.0,
+                    954.0,
+                    1240.0,
+                    998.0,
+                    1103.0,
+                    998.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1333.0,
+                    954.0,
+                    1409.0,
+                    954.0,
+                    1409.0,
+                    998.0,
+                    1333.0,
+                    998.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    631.0,
+                    436.0,
+                    636.0,
+                    436.0,
+                    636.0,
+                    479.0,
+                    631.0,
+                    479.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    366.0,
+                    523.0,
+                    516.0,
+                    523.0,
+                    516.0,
+                    560.0,
+                    366.0,
+                    560.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    534.0,
+                    523.0,
+                    616.0,
+                    523.0,
+                    616.0,
+                    560.0,
+                    534.0,
+                    560.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    637.0,
+                    523.0,
+                    683.0,
+                    523.0,
+                    683.0,
+                    560.0,
+                    637.0,
+                    560.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    732.0,
+                    523.0,
+                    1219.0,
+                    523.0,
+                    1219.0,
+                    560.0,
+                    732.0,
+                    560.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1239.0,
+                    523.0,
+                    1405.0,
+                    523.0,
+                    1405.0,
+                    560.0,
+                    1239.0,
+                    560.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    390.0,
+                    550.0,
+                    396.0,
+                    550.0,
+                    396.0,
+                    601.0,
+                    390.0,
+                    601.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    421.0,
+                    550.0,
+                    510.0,
+                    550.0,
+                    510.0,
+                    601.0,
+                    421.0,
+                    601.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    845.0,
+                    550.0,
+                    897.0,
+                    550.0,
+                    897.0,
+                    601.0,
+                    845.0,
+                    601.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1297.0,
+                    550.0,
+                    1409.0,
+                    550.0,
+                    1409.0,
+                    601.0,
+                    1297.0,
+                    601.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    587.0,
+                    396.0,
+                    587.0,
+                    396.0,
+                    629.0,
+                    392.0,
+                    629.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    479.0,
+                    587.0,
+                    527.0,
+                    587.0,
+                    527.0,
+                    629.0,
+                    479.0,
+                    629.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    688.0,
+                    587.0,
+                    737.0,
+                    587.0,
+                    737.0,
+                    629.0,
+                    688.0,
+                    629.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1069.0,
+                    587.0,
+                    1340.0,
+                    587.0,
+                    1340.0,
+                    629.0,
+                    1069.0,
+                    629.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1370.0,
+                    587.0,
+                    1383.0,
+                    587.0,
+                    1383.0,
+                    629.0,
+                    1370.0,
+                    629.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1808.0,
+                    476.0,
+                    1808.0,
+                    476.0,
+                    1852.0,
+                    293.0,
+                    1852.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    540.0,
+                    1808.0,
+                    696.0,
+                    1808.0,
+                    696.0,
+                    1852.0,
+                    540.0,
+                    1852.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    724.0,
+                    1808.0,
+                    981.0,
+                    1808.0,
+                    981.0,
+                    1852.0,
+                    724.0,
+                    1852.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1219.0,
+                    1808.0,
+                    1405.0,
+                    1808.0,
+                    1405.0,
+                    1852.0,
+                    1219.0,
+                    1852.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1843.0,
+                    470.0,
+                    1843.0,
+                    470.0,
+                    1883.0,
+                    294.0,
+                    1883.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    731.0,
+                    1843.0,
+                    742.0,
+                    1843.0,
+                    742.0,
+                    1883.0,
+                    731.0,
+                    1883.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1449.0,
+                    442.0,
+                    1449.0,
+                    442.0,
+                    1493.0,
+                    294.0,
+                    1493.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    718.0,
+                    1449.0,
+                    891.0,
+                    1449.0,
+                    891.0,
+                    1493.0,
+                    718.0,
+                    1493.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    911.0,
+                    1449.0,
+                    1131.0,
+                    1449.0,
+                    1131.0,
+                    1493.0,
+                    911.0,
+                    1493.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1156.0,
+                    1449.0,
+                    1202.0,
+                    1449.0,
+                    1202.0,
+                    1493.0,
+                    1156.0,
+                    1493.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1356.0,
+                    1449.0,
+                    1405.0,
+                    1449.0,
+                    1405.0,
+                    1493.0,
+                    1356.0,
+                    1493.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1485.0,
+                    297.0,
+                    1485.0,
+                    297.0,
+                    1539.0,
+                    292.0,
+                    1539.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    527.0,
+                    1485.0,
+                    582.0,
+                    1485.0,
+                    582.0,
+                    1539.0,
+                    527.0,
+                    1539.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    816.0,
+                    1485.0,
+                    1001.0,
+                    1485.0,
+                    1001.0,
+                    1539.0,
+                    816.0,
+                    1539.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1371.0,
+                    476.0,
+                    1371.0,
+                    476.0,
+                    1411.0,
+                    293.0,
+                    1411.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    536.0,
+                    1371.0,
+                    1243.0,
+                    1371.0,
+                    1243.0,
+                    1411.0,
+                    536.0,
+                    1411.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1271.0,
+                    1371.0,
+                    1405.0,
+                    1371.0,
+                    1405.0,
+                    1411.0,
+                    1271.0,
+                    1411.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1401.0,
+                    615.0,
+                    1401.0,
+                    615.0,
+                    1443.0,
+                    295.0,
+                    1443.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    642.0,
+                    1401.0,
+                    654.0,
+                    1401.0,
+                    654.0,
+                    1443.0,
+                    642.0,
+                    1443.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1965.0,
+                    764.0,
+                    1965.0,
+                    764.0,
+                    2010.0,
+                    292.0,
+                    2010.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1264.0,
+                    1965.0,
+                    1316.0,
+                    1965.0,
+                    1316.0,
+                    2010.0,
+                    1264.0,
+                    2010.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1404.0,
+                    1965.0,
+                    1408.0,
+                    1965.0,
+                    1408.0,
+                    2010.0,
+                    1404.0,
+                    2010.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1998.0,
+                    295.0,
+                    1998.0,
+                    295.0,
+                    2039.0,
+                    292.0,
+                    2039.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    617.0,
+                    1998.0,
+                    775.0,
+                    1998.0,
+                    775.0,
+                    2039.0,
+                    617.0,
+                    2039.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    997.0,
+                    837.0,
+                    997.0,
+                    837.0,
+                    1045.0,
+                    294.0,
+                    1045.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    867.0,
+                    997.0,
+                    980.0,
+                    997.0,
+                    980.0,
+                    1045.0,
+                    867.0,
+                    1045.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 15,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1939,
+                    1404,
+                    1939,
+                    1404,
+                    2037,
+                    298,
+                    2037
+                ],
+                "score": 0.972
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    302,
+                    433,
+                    1409,
+                    433,
+                    1409,
+                    530,
+                    302,
+                    530
+                ],
+                "score": 0.965
+            },
+            {
+                "category_id": 3,
+                "poly": [
+                    677,
+                    1555,
+                    1022,
+                    1555,
+                    1022,
+                    1825,
+                    677,
+                    1825
+                ],
+                "score": 0.96
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    694,
+                    1405,
+                    694,
+                    1405,
+                    789,
+                    298,
+                    789
+                ],
+                "score": 0.951
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    295,
+                    542,
+                    1482,
+                    542,
+                    1482,
+                    682,
+                    295,
+                    682
+                ],
+                "score": 0.951
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    687,
+                    846,
+                    1011,
+                    846,
+                    1011,
+                    892,
+                    687,
+                    892
+                ],
+                "score": 0.945
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    521,
+                    1126,
+                    1178,
+                    1126,
+                    1178,
+                    1196,
+                    521,
+                    1196
+                ],
+                "score": 0.94
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1210,
+                    852,
+                    1210,
+                    852,
+                    1248,
+                    297,
+                    1248
+                ],
+                "score": 0.936
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    494,
+                    939,
+                    1205,
+                    939,
+                    1205,
+                    984,
+                    494,
+                    984
+                ],
+                "score": 0.935
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1397,
+                    1407,
+                    1397,
+                    1407,
+                    1516,
+                    296,
+                    1516
+                ],
+                "score": 0.926
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    366,
+                    226,
+                    1412,
+                    226,
+                    1412,
+                    413,
+                    366,
+                    413
+                ],
+                "score": 0.921
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    799,
+                    897,
+                    799,
+                    897,
+                    833,
+                    297,
+                    833
+                ],
+                "score": 0.92
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    900,
+                    457,
+                    900,
+                    457,
+                    931,
+                    297,
+                    931
+                ],
+                "score": 0.918
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    74,
+                    817,
+                    74,
+                    817,
+                    106,
+                    298,
+                    106
+                ],
+                "score": 0.914
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    994,
+                    368,
+                    994,
+                    368,
+                    1024,
+                    296,
+                    1024
+                ],
+                "score": 0.903
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1085,
+                    509,
+                    1085,
+                    509,
+                    1117,
+                    298,
+                    1117
+                ],
+                "score": 0.897
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    835,
+                    2087,
+                    863,
+                    2087,
+                    863,
+                    2113,
+                    835,
+                    2113
+                ],
+                "score": 0.867
+            },
+            {
+                "category_id": 4,
+                "poly": [
+                    292,
+                    1854,
+                    1406,
+                    1854,
+                    1406,
+                    1918,
+                    292,
+                    1918
+                ],
+                "score": 0.833
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    297,
+                    1286,
+                    1035,
+                    1286,
+                    1035,
+                    1326,
+                    297,
+                    1326
+                ],
+                "score": 0.827
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    302,
+                    1356,
+                    1268,
+                    1356,
+                    1268,
+                    1392,
+                    302,
+                    1392
+                ],
+                "score": 0.773
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    291,
+                    1032,
+                    1401,
+                    1032,
+                    1401,
+                    1077,
+                    291,
+                    1077
+                ],
+                "score": 0.74
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    291,
+                    1032,
+                    1401,
+                    1032,
+                    1401,
+                    1077,
+                    291,
+                    1077
+                ],
+                "score": 0.135
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    292,
+                    1854,
+                    1406,
+                    1854,
+                    1406,
+                    1918,
+                    292,
+                    1918
+                ],
+                "score": 0.117
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1093,
+                    1428,
+                    1227,
+                    1428,
+                    1227,
+                    1483,
+                    1093,
+                    1483
+                ],
+                "score": 0.94,
+                "latex": "\\Omega \\left( \\frac { \\epsilon ^ { - 3 } } { \\ln ( 1 / \\delta ) } \\right)"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    578,
+                    739,
+                    875,
+                    739,
+                    875,
+                    790,
+                    578,
+                    790
+                ],
+                "score": 0.94,
+                "latex": "\\begin{array} { r } { \\bar { V } ^ { \\ast } ( \\bar { s } _ { s _ { 1 } , 1 } ) = \\frac { \\gamma ^ { H } } { 1 - \\gamma ^ { H } } V ^ { \\ast } ( s _ { 1 } ) } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    823,
+                    694,
+                    1123,
+                    694,
+                    1123,
+                    742,
+                    823,
+                    742
+                ],
+                "score": 0.94,
+                "latex": "\\begin{array} { r } { \\bar { V } ^ { \\bar { \\pi } } ( \\bar { s } _ { s _ { 1 } , 1 } ) = \\frac { \\gamma ^ { H } } { 1 - \\gamma ^ { H } } V ^ { \\pi } ( s _ { 1 } ) } \\end{array}"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    521,
+                    1123,
+                    1175,
+                    1123,
+                    1175,
+                    1199,
+                    521,
+                    1199
+                ],
+                "score": 0.93,
+                "latex": "{ V ^ { \\pi } } ^ { t } ( s _ { 1 } ) \\ge \\frac { 1 - \\gamma ^ { H } } { \\gamma ^ { H } } \\bar { V } ^ { * } ( \\bar { s } _ { s 1 , 1 } ) - \\epsilon / \\gamma ^ { H } = V ^ { * } ( s _ { 1 } ) - \\epsilon / \\gamma ^ { H } ,"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1102,
+                    2004,
+                    1229,
+                    2004,
+                    1229,
+                    2036,
+                    1102,
+                    2036
+                ],
+                "score": 0.92,
+                "latex": "R ( c , \\cdot ) = 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    1973,
+                    391,
+                    1973,
+                    391,
+                    2005,
+                    298,
+                    2005
+                ],
+                "score": 0.92,
+                "latex": "\\{ a , b , c \\}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    488,
+                    1939,
+                    632,
+                    1939,
+                    632,
+                    1976,
+                    488,
+                    1976
+                ],
+                "score": 0.92,
+                "latex": "0 < \\epsilon < \\frac { 1 } { 1 0 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    904,
+                    436,
+                    1167,
+                    436,
+                    1167,
+                    470,
+                    904,
+                    470
+                ],
+                "score": 0.92,
+                "latex": "\\{ ( s _ { 1 } , a _ { 1 } ) , ( s _ { 2 } , a _ { 2 } ) , \\cdot \\cdot \\cdot \\}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    436,
+                    379,
+                    595,
+                    379,
+                    595,
+                    410,
+                    436,
+                    410
+                ],
+                "score": 0.92,
+                "latex": "\\bar { r } ( \\bar { s } _ { s , h } , a ) = 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    859,
+                    345,
+                    1204,
+                    345,
+                    1204,
+                    380,
+                    859,
+                    380
+                ],
+                "score": 0.91,
+                "latex": "\\bar { p } ( \\bar { s } _ { s ^ { \\prime } , h + 1 } \\mid \\bar { s } _ { s , h } , a ) = p _ { h } ( s , h )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    590,
+                    1210,
+                    674,
+                    1210,
+                    674,
+                    1247,
+                    590,
+                    1247
+                ],
+                "score": 0.91,
+                "latex": "( \\epsilon / \\gamma ^ { H } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    297,
+                    1478,
+                    463,
+                    1478,
+                    463,
+                    1516,
+                    297,
+                    1516
+                ],
+                "score": 0.91,
+                "latex": "\\ln ( 1 / \\delta ) < \\epsilon ^ { - 2 }"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    685,
+                    844,
+                    1012,
+                    844,
+                    1012,
+                    890,
+                    685,
+                    890
+                ],
+                "score": 0.91,
+                "latex": "\\begin{array} { r } { \\bar { V } ^ { \\bar { \\pi } ^ { t } } ( \\bar { s } _ { s _ { 1 } , 1 } ) \\geq \\bar { V } ^ { * } ( \\bar { s } _ { s _ { 1 } , 1 } ) - \\epsilon . } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    595,
+                    1973,
+                    727,
+                    1973,
+                    727,
+                    2005,
+                    595,
+                    2005
+                ],
+                "score": 0.91,
+                "latex": "\\overset { \\vartriangle } { \\mathcal { A } } = \\{ \\ v { x } , \\ v { y } \\}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    350,
+                    2003,
+                    508,
+                    2003,
+                    508,
+                    2036,
+                    350,
+                    2036
+                ],
+                "score": 0.91,
+                "latex": "P ( b | a , x ) = 1"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1226,
+                    472,
+                    1362,
+                    472,
+                    1362,
+                    500,
+                    1226,
+                    500
+                ],
+                "score": 0.9,
+                "latex": "s _ { t H + 1 } = s _ { 1 }"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    310,
+                    540,
+                    1428,
+                    540,
+                    1428,
+                    683,
+                    310,
+                    683
+                ],
+                "score": 0.9,
+                "latex": "\\begin{array} { r l } & { \\bar { \\gamma } ^ { \\pi ^ { t } } ( \\bar { s } _ { s _ { 1 } , 1 } ) = \\mathbb { E } \\left[ \\bar { r } ( \\bar { s } _ { s _ { 1 } , 1 } , \\bar { a } _ { 1 } ) + \\gamma \\bar { r } ( \\bar { s } _ { s _ { 2 } , 2 } , \\bar { a } _ { 2 } ) + \\cdot \\cdot \\cdot + \\gamma ^ { H - 1 } \\bar { r } ( \\bar { s } _ { s _ { H - 1 } , H - 1 } , \\bar { a } _ { H - 1 } ) + \\gamma ^ { H } \\bar { V } ^ { \\pi _ { t + H - 1 } } ( \\bar { s } _ { s _ { H + 1 } , 1 } ) \\right] } \\\\ & { \\phantom { \\frac { 1 } { 1 } } = \\gamma ^ { H } \\mathbb { E } \\left[ r _ { 1 } ( s _ { 1 } , a _ { 1 } ) + r _ { 2 } ( s _ { 2 } , a _ { 2 } ) + \\cdot \\cdot \\cdot + r _ { H - 1 } ( s _ { H - 1 } , a _ { H - 1 } ) + \\bar { V } ^ { \\pi _ { t + H } } ( \\bar { s } _ { s _ { H + 1 } , 1 } ) \\right] } \\\\ & { \\phantom { \\frac { 1 } { 1 } } = \\gamma ^ { H } V ^ { \\pi ^ { t } } ( s _ { 1 } ) + \\gamma ^ { H } \\bar { V } ^ { \\pi + H } ( \\bar { s } _ { s _ { 1 } , 1 } ) . } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    474,
+                    344,
+                    805,
+                    344,
+                    805,
+                    378,
+                    474,
+                    378
+                ],
+                "score": 0.9,
+                "latex": "\\bar { r } ( \\bar { s } _ { s , h } , a ) = \\gamma ^ { H - h + 1 } r _ { h } ( s , a )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1314,
+                    346,
+                    1397,
+                    346,
+                    1397,
+                    375,
+                    1314,
+                    375
+                ],
+                "score": 0.89,
+                "latex": "h = H"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    333,
+                    499,
+                    395,
+                    499,
+                    395,
+                    528,
+                    333,
+                    528
+                ],
+                "score": 0.89,
+                "latex": "t \\geq 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    646,
+                    378,
+                    978,
+                    378,
+                    978,
+                    410,
+                    646,
+                    410
+                ],
+                "score": 0.89,
+                "latex": "\\bar { p } ( \\bar { s } _ { s ^ { \\prime } , 1 } \\mid \\bar { s } _ { s , h } , a ) = I [ s ^ { \\prime } = s _ { 1 } ]"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    674,
+                    316,
+                    721,
+                    316,
+                    721,
+                    345,
+                    674,
+                    345
+                ],
+                "score": 0.88,
+                "latex": "\\bar { s } _ { s , h }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    519,
+                    2004,
+                    804,
+                    2004,
+                    804,
+                    2036,
+                    519,
+                    2036
+                ],
+                "score": 0.88,
+                "latex": "P ( a | b , \\cdot ) = P ( a | c , \\cdot ) = 1"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    497,
+                    1213,
+                    527,
+                    1213,
+                    527,
+                    1241,
+                    497,
+                    1241
+                ],
+                "score": 0.88,
+                "latex": "\\pi ^ { t }"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    494,
+                    936,
+                    1200,
+                    936,
+                    1200,
+                    983,
+                    494,
+                    983
+                ],
+                "score": 0.88,
+                "latex": "\\gamma ^ { H } V ^ { \\pi ^ { t } } ( s _ { 1 } ) + \\gamma ^ { H } \\bar { V } ^ { \\pi _ { t + H } } ( \\bar { s } _ { s _ { 1 } , 1 } ) = \\bar { V } ^ { \\bar { \\pi } } ( \\bar { s } _ { s _ { 1 } , 1 } ) \\geq \\bar { V } ^ { * } ( \\bar { s } _ { s _ { 1 } , 1 } ) - \\epsilon ,"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    807,
+                    497,
+                    836,
+                    497,
+                    836,
+                    525,
+                    807,
+                    525
+                ],
+                "score": 0.87,
+                "latex": "\\bar { \\pi } ^ { t }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    472,
+                    436,
+                    791,
+                    436,
+                    791,
+                    470,
+                    472,
+                    470
+                ],
+                "score": 0.87,
+                "latex": "\\left\\{ { \\left( { \\bar { s } } _ { s _ { 1 } , 1 } , { \\bar { a } } _ { 1 } \\right) } , { \\left( { \\bar { s } } _ { s _ { 2 } , 2 } , { \\bar { a } } _ { 2 } \\right) } , \\cdot \\cdot \\cdot \\right\\}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    988,
+                    474,
+                    1016,
+                    474,
+                    1016,
+                    498,
+                    988,
+                    498
+                ],
+                "score": 0.87,
+                "latex": "s _ { 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    870,
+                    497,
+                    899,
+                    497,
+                    899,
+                    525,
+                    870,
+                    525
+                ],
+                "score": 0.87,
+                "latex": "\\pi ^ { t }"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    310,
+                    1032,
+                    1402,
+                    1032,
+                    1402,
+                    1076,
+                    310,
+                    1076
+                ],
+                "score": 0.86,
+                "latex": "^ { H } V ^ { \\pi ^ { \\varepsilon } } ( s _ { 1 } ) \\geq ( 1 - \\gamma ^ { H } ) \\bar { V } ^ { * } ( \\bar { s } _ { s _ { 1 } , 1 } ) + \\gamma ^ { H } ( \\bar { V } ^ { * } ( \\bar { s } _ { s _ { 1 } , 1 } ) - \\bar { V } ^ { \\pi _ { t + H } } ( \\bar { s } _ { s _ { 1 } , 1 } ) ) - \\epsilon \\geq ( 1 - \\gamma ^ { H } ) \\bar { V } ^ { * } ( \\bar { s } _ { s _ { 1 } , 1 } ) - \\epsilon ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1346,
+                    1944,
+                    1404,
+                    1944,
+                    1404,
+                    1972,
+                    1346,
+                    1972
+                ],
+                "score": 0.86,
+                "latex": "{ \\boldsymbol { s } } ="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1374,
+                    314,
+                    1396,
+                    314,
+                    1396,
+                    340,
+                    1374,
+                    340
+                ],
+                "score": 0.85,
+                "latex": "s ^ { \\prime }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    822,
+                    434,
+                    858,
+                    434,
+                    858,
+                    466,
+                    822,
+                    466
+                ],
+                "score": 0.85,
+                "latex": "\\bar { \\mathcal { M } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    751,
+                    329,
+                    751,
+                    329,
+                    777,
+                    298,
+                    777
+                ],
+                "score": 0.85,
+                "latex": "\\bar { \\pi } ^ { * }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1250,
+                    383,
+                    1277,
+                    383,
+                    1277,
+                    407,
+                    1250,
+                    407
+                ],
+                "score": 0.84,
+                "latex": "s _ { 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    596,
+                    470,
+                    630,
+                    470,
+                    630,
+                    494,
+                    596,
+                    494
+                ],
+                "score": 0.84,
+                "latex": "\\mathcal { M }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    439,
+                    469,
+                    474,
+                    469,
+                    474,
+                    494,
+                    439,
+                    494
+                ],
+                "score": 0.83,
+                "latex": "\\mathcal { M }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    395,
+                    226,
+                    624,
+                    226,
+                    624,
+                    262,
+                    395,
+                    262
+                ],
+                "score": 0.81,
+                "latex": "\\bar { S } = S \\times H , \\bar { A } = A"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    604,
+                    707,
+                    623,
+                    707,
+                    623,
+                    730,
+                    604,
+                    730
+                ],
+                "score": 0.8,
+                "latex": "\\bar { \\pi }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    457,
+                    804,
+                    476,
+                    804,
+                    476,
+                    828,
+                    457,
+                    828
+                ],
+                "score": 0.79,
+                "latex": "\\bar { \\pi }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    984,
+                    1399,
+                    1006,
+                    1399,
+                    1006,
+                    1426,
+                    984,
+                    1426
+                ],
+                "score": 0.78,
+                "latex": "S"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    610,
+                    314,
+                    629,
+                    314,
+                    629,
+                    341,
+                    610,
+                    341
+                ],
+                "score": 0.78,
+                "latex": "h"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    513,
+                    320,
+                    529,
+                    320,
+                    529,
+                    340,
+                    513,
+                    340
+                ],
+                "score": 0.76,
+                "latex": "s"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1194,
+                    320,
+                    1212,
+                    320,
+                    1212,
+                    340,
+                    1194,
+                    340
+                ],
+                "score": 0.75,
+                "latex": "a"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    752,
+                    804,
+                    766,
+                    804,
+                    766,
+                    828,
+                    752,
+                    828
+                ],
+                "score": 0.74,
+                "latex": "t"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    396,
+                    270,
+                    575,
+                    270,
+                    575,
+                    305,
+                    396,
+                    305
+                ],
+                "score": 0.73,
+                "latex": "\\gamma = ( 1 - 1 / H )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1028,
+                    1973,
+                    1250,
+                    1973,
+                    1250,
+                    2005,
+                    1028,
+                    2005
+                ],
+                "score": 0.73,
+                "latex": "P ( b | a , y ) = 1 - 1 0 \\epsilon"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    506,
+                    807,
+                    520,
+                    807,
+                    520,
+                    828,
+                    506,
+                    828
+                ],
+                "score": 0.73,
+                "latex": "\\epsilon"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1066,
+                    1400,
+                    1089,
+                    1400,
+                    1089,
+                    1426,
+                    1066,
+                    1426
+                ],
+                "score": 0.71,
+                "latex": "A"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    473,
+                    1440,
+                    496,
+                    1440,
+                    496,
+                    1470,
+                    473,
+                    1470
+                ],
+                "score": 0.71,
+                "latex": "Q"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    296,
+                    1437,
+                    360,
+                    1437,
+                    360,
+                    1469,
+                    296,
+                    1469
+                ],
+                "score": 0.71,
+                "latex": "1 - \\delta"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1265,
+                    1973,
+                    1405,
+                    1973,
+                    1405,
+                    2006,
+                    1265,
+                    2006
+                ],
+                "score": 0.61,
+                "latex": "P ( c | a , y ) ="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    971,
+                    1598,
+                    985,
+                    1598,
+                    985,
+                    1621,
+                    971,
+                    1621
+                ],
+                "score": 0.44,
+                "latex": "b"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    788,
+                    1563,
+                    837,
+                    1563,
+                    837,
+                    1586,
+                    788,
+                    1586
+                ],
+                "score": 0.27,
+                "latex": "x , y"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    780.0,
+                    1553.0,
+                    787.0,
+                    1553.0,
+                    787.0,
+                    1591.0,
+                    780.0,
+                    1591.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    838.0,
+                    1553.0,
+                    847.0,
+                    1553.0,
+                    847.0,
+                    1591.0,
+                    838.0,
+                    1591.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    966.0,
+                    1592.0,
+                    970.0,
+                    1592.0,
+                    970.0,
+                    1624.0,
+                    966.0,
+                    1624.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    986.0,
+                    1592.0,
+                    994.0,
+                    1592.0,
+                    994.0,
+                    1624.0,
+                    986.0,
+                    1624.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    795.0,
+                    1627.0,
+                    826.0,
+                    1627.0,
+                    826.0,
+                    1656.0,
+                    795.0,
+                    1656.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    847.0,
+                    1645.0,
+                    970.0,
+                    1645.0,
+                    970.0,
+                    1670.0,
+                    847.0,
+                    1670.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    702.0,
+                    1677.0,
+                    736.0,
+                    1677.0,
+                    736.0,
+                    1709.0,
+                    702.0,
+                    1709.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    835.0,
+                    1684.0,
+                    842.0,
+                    1684.0,
+                    842.0,
+                    1694.0,
+                    835.0,
+                    1694.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    794.0,
+                    1689.0,
+                    825.0,
+                    1689.0,
+                    825.0,
+                    1724.0,
+                    794.0,
+                    1724.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    891.0,
+                    1756.0,
+                    942.0,
+                    1756.0,
+                    942.0,
+                    1775.0,
+                    891.0,
+                    1775.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    966.0,
+                    1756.0,
+                    995.0,
+                    1756.0,
+                    995.0,
+                    1784.0,
+                    966.0,
+                    1784.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    887.0,
+                    1757.0,
+                    895.0,
+                    1757.0,
+                    895.0,
+                    1765.0,
+                    887.0,
+                    1765.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    784.0,
+                    1789.0,
+                    849.0,
+                    1789.0,
+                    849.0,
+                    1833.0,
+                    784.0,
+                    1833.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    871.0,
+                    1740.5,
+                    876.0,
+                    1740.5,
+                    876.0,
+                    1745.5,
+                    871.0,
+                    1745.5
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    72.0,
+                    817.0,
+                    72.0,
+                    817.0,
+                    109.0,
+                    295.0,
+                    109.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    831.0,
+                    2085.0,
+                    868.0,
+                    2085.0,
+                    868.0,
+                    2125.0,
+                    831.0,
+                    2125.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1854.0,
+                    1408.0,
+                    1854.0,
+                    1408.0,
+                    1890.0,
+                    295.0,
+                    1890.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1886.0,
+                    570.0,
+                    1886.0,
+                    570.0,
+                    1922.0,
+                    294.0,
+                    1922.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1281.0,
+                    1038.0,
+                    1281.0,
+                    1038.0,
+                    1335.0,
+                    292.0,
+                    1335.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1936.0,
+                    487.0,
+                    1936.0,
+                    487.0,
+                    1982.0,
+                    292.0,
+                    1982.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    633.0,
+                    1936.0,
+                    1345.0,
+                    1936.0,
+                    1345.0,
+                    1982.0,
+                    633.0,
+                    1982.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1405.0,
+                    1936.0,
+                    1408.0,
+                    1936.0,
+                    1408.0,
+                    1982.0,
+                    1405.0,
+                    1982.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    1971.0,
+                    594.0,
+                    1971.0,
+                    594.0,
+                    2009.0,
+                    392.0,
+                    2009.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    728.0,
+                    1971.0,
+                    1027.0,
+                    1971.0,
+                    1027.0,
+                    2009.0,
+                    728.0,
+                    2009.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1251.0,
+                    1971.0,
+                    1264.0,
+                    1971.0,
+                    1264.0,
+                    2009.0,
+                    1251.0,
+                    2009.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    2000.0,
+                    349.0,
+                    2000.0,
+                    349.0,
+                    2038.0,
+                    293.0,
+                    2038.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    509.0,
+                    2000.0,
+                    518.0,
+                    2000.0,
+                    518.0,
+                    2038.0,
+                    509.0,
+                    2038.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    805.0,
+                    2000.0,
+                    1101.0,
+                    2000.0,
+                    1101.0,
+                    2038.0,
+                    805.0,
+                    2038.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1230.0,
+                    2000.0,
+                    1240.0,
+                    2000.0,
+                    1240.0,
+                    2038.0,
+                    1230.0,
+                    2038.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    432.0,
+                    471.0,
+                    432.0,
+                    471.0,
+                    474.0,
+                    293.0,
+                    474.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    792.0,
+                    432.0,
+                    821.0,
+                    432.0,
+                    821.0,
+                    474.0,
+                    792.0,
+                    474.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    859.0,
+                    432.0,
+                    903.0,
+                    432.0,
+                    903.0,
+                    474.0,
+                    859.0,
+                    474.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1168.0,
+                    432.0,
+                    1406.0,
+                    432.0,
+                    1406.0,
+                    474.0,
+                    1168.0,
+                    474.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    464.0,
+                    438.0,
+                    464.0,
+                    438.0,
+                    502.0,
+                    295.0,
+                    502.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    475.0,
+                    464.0,
+                    595.0,
+                    464.0,
+                    595.0,
+                    502.0,
+                    475.0,
+                    502.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    631.0,
+                    464.0,
+                    987.0,
+                    464.0,
+                    987.0,
+                    502.0,
+                    631.0,
+                    502.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1017.0,
+                    464.0,
+                    1225.0,
+                    464.0,
+                    1225.0,
+                    502.0,
+                    1017.0,
+                    502.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1363.0,
+                    464.0,
+                    1405.0,
+                    464.0,
+                    1405.0,
+                    502.0,
+                    1363.0,
+                    502.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    498.0,
+                    332.0,
+                    498.0,
+                    332.0,
+                    532.0,
+                    296.0,
+                    532.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    396.0,
+                    498.0,
+                    806.0,
+                    498.0,
+                    806.0,
+                    532.0,
+                    396.0,
+                    532.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    837.0,
+                    498.0,
+                    869.0,
+                    498.0,
+                    869.0,
+                    532.0,
+                    837.0,
+                    532.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    900.0,
+                    498.0,
+                    1336.0,
+                    498.0,
+                    1336.0,
+                    532.0,
+                    900.0,
+                    532.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    280.0,
+                    682.0,
+                    603.0,
+                    682.0,
+                    603.0,
+                    751.0,
+                    280.0,
+                    751.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    624.0,
+                    682.0,
+                    822.0,
+                    682.0,
+                    822.0,
+                    751.0,
+                    624.0,
+                    751.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1124.0,
+                    682.0,
+                    1417.0,
+                    682.0,
+                    1417.0,
+                    751.0,
+                    1124.0,
+                    751.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    287.0,
+                    740.0,
+                    297.0,
+                    740.0,
+                    297.0,
+                    796.0,
+                    287.0,
+                    796.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    330.0,
+                    740.0,
+                    577.0,
+                    740.0,
+                    577.0,
+                    796.0,
+                    330.0,
+                    796.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    876.0,
+                    740.0,
+                    893.0,
+                    740.0,
+                    893.0,
+                    796.0,
+                    876.0,
+                    796.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    731.0,
+                    737.0,
+                    783.0,
+                    737.0,
+                    783.0,
+                    769.0,
+                    731.0,
+                    769.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1203.0,
+                    496.0,
+                    1203.0,
+                    496.0,
+                    1254.0,
+                    292.0,
+                    1254.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    528.0,
+                    1203.0,
+                    589.0,
+                    1203.0,
+                    589.0,
+                    1254.0,
+                    528.0,
+                    1254.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    675.0,
+                    1203.0,
+                    853.0,
+                    1203.0,
+                    853.0,
+                    1254.0,
+                    675.0,
+                    1254.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1392.0,
+                    983.0,
+                    1392.0,
+                    983.0,
+                    1435.0,
+                    294.0,
+                    1435.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1007.0,
+                    1392.0,
+                    1065.0,
+                    1392.0,
+                    1065.0,
+                    1435.0,
+                    1007.0,
+                    1435.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1090.0,
+                    1392.0,
+                    1404.0,
+                    1392.0,
+                    1404.0,
+                    1435.0,
+                    1090.0,
+                    1435.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1432.0,
+                    295.0,
+                    1432.0,
+                    295.0,
+                    1478.0,
+                    291.0,
+                    1478.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    361.0,
+                    1432.0,
+                    472.0,
+                    1432.0,
+                    472.0,
+                    1478.0,
+                    361.0,
+                    1478.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    497.0,
+                    1432.0,
+                    1092.0,
+                    1432.0,
+                    1092.0,
+                    1478.0,
+                    497.0,
+                    1478.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1230.0,
+                    1436.0,
+                    1405.0,
+                    1436.0,
+                    1405.0,
+                    1473.0,
+                    1230.0,
+                    1473.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1477.0,
+                    296.0,
+                    1477.0,
+                    296.0,
+                    1512.0,
+                    292.0,
+                    1512.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    464.0,
+                    1477.0,
+                    472.0,
+                    1477.0,
+                    472.0,
+                    1512.0,
+                    464.0,
+                    1512.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1145.0,
+                    1426.5,
+                    1201.0,
+                    1426.5,
+                    1201.0,
+                    1456.5,
+                    1145.0,
+                    1456.5
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    365.0,
+                    222.0,
+                    394.0,
+                    222.0,
+                    394.0,
+                    265.0,
+                    365.0,
+                    265.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    625.0,
+                    222.0,
+                    636.0,
+                    222.0,
+                    636.0,
+                    265.0,
+                    625.0,
+                    265.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    365.0,
+                    270.0,
+                    395.0,
+                    270.0,
+                    395.0,
+                    305.0,
+                    365.0,
+                    305.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    576.0,
+                    270.0,
+                    588.0,
+                    270.0,
+                    588.0,
+                    305.0,
+                    576.0,
+                    305.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    366.0,
+                    309.0,
+                    512.0,
+                    309.0,
+                    512.0,
+                    348.0,
+                    366.0,
+                    348.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    530.0,
+                    309.0,
+                    609.0,
+                    309.0,
+                    609.0,
+                    348.0,
+                    530.0,
+                    348.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    630.0,
+                    309.0,
+                    673.0,
+                    309.0,
+                    673.0,
+                    348.0,
+                    630.0,
+                    348.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    722.0,
+                    309.0,
+                    1193.0,
+                    309.0,
+                    1193.0,
+                    348.0,
+                    722.0,
+                    348.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1213.0,
+                    309.0,
+                    1373.0,
+                    309.0,
+                    1373.0,
+                    348.0,
+                    1213.0,
+                    348.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1397.0,
+                    309.0,
+                    1409.0,
+                    309.0,
+                    1409.0,
+                    348.0,
+                    1397.0,
+                    348.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    390.0,
+                    339.0,
+                    473.0,
+                    339.0,
+                    473.0,
+                    385.0,
+                    390.0,
+                    385.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    806.0,
+                    339.0,
+                    858.0,
+                    339.0,
+                    858.0,
+                    385.0,
+                    806.0,
+                    385.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1205.0,
+                    339.0,
+                    1313.0,
+                    339.0,
+                    1313.0,
+                    385.0,
+                    1205.0,
+                    385.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1398.0,
+                    339.0,
+                    1415.0,
+                    339.0,
+                    1415.0,
+                    385.0,
+                    1398.0,
+                    385.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    391.0,
+                    373.0,
+                    435.0,
+                    373.0,
+                    435.0,
+                    414.0,
+                    391.0,
+                    414.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    596.0,
+                    373.0,
+                    645.0,
+                    373.0,
+                    645.0,
+                    414.0,
+                    596.0,
+                    414.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    979.0,
+                    373.0,
+                    1249.0,
+                    373.0,
+                    1249.0,
+                    414.0,
+                    979.0,
+                    414.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1278.0,
+                    373.0,
+                    1291.0,
+                    373.0,
+                    1291.0,
+                    414.0,
+                    1278.0,
+                    414.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    797.0,
+                    456.0,
+                    797.0,
+                    456.0,
+                    837.0,
+                    296.0,
+                    837.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    477.0,
+                    797.0,
+                    505.0,
+                    797.0,
+                    505.0,
+                    837.0,
+                    477.0,
+                    837.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    521.0,
+                    797.0,
+                    751.0,
+                    797.0,
+                    751.0,
+                    837.0,
+                    521.0,
+                    837.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    767.0,
+                    797.0,
+                    896.0,
+                    797.0,
+                    896.0,
+                    837.0,
+                    767.0,
+                    837.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    896.0,
+                    461.0,
+                    896.0,
+                    461.0,
+                    934.0,
+                    293.0,
+                    934.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    991.0,
+                    371.0,
+                    991.0,
+                    371.0,
+                    1030.0,
+                    294.0,
+                    1030.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1081.0,
+                    511.0,
+                    1081.0,
+                    511.0,
+                    1120.0,
+                    294.0,
+                    1120.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1349.0,
+                    1267.0,
+                    1349.0,
+                    1267.0,
+                    1401.0,
+                    292.0,
+                    1401.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1026.0,
+                    309.0,
+                    1026.0,
+                    309.0,
+                    1083.0,
+                    292.0,
+                    1083.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1403.0,
+                    1026.0,
+                    1408.0,
+                    1026.0,
+                    1408.0,
+                    1083.0,
+                    1403.0,
+                    1083.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1854.0,
+                    1408.0,
+                    1854.0,
+                    1408.0,
+                    1890.0,
+                    295.0,
+                    1890.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1886.0,
+                    570.0,
+                    1886.0,
+                    570.0,
+                    1922.0,
+                    294.0,
+                    1922.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 16,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    226,
+                    1405,
+                    226,
+                    1405,
+                    470,
+                    297,
+                    470
+                ],
+                "score": 0.981
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    603,
+                    1405,
+                    603,
+                    1405,
+                    763,
+                    296,
+                    763
+                ],
+                "score": 0.979
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    485,
+                    1406,
+                    485,
+                    1406,
+                    593,
+                    298,
+                    593
+                ],
+                "score": 0.972
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    715,
+                    778,
+                    983,
+                    778,
+                    983,
+                    854,
+                    715,
+                    854
+                ],
+                "score": 0.956
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    867,
+                    1058,
+                    867,
+                    1058,
+                    907,
+                    295,
+                    907
+                ],
+                "score": 0.929
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    299,
+                    75,
+                    816,
+                    75,
+                    816,
+                    105,
+                    299,
+                    105
+                ],
+                "score": 0.906
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    836,
+                    2088,
+                    864,
+                    2088,
+                    864,
+                    2112,
+                    836,
+                    2112
+                ],
+                "score": 0.843
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    1374,
+                    871,
+                    1403,
+                    871,
+                    1403,
+                    900,
+                    1374,
+                    900
+                ],
+                "score": 0.822
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    627,
+                    335,
+                    714,
+                    335,
+                    714,
+                    372,
+                    627,
+                    372
+                ],
+                "score": 0.95,
+                "latex": "\\hat { Q } ( a , y )"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    714,
+                    776,
+                    984,
+                    776,
+                    984,
+                    854,
+                    714,
+                    854
+                ],
+                "score": 0.94,
+                "latex": "t _ { 0 } = \\Omega \\left( { \\frac { 1 } { \\epsilon ^ { 3 } \\left( \\ln { 1 / \\delta } \\right) } } \\right) ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1243,
+                    483,
+                    1331,
+                    483,
+                    1331,
+                    522,
+                    1243,
+                    522
+                ],
+                "score": 0.94,
+                "latex": "\\hat { Q } ( a , y )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    610,
+                    696,
+                    697,
+                    696,
+                    697,
+                    733,
+                    610,
+                    733
+                ],
+                "score": 0.94,
+                "latex": "\\hat { Q } ( a , y )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1260,
+                    300,
+                    1349,
+                    300,
+                    1349,
+                    338,
+                    1260,
+                    338
+                ],
+                "score": 0.93,
+                "latex": "\\hat { Q } ( a , x )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    663,
+                    430,
+                    749,
+                    430,
+                    749,
+                    469,
+                    663,
+                    469
+                ],
+                "score": 0.93,
+                "latex": "\\hat { Q } ( a , y )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    752,
+                    866,
+                    1051,
+                    866,
+                    1051,
+                    908,
+                    752,
+                    908
+                ],
+                "score": 0.93,
+                "latex": "\\begin{array} { r } { C = 3 \\ln \\frac { 1 } { \\delta } + 1 < \\frac { 4 } { \\epsilon ^ { 2 } } < m } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    803,
+                    555,
+                    942,
+                    555,
+                    942,
+                    594,
+                    803,
+                    594
+                ],
+                "score": 0.93,
+                "latex": "\\begin{array} { r } { m = \\Omega \\left( \\frac { 1 } { \\epsilon ^ { 2 } } \\right) } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    722,
+                    483,
+                    796,
+                    483,
+                    796,
+                    522,
+                    722,
+                    522
+                ],
+                "score": 0.93,
+                "latex": "\\hat { Q } ( \\cdot , \\cdot )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    990,
+                    487,
+                    1104,
+                    487,
+                    1104,
+                    522,
+                    990,
+                    522
+                ],
+                "score": 0.92,
+                "latex": "1 / ( 1 - \\gamma )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    573,
+                    633,
+                    752,
+                    633,
+                    752,
+                    670,
+                    573,
+                    670
+                ],
+                "score": 0.92,
+                "latex": "\\begin{array} { r } { C ^ { ' } = 3 \\ln \\frac { 1 } { \\delta } + 1 } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1327,
+                    227,
+                    1401,
+                    227,
+                    1401,
+                    267,
+                    1327,
+                    267
+                ],
+                "score": 0.92,
+                "latex": "\\begin{array} { r } { \\gamma > \\frac { 1 } { 2 } } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    369,
+                    868,
+                    535,
+                    868,
+                    535,
+                    904,
+                    369,
+                    904
+                ],
+                "score": 0.92,
+                "latex": "\\ln ( 1 / \\delta ) < \\epsilon ^ { - 2 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    371,
+                    645,
+                    371,
+                    645,
+                    404,
+                    298,
+                    404
+                ],
+                "score": 0.91,
+                "latex": "Q ( a , x ) - Q ( a , y ) = 1 0 \\epsilon \\gamma > \\epsilon"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    335,
+                    384,
+                    335,
+                    384,
+                    372,
+                    298,
+                    372
+                ],
+                "score": 0.91,
+                "latex": "\\hat { Q } ( a , y )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    297,
+                    634,
+                    483,
+                    634,
+                    483,
+                    668,
+                    297,
+                    668
+                ],
+                "score": 0.91,
+                "latex": "t _ { 0 } = m / ( 1 0 \\epsilon C )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1012,
+                    636,
+                    1101,
+                    636,
+                    1101,
+                    665,
+                    1012,
+                    665
+                ],
+                "score": 0.91,
+                "latex": "C \\leq m"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1073,
+                    524,
+                    1194,
+                    524,
+                    1194,
+                    558,
+                    1073,
+                    558
+                ],
+                "score": 0.9,
+                "latex": "1 / ( 1 - \\gamma ) )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1243,
+                    636,
+                    1282,
+                    636,
+                    1282,
+                    666,
+                    1243,
+                    666
+                ],
+                "score": 0.89,
+                "latex": "2 t _ { 0 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1053,
+                    701,
+                    1092,
+                    701,
+                    1092,
+                    731,
+                    1053,
+                    731
+                ],
+                "score": 0.89,
+                "latex": "2 t _ { 0 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    563,
+                    520,
+                    641,
+                    520,
+                    641,
+                    558,
+                    563,
+                    558
+                ],
+                "score": 0.88,
+                "latex": "\\hat { Q } ( c , \\cdot )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1035,
+                    667,
+                    1099,
+                    667,
+                    1099,
+                    695,
+                    1035,
+                    695
+                ],
+                "score": 0.87,
+                "latex": "1 - \\delta"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    426,
+                    731,
+                    490,
+                    731,
+                    490,
+                    760,
+                    426,
+                    760
+                ],
+                "score": 0.87,
+                "latex": "1 - \\delta"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    486,
+                    668,
+                    512,
+                    668,
+                    512,
+                    696,
+                    486,
+                    696
+                ],
+                "score": 0.87,
+                "latex": "t _ { 0 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1201,
+                    264,
+                    1227,
+                    264,
+                    1227,
+                    302,
+                    1201,
+                    302
+                ],
+                "score": 0.86,
+                "latex": "\\hat { Q }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    716,
+                    270,
+                    743,
+                    270,
+                    743,
+                    302,
+                    716,
+                    302
+                ],
+                "score": 0.84,
+                "latex": "Q"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1187,
+                    344,
+                    1207,
+                    344,
+                    1207,
+                    372,
+                    1187,
+                    372
+                ],
+                "score": 0.79,
+                "latex": "y"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    925,
+                    376,
+                    944,
+                    376,
+                    944,
+                    402,
+                    925,
+                    402
+                ],
+                "score": 0.76,
+                "latex": "y"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1032,
+                    310,
+                    1052,
+                    310,
+                    1052,
+                    337,
+                    1032,
+                    337
+                ],
+                "score": 0.76,
+                "latex": "y"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    678,
+                    563,
+                    694,
+                    563,
+                    694,
+                    585,
+                    678,
+                    585
+                ],
+                "score": 0.74,
+                "latex": "c"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    722,
+                    612,
+                    739,
+                    612,
+                    739,
+                    632,
+                    722,
+                    632
+                ],
+                "score": 0.74,
+                "latex": "a"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1169,
+                    671,
+                    1185,
+                    671,
+                    1185,
+                    693,
+                    1169,
+                    693
+                ],
+                "score": 0.73,
+                "latex": "c"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    362,
+                    441,
+                    380,
+                    441,
+                    380,
+                    463,
+                    362,
+                    463
+                ],
+                "score": 0.73,
+                "latex": "a"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    353,
+                    705,
+                    382,
+                    705,
+                    382,
+                    729,
+                    353,
+                    729
+                ],
+                "score": 0.73,
+                "latex": "m"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1139,
+                    237,
+                    1157,
+                    237,
+                    1157,
+                    259,
+                    1139,
+                    259
+                ],
+                "score": 0.72,
+                "latex": "a"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1300,
+                    346,
+                    1318,
+                    346,
+                    1318,
+                    367,
+                    1300,
+                    367
+                ],
+                "score": 0.71,
+                "latex": "a"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1033,
+                    376,
+                    1051,
+                    376,
+                    1051,
+                    398,
+                    1033,
+                    398
+                ],
+                "score": 0.66,
+                "latex": "a"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    672,
+                    316,
+                    672,
+                    316,
+                    693,
+                    298,
+                    693
+                ],
+                "score": 0.64,
+                "latex": "a"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    960,
+                    606,
+                    1003,
+                    606,
+                    1003,
+                    633,
+                    960,
+                    633
+                ],
+                "score": 0.61,
+                "latex": "1 0 \\epsilon"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    408,
+                    312,
+                    408,
+                    312,
+                    428,
+                    298,
+                    428
+                ],
+                "score": 0.59,
+                "latex": "\\epsilon"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1323,
+                    611,
+                    1339,
+                    611,
+                    1339,
+                    632,
+                    1323,
+                    632
+                ],
+                "score": 0.57,
+                "latex": "c"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    767,
+                    635,
+                    784,
+                    635,
+                    784,
+                    662,
+                    767,
+                    662
+                ],
+                "score": 0.55,
+                "latex": "\\delta"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    539,
+                    276,
+                    555,
+                    276,
+                    555,
+                    297,
+                    539,
+                    297
+                ],
+                "score": 0.49,
+                "latex": "\\epsilon"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    73.0,
+                    817.0,
+                    73.0,
+                    817.0,
+                    108.0,
+                    295.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    831.0,
+                    2084.0,
+                    868.0,
+                    2084.0,
+                    868.0,
+                    2122.0,
+                    831.0,
+                    2122.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1378.0,
+                    875.0,
+                    1403.0,
+                    875.0,
+                    1403.0,
+                    901.0,
+                    1378.0,
+                    901.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    226.0,
+                    1138.0,
+                    226.0,
+                    1138.0,
+                    270.0,
+                    292.0,
+                    270.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1158.0,
+                    226.0,
+                    1326.0,
+                    226.0,
+                    1326.0,
+                    270.0,
+                    1158.0,
+                    270.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1402.0,
+                    226.0,
+                    1406.0,
+                    226.0,
+                    1406.0,
+                    270.0,
+                    1402.0,
+                    270.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    269.0,
+                    538.0,
+                    269.0,
+                    538.0,
+                    303.0,
+                    294.0,
+                    303.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    556.0,
+                    269.0,
+                    715.0,
+                    269.0,
+                    715.0,
+                    303.0,
+                    556.0,
+                    303.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    744.0,
+                    269.0,
+                    1200.0,
+                    269.0,
+                    1200.0,
+                    303.0,
+                    744.0,
+                    303.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1228.0,
+                    269.0,
+                    1405.0,
+                    269.0,
+                    1405.0,
+                    303.0,
+                    1228.0,
+                    303.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    300.0,
+                    1031.0,
+                    300.0,
+                    1031.0,
+                    340.0,
+                    291.0,
+                    340.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1053.0,
+                    300.0,
+                    1259.0,
+                    300.0,
+                    1259.0,
+                    340.0,
+                    1053.0,
+                    340.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1350.0,
+                    300.0,
+                    1406.0,
+                    300.0,
+                    1406.0,
+                    340.0,
+                    1350.0,
+                    340.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    335.0,
+                    297.0,
+                    335.0,
+                    297.0,
+                    377.0,
+                    294.0,
+                    377.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    385.0,
+                    335.0,
+                    626.0,
+                    335.0,
+                    626.0,
+                    377.0,
+                    385.0,
+                    377.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    715.0,
+                    335.0,
+                    1186.0,
+                    335.0,
+                    1186.0,
+                    377.0,
+                    715.0,
+                    377.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1208.0,
+                    335.0,
+                    1299.0,
+                    335.0,
+                    1299.0,
+                    377.0,
+                    1208.0,
+                    377.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1319.0,
+                    335.0,
+                    1406.0,
+                    335.0,
+                    1406.0,
+                    377.0,
+                    1319.0,
+                    377.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    368.0,
+                    297.0,
+                    368.0,
+                    297.0,
+                    407.0,
+                    294.0,
+                    407.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    646.0,
+                    368.0,
+                    924.0,
+                    368.0,
+                    924.0,
+                    407.0,
+                    646.0,
+                    407.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    945.0,
+                    368.0,
+                    1032.0,
+                    368.0,
+                    1032.0,
+                    407.0,
+                    945.0,
+                    407.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1052.0,
+                    368.0,
+                    1407.0,
+                    368.0,
+                    1407.0,
+                    407.0,
+                    1052.0,
+                    407.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    313.0,
+                    402.0,
+                    1405.0,
+                    402.0,
+                    1405.0,
+                    435.0,
+                    313.0,
+                    435.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    433.0,
+                    361.0,
+                    433.0,
+                    361.0,
+                    472.0,
+                    292.0,
+                    472.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    381.0,
+                    433.0,
+                    662.0,
+                    433.0,
+                    662.0,
+                    472.0,
+                    381.0,
+                    472.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    750.0,
+                    433.0,
+                    762.0,
+                    433.0,
+                    762.0,
+                    472.0,
+                    750.0,
+                    472.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    604.0,
+                    721.0,
+                    604.0,
+                    721.0,
+                    638.0,
+                    295.0,
+                    638.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    740.0,
+                    604.0,
+                    959.0,
+                    604.0,
+                    959.0,
+                    638.0,
+                    740.0,
+                    638.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1004.0,
+                    604.0,
+                    1322.0,
+                    604.0,
+                    1322.0,
+                    638.0,
+                    1004.0,
+                    638.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1340.0,
+                    604.0,
+                    1405.0,
+                    604.0,
+                    1405.0,
+                    638.0,
+                    1340.0,
+                    638.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    632.0,
+                    296.0,
+                    632.0,
+                    296.0,
+                    674.0,
+                    293.0,
+                    674.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    484.0,
+                    632.0,
+                    572.0,
+                    632.0,
+                    572.0,
+                    674.0,
+                    484.0,
+                    674.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    753.0,
+                    632.0,
+                    766.0,
+                    632.0,
+                    766.0,
+                    674.0,
+                    753.0,
+                    674.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    785.0,
+                    632.0,
+                    1011.0,
+                    632.0,
+                    1011.0,
+                    674.0,
+                    785.0,
+                    674.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1102.0,
+                    632.0,
+                    1242.0,
+                    632.0,
+                    1242.0,
+                    674.0,
+                    1102.0,
+                    674.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1283.0,
+                    632.0,
+                    1408.0,
+                    632.0,
+                    1408.0,
+                    674.0,
+                    1283.0,
+                    674.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    665.0,
+                    297.0,
+                    665.0,
+                    297.0,
+                    699.0,
+                    294.0,
+                    699.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    317.0,
+                    665.0,
+                    485.0,
+                    665.0,
+                    485.0,
+                    699.0,
+                    317.0,
+                    699.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    513.0,
+                    665.0,
+                    1034.0,
+                    665.0,
+                    1034.0,
+                    699.0,
+                    513.0,
+                    699.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1100.0,
+                    665.0,
+                    1168.0,
+                    665.0,
+                    1168.0,
+                    699.0,
+                    1100.0,
+                    699.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1186.0,
+                    665.0,
+                    1405.0,
+                    665.0,
+                    1405.0,
+                    699.0,
+                    1186.0,
+                    699.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    698.0,
+                    352.0,
+                    698.0,
+                    352.0,
+                    736.0,
+                    295.0,
+                    736.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    383.0,
+                    698.0,
+                    609.0,
+                    698.0,
+                    609.0,
+                    736.0,
+                    383.0,
+                    736.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    698.0,
+                    698.0,
+                    1052.0,
+                    698.0,
+                    1052.0,
+                    736.0,
+                    698.0,
+                    736.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1093.0,
+                    698.0,
+                    1405.0,
+                    698.0,
+                    1405.0,
+                    736.0,
+                    1093.0,
+                    736.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    730.0,
+                    425.0,
+                    730.0,
+                    425.0,
+                    767.0,
+                    294.0,
+                    767.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    491.0,
+                    730.0,
+                    992.0,
+                    730.0,
+                    992.0,
+                    767.0,
+                    491.0,
+                    767.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    482.0,
+                    721.0,
+                    482.0,
+                    721.0,
+                    526.0,
+                    292.0,
+                    526.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    797.0,
+                    482.0,
+                    989.0,
+                    482.0,
+                    989.0,
+                    526.0,
+                    797.0,
+                    526.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1105.0,
+                    482.0,
+                    1242.0,
+                    482.0,
+                    1242.0,
+                    526.0,
+                    1105.0,
+                    526.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1332.0,
+                    482.0,
+                    1406.0,
+                    482.0,
+                    1406.0,
+                    526.0,
+                    1332.0,
+                    526.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    519.0,
+                    562.0,
+                    519.0,
+                    562.0,
+                    561.0,
+                    293.0,
+                    561.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    642.0,
+                    519.0,
+                    1072.0,
+                    519.0,
+                    1072.0,
+                    561.0,
+                    642.0,
+                    561.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1195.0,
+                    519.0,
+                    1404.0,
+                    519.0,
+                    1404.0,
+                    561.0,
+                    1195.0,
+                    561.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    555.0,
+                    677.0,
+                    555.0,
+                    677.0,
+                    595.0,
+                    295.0,
+                    595.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    695.0,
+                    555.0,
+                    802.0,
+                    555.0,
+                    802.0,
+                    595.0,
+                    695.0,
+                    595.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    943.0,
+                    555.0,
+                    1023.0,
+                    555.0,
+                    1023.0,
+                    595.0,
+                    943.0,
+                    595.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    857.0,
+                    368.0,
+                    857.0,
+                    368.0,
+                    913.0,
+                    292.0,
+                    913.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    536.0,
+                    857.0,
+                    751.0,
+                    857.0,
+                    751.0,
+                    913.0,
+                    536.0,
+                    913.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1052.0,
+                    857.0,
+                    1064.0,
+                    857.0,
+                    1064.0,
+                    913.0,
+                    1052.0,
+                    913.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 17,
+            "width": 1700,
+            "height": 2200
+        }
+    }
+]
\ No newline at end of file
diff --git a/parse/train/LAKplpLMbP8/LAKplpLMbP8.md b/parse/train/LAKplpLMbP8/LAKplpLMbP8.md
new file mode 100644
index 0000000000000000000000000000000000000000..b6199876b438099afe82fd7180249a7cb6ab5375
--- /dev/null
+++ b/parse/train/LAKplpLMbP8/LAKplpLMbP8.md
@@ -0,0 +1,387 @@
+# Repulsive Deep Ensembles are Bayesian
+
+Francesco D’Angelo ETH Zürich Zürich, Switzerland dngfra@gmail.com
+
+Vincent Fortuin   
+ETH Zürich   
+Zürich, Switzerland   
+fortuin@inf.ethz.ch
+
+# Abstract
+
+Deep ensembles have recently gained popularity in the deep learning community for their conceptual simplicity and efficiency. However, maintaining functional diversity between ensemble members that are independently trained with gradient descent is challenging. This can lead to pathologies when adding more ensemble members, such as a saturation of the ensemble performance, which converges to the performance of a single model. Moreover, this does not only affect the quality of its predictions, but even more so the uncertainty estimates of the ensemble, and thus its performance on out-of-distribution data. We hypothesize that this limitation can be overcome by discouraging different ensemble members from collapsing to the same function. To this end, we introduce a kernelized repulsive term in the update rule of the deep ensembles. We show that this simple modification not only enforces and maintains diversity among the members but, even more importantly, transforms the maximum a posteriori inference into proper Bayesian inference. Namely, we show that the training dynamics of our proposed repulsive ensembles follow a Wasserstein gradient flow of the KL divergence to the true posterior. We study repulsive terms in weight and function space and empirically compare their performance to standard ensembles and Bayesian baselines on synthetic and real-world prediction tasks.
+
+# 1 Introduction
+
+There have been many recent advances on the theoretical properties of sampling algorithms for approximate Bayesian inference, which changed our interpretation and understanding of them. Particularly worth mentioning is the work of Jordan et al. [38], who reinterpret Markov Chain Monte Carlo (MCMC) as a gradient flow of the KL divergence over the Wasserstein space of probability measures. This new formulation allowed for a deeper understanding of approximate inference methods but also inspired the inception of new and more efficient inference strategies. Following this direction, Liu and Wang $\pmb { \mathbb { B } } \mathbf { \mathbb { 1 } }$ recently proposed the Stein Variational Gradient Descent (SVGD) method to perform approximate Wasserstein gradient descent. Conceptually, this method, which belongs to the family of particle-optimization variational inference (POVI), introduces a repulsive force through a kernel acting in the parameter space to evolve a set of samples towards high-density regions of the target distribution without collapsing to a point estimate.
+
+Another method which has achieved great success recently are ensembles of neural networks (socalled deep ensembles), which work well both in terms of predictive performance $\pm 2 \sqrt { 8 0 }$ as well as uncertainty estimation $\begin{array} { r l } {  { \| 6 5 \| } } \end{array}$ , and have also been proposed as a way to perform approximate inference in Bayesian neural networks [82, 36]. That being said, while they might allow for the averaging of predictions over several hypotheses, they do not offer any guarantees for the diversity between those hypotheses nor do they provably converge to the true Bayesian posterior under any meaningful limit. In this work, we show how the introduction of a repulsive term between the members in the ensemble, inspired by SVGD, not only naïvely guarantees the diversity among the members, avoiding their collapse in parameter space, but also allows for a reformulation of the method as a gradient flow of the KL divergence in the Wasserstein space of distributions. It thus allows to endow deep ensembles with convergence guarantees to the true Bayesian posterior.
+
+![](images/c87b35667fe31cb24e44c323fe8bffeb4df13996d7df41a00bfd504161843062.jpg)  
+Figure 1: BNN 1D regression. The function-space methods (SVGD and WGD) approach the HMC posterior more closely, while the standard deep ensembles and weight-space methods fail to properly account for the uncertainty, especially the in-between uncertainty.
+
+An additional problem is that BNN inference in weight space can lead to degenerate solutions, due to the overparametrization of these models. That is, several samples could have very different weights but map to the same function, thus giving a false sense of diversity in the ensemble. This property, that we will refer to as non-identifiability of neural networks (see Appendix $\boxed { \mathrm { A } }$ , can lead to redundancies in the posterior distribution. It implies that methods like MCMC sampling, deep ensembles, and SVGD waste computation in local modes that account for equivalent functions. Predictive distributions approximated using samples from these modes do not improve over a simple point estimate and lead to a poor uncertainty estimation. Following this idea, Wang et al. $\mathbb { \left[ \left] \right. \right]} 2 $ introduced a new method to extend POVI methods to function space, overcoming this limitation. Here, we also study an update rule that allows for an approximation of the gradient flow of the KL divergence in function space in our proposed repulsive ensembles.
+
+We make the following contributions:
+
+• We derive several different repulsion terms that can be added as regularizers to the gradient updates of deep ensembles to endow them with Bayesian convergence properties.   
+• We show that these terms approximate Wasserstein gradient flows of the KL divergence and can be used both in weight space and function space.   
+• We compare these proposed methods theoretically to standard deep ensembles and SVGD and highlight their different guarantees.   
+• We assess all these methods on synthetic and real-world deep learning tasks and show that our proposed repulsive ensembles can achieve competitive performance and improved uncertainty estimation.
+
+# 2 Repulsive Deep Ensembles
+
+In supervised deep learning, we typically consider a likelihood function $p ( \pmb { y } | f ( \pmb { x } ; \mathbf { w } ) )$ (e.g., Gaussian for regression or Categorical for classification) parameterized by a neural network $f ( \pmb { x } ; \mathbf { w } )$ and training data $\textit { D } = \{ ( \boldsymbol { \mathbf { { x } } } _ { i } , \boldsymbol { \mathbf { { y } } } _ { i } ) \} _ { i = 1 } ^ { n }$ with $\textbf { \textit { x } } \in \textbf { \textit { X } }$ and $\textbf { \textit { y } } \in \textbf { \textit { y } }$ . In Bayesian neural networks (BNNs), we are interested in the posterior distribution of all likely networks given by $\begin{array} { r } { p ( \mathbf { w } | \mathcal { D } ) \propto \prod _ { i = 1 } ^ { n } p ( \pmb { y } _ { i } | f ( \pmb { x } _ { i } ; \mathbf { w } ) ) p ( \mathbf { w } ) } \end{array}$ , where $p ( \mathbf { w } )$ is the prior distribution over weights. Crucially, when making a prediction on a test point $\mathbf { \boldsymbol { x } } ^ { * }$ , in the Bayesian approach we do not only use a single parameter $\widehat { \bf w }$ to predict ${ \pmb y } ^ { * } = f ( { \pmb x } ^ { * } ; \widehat { \mathbf { w } } )$ , but we marginalize over the whole posterior, thus taking all possible explanations of the data into account:
+
+$$
+p ( \pmb { y } ^ { * } | \pmb { x } ^ { * } , \mathcal { D } ) = \int p ( \pmb { y } ^ { * } | f ( \pmb { x } ^ { * } ; \mathbf { w } ) ) p ( \mathbf { w } | \mathcal { D } ) \mathrm { d } \mathbf { w }
+$$
+
+While approximating the posterior of Bayesian neural networks (or sampling from it) is a challenging task, performing maximum a posteriori (MAP) estimation, which corresponds to finding the mode of the posterior, is usually simple. Ensembles of neural networks use the non-convexity of the MAP optimization problem to create a collection of $K$ independent—and possibly different— solutions. Considering $n$ weight configurations of a neural network $\{ { \bf w } _ { i } \} _ { i = 1 } ^ { n }$ with ${ \bf w } _ { i } \in \mathbb { R } ^ { d }$ , the dynamics of the ensemble under the gradient of the posterior lead to the following update rule at iteration $t$ :
+
+$$
+\begin{array} { r l } & { \mathbf { w } _ { i } ^ { t + 1 }  \mathbf { w } _ { i } ^ { t } + \epsilon _ { t } \phi ( \mathbf { w } _ { i } ^ { t } ) } \\ { \mathrm { w i t h } \quad } & { \phi ( \mathbf { w } _ { i } ^ { t } ) = \nabla _ { \mathbf { w } _ { i } ^ { t } } \log p ( \mathbf { w } _ { i } ^ { t } | \mathcal { D } ) , } \end{array}
+$$
+
+with step size $\epsilon _ { t }$ . Ensemble methods have a long history [e.g., 45, 26, 6] and were recently revisited for neural networks $\pm 2 \|$ and coined deep ensembles. The predictions of the different members are combined to create a predictive distribution by using the solutions to compute the Bayesian model average (BMA) in Eq. $\mathbb { D }$ . Recent works $\mathbb { \lVert \rVert }$ have shown that deep ensembles can outperform some of the Bayesian approaches for uncertainty estimation. Even more recently, Wilson and Izmailov $\pmb { \Vert 8 2 \Vert }$ argued that deep ensembles can be considered a compelling approach to Bayesian model averaging. Despite these ideas, the ability of deep ensembles to efficiently average over multiple hypotheses and to explore the functional landscape of the posterior distribution studied in $[ \overline { { 1 8 } } ]$ does not guarantee sampling from the right distribution. Indeed, the additional Langevin noise introduced in $\mathbb { [ \breve { ] { ] \mathrm { ~ Z ~ Z ~ } ] } } }$ , which is not considered in deep ensembles, is crucial to ensure samples from the true Bayesian posterior.
+
+From a practical standpoint, since the quality of an ensemble hinges on the diversity of its members, many methods were recently proposed to improve this diversity without compromising the individual accuracy. For instance, Wenzel et al. [80] propose hyper-deep ensembles that combine deep networks with different hyperparameters. Similarly, cyclical learning-rate schedules can explore several local minima for the ensemble members $\pmb { \mathbb { B 3 } }$ . Alternatively, Rame and Cord $ { \mathbb { I } }  { \mathbb { I } }$ proposed an informationtheoretic framework to avoid redundancy in the members and Oswald et al. $\overline { { \| 6 3 \| } }$ studied possible interactions between members based on weight sharing. However, the absence of a constraint that prevents particles from converging to the same mode limits the possibility of improvement by introducing more ensemble members. This means that any hopes to converge to different modes must exclusively rely on:
+
+1. the randomness of the initialization   
+2. the noise in the estimation of the gradients due to minibatching   
+3. the number of local optima that might be reached during gradient descent.
+
+Moreover, the recent study of Geiger et al. $\pmb { \left. \pmb { \left. \bar { 2 5 } \right. } \right. }$ showed how the empirical test error of the ensemble converges to the one of a single trained model when the number of parameters goes to infinity, leading to deterioration of the performance. In other words, the bigger the model, the harder it is to maintain diversity in the ensemble and avoid collapse to the same solution. This is intuitively due to the fact that bigger models are less sensitive to the initialization. Namely, in order for them to get stuck in a local minimum, they must have second derivatives that are positive simultaneously in all directions. As the number of hidden units gets larger, this becomes less likely.
+
+# 2.1 Repulsive force in weight space
+
+To overcome the aforementioned limitations of standard deep ensembles, we introduce, inspired by SVGD $\mathbb { \left[ \left[ 5 1 \right] \right] }$ , a deep ensemble with members that interact with each other through a repulsive component. Using a kernel function to model this interaction, the single models repel each other based on their position in the weight space, so that two members can never assume the same weights. Considering a stationary kernel $\bar { k } ( \cdot , \cdot ) : \mathbb { R } ^ { d } \times \mathbb { R } ^ { d } \to \mathbb { R }$ acting in the parameter space of the neural network, a repulsive term $\mathcal { R }$ can be parameterized through its gradient:
+
+$$
+\phi ( \mathbf { w } _ { i } ^ { t } ) = \nabla _ { \mathbf { w } _ { i } ^ { t } } \log p ( \mathbf { w } _ { i } ^ { t } | \mathcal { D } ) - \mathcal { R } \left( \left\{ \nabla _ { \mathbf { w } _ { i } ^ { t } } k ( \mathbf { w } _ { i } ^ { t } , \mathbf { w } _ { j } ^ { t } ) \right\} _ { j = 1 } ^ { n } \right) .
+$$
+
+To get an intuition for the behavior of this repulsive term and its gradients, we can consider the RBF kernel $\begin{array} { r } { k ( \mathbf { w } _ { i } , \mathbf { w } _ { j } ) = \exp \big ( - \frac { 1 } { h } | | \mathbf { w } _ { i } - \mathbf { w } _ { j } | | ^ { 2 } \big ) } \end{array}$ with lengthscale $h$ and notice how its gradient
+
+$$
+\nabla _ { \mathbf { w } _ { i } ^ { t } } k ( \mathbf { w } _ { i } ^ { t } , \mathbf { w } _ { j } ^ { t } ) = \frac { 2 } { h } ( \mathbf { w } _ { j } ^ { t } - \mathbf { w } _ { i } ^ { t } ) k ( \mathbf { w } _ { i } ^ { t } , \mathbf { w } _ { j } ^ { t } )
+$$
+
+drives $\mathbf { w } _ { i }$ away from its neighboring members ${ \bf w } _ { j }$ , thus creating a repulsive effect. Naturally, not all the choices of $\mathcal { R }$ induce this effect. One of the simplest formulations to obtain it is via a linear combination of the kernel gradients scaled by a positive factor, that is, $\begin{array} { r } { \beta \sum _ { j = 1 } ^ { n } \nabla _ { \mathbf { w } _ { i } ^ { t } } k ( \mathbf { w } _ { i } ^ { t } , \mathbf { w } _ { j } ^ { t } ) } \end{array}$ with $\beta \in \mathbb { R } _ { * } ^ { + }$ . We will see in Section $\begin{array} { l } { 3 } \\ { . } \end{array}$ how the choice of $\beta$ can be justified in order to obtain convergence to the Bayesian posterior together with alternative possible formulations of $\mathcal { R }$ that preserve this convergence.
+
+# 2.2 Repulsive force in function space
+
+To overcome the aforementioned overparameterization issue, the update in Eq. $\textcircled { 3 }$ can be formulated in function space instead of weight space. Let $f : \mathbf { w } \mapsto f ( \cdot ; \mathbf { w } )$ be the map that maps a configuration of weights $\mathbf { w } \in \mathbb { R } ^ { d }$ to the corresponding neural network regression function and denote as $f _ { i } : = f ( \cdot ; { \mathbf w } _ { i } )$ the function with a certain configuration of weights $\mathbf { w } _ { i }$ . We can now consider $n$ particles in function space $\{ f _ { i } \} _ { i = 1 } ^ { n }$ with $\pmb { f } \in \mathcal { F }$ and model their interaction with a general positive definite kernel $k ( \cdot , \cdot )$ . We also consider the implicit functional likelihood $p ( \pmb { y } | \pmb { x } , \pmb { f } )$ , determined by the measure $p ( \pmb { y } | \pmb { x } , \mathbf { w } )$ in the weight space, as well as the functional prior $p ( f )$ , which can either be defined separately (e.g., using a GP) or modeled as a push-forward measure of the weight-space prior $p ( \mathbf { w } )$ . Together, they determine the posterior in function space $p ( \pmb { f } | \mathcal { D } )$ . The functional evolution of a particle can then be written as:
+
+$$
+\begin{array} { r l } & { f _ { i } ^ { t + 1 } \gets f _ { i } ^ { t } + \epsilon _ { t } \phi ( f _ { i } ^ { t } ) } \\ { \mathrm { t h } \quad } & { \phi ( f _ { i } ^ { t } ) = \nabla _ { f _ { i } ^ { t } } \log p ( f _ { i } ^ { t } | \mathcal { D } ) - \mathcal { R } \left( \left\{ \nabla _ { f _ { i } ^ { t } } k ( f _ { i } ^ { t } , f _ { j } ^ { t } ) \right\} _ { j = 1 } ^ { n } \right) . } \end{array}
+$$
+
+However, computing the update in function space is neither tractable nor practical, which is why two additional considerations are needed. The first one regards the infinite dimensionality of function space, which we circumvent using a canonical projection into a subspace:
+
+Definition 1 (Canonical projection). For any $A \subset { \mathcal { X } }$ , we define $\pi _ { A } : \mathbb { R } ^ { \mathcal { X } } \to \mathbb { R } ^ { A }$ as the canonical projection onto $A$ , that is, $\pi _ { A } ( f ) = \{ f ( a ) \} _ { a \in A }$ .
+
+In other words, the kernel will not be evaluated directly in function space, but on the projection $k \big ( \pi _ { B } ( f ) , \pi _ { B } ( f ^ { \prime } ) \big )$ , with $B$ being a subset of the input space given by a batch of training data points. The second consideration is to project this update back into the parameter space and evolve a set of particles there, because ultimately we are interested in representing the functions by parameterized neural networks. For this purpose, we can use the Jacobian of the $i$ -th particle as a projector:
+
+$$
+\phi ( { \mathbf w } _ { i } ^ { t } ) = \left( \frac { \partial f _ { i } ^ { t } } { \partial { \mathbf w } _ { i } ^ { t } } \right) ^ { \top } \left[ \nabla _ { f _ { i } ^ { t } } \log p ( f _ { i } ^ { t } | { \mathcal D } ) - { \mathcal R } \left( \left\{ \nabla _ { f _ { i } ^ { t } } k ( \pi _ { B } ( f _ { i } ^ { t } ) , \pi _ { B } ( f _ { j } ^ { t } ) ) \right\} _ { j = 1 } ^ { n } \right) \right] .
+$$
+
+# 2.3 Comparison to Stein variational gradient descent
+
+Note that our update is reminiscent of SVGD $\mathbb { \left[ 5 1 \right] }$ , which in parameter space can be written as:
+
+$$
+\phi ( \mathbf { w } _ { i } ^ { t } ) = \sum _ { j = 1 } ^ { n } k ( \mathbf { w } _ { i } ^ { t } , \mathbf { w } _ { j } ^ { t } ) \nabla _ { \mathbf { w } _ { i } ^ { t } } \log p ( \mathbf { w } _ { i } ^ { t } | \mathcal { D } ) + \sum _ { j = 1 } ^ { n } \nabla _ { \mathbf { w } _ { j } ^ { t } } k ( \mathbf { w } _ { j } ^ { t } , \mathbf { w } _ { i } ^ { t } ) .
+$$
+
+It is important to notice that here, the gradients are averaged across all the particles using the kernel matrix. Interestingly, SVGD can be asymptotically interpreted as gradient flow of the KL divergence under a new metric induced by the Stein operator [16, 50] (see Appendix D for more details). Moving the inference from parameter to function space $\pmb { \mathbb { Z } } 6 \|$ leads to the update rule
+
+$$
+\phi ( \mathbf { w } _ { i } ^ { t } ) = \left( \frac { \partial f _ { i } ^ { t } } { \partial \mathbf { w } _ { i } ^ { t } } \right) ^ { \top } \left( \frac { 1 } { n } \sum _ { j = 1 } ^ { n } k ( f _ { i } ^ { t } , f _ { j } ^ { t } ) \nabla _ { f _ { j } ^ { t } } \log p ( f _ { j } ^ { t } | \mathcal { D } ) + \nabla _ { f _ { j } ^ { t } } k ( f _ { i } ^ { t } , f _ { j } ^ { t } ) \right) .
+$$
+
+This way of averaging gradients using a kernel can be dangerous in high-dimensional settings, where kernel methods often suffer from the curse of dimensionality. Moreover, in Eq. $\textcircled{6}$ , the posterior gradients of the particles are averaged using their similarity in weight space, which can be misleading in multi-modal posteriors. Worse yet, in Eq. $\textcircled{7}$ , the gradients are averaged in function space and are then projected back using exclusively the $i$ -th Jacobian, which can be harmful given that it is not guaranteed that distances between functions evaluated on a subset of their input space resemble their true distance. Our proposed method, on the other hand, does not employ any averaging of the posterior gradients and thus comes closest to the true particle gradients in deep ensembles.
+
+# 3 Repulsive deep ensembles are Bayesian
+
+So far, we represented the repulsive force as a general function of the gradients of a kernel. In this section, we show how to determine the explicit form of the repulsive term, such that the resulting update rule is equivalent to the discretization of the gradient flow dynamics of the KL divergence in Wasserstein space. We begin by introducing the concepts of particle approximation and gradient flow.
+
+# 3.1 Particle approximation
+
+A particle-based approximation of a target measure depends on a set of weighted samples $\{ ( \bar { x _ { i } } , w _ { i } ) \} _ { i = 1 } ^ { n }$ , for which an empirical measure can be defined as
+
+$$
+\rho ( x ) = \sum _ { i = 1 } ^ { n } w _ { i } \delta ( x - x _ { i } ) ,
+$$
+
+where $\delta ( \cdot )$ is the Dirac delta function and the weights $w _ { i }$ satisfy $w _ { i } \in [ 0 , 1 ]$ and $\textstyle \sum _ { i = 1 } ^ { n } w _ { i } = 1$ . To approximate a target distribution $\pi ( x )$ using the empirical measure, the particles and their weights need to be selected in a principled manner that minimizes some measure of distance between $\pi ( x )$ and $\rho ( x )$ (e.g., a set of $N$ samples with weights $w _ { i } = 1 / N$ obtained using an MCMC method).
+
+# 3.2 Gradient flow in parameter space
+
+Given a smooth function $J : \mathbb { R } ^ { d }  \mathbb { R }$ in Euclidean space, we can minimize it by creating a path that follows its negative gradient starting from some initial conditions $x _ { 0 }$ . The curve $x ( t )$ with starting point $x _ { 0 }$ described by that path is called gradient flow. The dynamics and evolution in time of a considered point in the space under this minimization problem can be described as the ODE1
+
+$$
+\frac { d \boldsymbol { x } } { d t } = - \boldsymbol { \nabla } J ( \boldsymbol { x } ) .
+$$
+
+We can extend this concept to the space of probability distributions (Wasserstein gradient flow) [3]. Let us consider the space of probability measures $\mathcal { P } _ { 2 } ( \mathcal { M } )$ , that is, the set of probability measures with finite second moments defined on the manifold $\mathcal { M }$ :
+
+$$
+\mathcal { P } _ { 2 } ( \mathcal { M } ) = \left\{ \varphi : \mathcal { M } \to [ 0 , \infty ) \bigg | \int _ { \mathcal { M } } \mathrm { d } \varphi = 1 , ~ \int _ { \mathcal { M } } | x | ^ { 2 } \varphi ( x ) \mathrm { d } x < + \infty \right\} .
+$$
+
+Taking $\Pi ( \mu , \nu )$ as the set of joint probability measures with marginals $\mu , \nu$ , we can define the Wasserstein metric on the space $\mathcal { P } _ { 2 } ( \mathcal { M } )$ as:
+
+$$
+W _ { 2 } ^ { 2 } ( \mu , \nu ) = \operatorname* { i n f } _ { \pi \in \Pi ( \mu , \nu ) } \int | x - y | ^ { 2 } { \mathrm { d } } \pi ( x , y ) .
+$$
+
+Considering the optimization problem of a functional $J : \mathcal { P } _ { 2 } ( \mathcal { M } )  \mathbb { R }$ , such as the $\mathrm { K L }$ divergence between the particle approximation in Eq. $\textcircled { 8 }$ and the target posterior $\pi ( x )$ ,
+
+$$
+\operatorname* { i n f } _ { \rho \in \mathcal { P } _ { 2 } ( \mathcal { M } ) } D _ { K L } ( \rho , \pi ) = \int _ { \mathcal { M } } ( \log \rho ( x ) - \log \pi ( x ) ) \rho ( x ) \mathrm { d } x ,
+$$
+
+the evolution in time of the measure $\rho$ under the equivalent of the gradient, the Wasserstein gradient flow, is described by the Liouville equation2 [38, 3, 64]:
+
+$$
+\begin{array} { l } { \displaystyle \frac { \partial \rho ( \boldsymbol { x } ) } { \partial t } = \nabla \cdot \left( \rho ( \boldsymbol { x } ) \nabla \frac { \delta } { \delta \rho } D _ { K L } ( \rho , \pi ) \right) } \\ { \displaystyle = \nabla \cdot \left( \rho ( \boldsymbol { x } ) \nabla \big ( \log \rho ( \boldsymbol { x } ) - \log \pi ( \boldsymbol { x } ) \big ) \right) , } \end{array}
+$$
+
+where $\nabla _ { \delta \rho } ^ { \delta } D _ { K L } ( \rho , \pi ) \ = : \ \nabla _ { \mathcal { W } _ { 2 } } D _ { K L } ( \rho , \pi )$ is the Wasserstein gradient and the operator $\frac { \delta } { \delta \rho }$ $\mathcal { P } _ { 2 } ( \mathcal { M } ) \stackrel { \cdot } {  } \mathbb { R }$ represents the functional derivative or first variation (see Appendix $\boxed { \mathsf { C } }$ for more details). In the particular case of the KL functional, we can recover the Fokker-Planck equation,
+
+$$
+\begin{array} { r l r } & { } & { \frac { \partial \rho ( x ) } { \partial t } = \nabla \cdot \left( \rho ( x ) \nabla ( \log \rho ( x ) - \log \pi ( x ) ) \right) } \\ & { } & { = - \nabla \cdot \left( \rho ( x ) \nabla \log \pi ( x ) \right) + \nabla ^ { 2 } \rho ( x ) , } \end{array}
+$$
+
+that admits as unique stationary distribution the posterior $\pi ( x )$ . The deterministic particle dynamics ODE $\left[ \left[ 2 \right] \right]$ related to Eq. $\mathbb { ( 1 1 ) }$ , namely mean-field Wasserstein dynamics, is then given by:
+
+$$
+\frac { d x } { d t } = - \nabla \big ( \log \rho ( x ) - \log \pi ( x ) \big ) .
+$$
+
+Considering a discretization of Eq. (12) for a particle system $\{ x \} _ { i = 1 } ^ { n }$ and small stepsize $\epsilon _ { t }$ , we can rewrite Eq. $\mathbb { \underline { { ( 1 2 ) } } }$ as:
+
+$$
+x _ { i } ^ { t + 1 } = x _ { i } ^ { t } + \epsilon _ { t } \bigl ( \nabla \log \pi ( x _ { i } ^ { t } ) - \nabla \log \rho ( x _ { i } ^ { t } ) \bigr ) .
+$$
+
+Unfortunately, we do not have access to the analytical form of the gradient $\nabla \log \rho$ , so an approximation is needed. At this point, it is crucial to observe the similarity between the discretization of the Wasserstein gradient flow in Eq. $\textcircled { 1 3 }$ and the repulsive update in Eq. $( 3 )$ to notice how, if the kernelized repulsion is an approximation of the gradient of the empirical particle measure, the update rule minimizes the KL divergence between the particle measure and the target posterior. Different sample-based approximations of the gradient that use a kernel function have been recently studied. The simplest one is given by the kernel density estimation (KDE) (details in Appendix $\dot { \mathrm { ~ E ~ } } )$ $\begin{array} { r } { \tilde { \rho } _ { t } ( x ) = \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \dot { k } ( x , x _ { t } ^ { i } ) } \end{array}$ , where $\boldsymbol { k } ( \cdot , \cdot ) : \mathbb { R } ^ { d } \times \mathbb { R } ^ { d }  \dot { \mathbb { R } }$ and the gradient of its log density is given by $\mathbb { \ m }$ :
+
+$$
+\nabla \log \rho ( x _ { i } ^ { t } ) \approx \frac { \sum _ { j = 1 } ^ { n } \nabla _ { x _ { i } ^ { t } } k ( x _ { i } ^ { t } , x _ { j } ^ { t } ) } { \sum _ { j = 1 } ^ { n } k ( x _ { i } ^ { t } , x _ { j } ^ { t } ) } .
+$$
+
+Using this approximation in Eq. $( 1 3 )$ we obtain:
+
+$$
+x _ { i } ^ { t + 1 } = x _ { i } ^ { t } + \epsilon _ { t } \Bigg ( \nabla \log \pi ( x _ { i } ^ { t } ) - \frac { \sum _ { j = 1 } ^ { n } \nabla _ { x _ { i } ^ { t } } k ( x _ { i } ^ { t } , x _ { j } ^ { t } ) } { \sum _ { j = 1 } ^ { n } k ( x _ { i } ^ { t } , x _ { j } ^ { t } ) } \Bigg ) ,
+$$
+
+where, if we substitute the posterior for $\pi$ , we obtain an expression for the repulsive force in Eq. $\textcircled{3}$ . This shows that if the repulsive term in Eq. $( 3 )$ is the normalized sum of the gradients $\mathcal { R } =$ $\begin{array} { r } { \left( \bar { \sum _ { j = 1 } ^ { n } } k ( \mathbf { w } _ { i } ^ { t } , \mathbf { w } _ { j } ^ { t } ) \right) ^ { - 1 } \sum _ { j = 1 } ^ { n } \nabla _ { \mathbf { w } _ { i } ^ { t } } k ( \mathbf { w } _ { i } ^ { t } , \mathbf { w } _ { j } ^ { t } ) } \end{array}$ , we do not only encourage diversity of the ensemble members and thus avoid collapse, but surprisingly—in the asymptotic limit of , where the KDE approximation is exact $\left[ \left[ 6 6 \right] \right]$ —also converge to the true Bayesian posterior!
+
+Nevertheless, approximating the gradient of the empirical measure with the KDE can lead to suboptimal performance, as already studied by Li and Turner $[ \overline { { | 4 6 | } }$ . They instead introduced a new Stein gradient estimator (SGE) that offers better performance, while maintaining the same computational cost. Even more recently, Shi et al. $\mathbb { \left. \boldsymbol { \mathfrak { G } } \boldsymbol { \mathfrak { A } } \right. }$ introduced a spectral method for gradient estimation (SSGE), that also allows for a simple estimation on out-of-sample points. These two estimators can be used in Eq. $\textcircled { 1 3 }$ , to formulate the following update rules with two alternative repulsive forces. The one using the Stein estimator, that we will call SGE-WGD, is:
+
+$$
+x _ { i } ^ { t + 1 } = x _ { i } ^ { t } + \epsilon _ { t } \bigg ( \nabla \log \pi ( x _ { i } ^ { t } ) + \sum _ { j = 1 } ^ { n } ( K + \eta \mathbb { I } ) _ { i j } ^ { - 1 } \sum _ { k = 1 } ^ { n } \nabla _ { x _ { k } ^ { t } } k ( x _ { k } ^ { t } , x _ { j } ^ { t } ) \bigg ) ,
+$$
+
+where $K$ is the kernel Gram matrix, $\eta$ a small constant, and I the identity matrix. We can notice an important difference between KDE and SGE, in that the former is only considering the interaction of the $i$ -th particle being updated with all the others, while the latter is simultaneously considering also the interactions between the remaining particles. The spectral method, that we will call SSGE-WGD, leads to the following update rule:
+
+$$
+x _ { t + 1 } ^ { i } = x _ { t } ^ { i } + \epsilon _ { t } \bigg ( \nabla \log \pi ( x _ { t } ^ { i } ) + \sum _ { j = 1 } ^ { J } \frac { 1 } { \lambda _ { j } ^ { 2 } } \sum _ { m = 1 } ^ { n } \sum _ { k = 1 } ^ { n } u _ { j k } \nabla _ { x _ { m } } k ( x _ { m } ^ { t } , x _ { k } ^ { t } ) \cdot \sum _ { l = 1 } ^ { n } u _ { j l } k ( x _ { i } ^ { t } , x _ { l } ^ { t } ) \bigg )
+$$
+
+where $\lambda _ { j }$ is the $j$ -th eigenvalue of the kernel matrix and $u _ { j k }$ is the $k$ -th component of the $j$ -th eigenvector. Computationally, both SSGE and SGE have a cost of $\mathcal { O } ( M ^ { 3 } + M ^ { 2 } d )$ , with $M$ being the number of points and $d$ their dimensionality. SSGE has an additional cost for predictions of $\mathcal { O } ( M ( d + J ) )$ , where $J$ is the number of eigenvalues.
+
+![](images/909c60e208223cd54336af828c72fc5777f5cbee78dd1b5dffc27345c64eca36.jpg)  
+Figure 2: Single Gaussian. We show samples from SVGD, KDE-WGD, SGE-WGD, and SSGEWGD (from left to right). The upper and right plots show the empirical one-dimensional marginal distributions obtained using KDE on the samples (red) and on the particles (blue).
+
+# 3.3 Gradient flow in function space
+
+To theoretically justify the update rule introduced in function space in Eq. $\textcircled{5}$ , we can rewrite the Liouville equation for the gradient flow in Eq. $\textcircled { 1 1 }$ in function space as
+
+$$
+\begin{array} { l } { \displaystyle \frac { \partial \rho ( { \pmb f } ) } { \partial t } = \nabla \cdot \left( \rho ( { \pmb f } ) \nabla \frac { \delta } { \delta \rho } D _ { K L } ( \rho , \pi ) \right) } \\ { \displaystyle = \nabla \cdot \left( \rho ( { \pmb f } ) \nabla \big ( \log \rho ( { \pmb f } ) - \log \pi ( { \pmb f } ) \big ) \right) . } \end{array}
+$$
+
+Following this update, the mean field functional dynamics are
+
+$$
+\frac { d \pmb f } { d t } = - \nabla \big ( \log \rho ( \pmb f ) - \log \pi ( \pmb f ) \big ) .
+$$
+
+Using the same KDE approximation as above, we can obtain a discretized evolution in function space and with it an explicit form for the repulsive force in Eq. $\textcircled{4}$ as
+
+$$
+\pmb { f } _ { t + 1 } ^ { i } = \pmb { f } _ { t } ^ { i } + \epsilon _ { t } \bigg ( \nabla _ { \pmb { f } } \log \pi ( \pmb { f } _ { t } ^ { i } ) - \frac { \sum _ { j = 1 } ^ { n } \nabla _ { \pmb { f } _ { i } ^ { t } } k ( \pmb { f } _ { i } ^ { t } , \pmb { f } _ { j } ^ { t } ) } { \sum _ { j = 1 } ^ { n } k ( \pmb { f } _ { i } ^ { t } , \pmb { f } _ { j } ^ { t } ) } \bigg ) .
+$$
+
+The update rules using the SGE and SSGE approximations follow as for the parametric case. It is important to notice that this update rule requires the function space prior gradient: $\nabla _ { f _ { j } } \log { p ( f _ { j } | x , y ) } =$ $\nabla _ { f _ { j } } \log p ( \pmb { y } | \pmb { x } , \pmb { f _ { j } } ) + \nabla _ { f _ { j } } \log p ( \pmb { f _ { j } } )$ . If one wants to use an implicit prior defined in weight space, an additional estimator is needed due to its analytical intractability. We again adopted the SSGE, introduced by Shi et al. $\mathbb { \lVert \boldsymbol { 6 9 } \rVert }$ , which was already used for a similar purpose in Sun et al. $\pmb { \mathbb { Z } 1 }$ . It is also interesting to note that the update rule in Eq. $\textcircled { 1 2 0 }$ readily allows for the use of alternative priors that have an analytical form, such as Gaussian processes. This is an important feature of our method that allows for an explicit encoding of function space properties that can be useful for example in achieving better out of distribution detection capabilities $\checkmark$ .
+
+# 3.4 The choice of the kernel
+
+A repulsive effect can always be created in the ensemble by means of the gradient of any kernel function that is measuring the similarity between two members. Nevertheless, it is important to keep in mind that to ensure the asymptotic convergence to the Bayesian posterior, the repulsive component must be a consistent estimator of the gradient in Eq. $( 1 3 )$ , as shown in Section $\checkmark$ . Therefore, some important constraints over the kernel choice are needed. In particular, the SGE and SSGE need a kernel function belonging to the Stein class (see Shi et al. $\dot { \overline { { \vert 6 9 \vert } } }$ for more details). On the other hand, for the KDE, any symmetric probability density function can be used. On this subject, the work of Aggarwal et al. [1] has shown how the Manhattan distance metric (L1 norm) might be preferable over the Euclidean distance metric (L2 norm) for high-dimensional settings. We performed some additional experiments using the L1 norm (Laplace kernel) for the KDE but we could not observe any substantial difference compared to using the L2 norm. Further investigations regarding this hypothesis are left for future research.
+
+![](images/094ed7ba5611118de5688c3ddd1545168ced55dff3ababfdac0ee5e88615b714.jpg)  
+Figure 3: BNN 2D classification. We show the entropy of the predictive posteriors. Again, the function-space methods capture the uncertainty better than the weight-space ones, thus approaching the gold-standard HMC posterior.
+
+# 4 Experiments
+
+In this section, we compare the different proposed WGD methods with deep ensembles and SVGD on synthetic sampling, regression, and classification tasks and real-world image classification tasks. We use an RBF kernel (except where otherwise specified) with the popular median heuristic $\mathbb { \left[ \left[ 5 1 \right] \right] }$ to choose the kernel bandwidth. In our experiments, an adaptive bandwidth leads to better performance than fixing and tuning a single constant value for the entire evolution of the particles. We also quantitatively assess the uncertainty estimation of the methods in terms of calibration and OOD detection. In our experiments, we report the test accuracy, negative log-likelihood (NLL), and the expected calibration error (ECE) [58]. To assert the robustness on out-of-distribution (OOD) data, we report the ratio between predictive entropy on OOD and test data points $( H _ { o } / H _ { t } )$ , and the OOD detection area under the ROC curve AUROC(H) $\mathbb { H }$ . Moreover, to assess the diversity of the ensemble generated by the different methods in function space, we measure the functional diversity using the model disagreement (MD) (details in Appendix $\bar { \bigtriangledown } \bar { \bigtriangledown }$ . In particular, we report the ratio between the average model disagreement on the OOD and test data points $( M D _ { o } / M D _ { t } )$ and additionally the OOD detection AUROC(MD) computed using this measure instead of the entropy.
+
+Sampling from synthetic distributions As a sanity check, we first assessed the ability of our different approximations for Wasserstein gradient descent (using KDE, SGE, and SSGE) to sample from a two-dimensional Gaussian distribution (Figure $^ { 2 ) }$ . We see that our SGE-WGD, SSGE-WGD and the SVGD fit the target almost perfectly. We also tested the different methods in a more complex two-dimensional Funnel distribution $\mathbb { \left[ \left[ 5 9 \right] \right] }$ and present the results in Figure $\mathrm { F . l }$ in the Appendix. There, SGE-WGD and SVGD also perform best.
+
+BNN 1D regression We then assessed the different methods in fitting a BNN posterior on a synthetically generated one-dimensional regression task. The results are reported in Figure 1 consisting of the mean prediction and $\pm 1 , 2 , 3$ standard deviations of the predictive distribution. We can see that all methods performing inference in the weight space (DE, w-SVGD, WGD) are unable to capture the epistemic uncertainty between the two clusters of training data points. Conversely, the functional methods (f-SVGD, fWGD) are perfectly able to infer the diversity of the hypotheses in this region due to the lack of training evidence. They thereby achieve a predictive posterior that very closely resembles the one obtained with the gold-standard HMC sampling.
+
+BNN 2D classification Next, we investigated the predictive performance and quality of uncertainty estimation of the methods in a two-dimensional synthetic classification setting. The results are displayed in Figure $\textcircled { 3 }$ We can clearly observe that the weight-space methods are overconfident and do not capture the uncertainty well. Moreover, all the functions seems to collapse to the optimal classifier. These methods thus only account for uncertainty close to the decision boundaries and to the origin region, for which the uncertainty is purely aleatoric. In this setting, f-SVGD suffers from similar issues as the weight space methods, being overconfident away from the training data. Conversely, our fWGD methods are confident (low entropy) around the data but not out-of-distribution, thus representing the epistemic uncertainty better. This suggests that the functional diversity captured by this method naturally leads to a distance-aware uncertainty estimation $\mathbb { H 9 } \mathbb { L O }$ , a property that translates into confident predictions only in the proximity of the training data, allowing for a principled OOD detection.
+
+Table 1: BNN image classification. AUROC $\mathbf { ( H ) }$ is the AUROC computed using the entropy whereas AUROC(MD) is computed using the model disagreement. $\mathbf { H _ { o } / H _ { t } }$ is the ratio of the entropies on OOD and test points respectively and $\mathbf { M D _ { o } / M D _ { t } }$ is the ratio for model disagreement. We see that the best accuracy is achieved by our WGD methods, while our fWGD methods yield the best OOD detection and funtional diversity. All our proposed methods improve over standard deep ensembles in terms of accuracy and diversity, highlighting the effect of our repulsion.   
+
+<table><tr><td rowspan="11">Prroiiiie</td><td></td><td>AUROC(H)</td><td>AUROC(MD)</td><td>Accuracy</td><td>H/Ht</td><td>MD/MDt</td><td>ECE</td><td>NLL</td></tr><tr><td>Deep ensemble 4</td><td>0.958±0.001</td><td>0.975±0.001</td><td>91.122±0.013</td><td>6.257±0.005</td><td>6.394±0.001</td><td>0.012±0.001</td><td>0.129±0.001</td></tr><tr><td>SVGD [51</td><td>0.960±0.001</td><td>0.973±0.001</td><td>91.134±0.024</td><td>6.315±0.019</td><td>6.395±0.018</td><td>0.014±0.001</td><td>0.127±0.001</td></tr><tr><td>f-SVGD [76</td><td>0.956±0.001</td><td>0.975±0.001</td><td>89.884±0.015</td><td>5.652±0.009</td><td>6.531±0.005</td><td>0.013±0.001</td><td>0.150±0.001</td></tr><tr><td>hyper-DE [80]</td><td>0.968±0.001</td><td>0.981±0.001</td><td>91.160±0.007</td><td>6.682±0.065</td><td>7.059±0.152</td><td>0.014±0.001</td><td>0.128±0.001</td></tr><tr><td>kde-WGD (ours)</td><td>0.960±0.001</td><td>0.970±0.001</td><td>91.238±0.019</td><td>6.587±0.019</td><td>6.379±0.018</td><td>0.014±0.001</td><td>0.128±0.001</td></tr><tr><td>sge-WGD (ours)</td><td>0.960±0.001</td><td>0.970±0.001</td><td>91.312±0.016</td><td>6.562±0.007</td><td>6.363±0.009</td><td>0.012±0.001</td><td>0.128±0.001</td></tr><tr><td>ssge-WGD (ours)</td><td>0.968±0.001</td><td>0.979±0.001</td><td>91.198±0.024</td><td>6.522±0.009</td><td>6.610±0.012</td><td>0.012±0.001</td><td>0.130±0.001</td></tr><tr><td>kde-fWGD (ours)</td><td>0.971±0.001</td><td>0.980±0.001</td><td>91.260±0.011</td><td>7.079±0.016</td><td>6.887±0.015</td><td>0.015±0.001</td><td>0.125±0.001</td></tr><tr><td>sge-fWGD (ours)</td><td>0.969±0.001</td><td>0.978±0.001</td><td>91.192±0.013</td><td>7.076±0.004</td><td>6.900±0.005</td><td>0.015±0.001</td><td>0.125±0.001</td></tr><tr><td>ssge-fWGD (ours)</td><td>0.971±0.001</td><td>0.980±0.001</td><td>91.240±0.022</td><td>7.129±0.006</td><td>6.951±0.005</td><td>0.016±0.001</td><td>0.124±0.001</td></tr><tr><td rowspan="11">CITIIIO</td><td>Deep ensemble 42</td><td>0.843±0.004</td><td>0.736±0.005</td><td>85,552±0.076</td><td>2.244±0.006</td><td>1.667±0.008</td><td>0.049±0.001</td><td>0.277±0.001</td></tr><tr><td>SVGD [51</td><td>0.825±0.001</td><td>0.710±0.002</td><td>85.142±0.017</td><td>2.106±0.003</td><td>1.567±0.004</td><td>0.052±0.001</td><td>0.287±0.001</td></tr><tr><td>fSVGD 回</td><td>0.783±0.001</td><td>0.712±0.001</td><td>84.510±0.031</td><td>1.968±0.004</td><td>1.624±0.003</td><td>0.049±0.001</td><td>0.292±0.001</td></tr><tr><td>hyper-DE [80]</td><td>0.789±0.001</td><td>0.743±0.001</td><td>84.743±0.011</td><td>1.951±0.010</td><td>1.690±0.015</td><td>0.046±0.001</td><td>0.288±0.001</td></tr><tr><td>kde-WGD (ours)</td><td>0.838±0.001</td><td>0.735±0.004</td><td>85.904±0.030</td><td>2.205±0.003</td><td>1.661±0.008</td><td>0.053±0.001</td><td>0.276±0.001</td></tr><tr><td>sge-WGD (ours)</td><td>0.837±0.003</td><td>0.725±0.004</td><td>85.792±0.035</td><td>2.214±0.010</td><td>1.634±0.004</td><td>0.051±0.001</td><td>0.275±0.001</td></tr><tr><td>ssge-WGD (ours)</td><td>0.832±0.003</td><td>0.731±0.005</td><td>85.638±0.038</td><td>2.182±0.015</td><td>1.655±0.001</td><td>0.049±0.001</td><td>0.276±0.001</td></tr><tr><td>kde-fWGD (ours)</td><td>0.791±0.002</td><td>0.758±0.002</td><td>84.888±0.030</td><td>1.970±0.004</td><td>1.749±0.005</td><td>0.044±0.001</td><td>0.282±0.001</td></tr><tr><td>sge-fWGD (ours)</td><td>0.795±0.001</td><td>0.754±0.002</td><td>84.766±0.060</td><td>1.984±0.003</td><td>1.729±0.002</td><td>0.047±0.001</td><td>0.288±0.001</td></tr><tr><td>ssge-fWGD (ours)</td><td>0.792±0.002</td><td>0.752±0.002</td><td>84.762±0.034</td><td>1.970±0.006</td><td>1.723±0.005</td><td>0.046±0.001</td><td>0.286±0.001</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></table>
+
+FashionMNIST classification Moving on to real-world data, we used an image classification setting using the FashionMNIST dataset $\dot { \left[ \left| 8 3 \right| \right] }$ for training and the MNIST dataset $\bar { \mathbb { E } 3 } \mathbb { I }$ as an out-ofdistribution (OOD) task. The results are reported in Table $^ 1 { } _ { . }$ (top). We can see that all our methods improve upon standard deep ensembles and SVGD, highlighting the effectiveness of our proposed repulsion terms when training neural network ensembles. In particular, the sge-WGD offers the best accuracy, whereas the methods in function space all offer a better OOD detection. This is probably due to the fact that these methods achieve a higher entropy ratio and functional diversity measured via the model disagreement when compared to their weight-space counterparts. Interestingly, they also reach the lowest NLL values. We can also notice how the model disagreement (MD) not only serves its purpose as a metric for the functional heterogeneity of the ensemble but also allows for a better OOD detection in comparison to the entropy. To the best of our knowledge, this insight has not been described before, although it has been used in continual learning $\pmb { \mathbb { B } } \mathbf { \mathbb { 1 } }$ . Interestingly, using this metric, the hyper-deep ensemble $[ \textcircled { 8 0 } ]$ shows OOD detection performance comparable with our repulsive ensemble in function space.
+
+CIFAR classification Finally, we use a ResNet32 architecture $\mathbb { \left| \left[ 2 9 \right] \right| }$ on CIFAR-10 [41] with the SVHN dataset $\mathbb { \left[ 6 1 \right] }$ as OOD data. The results are reported in Table 1 (bottom). We can see that in this case, the weight-space methods achieve better performance in accuracy and OOD detection using the entropy than the ones in function space. Nevertheless, all our repulsive ensembles improve functional diversity, accuracy, and OOD detection when compared to standard SVGD, whereas the standard deep ensemble achieves the best OOD detection using the entropy.
+
+# 5 Related Work
+
+The theoretical and empirical properties of SVGD have been well studied [40, 48, 13] and it can also be seen as a Wasserstein gradient flow of the KL divergence in the Stein geometry [16, 50] (see Appendix D for more details). Interestingly, a gradient flow interpretation is also possible for (stochastic gradient) MCMC-type algorithms $\dot { \left. \overline { { 4 8 } } \right. }$ , which can be unified under a general particle inference framework [10]. Moreover, our Wasserstein gradient descent using the SGE approximation can also be derived using an alternative formulation as a gradient flow with smoothed test functions [48]. A projected version of WGD has been studied in Wang et al. $\mathbb { \left. \overline { { \boldsymbol { \mathscr { Q } } \boldsymbol { \cdot } \boldsymbol { \cdot } } } \right. }$ , which could also be readily applied in our framework. Besides particle methods, Bayesian neural networks $\pm \pm \infty$ have gained popularity recently [79, 22, 19, 36], using modern MCMC [59, 79, 22, 24, 21] and variational inference techniques [5, 72, 17, 34]. On the other hand, ensemble methods have also been extensively studied [42, 18, 82, 23, 80, 32, 85, 78].Moreover, repulsive interactions between the members have also been studied in Wabartha et al. [74]. Moreover, providing Bayesian interpretations for deep ensembles has been previously attempted through the lenses of stationary SGD distributions $[ \sqrt { 5 6 } , \sqrt ] { 8 } ]$ , ensembles of linear models $\dot { \bigtriangledown } 5 7 \big |$ , additional random functions $\boxed { 6 2 } , \boxed { 1 2 } , \boxed { 2 7 }$ , approximate inference $\lVert 8 2 \rVert$ , Stein variational inference [15], and marginal likelihood lower bounds $\bar { \| 5 3 \| }$ , and ensembles have also been shown to provide good approximations to the true BNN posterior in some settings $\left[ \left[ 3 6 \right] \right]$ . Furthermore, variational inference in function space has recently gained attention $\mathbb { \ m }$ and the limitations of the KL divergence have been studied in Burt et al. [7].
+
+# 6 Conclusion
+
+We have presented a simple and principled way to improve upon standard deep ensemble methods. To this end, we have shown that the introduction of a kernelized repulsion between members of the ensemble not only improves the accuracy of the predictions but—even more importantly—can be seen as Wasserstein gradient descent on the KL divergence, thus transforming the MAP inference of deep ensembles into proper Bayesian inference. Moreover, we have shown that incorporating functional repulsion between ensemble members can improve the quality of the estimated uncertainties on simple synthetic examples and OOD detection on real-world data and can approach the true Bayesian posterior more closely.
+
+In future work, it will be interesting to study the impact of the Jacobian in the fWGD update and its implications on the Liouville equation in more detail, also compared to other neural network Jacobian methods, such as neural tangent kernels $\pmb { \Vert 3 7 } \Vert$ and generalized Gauss-Newton approximations $\boldsymbol { \left[ \left[ 3 5 \right] \right] }$ . Moreover, it would be interesting to derive explicit convergence bounds for our proposed method and compare them to the existing bounds for SVGD [40].
+
+# Acknowledgments
+
+VF would like to acknowledge financial support from the Strategic Focus Area “Personalized Health and Related Technologies” of the ETH Domain through the grant #2017-110 and from the Swiss Data Science Center through a PhD fellowship. We thank Florian Wenzel, Alexander Immer, Andrew Gordon Wilson, Pavel Izmailov, Christian Henning, and Johannes von Oswald for helpful discussions. We also thank Dr. Sheldon Cooper, Dr. Leonard Hofstadter and Penny Hofstadter for their support and inspiration.
+
+# References
+
+[1] Charu C Aggarwal, Alexander Hinneburg, and Daniel A Keim. On the surprising behavior of distance metrics in high dimensional space. In International conference on database theory, pages 420–434. Springer, 2001.   
+[2] Luigi Ambrosio and Gianluca Crippa. Continuity equations and ode flows with non-smooth velocity. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 144(6): 1191–1244, 2014.   
+[3] Luigi Ambrosio, Nicola Gigli, and Giuseppe Savaré. Gradient flows: in metric spaces and in the space of probability measures. Springer Science & Business Media, 2008.   
+[4] Vijay Badrinarayanan, Bamdev Mishra, and Roberto Cipolla. Symmetry-invariant optimization in deep networks. arXiv preprint arXiv:1511.01754, 2015.   
+[5] Charles Blundell, Julien Cornebise, Koray Kavukcuoglu, and Daan Wierstra. Weight uncertainty in neural networks. arXiv preprint arXiv:1505.05424, 2015.
+
+[6] Leo Breiman. Bagging predictors. Machine learning, 24(2):123–140, 1996.
+
+[7] David R Burt, Sebastian W Ober, Adrià Garriga-Alonso, and Mark van der Wilk. Understanding variational inference in function-space. arXiv preprint arXiv:2011.09421, 2020.
+
+[8] Pratik Chaudhari and Stefano Soatto. Stochastic gradient descent performs variational inference, converges to limit cycles for deep networks. In 2018 Information Theory and Applications Workshop (ITA), pages 1–10. IEEE, 2018.
+
+[9] An Mei Chen, Haw-minn Lu, and Robert Hecht-Nielsen. On the geometry of feedforward neural network error surfaces. Neural computation, 5(6):910–927, 1993.
+
+[10] Changyou Chen, Ruiyi Zhang, Wenlin Wang, Bai Li, and Liqun Chen. A unified particleoptimization framework for scalable bayesian sampling. arXiv preprint arXiv:1805.11659, 2018.
+
+[11] Jiefeng Chen, Xi Wu, Yingyu Liang, Somesh Jha, et al. Robust out-of-distribution detection in neural networks. arXiv preprint arXiv:2003.09711, 2020.
+
+[12] Kamil Ciosek, Vincent Fortuin, Ryota Tomioka, Katja Hofmann, and Richard Turner. Conservative uncertainty estimation by fitting prior networks. In International Conference on Learning Representations, 2019.
+
+[13] Francesco D’Angelo and Vincent Fortuin. Annealed stein variational gradient descent. arXiv preprint arXiv:2101.09815, 2021.
+
+[14] Francesco D’Angelo and Christian Henning. Uncertainty-based out-of-distribution detection requires suitable function space priors. arXiv preprint arXiv:2110.06020, 2021.
+
+[15] Francesco D’Angelo, Vincent Fortuin, and Florian Wenzel. On stein variational neural network ensembles. arXiv preprint arXiv:2106.10760, 2021.
+
+[16] A Duncan, Nikolas Nuesken, and Lukasz Szpruch. On the geometry of stein variational gradient descent. arXiv preprint arXiv:1912.00894, 2019.
+
+[17] Michael W Dusenberry, Ghassen Jerfel, Yeming Wen, Yi-an Ma, Jasper Snoek, Katherine Heller, Balaji Lakshminarayanan, and Dustin Tran. Efficient and scalable bayesian neural nets with rank-1 factors. arXiv preprint arXiv:2005.07186, 2020.
+
+[18] Stanislav Fort, Huiyi Hu, and Balaji Lakshminarayanan. Deep ensembles: A loss landscape perspective. arXiv preprint arXiv:1912.02757, 2019.
+
+[19] Vincent Fortuin. Priors in bayesian deep learning: A review. arXiv preprint arXiv:2105.06868, 2021.
+
+[20] Vincent Fortuin, Mark Collier, Florian Wenzel, James Allingham, Jeremiah Liu, Dustin Tran, Balaji Lakshminarayanan, Jesse Berent, Rodolphe Jenatton, and Effrosyni Kokiopoulou. Deep classifiers with label noise modeling and distance awareness. arXiv preprint arXiv:2110.02609, 2021.
+
+[21] Vincent Fortuin, Adrià Garriga-Alonso, Mark van der Wilk, and Laurence Aitchison. Bnnpriors: A library for bayesian neural network inference with different prior distributions. Software Impacts, page 100079, 2021.
+
+[22] Vincent Fortuin, Adrià Garriga-Alonso, Florian Wenzel, Gunnar Rätsch, Richard Turner, Mark van der Wilk, and Laurence Aitchison. Bayesian neural network priors revisited. arXiv preprint arXiv:2102.06571, 2021.
+
+[23] Timur Garipov, Pavel Izmailov, Dmitrii Podoprikhin, Dmitry Vetrov, and Andrew Gordon Wilson. Loss surfaces, mode connectivity, and fast ensembling of dnns. arXiv preprint arXiv:1802.10026, 2018.
+
+[24] Adrià Garriga-Alonso and Vincent Fortuin. Exact langevin dynamics with stochastic gradients. arXiv preprint arXiv:2102.01691, 2021.
+
+[25] Mario Geiger, Arthur Jacot, Stefano Spigler, Franck Gabriel, Levent Sagun, Stéphane d’Ascoli, Giulio Biroli, Clément Hongler, and Matthieu Wyart. Scaling description of generalization with number of parameters in deep learning. Journal of Statistical Mechanics: Theory and Experiment, 2020(2):023401, 2020.   
+[26] L. K. Hansen and P. Salamon. Neural network ensembles. IEEE Trans. Pattern Anal. Mach. Intell., 12(10):993–1001, October 1990. ISSN 0162-8828. doi: 10.1109/34.58871. URL https://doi.org/10.1109/34.58871.   
+[27] Bobby He, Balaji Lakshminarayanan, and Yee Whye Teh. Bayesian deep ensembles via the neural tangent kernel. arXiv preprint arXiv:2007.05864, 2020.   
+[28] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Delving deep into rectifiers: Surpassing human-level performance on imagenet classification. In Proceedings of the IEEE international conference on computer vision, pages 1026–1034, 2015.   
+[29] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 770–778, 2016.   
+[30] Robert Hecht-Nielsen. On the algebraic structure of feedforward network weight spaces. In Advanced Neural Computers, pages 129–135. Elsevier, 1990.   
+[31] Christian Henning, Maria R Cervera, Francesco D’Angelo, Johannes von Oswald, Regina Traber, Benjamin Ehret, Seijin Kobayashi, João Sacramento, and Benjamin F Grewe. Posterior meta-replay for continual learning. arXiv preprint arXiv:2103.01133, 2021.   
+[32] Gao Huang, Yixuan Li, Geoff Pleiss, Zhuang Liu, John E Hopcroft, and Kilian Q Weinberger. Snapshot ensembles: Train 1, get m for free. arXiv preprint arXiv:1704.00109, 2017.   
+[33] Gao Huang, Yixuan Li, Geoff Pleiss, Zhuang Liu, John E. Hopcroft, and Kilian Q. Weinberger. Snapshot ensembles: Train 1, get M for free. CoRR, abs/1704.00109, 2017. URL http: //arxiv.org/abs/1704.00109.   
+[34] Alexander Immer, Matthias Bauer, Vincent Fortuin, Gunnar Rätsch, and Mohammad Emtiyaz Khan. Scalable marginal likelihood estimation for model selection in deep learning. arXiv preprint arXiv:2104.04975, 2021.   
+[35] Alexander Immer, Maciej Korzepa, and Matthias Bauer. Improving predictions of bayesian neural nets via local linearization. In International Conference on Artificial Intelligence and Statistics, pages 703–711. PMLR, 2021.   
+[36] Pavel Izmailov, Sharad Vikram, Matthew D Hoffman, and Andrew Gordon Wilson. What are bayesian neural network posteriors really like? arXiv preprint arXiv:2104.14421, 2021.   
+[37] Arthur Jacot, Franck Gabriel, and Clément Hongler. Neural tangent kernel: convergence and generalization in neural networks. In Proceedings of the 32nd International Conference on Neural Information Processing Systems, pages 8580–8589, 2018.   
+[38] Richard Jordan, David Kinderlehrer, and Felix Otto. The variational formulation of the fokker– planck equation. SIAM journal on mathematical analysis, 29(1):1–17, 1998.   
+[39] Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.   
+[40] Anna Korba, Adil Salim, Michael Arbel, Giulia Luise, and Arthur Gretton. A non-asymptotic analysis for stein variational gradient descent. Advances in Neural Information Processing Systems, 33, 2020.   
+[41] Alex Krizhevsky et al. Learning multiple layers of features from tiny images. 2009.   
+[42] Balaji Lakshminarayanan, Alexander Pritzel, and Charles Blundell. Simple and scalable predictive uncertainty estimation using deep ensembles. In Advances in neural information processing systems, pages 6402–6413, 2017.   
+[43] Yann LeCun. The mnist database of handwritten digits. http://yann. lecun. com/exdb/mnist/, 1998.   
+[44] Jaehoon Lee, Yasaman Bahri, Roman Novak, Samuel S Schoenholz, Jeffrey Pennington, and Jascha Sohl-Dickstein. Deep neural networks as gaussian processes. arXiv preprint arXiv:1711.00165, 2017.   
+[45] E. Levin, N. Tishby, and S. A. Solla. A statistical approach to learning and generalization in layered neural networks. Proc. of the IEEE – Special issue on Neural Networks, 1990.   
+[46] Yingzhen Li and Richard E Turner. Gradient estimators for implicit models. arXiv preprint arXiv:1705.07107, 2017.   
+[47] Shiyu Liang, Yixuan Li, and Rayadurgam Srikant. Enhancing the reliability of out-ofdistribution image detection in neural networks. arXiv preprint arXiv:1706.02690, 2017.   
+[48] Chang Liu, Jingwei Zhuo, Pengyu Cheng, Ruiyi Zhang, and Jun Zhu. Understanding and accelerating particle-based variational inference. In International Conference on Machine Learning, pages 4082–4092. PMLR, 2019.   
+[49] Jeremiah Zhe Liu, Zi Lin, Shreyas Padhy, Dustin Tran, Tania Bedrax-Weiss, and Balaji Lakshminarayanan. Simple and principled uncertainty estimation with deterministic deep learning via distance awareness. arXiv preprint arXiv:2006.10108, 2020.   
+[50] Qiang Liu. Stein variational gradient descent as gradient flow. In Advances in neural information processing systems, pages 3115–3123, 2017.   
+[51] Qiang Liu and Dilin Wang. Stein variational gradient descent: A general purpose bayesian inference algorithm. In Advances in neural information processing systems, pages 2378–2386, 2016.   
+[52] Qiang Liu, Jason Lee, and Michael Jordan. A kernelized stein discrepancy for goodness-of-fit tests. In International conference on machine learning, pages 276–284. PMLR, 2016.   
+[53] Clare Lyle, Lisa Schut, Robin Ru, Yarin Gal, and Mark van der Wilk. A bayesian perspective on training speed and model selection. Advances in Neural Information Processing Systems, 33, 2020.   
+[54] David JC MacKay. A practical bayesian framework for backpropagation networks. Neural computation, 4(3):448–472, 1992.   
+[55] Andrey Malinin, Bruno Mlodozeniec, and Mark Gales. Ensemble distribution distillation. arXiv preprint arXiv:1905.00076, 2019.   
+[56] Stephan Mandt, Matthew D Hoffman, and David M Blei. Stochastic gradient descent as approximate bayesian inference. arXiv preprint arXiv:1704.04289, 2017.   
+[57] Alexander G de G Matthews, Jiri Hron, Richard E Turner, and Zoubin Ghahramani. Samplethen-optimize posterior sampling for bayesian linear models. In NeurIPS Workshop on Advances in Approximate Bayesian Inference, 2017.   
+[58] Mahdi Pakdaman Naeini, Gregory Cooper, and Milos Hauskrecht. Obtaining well calibrated probabilities using bayesian binning. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 29, 2015.   
+[59] Radford M Neal. Bayesian learning for neural networks. 1995.   
+[60] Radford M Neal. Bayesian learning for neural networks, volume 118. Springer Science & Business Media, 2012.   
+[61] Yuval Netzer, Tao Wang, Adam Coates, Alessandro Bissacco, Bo Wu, and Andrew Y Ng. Reading digits in natural images with unsupervised feature learning. 2011.   
+[62] Ian Osband, Benjamin Van Roy, Daniel J Russo, Zheng Wen, et al. Deep exploration via randomized value functions. J. Mach. Learn. Res., 20(124):1–62, 2019.
+
+[63] Johannes Von Oswald, Seijin Kobayashi, Joao Sacramento, Alexander Meulemans, Christian Henning, and Benjamin F Grewe. Neural networks with late-phase weights. In International Conference on Learning Representations, 2021. URL https://openreview.net/forum? id=C0qJUx5dxFb.
+
+[64] Felix Otto. The geometry of dissipative evolution equations: the porous medium equation. 2001.
+
+[65] Yaniv Ovadia, Emily Fertig, Jie Ren, Zachary Nado, David Sculley, Sebastian Nowozin, Joshua Dillon, Balaji Lakshminarayanan, and Jasper Snoek. Can you trust your model’s uncertainty? evaluating predictive uncertainty under dataset shift. In Advances in Neural Information Processing Systems, pages 13991–14002, 2019.
+
+[66] Emanuel Parzen. On estimation of a probability density function and mode. The annals of mathematical statistics, 33(3):1065–1076, 1962.
+
+[67] Alexandre Rame and Matthieu Cord. Dice: Diversity in deep ensembles via conditional redundancy adversarial estimation. arXiv preprint arXiv:2101.05544, 2021.
+
+[68] Geoffrey Roeder, Luke Metz, and Diederik P Kingma. On linear identifiability of learned representations. arXiv preprint arXiv:2007.00810, 2020.
+
+[69] Jiaxin Shi, Shengyang Sun, and Jun Zhu. A spectral approach to gradient estimation for implicit distributions. In International Conference on Machine Learning, pages 4644–4653. PMLR, 2018.
+
+[70] Radhey S Singh. Improvement on some known nonparametric uniformly consistent estimators of derivatives of a density. The Annals of Statistics, pages 394–399, 1977.
+
+[71] Shengyang Sun, Guodong Zhang, Jiaxin Shi, and Roger Grosse. Functional variational bayesian neural networks. arXiv preprint arXiv:1903.05779, 2019.
+
+[72] Jakub Swiatkowski, Kevin Roth, Bastiaan S Veeling, Linh Tran, Joshua V Dillon, Stephan Mandt, Jasper Snoek, Tim Salimans, Rodolphe Jenatton, and Sebastian Nowozin. The k-tied normal distribution: A compact parameterization of gaussian mean field posteriors in bayesian neural networks. arXiv preprint arXiv:2002.02655, 2020.
+
+[73] Johannes von Oswald, Christian Henning, João Sacramento, and Benjamin F. Grewe. Continual learning with hypernetworks. In International Conference on Learning Representations, 2020. URL https://arxiv.org/abs/1906.00695.
+
+[74] Maxime Wabartha, Audrey Durand, Vincent François-Lavet, and Joelle Pineau. Handling black swan events in deep learning with diversely extrapolated neural networks. In IJCAI, pages 2140–2147, 2020.
+
+[75] Yifei Wang, Peng Chen, and Wuchen Li. Projected wasserstein gradient descent for highdimensional bayesian inference. arXiv preprint arXiv:2102.06350, 2021.
+
+[76] Ziyu Wang, Tongzheng Ren, Jun Zhu, and Bo Zhang. Function space particle optimization for bayesian neural networks. arXiv preprint arXiv:1902.09754, 2019.
+
+[77] Max Welling and Yee W Teh. Bayesian learning via stochastic gradient langevin dynamics. In Proceedings of the 28th international conference on machine learning (ICML-11), pages 681–688, 2011.
+
+[78] Yeming Wen, Dustin Tran, and Jimmy Ba. Batchensemble: an alternative approach to efficient ensemble and lifelong learning. arXiv preprint arXiv:2002.06715, 2020.
+
+[79] Florian Wenzel, Kevin Roth, Bastiaan S Veeling, Jakub Swiatkowski, Linh Tran, Stephan Mandt, ´ Jasper Snoek, Tim Salimans, Rodolphe Jenatton, and Sebastian Nowozin. How good is the bayes posterior in deep neural networks really? arXiv preprint arXiv:2002.02405, 2020.
+
+[80] Florian Wenzel, Jasper Snoek, Dustin Tran, and Rodolphe Jenatton. Hyperparameter ensembles for robustness and uncertainty quantification. In Advances in Neural Information Processing Systems, 2020.
+
+[81] Christopher KI Williams. Computation with infinite neural networks. Neural Computation, 10 (5):1203–1216, 1998.   
+[82] Andrew Gordon Wilson and Pavel Izmailov. Bayesian deep learning and a probabilistic perspective of generalization. arXiv preprint arXiv:2002.08791, 2020.   
+[83] Han Xiao, Kashif Rasul, and Roland Vollgraf. Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms. arXiv preprint arXiv:1708.07747, 2017.   
+[84] Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals. Understanding deep learning requires rethinking generalization. arXiv preprint arXiv:1611.03530, 2016.   
+[85] Ruqi Zhang, Chunyuan Li, Jianyi Zhang, Changyou Chen, and Andrew Gordon Wilson. Cyclical stochastic gradient mcmc for bayesian deep learning. arXiv preprint arXiv:1902.03932, 2019.
\ No newline at end of file
diff --git a/parse/train/LAKplpLMbP8/LAKplpLMbP8_content_list.json b/parse/train/LAKplpLMbP8/LAKplpLMbP8_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..c99047df4faf9a1a3cf8a0e0abab3c55896dde07
--- /dev/null
+++ b/parse/train/LAKplpLMbP8/LAKplpLMbP8_content_list.json
@@ -0,0 +1,1690 @@
+[
+    {
+        "type": "text",
+        "text": "Repulsive Deep Ensembles are Bayesian ",
+        "text_level": 1,
+        "bbox": [
+            254,
+            122,
+            743,
+            147
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Francesco D’Angelo ETH Zürich Zürich, Switzerland dngfra@gmail.com ",
+        "bbox": [
+            285,
+            200,
+            429,
+            257
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Vincent Fortuin   \nETH Zürich   \nZürich, Switzerland   \nfortuin@inf.ethz.ch ",
+        "bbox": [
+            547,
+            202,
+            712,
+            256
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract ",
+        "text_level": 1,
+        "bbox": [
+            462,
+            292,
+            535,
+            308
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Deep ensembles have recently gained popularity in the deep learning community for their conceptual simplicity and efficiency. However, maintaining functional diversity between ensemble members that are independently trained with gradient descent is challenging. This can lead to pathologies when adding more ensemble members, such as a saturation of the ensemble performance, which converges to the performance of a single model. Moreover, this does not only affect the quality of its predictions, but even more so the uncertainty estimates of the ensemble, and thus its performance on out-of-distribution data. We hypothesize that this limitation can be overcome by discouraging different ensemble members from collapsing to the same function. To this end, we introduce a kernelized repulsive term in the update rule of the deep ensembles. We show that this simple modification not only enforces and maintains diversity among the members but, even more importantly, transforms the maximum a posteriori inference into proper Bayesian inference. Namely, we show that the training dynamics of our proposed repulsive ensembles follow a Wasserstein gradient flow of the KL divergence to the true posterior. We study repulsive terms in weight and function space and empirically compare their performance to standard ensembles and Bayesian baselines on synthetic and real-world prediction tasks. ",
+        "bbox": [
+            233,
+            325,
+            766,
+            573
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 Introduction ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            599,
+            310,
+            616
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "There have been many recent advances on the theoretical properties of sampling algorithms for approximate Bayesian inference, which changed our interpretation and understanding of them. Particularly worth mentioning is the work of Jordan et al. [38], who reinterpret Markov Chain Monte Carlo (MCMC) as a gradient flow of the KL divergence over the Wasserstein space of probability measures. This new formulation allowed for a deeper understanding of approximate inference methods but also inspired the inception of new and more efficient inference strategies. Following this direction, Liu and Wang $\\pmb { \\mathbb { B } } \\mathbf { \\mathbb { 1 } }$ recently proposed the Stein Variational Gradient Descent (SVGD) method to perform approximate Wasserstein gradient descent. Conceptually, this method, which belongs to the family of particle-optimization variational inference (POVI), introduces a repulsive force through a kernel acting in the parameter space to evolve a set of samples towards high-density regions of the target distribution without collapsing to a point estimate. ",
+        "bbox": [
+            174,
+            631,
+            825,
+            784
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Another method which has achieved great success recently are ensembles of neural networks (socalled deep ensembles), which work well both in terms of predictive performance $\\pm 2 \\sqrt { 8 0 }$ as well as uncertainty estimation $\\begin{array} { r l } {  { \\| 6 5 \\| } } \\end{array}$ , and have also been proposed as a way to perform approximate inference in Bayesian neural networks [82, 36]. That being said, while they might allow for the averaging of predictions over several hypotheses, they do not offer any guarantees for the diversity between those hypotheses nor do they provably converge to the true Bayesian posterior under any meaningful limit. In this work, we show how the introduction of a repulsive term between the members in the ensemble, inspired by SVGD, not only naïvely guarantees the diversity among the members, avoiding their collapse in parameter space, but also allows for a reformulation of the method as a gradient flow of the KL divergence in the Wasserstein space of distributions. It thus allows to endow deep ensembles with convergence guarantees to the true Bayesian posterior. ",
+        "bbox": [
+            174,
+            790,
+            825,
+            900
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/c87b35667fe31cb24e44c323fe8bffeb4df13996d7df41a00bfd504161843062.jpg",
+        "image_caption": [
+            "Figure 1: BNN 1D regression. The function-space methods (SVGD and WGD) approach the HMC posterior more closely, while the standard deep ensembles and weight-space methods fail to properly account for the uncertainty, especially the in-between uncertainty. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            196,
+            85,
+            805,
+            251
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            176,
+            327,
+            821,
+            369
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "An additional problem is that BNN inference in weight space can lead to degenerate solutions, due to the overparametrization of these models. That is, several samples could have very different weights but map to the same function, thus giving a false sense of diversity in the ensemble. This property, that we will refer to as non-identifiability of neural networks (see Appendix $\\boxed { \\mathrm { A } }$ , can lead to redundancies in the posterior distribution. It implies that methods like MCMC sampling, deep ensembles, and SVGD waste computation in local modes that account for equivalent functions. Predictive distributions approximated using samples from these modes do not improve over a simple point estimate and lead to a poor uncertainty estimation. Following this idea, Wang et al. $\\mathbb { \\left[ \\left] \\right. \\right]} 2 $ introduced a new method to extend POVI methods to function space, overcoming this limitation. Here, we also study an update rule that allows for an approximation of the gradient flow of the KL divergence in function space in our proposed repulsive ensembles. ",
+        "bbox": [
+            173,
+            375,
+            825,
+            527
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We make the following contributions: ",
+        "bbox": [
+            176,
+            534,
+            421,
+            549
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "• We derive several different repulsion terms that can be added as regularizers to the gradient updates of deep ensembles to endow them with Bayesian convergence properties.   \n• We show that these terms approximate Wasserstein gradient flows of the KL divergence and can be used both in weight space and function space.   \n• We compare these proposed methods theoretically to standard deep ensembles and SVGD and highlight their different guarantees.   \n• We assess all these methods on synthetic and real-world deep learning tasks and show that our proposed repulsive ensembles can achieve competitive performance and improved uncertainty estimation. ",
+        "bbox": [
+            217,
+            560,
+            825,
+            705
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 Repulsive Deep Ensembles ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            732,
+            428,
+            750
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In supervised deep learning, we typically consider a likelihood function $p ( \\pmb { y } | f ( \\pmb { x } ; \\mathbf { w } ) )$ (e.g., Gaussian for regression or Categorical for classification) parameterized by a neural network $f ( \\pmb { x } ; \\mathbf { w } )$ and training data $\\textit { D } = \\{ ( \\boldsymbol { \\mathbf { { x } } } _ { i } , \\boldsymbol { \\mathbf { { y } } } _ { i } ) \\} _ { i = 1 } ^ { n }$ with $\\textbf { \\textit { x } } \\in \\textbf { \\textit { X } }$ and $\\textbf { \\textit { y } } \\in \\textbf { \\textit { y } }$ . In Bayesian neural networks (BNNs), we are interested in the posterior distribution of all likely networks given by $\\begin{array} { r } { p ( \\mathbf { w } | \\mathcal { D } ) \\propto \\prod _ { i = 1 } ^ { n } p ( \\pmb { y } _ { i } | f ( \\pmb { x } _ { i } ; \\mathbf { w } ) ) p ( \\mathbf { w } ) } \\end{array}$ , where $p ( \\mathbf { w } )$ is the prior distribution over weights. Crucially, when making a prediction on a test point $\\mathbf { \\boldsymbol { x } } ^ { * }$ , in the Bayesian approach we do not only use a single parameter $\\widehat { \\bf w }$ to predict ${ \\pmb y } ^ { * } = f ( { \\pmb x } ^ { * } ; \\widehat { \\mathbf { w } } )$ , but we marginalize over the whole posterior, thus taking all possible explanations of the data into account: ",
+        "bbox": [
+            173,
+            763,
+            826,
+            876
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "img_path": "images/ea58bf85c2893e1394390263ae7f97e3c6d3270c2715a883b91057d7c53c61ba.jpg",
+        "text": "$$\np ( \\pmb { y } ^ { * } | \\pmb { x } ^ { * } , \\mathcal { D } ) = \\int p ( \\pmb { y } ^ { * } | f ( \\pmb { x } ^ { * } ; \\mathbf { w } ) ) p ( \\mathbf { w } | \\mathcal { D } ) \\mathrm { d } \\mathbf { w }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            343,
+            883,
+            653,
+            916
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "While approximating the posterior of Bayesian neural networks (or sampling from it) is a challenging task, performing maximum a posteriori (MAP) estimation, which corresponds to finding the mode of the posterior, is usually simple. Ensembles of neural networks use the non-convexity of the MAP optimization problem to create a collection of $K$ independent—and possibly different— solutions. Considering $n$ weight configurations of a neural network $\\{ { \\bf w } _ { i } \\} _ { i = 1 } ^ { n }$ with ${ \\bf w } _ { i } \\in \\mathbb { R } ^ { d }$ , the dynamics of the ensemble under the gradient of the posterior lead to the following update rule at iteration $t$ : ",
+        "bbox": [
+            173,
+            90,
+            826,
+            175
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/dec175f126457d7570141af68aa834ee6aa688fa0490be6f7e2b319f4c374697.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\mathbf { w } _ { i } ^ { t + 1 }  \\mathbf { w } _ { i } ^ { t } + \\epsilon _ { t } \\phi ( \\mathbf { w } _ { i } ^ { t } ) } \\\\ { \\mathrm { w i t h } \\quad } & { \\phi ( \\mathbf { w } _ { i } ^ { t } ) = \\nabla _ { \\mathbf { w } _ { i } ^ { t } } \\log p ( \\mathbf { w } _ { i } ^ { t } | \\mathcal { D } ) , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            372,
+            179,
+            625,
+            223
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "with step size $\\epsilon _ { t }$ . Ensemble methods have a long history [e.g., 45, 26, 6] and were recently revisited for neural networks $\\pm 2 \\|$ and coined deep ensembles. The predictions of the different members are combined to create a predictive distribution by using the solutions to compute the Bayesian model average (BMA) in Eq. $\\mathbb { D }$ . Recent works $\\mathbb { \\lVert \\rVert }$ have shown that deep ensembles can outperform some of the Bayesian approaches for uncertainty estimation. Even more recently, Wilson and Izmailov $\\pmb { \\Vert 8 2 \\Vert }$ argued that deep ensembles can be considered a compelling approach to Bayesian model averaging. Despite these ideas, the ability of deep ensembles to efficiently average over multiple hypotheses and to explore the functional landscape of the posterior distribution studied in $[ \\overline { { 1 8 } } ]$ does not guarantee sampling from the right distribution. Indeed, the additional Langevin noise introduced in $\\mathbb { [ \\breve { ] { ] \\mathrm { ~ Z ~ Z ~ } ] } } }$ , which is not considered in deep ensembles, is crucial to ensure samples from the true Bayesian posterior. ",
+        "bbox": [
+            173,
+            224,
+            825,
+            364
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "From a practical standpoint, since the quality of an ensemble hinges on the diversity of its members, many methods were recently proposed to improve this diversity without compromising the individual accuracy. For instance, Wenzel et al. [80] propose hyper-deep ensembles that combine deep networks with different hyperparameters. Similarly, cyclical learning-rate schedules can explore several local minima for the ensemble members $\\pmb { \\mathbb { B 3 } }$ . Alternatively, Rame and Cord $ { \\mathbb { I } }  { \\mathbb { I } }$ proposed an informationtheoretic framework to avoid redundancy in the members and Oswald et al. $\\overline { { \\| 6 3 \\| } }$ studied possible interactions between members based on weight sharing. However, the absence of a constraint that prevents particles from converging to the same mode limits the possibility of improvement by introducing more ensemble members. This means that any hopes to converge to different modes must exclusively rely on: ",
+        "bbox": [
+            174,
+            371,
+            826,
+            510
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "1. the randomness of the initialization   \n2. the noise in the estimation of the gradients due to minibatching   \n3. the number of local optima that might be reached during gradient descent. ",
+        "bbox": [
+            210,
+            520,
+            717,
+            573
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Moreover, the recent study of Geiger et al. $\\pmb { \\left. \\pmb { \\left. \\bar { 2 5 } \\right. } \\right. }$ showed how the empirical test error of the ensemble converges to the one of a single trained model when the number of parameters goes to infinity, leading to deterioration of the performance. In other words, the bigger the model, the harder it is to maintain diversity in the ensemble and avoid collapse to the same solution. This is intuitively due to the fact that bigger models are less sensitive to the initialization. Namely, in order for them to get stuck in a local minimum, they must have second derivatives that are positive simultaneously in all directions. As the number of hidden units gets larger, this becomes less likely. ",
+        "bbox": [
+            174,
+            582,
+            826,
+            680
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.1 Repulsive force in weight space ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            695,
+            429,
+            712
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To overcome the aforementioned limitations of standard deep ensembles, we introduce, inspired by SVGD $\\mathbb { \\left[ \\left[ 5 1 \\right] \\right] }$ , a deep ensemble with members that interact with each other through a repulsive component. Using a kernel function to model this interaction, the single models repel each other based on their position in the weight space, so that two members can never assume the same weights. Considering a stationary kernel $\\bar { k } ( \\cdot , \\cdot ) : \\mathbb { R } ^ { d } \\times \\mathbb { R } ^ { d } \\to \\mathbb { R }$ acting in the parameter space of the neural network, a repulsive term $\\mathcal { R }$ can be parameterized through its gradient: ",
+        "bbox": [
+            173,
+            720,
+            826,
+            805
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/52631e0ed6e1a61e9e013d38c7585cc4709cd85b719f28114ba1570f9f671c2a.jpg",
+        "text": "$$\n\\phi ( \\mathbf { w } _ { i } ^ { t } ) = \\nabla _ { \\mathbf { w } _ { i } ^ { t } } \\log p ( \\mathbf { w } _ { i } ^ { t } | \\mathcal { D } ) - \\mathcal { R } \\left( \\left\\{ \\nabla _ { \\mathbf { w } _ { i } ^ { t } } k ( \\mathbf { w } _ { i } ^ { t } , \\mathbf { w } _ { j } ^ { t } ) \\right\\} _ { j = 1 } ^ { n } \\right) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            299,
+            810,
+            699,
+            845
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To get an intuition for the behavior of this repulsive term and its gradients, we can consider the RBF kernel $\\begin{array} { r } { k ( \\mathbf { w } _ { i } , \\mathbf { w } _ { j } ) = \\exp \\big ( - \\frac { 1 } { h } | | \\mathbf { w } _ { i } - \\mathbf { w } _ { j } | | ^ { 2 } \\big ) } \\end{array}$ with lengthscale $h$ and notice how its gradient ",
+        "bbox": [
+            173,
+            849,
+            825,
+            881
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/f23cff6e6b3dc3c8e61b222583d646eef0fa3e0251332d45f77faee6e2130a87.jpg",
+        "text": "$$\n\\nabla _ { \\mathbf { w } _ { i } ^ { t } } k ( \\mathbf { w } _ { i } ^ { t } , \\mathbf { w } _ { j } ^ { t } ) = \\frac { 2 } { h } ( \\mathbf { w } _ { j } ^ { t } - \\mathbf { w } _ { i } ^ { t } ) k ( \\mathbf { w } _ { i } ^ { t } , \\mathbf { w } _ { j } ^ { t } )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            357,
+            886,
+            638,
+            916
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "drives $\\mathbf { w } _ { i }$ away from its neighboring members ${ \\bf w } _ { j }$ , thus creating a repulsive effect. Naturally, not all the choices of $\\mathcal { R }$ induce this effect. One of the simplest formulations to obtain it is via a linear combination of the kernel gradients scaled by a positive factor, that is, $\\begin{array} { r } { \\beta \\sum _ { j = 1 } ^ { n } \\nabla _ { \\mathbf { w } _ { i } ^ { t } } k ( \\mathbf { w } _ { i } ^ { t } , \\mathbf { w } _ { j } ^ { t } ) } \\end{array}$ with $\\beta \\in \\mathbb { R } _ { * } ^ { + }$ . We will see in Section $\\begin{array} { l } { 3 } \\\\ { . } \\end{array}$ how the choice of $\\beta$ can be justified in order to obtain convergence to the Bayesian posterior together with alternative possible formulations of $\\mathcal { R }$ that preserve this convergence. ",
+        "bbox": [
+            173,
+            90,
+            826,
+            178
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "2.2 Repulsive force in function space ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            193,
+            441,
+            208
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To overcome the aforementioned overparameterization issue, the update in Eq. $\\textcircled { 3 }$ can be formulated in function space instead of weight space. Let $f : \\mathbf { w } \\mapsto f ( \\cdot ; \\mathbf { w } )$ be the map that maps a configuration of weights $\\mathbf { w } \\in \\mathbb { R } ^ { d }$ to the corresponding neural network regression function and denote as $f _ { i } : = f ( \\cdot ; { \\mathbf w } _ { i } )$ the function with a certain configuration of weights $\\mathbf { w } _ { i }$ . We can now consider $n$ particles in function space $\\{ f _ { i } \\} _ { i = 1 } ^ { n }$ with $\\pmb { f } \\in \\mathcal { F }$ and model their interaction with a general positive definite kernel $k ( \\cdot , \\cdot )$ . We also consider the implicit functional likelihood $p ( \\pmb { y } | \\pmb { x } , \\pmb { f } )$ , determined by the measure $p ( \\pmb { y } | \\pmb { x } , \\mathbf { w } )$ in the weight space, as well as the functional prior $p ( f )$ , which can either be defined separately (e.g., using a GP) or modeled as a push-forward measure of the weight-space prior $p ( \\mathbf { w } )$ . Together, they determine the posterior in function space $p ( \\pmb { f } | \\mathcal { D } )$ . The functional evolution of a particle can then be written as: ",
+        "bbox": [
+            173,
+            218,
+            826,
+            358
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/6e9ccd562a52a4d7474eb2dbb571b766cb26754c555d1761309dd914491e04b8.jpg",
+        "text": "$$\n\\begin{array} { r l } & { f _ { i } ^ { t + 1 } \\gets f _ { i } ^ { t } + \\epsilon _ { t } \\phi ( f _ { i } ^ { t } ) } \\\\ { \\mathrm { t h } \\quad } & { \\phi ( f _ { i } ^ { t } ) = \\nabla _ { f _ { i } ^ { t } } \\log p ( f _ { i } ^ { t } | \\mathcal { D } ) - \\mathcal { R } \\left( \\left\\{ \\nabla _ { f _ { i } ^ { t } } k ( f _ { i } ^ { t } , f _ { j } ^ { t } ) \\right\\} _ { j = 1 } ^ { n } \\right) . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            297,
+            362,
+            720,
+            419
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "However, computing the update in function space is neither tractable nor practical, which is why two additional considerations are needed. The first one regards the infinite dimensionality of function space, which we circumvent using a canonical projection into a subspace: ",
+        "bbox": [
+            178,
+            422,
+            823,
+            465
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Definition 1 (Canonical projection). For any $A \\subset { \\mathcal { X } }$ , we define $\\pi _ { A } : \\mathbb { R } ^ { \\mathcal { X } } \\to \\mathbb { R } ^ { A }$ as the canonical projection onto $A$ , that is, $\\pi _ { A } ( f ) = \\{ f ( a ) \\} _ { a \\in A }$ . ",
+        "bbox": [
+            174,
+            468,
+            821,
+            500
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In other words, the kernel will not be evaluated directly in function space, but on the projection $k \\big ( \\pi _ { B } ( f ) , \\pi _ { B } ( f ^ { \\prime } ) \\big )$ , with $B$ being a subset of the input space given by a batch of training data points. The second consideration is to project this update back into the parameter space and evolve a set of particles there, because ultimately we are interested in representing the functions by parameterized neural networks. For this purpose, we can use the Jacobian of the $i$ -th particle as a projector: ",
+        "bbox": [
+            174,
+            507,
+            825,
+            578
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/d7dea1ea5314c734775cfe499bded9ea6e655f30206ef90295c8a3d5d82d37d3.jpg",
+        "text": "$$\n\\phi ( { \\mathbf w } _ { i } ^ { t } ) = \\left( \\frac { \\partial f _ { i } ^ { t } } { \\partial { \\mathbf w } _ { i } ^ { t } } \\right) ^ { \\top } \\left[ \\nabla _ { f _ { i } ^ { t } } \\log p ( f _ { i } ^ { t } | { \\mathcal D } ) - { \\mathcal R } \\left( \\left\\{ \\nabla _ { f _ { i } ^ { t } } k ( \\pi _ { B } ( f _ { i } ^ { t } ) , \\pi _ { B } ( f _ { j } ^ { t } ) ) \\right\\} _ { j = 1 } ^ { n } \\right) \\right] .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            230,
+            593,
+            767,
+            631
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "2.3 Comparison to Stein variational gradient descent ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            645,
+            555,
+            661
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Note that our update is reminiscent of SVGD $\\mathbb { \\left[ 5 1 \\right] }$ , which in parameter space can be written as: ",
+        "bbox": [
+            173,
+            669,
+            795,
+            685
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/ed4ba25f1f792a3ef21feee9794a7aaba9ed6181f2313384dd85bba5b6760967.jpg",
+        "text": "$$\n\\phi ( \\mathbf { w } _ { i } ^ { t } ) = \\sum _ { j = 1 } ^ { n } k ( \\mathbf { w } _ { i } ^ { t } , \\mathbf { w } _ { j } ^ { t } ) \\nabla _ { \\mathbf { w } _ { i } ^ { t } } \\log p ( \\mathbf { w } _ { i } ^ { t } | \\mathcal { D } ) + \\sum _ { j = 1 } ^ { n } \\nabla _ { \\mathbf { w } _ { j } ^ { t } } k ( \\mathbf { w } _ { j } ^ { t } , \\mathbf { w } _ { i } ^ { t } ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            282,
+            690,
+            715,
+            734
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "It is important to notice that here, the gradients are averaged across all the particles using the kernel matrix. Interestingly, SVGD can be asymptotically interpreted as gradient flow of the KL divergence under a new metric induced by the Stein operator [16, 50] (see Appendix D for more details). Moving the inference from parameter to function space $\\pmb { \\mathbb { Z } } 6 \\|$ leads to the update rule ",
+        "bbox": [
+            173,
+            738,
+            826,
+            795
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/da910223233132ed75eba544433552d88de5b055ed7c20ab997ee811df84045c.jpg",
+        "text": "$$\n\\phi ( \\mathbf { w } _ { i } ^ { t } ) = \\left( \\frac { \\partial f _ { i } ^ { t } } { \\partial \\mathbf { w } _ { i } ^ { t } } \\right) ^ { \\top } \\left( \\frac { 1 } { n } \\sum _ { j = 1 } ^ { n } k ( f _ { i } ^ { t } , f _ { j } ^ { t } ) \\nabla _ { f _ { j } ^ { t } } \\log p ( f _ { j } ^ { t } | \\mathcal { D } ) + \\nabla _ { f _ { j } ^ { t } } k ( f _ { i } ^ { t } , f _ { j } ^ { t } ) \\right) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            251,
+            799,
+            746,
+            843
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "This way of averaging gradients using a kernel can be dangerous in high-dimensional settings, where kernel methods often suffer from the curse of dimensionality. Moreover, in Eq. $\\textcircled{6}$ , the posterior gradients of the particles are averaged using their similarity in weight space, which can be misleading in multi-modal posteriors. Worse yet, in Eq. $\\textcircled{7}$ , the gradients are averaged in function space and are then projected back using exclusively the $i$ -th Jacobian, which can be harmful given that it is not guaranteed that distances between functions evaluated on a subset of their input space resemble their true distance. Our proposed method, on the other hand, does not employ any averaging of the posterior gradients and thus comes closest to the true particle gradients in deep ensembles. ",
+        "bbox": [
+            174,
+            854,
+            825,
+            912
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            90,
+            825,
+            147
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3 Repulsive deep ensembles are Bayesian ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            165,
+            532,
+            183
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "So far, we represented the repulsive force as a general function of the gradients of a kernel. In this section, we show how to determine the explicit form of the repulsive term, such that the resulting update rule is equivalent to the discretization of the gradient flow dynamics of the KL divergence in Wasserstein space. We begin by introducing the concepts of particle approximation and gradient flow. ",
+        "bbox": [
+            173,
+            195,
+            826,
+            252
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.1 Particle approximation ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            267,
+            374,
+            282
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "A particle-based approximation of a target measure depends on a set of weighted samples $\\{ ( \\bar { x _ { i } } , w _ { i } ) \\} _ { i = 1 } ^ { n }$ , for which an empirical measure can be defined as ",
+        "bbox": [
+            173,
+            292,
+            823,
+            321
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/b51a8eebc42b5a02f34979b6c46328fac936b6561c35ce4b3a464937651a8dd3.jpg",
+        "text": "$$\n\\rho ( x ) = \\sum _ { i = 1 } ^ { n } w _ { i } \\delta ( x - x _ { i } ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            413,
+            325,
+            584,
+            366
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $\\delta ( \\cdot )$ is the Dirac delta function and the weights $w _ { i }$ satisfy $w _ { i } \\in [ 0 , 1 ]$ and $\\textstyle \\sum _ { i = 1 } ^ { n } w _ { i } = 1$ . To approximate a target distribution $\\pi ( x )$ using the empirical measure, the particles and their weights need to be selected in a principled manner that minimizes some measure of distance between $\\pi ( x )$ and $\\rho ( x )$ (e.g., a set of $N$ samples with weights $w _ { i } = 1 / N$ obtained using an MCMC method). ",
+        "bbox": [
+            173,
+            369,
+            825,
+            426
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.2 Gradient flow in parameter space ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            441,
+            446,
+            457
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Given a smooth function $J : \\mathbb { R } ^ { d }  \\mathbb { R }$ in Euclidean space, we can minimize it by creating a path that follows its negative gradient starting from some initial conditions $x _ { 0 }$ . The curve $x ( t )$ with starting point $x _ { 0 }$ described by that path is called gradient flow. The dynamics and evolution in time of a considered point in the space under this minimization problem can be described as the ODE1 ",
+        "bbox": [
+            173,
+            465,
+            825,
+            522
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/4af9c8caebc8dd0f4bb240ad868ba49b8044f29f61003074e861ae4833cdfbee.jpg",
+        "text": "$$\n\\frac { d \\boldsymbol { x } } { d t } = - \\boldsymbol { \\nabla } J ( \\boldsymbol { x } ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            442,
+            526,
+            555,
+            556
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We can extend this concept to the space of probability distributions (Wasserstein gradient flow) [3]. Let us consider the space of probability measures $\\mathcal { P } _ { 2 } ( \\mathcal { M } )$ , that is, the set of probability measures with finite second moments defined on the manifold $\\mathcal { M }$ : ",
+        "bbox": [
+            173,
+            558,
+            825,
+            599
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/c1e5d77c719b4d2fa7a0247805d6e0144779c241f5db03b43a6f1d113276ff19.jpg",
+        "text": "$$\n\\mathcal { P } _ { 2 } ( \\mathcal { M } ) = \\left\\{ \\varphi : \\mathcal { M } \\to [ 0 , \\infty ) \\bigg | \\int _ { \\mathcal { M } } \\mathrm { d } \\varphi = 1 , ~ \\int _ { \\mathcal { M } } | x | ^ { 2 } \\varphi ( x ) \\mathrm { d } x < + \\infty \\right\\} .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            259,
+            601,
+            736,
+            636
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Taking $\\Pi ( \\mu , \\nu )$ as the set of joint probability measures with marginals $\\mu , \\nu$ , we can define the Wasserstein metric on the space $\\mathcal { P } _ { 2 } ( \\mathcal { M } )$ as: ",
+        "bbox": [
+            178,
+            638,
+            820,
+            667
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/22875a9421a3c955c184f36bee03fad9988e4e0d847133375befe3e5951b4f25.jpg",
+        "text": "$$\nW _ { 2 } ^ { 2 } ( \\mu , \\nu ) = \\operatorname* { i n f } _ { \\pi \\in \\Pi ( \\mu , \\nu ) } \\int | x - y | ^ { 2 } { \\mathrm { d } } \\pi ( x , y ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            354,
+            670,
+            642,
+            703
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Considering the optimization problem of a functional $J : \\mathcal { P } _ { 2 } ( \\mathcal { M } )  \\mathbb { R }$ , such as the $\\mathrm { K L }$ divergence between the particle approximation in Eq. $\\textcircled { 8 }$ and the target posterior $\\pi ( x )$ , ",
+        "bbox": [
+            173,
+            707,
+            823,
+            736
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/202eca2cfd27979881321c7e7947951e3cc456330188130d02fcab3cc4c0abde.jpg",
+        "text": "$$\n\\operatorname* { i n f } _ { \\rho \\in \\mathcal { P } _ { 2 } ( \\mathcal { M } ) } D _ { K L } ( \\rho , \\pi ) = \\int _ { \\mathcal { M } } ( \\log \\rho ( x ) - \\log \\pi ( x ) ) \\rho ( x ) \\mathrm { d } x ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            305,
+            739,
+            691,
+            772
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "the evolution in time of the measure $\\rho$ under the equivalent of the gradient, the Wasserstein gradient flow, is described by the Liouville equation2 [38, 3, 64]: ",
+        "bbox": [
+            174,
+            775,
+            825,
+            804
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/319c5dba11def8b47c62bbed7e518cec22d2bb6447df21ccd8c8f0ceacda0468.jpg",
+        "text": "$$\n\\begin{array} { l } { \\displaystyle \\frac { \\partial \\rho ( \\boldsymbol { x } ) } { \\partial t } = \\nabla \\cdot \\left( \\rho ( \\boldsymbol { x } ) \\nabla \\frac { \\delta } { \\delta \\rho } D _ { K L } ( \\rho , \\pi ) \\right) } \\\\ { \\displaystyle = \\nabla \\cdot \\left( \\rho ( \\boldsymbol { x } ) \\nabla \\big ( \\log \\rho ( \\boldsymbol { x } ) - \\log \\pi ( \\boldsymbol { x } ) \\big ) \\right) , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            339,
+            806,
+            656,
+            877
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $\\nabla _ { \\delta \\rho } ^ { \\delta } D _ { K L } ( \\rho , \\pi ) \\ = : \\ \\nabla _ { \\mathcal { W } _ { 2 } } D _ { K L } ( \\rho , \\pi )$ is the Wasserstein gradient and the operator $\\frac { \\delta } { \\delta \\rho }$ $\\mathcal { P } _ { 2 } ( \\mathcal { M } ) \\stackrel { \\cdot } {  } \\mathbb { R }$ represents the functional derivative or first variation (see Appendix $\\boxed { \\mathsf { C } }$ for more details). In the particular case of the KL functional, we can recover the Fokker-Planck equation, ",
+        "bbox": [
+            173,
+            89,
+            826,
+            136
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/bc5069e97a8be7662b9fea29c7dc30021ca7cea5d088b0d8d45da5c537562e37.jpg",
+        "text": "$$\n\\begin{array} { r l r } & { } & { \\frac { \\partial \\rho ( x ) } { \\partial t } = \\nabla \\cdot \\left( \\rho ( x ) \\nabla ( \\log \\rho ( x ) - \\log \\pi ( x ) ) \\right) } \\\\ & { } & { = - \\nabla \\cdot \\left( \\rho ( x ) \\nabla \\log \\pi ( x ) \\right) + \\nabla ^ { 2 } \\rho ( x ) , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            348,
+            137,
+            647,
+            189
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "that admits as unique stationary distribution the posterior $\\pi ( x )$ . The deterministic particle dynamics ODE $\\left[ \\left[ 2 \\right] \\right]$ related to Eq. $\\mathbb { ( 1 1 ) }$ , namely mean-field Wasserstein dynamics, is then given by: ",
+        "bbox": [
+            173,
+            189,
+            823,
+            217
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/dd2081dc85db6793f99ac9a48cbba2bf3fdd0b388e3458acd6fdadb5a243ac7b.jpg",
+        "text": "$$\n\\frac { d x } { d t } = - \\nabla \\big ( \\log \\rho ( x ) - \\log \\pi ( x ) \\big ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            385,
+            218,
+            612,
+            247
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Considering a discretization of Eq. (12) for a particle system $\\{ x \\} _ { i = 1 } ^ { n }$ and small stepsize $\\epsilon _ { t }$ , we can rewrite Eq. $\\mathbb { \\underline { { ( 1 2 ) } } }$ as: ",
+        "bbox": [
+            171,
+            253,
+            823,
+            284
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/8a84c16f9a2296b238e38136d0db6478f4239c987d86ac3eef254ae1bde2a3a0.jpg",
+        "text": "$$\nx _ { i } ^ { t + 1 } = x _ { i } ^ { t } + \\epsilon _ { t } \\bigl ( \\nabla \\log \\pi ( x _ { i } ^ { t } ) - \\nabla \\log \\rho ( x _ { i } ^ { t } ) \\bigr ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            348,
+            281,
+            648,
+            300
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Unfortunately, we do not have access to the analytical form of the gradient $\\nabla \\log \\rho$ , so an approximation is needed. At this point, it is crucial to observe the similarity between the discretization of the Wasserstein gradient flow in Eq. $\\textcircled { 1 3 }$ and the repulsive update in Eq. $( 3 )$ to notice how, if the kernelized repulsion is an approximation of the gradient of the empirical particle measure, the update rule minimizes the KL divergence between the particle measure and the target posterior. Different sample-based approximations of the gradient that use a kernel function have been recently studied. The simplest one is given by the kernel density estimation (KDE) (details in Appendix $\\dot { \\mathrm { ~ E ~ } } )$ $\\begin{array} { r } { \\tilde { \\rho } _ { t } ( x ) = \\frac { 1 } { n } \\sum _ { i = 1 } ^ { n } \\dot { k } ( x , x _ { t } ^ { i } ) } \\end{array}$ , where $\\boldsymbol { k } ( \\cdot , \\cdot ) : \\mathbb { R } ^ { d } \\times \\mathbb { R } ^ { d }  \\dot { \\mathbb { R } }$ and the gradient of its log density is given by $\\mathbb { \\ m }$ : ",
+        "bbox": [
+            173,
+            299,
+            826,
+            422
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/690e51dceea0054b390381bde15c30e9e687f9c712f52307c2e07985d9200e39.jpg",
+        "text": "$$\n\\nabla \\log \\rho ( x _ { i } ^ { t } ) \\approx \\frac { \\sum _ { j = 1 } ^ { n } \\nabla _ { x _ { i } ^ { t } } k ( x _ { i } ^ { t } , x _ { j } ^ { t } ) } { \\sum _ { j = 1 } ^ { n } k ( x _ { i } ^ { t } , x _ { j } ^ { t } ) } .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            377,
+            421,
+            620,
+            460
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Using this approximation in Eq. $( 1 3 )$ we obtain: ",
+        "bbox": [
+            174,
+            458,
+            488,
+            473
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/371ffb0715cb9a3b57e74ec4c78b9d2ce1313431a8e5f80ccc30135a0cfa4053.jpg",
+        "text": "$$\nx _ { i } ^ { t + 1 } = x _ { i } ^ { t } + \\epsilon _ { t } \\Bigg ( \\nabla \\log \\pi ( x _ { i } ^ { t } ) - \\frac { \\sum _ { j = 1 } ^ { n } \\nabla _ { x _ { i } ^ { t } } k ( x _ { i } ^ { t } , x _ { j } ^ { t } ) } { \\sum _ { j = 1 } ^ { n } k ( x _ { i } ^ { t } , x _ { j } ^ { t } ) } \\Bigg ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            315,
+            473,
+            681,
+            512
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where, if we substitute the posterior for $\\pi$ , we obtain an expression for the repulsive force in Eq. $\\textcircled{3}$ . This shows that if the repulsive term in Eq. $( 3 )$ is the normalized sum of the gradients $\\mathcal { R } =$ $\\begin{array} { r } { \\left( \\bar { \\sum _ { j = 1 } ^ { n } } k ( \\mathbf { w } _ { i } ^ { t } , \\mathbf { w } _ { j } ^ { t } ) \\right) ^ { - 1 } \\sum _ { j = 1 } ^ { n } \\nabla _ { \\mathbf { w } _ { i } ^ { t } } k ( \\mathbf { w } _ { i } ^ { t } , \\mathbf { w } _ { j } ^ { t } ) } \\end{array}$ , we do not only encourage diversity of the ensemble members and thus avoid collapse, but surprisingly—in the asymptotic limit of , where the KDE approximation is exact $\\left[ \\left[ 6 6 \\right] \\right]$ —also converge to the true Bayesian posterior! ",
+        "bbox": [
+            173,
+            512,
+            825,
+            594
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Nevertheless, approximating the gradient of the empirical measure with the KDE can lead to suboptimal performance, as already studied by Li and Turner $[ \\overline { { | 4 6 | } }$ . They instead introduced a new Stein gradient estimator (SGE) that offers better performance, while maintaining the same computational cost. Even more recently, Shi et al. $\\mathbb { \\left. \\boldsymbol { \\mathfrak { G } } \\boldsymbol { \\mathfrak { A } } \\right. }$ introduced a spectral method for gradient estimation (SSGE), that also allows for a simple estimation on out-of-sample points. These two estimators can be used in Eq. $\\textcircled { 1 3 }$ , to formulate the following update rules with two alternative repulsive forces. The one using the Stein estimator, that we will call SGE-WGD, is: ",
+        "bbox": [
+            173,
+            598,
+            826,
+            696
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/fc8beab1c532557f6b4c53d364e88ab075d4917c7571f2c182526373978fd6c4.jpg",
+        "text": "$$\nx _ { i } ^ { t + 1 } = x _ { i } ^ { t } + \\epsilon _ { t } \\bigg ( \\nabla \\log \\pi ( x _ { i } ^ { t } ) + \\sum _ { j = 1 } ^ { n } ( K + \\eta \\mathbb { I } ) _ { i j } ^ { - 1 } \\sum _ { k = 1 } ^ { n } \\nabla _ { x _ { k } ^ { t } } k ( x _ { k } ^ { t } , x _ { j } ^ { t } ) \\bigg ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            269,
+            696,
+            725,
+            738
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $K$ is the kernel Gram matrix, $\\eta$ a small constant, and I the identity matrix. We can notice an important difference between KDE and SGE, in that the former is only considering the interaction of the $i$ -th particle being updated with all the others, while the latter is simultaneously considering also the interactions between the remaining particles. The spectral method, that we will call SSGE-WGD, leads to the following update rule: ",
+        "bbox": [
+            174,
+            739,
+            825,
+            809
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/22b05cdc924e14a9f81460eed44ce5ae2949169ff1032670bb23204d0bc3d3f9.jpg",
+        "text": "$$\nx _ { t + 1 } ^ { i } = x _ { t } ^ { i } + \\epsilon _ { t } \\bigg ( \\nabla \\log \\pi ( x _ { t } ^ { i } ) + \\sum _ { j = 1 } ^ { J } \\frac { 1 } { \\lambda _ { j } ^ { 2 } } \\sum _ { m = 1 } ^ { n } \\sum _ { k = 1 } ^ { n } u _ { j k } \\nabla _ { x _ { m } } k ( x _ { m } ^ { t } , x _ { k } ^ { t } ) \\cdot \\sum _ { l = 1 } ^ { n } u _ { j l } k ( x _ { i } ^ { t } , x _ { l } ^ { t } ) \\bigg )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            197,
+            809,
+            772,
+            853
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $\\lambda _ { j }$ is the $j$ -th eigenvalue of the kernel matrix and $u _ { j k }$ is the $k$ -th component of the $j$ -th eigenvector. Computationally, both SSGE and SGE have a cost of $\\mathcal { O } ( M ^ { 3 } + M ^ { 2 } d )$ , with $M$ being the number of points and $d$ their dimensionality. SSGE has an additional cost for predictions of $\\mathcal { O } ( M ( d + J ) )$ , where $J$ is the number of eigenvalues. ",
+        "bbox": [
+            174,
+            854,
+            825,
+            912
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/909c60e208223cd54336af828c72fc5777f5cbee78dd1b5dffc27345c64eca36.jpg",
+        "image_caption": [
+            "Figure 2: Single Gaussian. We show samples from SVGD, KDE-WGD, SGE-WGD, and SSGEWGD (from left to right). The upper and right plots show the empirical one-dimensional marginal distributions obtained using KDE on the samples (red) and on the particles (blue). "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            181,
+            85,
+            820,
+            212
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "3.3 Gradient flow in function space ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            287,
+            429,
+            303
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To theoretically justify the update rule introduced in function space in Eq. $\\textcircled{5}$ , we can rewrite the Liouville equation for the gradient flow in Eq. $\\textcircled { 1 1 }$ in function space as ",
+        "bbox": [
+            173,
+            314,
+            823,
+            344
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "img_path": "images/5c17155651b4b8a9222af9e3b20c3d19517ca6b37f38c6cba7442ed799860e6c.jpg",
+        "text": "$$\n\\begin{array} { l } { \\displaystyle \\frac { \\partial \\rho ( { \\pmb f } ) } { \\partial t } = \\nabla \\cdot \\left( \\rho ( { \\pmb f } ) \\nabla \\frac { \\delta } { \\delta \\rho } D _ { K L } ( \\rho , \\pi ) \\right) } \\\\ { \\displaystyle = \\nabla \\cdot \\left( \\rho ( { \\pmb f } ) \\nabla \\big ( \\log \\rho ( { \\pmb f } ) - \\log \\pi ( { \\pmb f } ) \\big ) \\right) . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            336,
+            352,
+            663,
+            422
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Following this update, the mean field functional dynamics are ",
+        "bbox": [
+            173,
+            429,
+            580,
+            444
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "img_path": "images/6ec49c1866059fd222d901856c6fd87a5e5117e19a3da56886cb693721fd87d0.jpg",
+        "text": "$$\n\\frac { d \\pmb f } { d t } = - \\nabla \\big ( \\log \\rho ( \\pmb f ) - \\log \\pi ( \\pmb f ) \\big ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            382,
+            452,
+            616,
+            483
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Using the same KDE approximation as above, we can obtain a discretized evolution in function space and with it an explicit form for the repulsive force in Eq. $\\textcircled{4}$ as ",
+        "bbox": [
+            171,
+            489,
+            825,
+            520
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "img_path": "images/413dc39054cf2ffe58aac203b1f546f1178b0fd741a1e970d847b042475c73d1.jpg",
+        "text": "$$\n\\pmb { f } _ { t + 1 } ^ { i } = \\pmb { f } _ { t } ^ { i } + \\epsilon _ { t } \\bigg ( \\nabla _ { \\pmb { f } } \\log \\pi ( \\pmb { f } _ { t } ^ { i } ) - \\frac { \\sum _ { j = 1 } ^ { n } \\nabla _ { \\pmb { f } _ { i } ^ { t } } k ( \\pmb { f } _ { i } ^ { t } , \\pmb { f } _ { j } ^ { t } ) } { \\sum _ { j = 1 } ^ { n } k ( \\pmb { f } _ { i } ^ { t } , \\pmb { f } _ { j } ^ { t } ) } \\bigg ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            307,
+            526,
+            691,
+            568
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The update rules using the SGE and SSGE approximations follow as for the parametric case. It is important to notice that this update rule requires the function space prior gradient: $\\nabla _ { f _ { j } } \\log { p ( f _ { j } | x , y ) } =$ $\\nabla _ { f _ { j } } \\log p ( \\pmb { y } | \\pmb { x } , \\pmb { f _ { j } } ) + \\nabla _ { f _ { j } } \\log p ( \\pmb { f _ { j } } )$ . If one wants to use an implicit prior defined in weight space, an additional estimator is needed due to its analytical intractability. We again adopted the SSGE, introduced by Shi et al. $\\mathbb { \\lVert \\boldsymbol { 6 9 } \\rVert }$ , which was already used for a similar purpose in Sun et al. $\\pmb { \\mathbb { Z } 1 }$ . It is also interesting to note that the update rule in Eq. $\\textcircled { 1 2 0 }$ readily allows for the use of alternative priors that have an analytical form, such as Gaussian processes. This is an important feature of our method that allows for an explicit encoding of function space properties that can be useful for example in achieving better out of distribution detection capabilities $\\checkmark$ . ",
+        "bbox": [
+            173,
+            574,
+            826,
+            700
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "3.4 The choice of the kernel ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            718,
+            379,
+            733
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "A repulsive effect can always be created in the ensemble by means of the gradient of any kernel function that is measuring the similarity between two members. Nevertheless, it is important to keep in mind that to ensure the asymptotic convergence to the Bayesian posterior, the repulsive component must be a consistent estimator of the gradient in Eq. $( 1 3 )$ , as shown in Section $\\checkmark$ . Therefore, some important constraints over the kernel choice are needed. In particular, the SGE and SSGE need a kernel function belonging to the Stein class (see Shi et al. $\\dot { \\overline { { \\vert 6 9 \\vert } } }$ for more details). On the other hand, for the KDE, any symmetric probability density function can be used. On this subject, the work of Aggarwal et al. [1] has shown how the Manhattan distance metric (L1 norm) might be preferable over the Euclidean distance metric (L2 norm) for high-dimensional settings. We performed some additional experiments using the L1 norm (Laplace kernel) for the KDE but we could not observe any substantial difference compared to using the L2 norm. Further investigations regarding this hypothesis are left for future research. ",
+        "bbox": [
+            173,
+            744,
+            825,
+            911
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/094ed7ba5611118de5688c3ddd1545168ced55dff3ababfdac0ee5e88615b714.jpg",
+        "image_caption": [
+            "Figure 3: BNN 2D classification. We show the entropy of the predictive posteriors. Again, the function-space methods capture the uncertainty better than the weight-space ones, thus approaching the gold-standard HMC posterior. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            196,
+            93,
+            831,
+            292
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4 Experiments ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            373,
+            312,
+            391
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this section, we compare the different proposed WGD methods with deep ensembles and SVGD on synthetic sampling, regression, and classification tasks and real-world image classification tasks. We use an RBF kernel (except where otherwise specified) with the popular median heuristic $\\mathbb { \\left[ \\left[ 5 1 \\right] \\right] }$ to choose the kernel bandwidth. In our experiments, an adaptive bandwidth leads to better performance than fixing and tuning a single constant value for the entire evolution of the particles. We also quantitatively assess the uncertainty estimation of the methods in terms of calibration and OOD detection. In our experiments, we report the test accuracy, negative log-likelihood (NLL), and the expected calibration error (ECE) [58]. To assert the robustness on out-of-distribution (OOD) data, we report the ratio between predictive entropy on OOD and test data points $( H _ { o } / H _ { t } )$ , and the OOD detection area under the ROC curve AUROC(H) $\\mathbb { H }$ . Moreover, to assess the diversity of the ensemble generated by the different methods in function space, we measure the functional diversity using the model disagreement (MD) (details in Appendix $\\bar { \\bigtriangledown } \\bar { \\bigtriangledown }$ . In particular, we report the ratio between the average model disagreement on the OOD and test data points $( M D _ { o } / M D _ { t } )$ and additionally the OOD detection AUROC(MD) computed using this measure instead of the entropy. ",
+        "bbox": [
+            174,
+            405,
+            825,
+            599
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Sampling from synthetic distributions As a sanity check, we first assessed the ability of our different approximations for Wasserstein gradient descent (using KDE, SGE, and SSGE) to sample from a two-dimensional Gaussian distribution (Figure $^ { 2 ) }$ . We see that our SGE-WGD, SSGE-WGD and the SVGD fit the target almost perfectly. We also tested the different methods in a more complex two-dimensional Funnel distribution $\\mathbb { \\left[ \\left[ 5 9 \\right] \\right] }$ and present the results in Figure $\\mathrm { F . l }$ in the Appendix. There, SGE-WGD and SVGD also perform best. ",
+        "bbox": [
+            173,
+            616,
+            825,
+            699
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "BNN 1D regression We then assessed the different methods in fitting a BNN posterior on a synthetically generated one-dimensional regression task. The results are reported in Figure 1 consisting of the mean prediction and $\\pm 1 , 2 , 3$ standard deviations of the predictive distribution. We can see that all methods performing inference in the weight space (DE, w-SVGD, WGD) are unable to capture the epistemic uncertainty between the two clusters of training data points. Conversely, the functional methods (f-SVGD, fWGD) are perfectly able to infer the diversity of the hypotheses in this region due to the lack of training evidence. They thereby achieve a predictive posterior that very closely resembles the one obtained with the gold-standard HMC sampling. ",
+        "bbox": [
+            173,
+            714,
+            825,
+            825
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "BNN 2D classification Next, we investigated the predictive performance and quality of uncertainty estimation of the methods in a two-dimensional synthetic classification setting. The results are displayed in Figure $\\textcircled { 3 }$ We can clearly observe that the weight-space methods are overconfident and do not capture the uncertainty well. Moreover, all the functions seems to collapse to the optimal classifier. These methods thus only account for uncertainty close to the decision boundaries and to the origin region, for which the uncertainty is purely aleatoric. In this setting, f-SVGD suffers from similar issues as the weight space methods, being overconfident away from the training data. Conversely, our fWGD methods are confident (low entropy) around the data but not out-of-distribution, thus representing the epistemic uncertainty better. This suggests that the functional diversity captured by this method naturally leads to a distance-aware uncertainty estimation $\\mathbb { H 9 } \\mathbb { L O }$ , a property that translates into confident predictions only in the proximity of the training data, allowing for a principled OOD detection. ",
+        "bbox": [
+            174,
+            842,
+            825,
+            911
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/c10e7e6db9d6afe7b283337a217b0daf6bdc8ff99b073aef9c58623cfb518d7c.jpg",
+        "table_caption": [
+            "Table 1: BNN image classification. AUROC $\\mathbf { ( H ) }$ is the AUROC computed using the entropy whereas AUROC(MD) is computed using the model disagreement. $\\mathbf { H _ { o } / H _ { t } }$ is the ratio of the entropies on OOD and test points respectively and $\\mathbf { M D _ { o } / M D _ { t } }$ is the ratio for model disagreement. We see that the best accuracy is achieved by our WGD methods, while our fWGD methods yield the best OOD detection and funtional diversity. All our proposed methods improve over standard deep ensembles in terms of accuracy and diversity, highlighting the effect of our repulsion. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"11\">Prroiiiie</td><td></td><td>AUROC(H)</td><td>AUROC(MD)</td><td>Accuracy</td><td>H/Ht</td><td>MD/MDt</td><td>ECE</td><td>NLL</td></tr><tr><td>Deep ensemble 4</td><td>0.958±0.001</td><td>0.975±0.001</td><td>91.122±0.013</td><td>6.257±0.005</td><td>6.394±0.001</td><td>0.012±0.001</td><td>0.129±0.001</td></tr><tr><td>SVGD [51</td><td>0.960±0.001</td><td>0.973±0.001</td><td>91.134±0.024</td><td>6.315±0.019</td><td>6.395±0.018</td><td>0.014±0.001</td><td>0.127±0.001</td></tr><tr><td>f-SVGD [76</td><td>0.956±0.001</td><td>0.975±0.001</td><td>89.884±0.015</td><td>5.652±0.009</td><td>6.531±0.005</td><td>0.013±0.001</td><td>0.150±0.001</td></tr><tr><td>hyper-DE [80]</td><td>0.968±0.001</td><td>0.981±0.001</td><td>91.160±0.007</td><td>6.682±0.065</td><td>7.059±0.152</td><td>0.014±0.001</td><td>0.128±0.001</td></tr><tr><td>kde-WGD (ours)</td><td>0.960±0.001</td><td>0.970±0.001</td><td>91.238±0.019</td><td>6.587±0.019</td><td>6.379±0.018</td><td>0.014±0.001</td><td>0.128±0.001</td></tr><tr><td>sge-WGD (ours)</td><td>0.960±0.001</td><td>0.970±0.001</td><td>91.312±0.016</td><td>6.562±0.007</td><td>6.363±0.009</td><td>0.012±0.001</td><td>0.128±0.001</td></tr><tr><td>ssge-WGD (ours)</td><td>0.968±0.001</td><td>0.979±0.001</td><td>91.198±0.024</td><td>6.522±0.009</td><td>6.610±0.012</td><td>0.012±0.001</td><td>0.130±0.001</td></tr><tr><td>kde-fWGD (ours)</td><td>0.971±0.001</td><td>0.980±0.001</td><td>91.260±0.011</td><td>7.079±0.016</td><td>6.887±0.015</td><td>0.015±0.001</td><td>0.125±0.001</td></tr><tr><td>sge-fWGD (ours)</td><td>0.969±0.001</td><td>0.978±0.001</td><td>91.192±0.013</td><td>7.076±0.004</td><td>6.900±0.005</td><td>0.015±0.001</td><td>0.125±0.001</td></tr><tr><td>ssge-fWGD (ours)</td><td>0.971±0.001</td><td>0.980±0.001</td><td>91.240±0.022</td><td>7.129±0.006</td><td>6.951±0.005</td><td>0.016±0.001</td><td>0.124±0.001</td></tr><tr><td rowspan=\"11\">CITIIIO</td><td>Deep ensemble 42</td><td>0.843±0.004</td><td>0.736±0.005</td><td>85,552±0.076</td><td>2.244±0.006</td><td>1.667±0.008</td><td>0.049±0.001</td><td>0.277±0.001</td></tr><tr><td>SVGD [51</td><td>0.825±0.001</td><td>0.710±0.002</td><td>85.142±0.017</td><td>2.106±0.003</td><td>1.567±0.004</td><td>0.052±0.001</td><td>0.287±0.001</td></tr><tr><td>fSVGD 回</td><td>0.783±0.001</td><td>0.712±0.001</td><td>84.510±0.031</td><td>1.968±0.004</td><td>1.624±0.003</td><td>0.049±0.001</td><td>0.292±0.001</td></tr><tr><td>hyper-DE [80]</td><td>0.789±0.001</td><td>0.743±0.001</td><td>84.743±0.011</td><td>1.951±0.010</td><td>1.690±0.015</td><td>0.046±0.001</td><td>0.288±0.001</td></tr><tr><td>kde-WGD (ours)</td><td>0.838±0.001</td><td>0.735±0.004</td><td>85.904±0.030</td><td>2.205±0.003</td><td>1.661±0.008</td><td>0.053±0.001</td><td>0.276±0.001</td></tr><tr><td>sge-WGD (ours)</td><td>0.837±0.003</td><td>0.725±0.004</td><td>85.792±0.035</td><td>2.214±0.010</td><td>1.634±0.004</td><td>0.051±0.001</td><td>0.275±0.001</td></tr><tr><td>ssge-WGD (ours)</td><td>0.832±0.003</td><td>0.731±0.005</td><td>85.638±0.038</td><td>2.182±0.015</td><td>1.655±0.001</td><td>0.049±0.001</td><td>0.276±0.001</td></tr><tr><td>kde-fWGD (ours)</td><td>0.791±0.002</td><td>0.758±0.002</td><td>84.888±0.030</td><td>1.970±0.004</td><td>1.749±0.005</td><td>0.044±0.001</td><td>0.282±0.001</td></tr><tr><td>sge-fWGD (ours)</td><td>0.795±0.001</td><td>0.754±0.002</td><td>84.766±0.060</td><td>1.984±0.003</td><td>1.729±0.002</td><td>0.047±0.001</td><td>0.288±0.001</td></tr><tr><td>ssge-fWGD (ours)</td><td>0.792±0.002</td><td>0.752±0.002</td><td>84.762±0.034</td><td>1.970±0.006</td><td>1.723±0.005</td><td>0.046±0.001</td><td>0.286±0.001</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></table>",
+        "bbox": [
+            174,
+            180,
+            825,
+            393
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            173,
+            421,
+            825,
+            518
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "FashionMNIST classification Moving on to real-world data, we used an image classification setting using the FashionMNIST dataset $\\dot { \\left[ \\left| 8 3 \\right| \\right] }$ for training and the MNIST dataset $\\bar { \\mathbb { E } 3 } \\mathbb { I }$ as an out-ofdistribution (OOD) task. The results are reported in Table $^ 1 { } _ { . }$ (top). We can see that all our methods improve upon standard deep ensembles and SVGD, highlighting the effectiveness of our proposed repulsion terms when training neural network ensembles. In particular, the sge-WGD offers the best accuracy, whereas the methods in function space all offer a better OOD detection. This is probably due to the fact that these methods achieve a higher entropy ratio and functional diversity measured via the model disagreement when compared to their weight-space counterparts. Interestingly, they also reach the lowest NLL values. We can also notice how the model disagreement (MD) not only serves its purpose as a metric for the functional heterogeneity of the ensemble but also allows for a better OOD detection in comparison to the entropy. To the best of our knowledge, this insight has not been described before, although it has been used in continual learning $\\pmb { \\mathbb { B } } \\mathbf { \\mathbb { 1 } }$ . Interestingly, using this metric, the hyper-deep ensemble $[ \\textcircled { 8 0 } ]$ shows OOD detection performance comparable with our repulsive ensemble in function space. ",
+        "bbox": [
+            173,
+            536,
+            825,
+            729
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "CIFAR classification Finally, we use a ResNet32 architecture $\\mathbb { \\left| \\left[ 2 9 \\right] \\right| }$ on CIFAR-10 [41] with the SVHN dataset $\\mathbb { \\left[ 6 1 \\right] }$ as OOD data. The results are reported in Table 1 (bottom). We can see that in this case, the weight-space methods achieve better performance in accuracy and OOD detection using the entropy than the ones in function space. Nevertheless, all our repulsive ensembles improve functional diversity, accuracy, and OOD detection when compared to standard SVGD, whereas the standard deep ensemble achieves the best OOD detection using the entropy. ",
+        "bbox": [
+            174,
+            746,
+            825,
+            829
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5 Related Work ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            849,
+            321,
+            867
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "The theoretical and empirical properties of SVGD have been well studied [40, 48, 13] and it can also be seen as a Wasserstein gradient flow of the KL divergence in the Stein geometry [16, 50] (see Appendix D for more details). Interestingly, a gradient flow interpretation is also possible for (stochastic gradient) MCMC-type algorithms $\\dot { \\left. \\overline { { 4 8 } } \\right. }$ , which can be unified under a general particle inference framework [10]. Moreover, our Wasserstein gradient descent using the SGE approximation can also be derived using an alternative formulation as a gradient flow with smoothed test functions [48]. A projected version of WGD has been studied in Wang et al. $\\mathbb { \\left. \\overline { { \\boldsymbol { \\mathscr { Q } } \\boldsymbol { \\cdot } \\boldsymbol { \\cdot } } } \\right. }$ , which could also be readily applied in our framework. Besides particle methods, Bayesian neural networks $\\pm \\pm \\infty$ have gained popularity recently [79, 22, 19, 36], using modern MCMC [59, 79, 22, 24, 21] and variational inference techniques [5, 72, 17, 34]. On the other hand, ensemble methods have also been extensively studied [42, 18, 82, 23, 80, 32, 85, 78].Moreover, repulsive interactions between the members have also been studied in Wabartha et al. [74]. Moreover, providing Bayesian interpretations for deep ensembles has been previously attempted through the lenses of stationary SGD distributions $[ \\sqrt { 5 6 } , \\sqrt ] { 8 } ]$ , ensembles of linear models $\\dot { \\bigtriangledown } 5 7 \\big |$ , additional random functions $\\boxed { 6 2 } , \\boxed { 1 2 } , \\boxed { 2 7 }$ , approximate inference $\\lVert 8 2 \\rVert$ , Stein variational inference [15], and marginal likelihood lower bounds $\\bar { \\| 5 3 \\| }$ , and ensembles have also been shown to provide good approximations to the true BNN posterior in some settings $\\left[ \\left[ 3 6 \\right] \\right]$ . Furthermore, variational inference in function space has recently gained attention $\\mathbb { \\ m }$ and the limitations of the KL divergence have been studied in Burt et al. [7]. ",
+        "bbox": [
+            174,
+            882,
+            821,
+            911
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            90,
+            825,
+            313
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "6 Conclusion ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            330,
+            299,
+            348
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "We have presented a simple and principled way to improve upon standard deep ensemble methods. To this end, we have shown that the introduction of a kernelized repulsion between members of the ensemble not only improves the accuracy of the predictions but—even more importantly—can be seen as Wasserstein gradient descent on the KL divergence, thus transforming the MAP inference of deep ensembles into proper Bayesian inference. Moreover, we have shown that incorporating functional repulsion between ensemble members can improve the quality of the estimated uncertainties on simple synthetic examples and OOD detection on real-world data and can approach the true Bayesian posterior more closely. ",
+        "bbox": [
+            174,
+            361,
+            825,
+            472
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "In future work, it will be interesting to study the impact of the Jacobian in the fWGD update and its implications on the Liouville equation in more detail, also compared to other neural network Jacobian methods, such as neural tangent kernels $\\pmb { \\Vert 3 7 } \\Vert$ and generalized Gauss-Newton approximations $\\boldsymbol { \\left[ \\left[ 3 5 \\right] \\right] }$ . Moreover, it would be interesting to derive explicit convergence bounds for our proposed method and compare them to the existing bounds for SVGD [40]. ",
+        "bbox": [
+            174,
+            478,
+            825,
+            547
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgments ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            563,
+            303,
+            578
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "VF would like to acknowledge financial support from the Strategic Focus Area “Personalized Health and Related Technologies” of the ETH Domain through the grant #2017-110 and from the Swiss Data Science Center through a PhD fellowship. We thank Florian Wenzel, Alexander Immer, Andrew Gordon Wilson, Pavel Izmailov, Christian Henning, and Johannes von Oswald for helpful discussions. We also thank Dr. Sheldon Cooper, Dr. Leonard Hofstadter and Penny Hofstadter for their support and inspiration. ",
+        "bbox": [
+            174,
+            588,
+            825,
+            671
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "References ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            690,
+            266,
+            707
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "[1] Charu C Aggarwal, Alexander Hinneburg, and Daniel A Keim. On the surprising behavior of distance metrics in high dimensional space. In International conference on database theory, pages 420–434. Springer, 2001.   \n[2] Luigi Ambrosio and Gianluca Crippa. Continuity equations and ode flows with non-smooth velocity. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 144(6): 1191–1244, 2014.   \n[3] Luigi Ambrosio, Nicola Gigli, and Giuseppe Savaré. Gradient flows: in metric spaces and in the space of probability measures. Springer Science & Business Media, 2008.   \n[4] Vijay Badrinarayanan, Bamdev Mishra, and Roberto Cipolla. Symmetry-invariant optimization in deep networks. arXiv preprint arXiv:1511.01754, 2015.   \n[5] Charles Blundell, Julien Cornebise, Koray Kavukcuoglu, and Daan Wierstra. Weight uncertainty in neural networks. arXiv preprint arXiv:1505.05424, 2015. ",
+        "bbox": [
+            179,
+            713,
+            826,
+            911
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "[6] Leo Breiman. Bagging predictors. Machine learning, 24(2):123–140, 1996. ",
+        "bbox": [
+            179,
+            90,
+            707,
+            107
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "[7] David R Burt, Sebastian W Ober, Adrià Garriga-Alonso, and Mark van der Wilk. Understanding variational inference in function-space. arXiv preprint arXiv:2011.09421, 2020. ",
+        "bbox": [
+            178,
+            114,
+            823,
+            145
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "[8] Pratik Chaudhari and Stefano Soatto. Stochastic gradient descent performs variational inference, converges to limit cycles for deep networks. In 2018 Information Theory and Applications Workshop (ITA), pages 1–10. IEEE, 2018. ",
+        "bbox": [
+            178,
+            152,
+            823,
+            195
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "[9] An Mei Chen, Haw-minn Lu, and Robert Hecht-Nielsen. On the geometry of feedforward neural network error surfaces. Neural computation, 5(6):910–927, 1993. ",
+        "bbox": [
+            178,
+            204,
+            825,
+            234
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "[10] Changyou Chen, Ruiyi Zhang, Wenlin Wang, Bai Li, and Liqun Chen. A unified particleoptimization framework for scalable bayesian sampling. arXiv preprint arXiv:1805.11659, 2018. ",
+        "bbox": [
+            173,
+            242,
+            825,
+            285
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "[11] Jiefeng Chen, Xi Wu, Yingyu Liang, Somesh Jha, et al. Robust out-of-distribution detection in neural networks. arXiv preprint arXiv:2003.09711, 2020. ",
+        "bbox": [
+            173,
+            294,
+            825,
+            323
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "[12] Kamil Ciosek, Vincent Fortuin, Ryota Tomioka, Katja Hofmann, and Richard Turner. Conservative uncertainty estimation by fitting prior networks. In International Conference on Learning Representations, 2019. ",
+        "bbox": [
+            174,
+            332,
+            823,
+            375
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "[13] Francesco D’Angelo and Vincent Fortuin. Annealed stein variational gradient descent. arXiv preprint arXiv:2101.09815, 2021. ",
+        "bbox": [
+            173,
+            382,
+            821,
+            412
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "[14] Francesco D’Angelo and Christian Henning. Uncertainty-based out-of-distribution detection requires suitable function space priors. arXiv preprint arXiv:2110.06020, 2021. ",
+        "bbox": [
+            173,
+            421,
+            821,
+            450
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "[15] Francesco D’Angelo, Vincent Fortuin, and Florian Wenzel. On stein variational neural network ensembles. arXiv preprint arXiv:2106.10760, 2021. ",
+        "bbox": [
+            174,
+            458,
+            823,
+            488
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "[16] A Duncan, Nikolas Nuesken, and Lukasz Szpruch. On the geometry of stein variational gradient descent. arXiv preprint arXiv:1912.00894, 2019. ",
+        "bbox": [
+            173,
+            496,
+            823,
+            526
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "[17] Michael W Dusenberry, Ghassen Jerfel, Yeming Wen, Yi-an Ma, Jasper Snoek, Katherine Heller, Balaji Lakshminarayanan, and Dustin Tran. Efficient and scalable bayesian neural nets with rank-1 factors. arXiv preprint arXiv:2005.07186, 2020. ",
+        "bbox": [
+            174,
+            535,
+            823,
+            578
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "[18] Stanislav Fort, Huiyi Hu, and Balaji Lakshminarayanan. Deep ensembles: A loss landscape perspective. arXiv preprint arXiv:1912.02757, 2019. ",
+        "bbox": [
+            174,
+            587,
+            823,
+            616
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "[19] Vincent Fortuin. Priors in bayesian deep learning: A review. arXiv preprint arXiv:2105.06868, 2021. ",
+        "bbox": [
+            173,
+            625,
+            823,
+            654
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "[20] Vincent Fortuin, Mark Collier, Florian Wenzel, James Allingham, Jeremiah Liu, Dustin Tran, Balaji Lakshminarayanan, Jesse Berent, Rodolphe Jenatton, and Effrosyni Kokiopoulou. Deep classifiers with label noise modeling and distance awareness. arXiv preprint arXiv:2110.02609, 2021. ",
+        "bbox": [
+            174,
+            661,
+            826,
+            718
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "[21] Vincent Fortuin, Adrià Garriga-Alonso, Mark van der Wilk, and Laurence Aitchison. Bnnpriors: A library for bayesian neural network inference with different prior distributions. Software Impacts, page 100079, 2021. ",
+        "bbox": [
+            173,
+            727,
+            823,
+            771
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "[22] Vincent Fortuin, Adrià Garriga-Alonso, Florian Wenzel, Gunnar Rätsch, Richard Turner, Mark van der Wilk, and Laurence Aitchison. Bayesian neural network priors revisited. arXiv preprint arXiv:2102.06571, 2021. ",
+        "bbox": [
+            174,
+            779,
+            823,
+            821
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "[23] Timur Garipov, Pavel Izmailov, Dmitrii Podoprikhin, Dmitry Vetrov, and Andrew Gordon Wilson. Loss surfaces, mode connectivity, and fast ensembling of dnns. arXiv preprint arXiv:1802.10026, 2018. ",
+        "bbox": [
+            174,
+            830,
+            821,
+            875
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "[24] Adrià Garriga-Alonso and Vincent Fortuin. Exact langevin dynamics with stochastic gradients. arXiv preprint arXiv:2102.01691, 2021. ",
+        "bbox": [
+            173,
+            882,
+            820,
+            911
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "[25] Mario Geiger, Arthur Jacot, Stefano Spigler, Franck Gabriel, Levent Sagun, Stéphane d’Ascoli, Giulio Biroli, Clément Hongler, and Matthieu Wyart. Scaling description of generalization with number of parameters in deep learning. Journal of Statistical Mechanics: Theory and Experiment, 2020(2):023401, 2020.   \n[26] L. K. Hansen and P. Salamon. Neural network ensembles. IEEE Trans. Pattern Anal. Mach. Intell., 12(10):993–1001, October 1990. ISSN 0162-8828. doi: 10.1109/34.58871. URL https://doi.org/10.1109/34.58871.   \n[27] Bobby He, Balaji Lakshminarayanan, and Yee Whye Teh. Bayesian deep ensembles via the neural tangent kernel. arXiv preprint arXiv:2007.05864, 2020.   \n[28] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Delving deep into rectifiers: Surpassing human-level performance on imagenet classification. In Proceedings of the IEEE international conference on computer vision, pages 1026–1034, 2015.   \n[29] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 770–778, 2016.   \n[30] Robert Hecht-Nielsen. On the algebraic structure of feedforward network weight spaces. In Advanced Neural Computers, pages 129–135. Elsevier, 1990.   \n[31] Christian Henning, Maria R Cervera, Francesco D’Angelo, Johannes von Oswald, Regina Traber, Benjamin Ehret, Seijin Kobayashi, João Sacramento, and Benjamin F Grewe. Posterior meta-replay for continual learning. arXiv preprint arXiv:2103.01133, 2021.   \n[32] Gao Huang, Yixuan Li, Geoff Pleiss, Zhuang Liu, John E Hopcroft, and Kilian Q Weinberger. Snapshot ensembles: Train 1, get m for free. arXiv preprint arXiv:1704.00109, 2017.   \n[33] Gao Huang, Yixuan Li, Geoff Pleiss, Zhuang Liu, John E. Hopcroft, and Kilian Q. Weinberger. Snapshot ensembles: Train 1, get M for free. CoRR, abs/1704.00109, 2017. URL http: //arxiv.org/abs/1704.00109.   \n[34] Alexander Immer, Matthias Bauer, Vincent Fortuin, Gunnar Rätsch, and Mohammad Emtiyaz Khan. Scalable marginal likelihood estimation for model selection in deep learning. arXiv preprint arXiv:2104.04975, 2021.   \n[35] Alexander Immer, Maciej Korzepa, and Matthias Bauer. Improving predictions of bayesian neural nets via local linearization. In International Conference on Artificial Intelligence and Statistics, pages 703–711. PMLR, 2021.   \n[36] Pavel Izmailov, Sharad Vikram, Matthew D Hoffman, and Andrew Gordon Wilson. What are bayesian neural network posteriors really like? arXiv preprint arXiv:2104.14421, 2021.   \n[37] Arthur Jacot, Franck Gabriel, and Clément Hongler. Neural tangent kernel: convergence and generalization in neural networks. In Proceedings of the 32nd International Conference on Neural Information Processing Systems, pages 8580–8589, 2018.   \n[38] Richard Jordan, David Kinderlehrer, and Felix Otto. The variational formulation of the fokker– planck equation. SIAM journal on mathematical analysis, 29(1):1–17, 1998.   \n[39] Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.   \n[40] Anna Korba, Adil Salim, Michael Arbel, Giulia Luise, and Arthur Gretton. A non-asymptotic analysis for stein variational gradient descent. Advances in Neural Information Processing Systems, 33, 2020.   \n[41] Alex Krizhevsky et al. Learning multiple layers of features from tiny images. 2009.   \n[42] Balaji Lakshminarayanan, Alexander Pritzel, and Charles Blundell. Simple and scalable predictive uncertainty estimation using deep ensembles. In Advances in neural information processing systems, pages 6402–6413, 2017.   \n[43] Yann LeCun. The mnist database of handwritten digits. http://yann. lecun. com/exdb/mnist/, 1998.   \n[44] Jaehoon Lee, Yasaman Bahri, Roman Novak, Samuel S Schoenholz, Jeffrey Pennington, and Jascha Sohl-Dickstein. Deep neural networks as gaussian processes. arXiv preprint arXiv:1711.00165, 2017.   \n[45] E. Levin, N. Tishby, and S. A. Solla. A statistical approach to learning and generalization in layered neural networks. Proc. of the IEEE – Special issue on Neural Networks, 1990.   \n[46] Yingzhen Li and Richard E Turner. Gradient estimators for implicit models. arXiv preprint arXiv:1705.07107, 2017.   \n[47] Shiyu Liang, Yixuan Li, and Rayadurgam Srikant. Enhancing the reliability of out-ofdistribution image detection in neural networks. arXiv preprint arXiv:1706.02690, 2017.   \n[48] Chang Liu, Jingwei Zhuo, Pengyu Cheng, Ruiyi Zhang, and Jun Zhu. Understanding and accelerating particle-based variational inference. In International Conference on Machine Learning, pages 4082–4092. PMLR, 2019.   \n[49] Jeremiah Zhe Liu, Zi Lin, Shreyas Padhy, Dustin Tran, Tania Bedrax-Weiss, and Balaji Lakshminarayanan. Simple and principled uncertainty estimation with deterministic deep learning via distance awareness. arXiv preprint arXiv:2006.10108, 2020.   \n[50] Qiang Liu. Stein variational gradient descent as gradient flow. In Advances in neural information processing systems, pages 3115–3123, 2017.   \n[51] Qiang Liu and Dilin Wang. Stein variational gradient descent: A general purpose bayesian inference algorithm. In Advances in neural information processing systems, pages 2378–2386, 2016.   \n[52] Qiang Liu, Jason Lee, and Michael Jordan. A kernelized stein discrepancy for goodness-of-fit tests. In International conference on machine learning, pages 276–284. PMLR, 2016.   \n[53] Clare Lyle, Lisa Schut, Robin Ru, Yarin Gal, and Mark van der Wilk. A bayesian perspective on training speed and model selection. Advances in Neural Information Processing Systems, 33, 2020.   \n[54] David JC MacKay. A practical bayesian framework for backpropagation networks. Neural computation, 4(3):448–472, 1992.   \n[55] Andrey Malinin, Bruno Mlodozeniec, and Mark Gales. Ensemble distribution distillation. arXiv preprint arXiv:1905.00076, 2019.   \n[56] Stephan Mandt, Matthew D Hoffman, and David M Blei. Stochastic gradient descent as approximate bayesian inference. arXiv preprint arXiv:1704.04289, 2017.   \n[57] Alexander G de G Matthews, Jiri Hron, Richard E Turner, and Zoubin Ghahramani. Samplethen-optimize posterior sampling for bayesian linear models. In NeurIPS Workshop on Advances in Approximate Bayesian Inference, 2017.   \n[58] Mahdi Pakdaman Naeini, Gregory Cooper, and Milos Hauskrecht. Obtaining well calibrated probabilities using bayesian binning. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 29, 2015.   \n[59] Radford M Neal. Bayesian learning for neural networks. 1995.   \n[60] Radford M Neal. Bayesian learning for neural networks, volume 118. Springer Science & Business Media, 2012.   \n[61] Yuval Netzer, Tao Wang, Adam Coates, Alessandro Bissacco, Bo Wu, and Andrew Y Ng. Reading digits in natural images with unsupervised feature learning. 2011.   \n[62] Ian Osband, Benjamin Van Roy, Daniel J Russo, Zheng Wen, et al. Deep exploration via randomized value functions. J. Mach. Learn. Res., 20(124):1–62, 2019. ",
+        "bbox": [
+            168,
+            42,
+            828,
+            915
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            171,
+            56,
+            828,
+            919
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "[63] Johannes Von Oswald, Seijin Kobayashi, Joao Sacramento, Alexander Meulemans, Christian Henning, and Benjamin F Grewe. Neural networks with late-phase weights. In International Conference on Learning Representations, 2021. URL https://openreview.net/forum? id=C0qJUx5dxFb. ",
+        "bbox": [
+            174,
+            90,
+            826,
+            148
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "[64] Felix Otto. The geometry of dissipative evolution equations: the porous medium equation. 2001. ",
+        "bbox": [
+            169,
+            155,
+            825,
+            184
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "[65] Yaniv Ovadia, Emily Fertig, Jie Ren, Zachary Nado, David Sculley, Sebastian Nowozin, Joshua Dillon, Balaji Lakshminarayanan, and Jasper Snoek. Can you trust your model’s uncertainty? evaluating predictive uncertainty under dataset shift. In Advances in Neural Information Processing Systems, pages 13991–14002, 2019. ",
+        "bbox": [
+            174,
+            193,
+            825,
+            248
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "[66] Emanuel Parzen. On estimation of a probability density function and mode. The annals of mathematical statistics, 33(3):1065–1076, 1962. ",
+        "bbox": [
+            173,
+            256,
+            823,
+            285
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "[67] Alexandre Rame and Matthieu Cord. Dice: Diversity in deep ensembles via conditional redundancy adversarial estimation. arXiv preprint arXiv:2101.05544, 2021. ",
+        "bbox": [
+            173,
+            292,
+            823,
+            321
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "[68] Geoffrey Roeder, Luke Metz, and Diederik P Kingma. On linear identifiability of learned representations. arXiv preprint arXiv:2007.00810, 2020. ",
+        "bbox": [
+            173,
+            329,
+            823,
+            359
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "[69] Jiaxin Shi, Shengyang Sun, and Jun Zhu. A spectral approach to gradient estimation for implicit distributions. In International Conference on Machine Learning, pages 4644–4653. PMLR, 2018. ",
+        "bbox": [
+            173,
+            366,
+            825,
+            409
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "[70] Radhey S Singh. Improvement on some known nonparametric uniformly consistent estimators of derivatives of a density. The Annals of Statistics, pages 394–399, 1977. ",
+        "bbox": [
+            173,
+            416,
+            823,
+            446
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "[71] Shengyang Sun, Guodong Zhang, Jiaxin Shi, and Roger Grosse. Functional variational bayesian neural networks. arXiv preprint arXiv:1903.05779, 2019. ",
+        "bbox": [
+            173,
+            454,
+            823,
+            483
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "[72] Jakub Swiatkowski, Kevin Roth, Bastiaan S Veeling, Linh Tran, Joshua V Dillon, Stephan Mandt, Jasper Snoek, Tim Salimans, Rodolphe Jenatton, and Sebastian Nowozin. The k-tied normal distribution: A compact parameterization of gaussian mean field posteriors in bayesian neural networks. arXiv preprint arXiv:2002.02655, 2020. ",
+        "bbox": [
+            174,
+            491,
+            826,
+            546
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "[73] Johannes von Oswald, Christian Henning, João Sacramento, and Benjamin F. Grewe. Continual learning with hypernetworks. In International Conference on Learning Representations, 2020. URL https://arxiv.org/abs/1906.00695. ",
+        "bbox": [
+            178,
+            555,
+            823,
+            598
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "[74] Maxime Wabartha, Audrey Durand, Vincent François-Lavet, and Joelle Pineau. Handling black swan events in deep learning with diversely extrapolated neural networks. In IJCAI, pages 2140–2147, 2020. ",
+        "bbox": [
+            176,
+            606,
+            823,
+            647
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "[75] Yifei Wang, Peng Chen, and Wuchen Li. Projected wasserstein gradient descent for highdimensional bayesian inference. arXiv preprint arXiv:2102.06350, 2021. ",
+        "bbox": [
+            174,
+            656,
+            823,
+            685
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "[76] Ziyu Wang, Tongzheng Ren, Jun Zhu, and Bo Zhang. Function space particle optimization for bayesian neural networks. arXiv preprint arXiv:1902.09754, 2019. ",
+        "bbox": [
+            173,
+            693,
+            825,
+            722
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "[77] Max Welling and Yee W Teh. Bayesian learning via stochastic gradient langevin dynamics. In Proceedings of the 28th international conference on machine learning (ICML-11), pages 681–688, 2011. ",
+        "bbox": [
+            176,
+            729,
+            825,
+            772
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "[78] Yeming Wen, Dustin Tran, and Jimmy Ba. Batchensemble: an alternative approach to efficient ensemble and lifelong learning. arXiv preprint arXiv:2002.06715, 2020. ",
+        "bbox": [
+            171,
+            780,
+            825,
+            809
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "[79] Florian Wenzel, Kevin Roth, Bastiaan S Veeling, Jakub Swiatkowski, Linh Tran, Stephan Mandt, ´ Jasper Snoek, Tim Salimans, Rodolphe Jenatton, and Sebastian Nowozin. How good is the bayes posterior in deep neural networks really? arXiv preprint arXiv:2002.02405, 2020. ",
+        "bbox": [
+            173,
+            818,
+            825,
+            861
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "[80] Florian Wenzel, Jasper Snoek, Dustin Tran, and Rodolphe Jenatton. Hyperparameter ensembles for robustness and uncertainty quantification. In Advances in Neural Information Processing Systems, 2020. ",
+        "bbox": [
+            174,
+            869,
+            825,
+            911
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "[81] Christopher KI Williams. Computation with infinite neural networks. Neural Computation, 10 (5):1203–1216, 1998.   \n[82] Andrew Gordon Wilson and Pavel Izmailov. Bayesian deep learning and a probabilistic perspective of generalization. arXiv preprint arXiv:2002.08791, 2020.   \n[83] Han Xiao, Kashif Rasul, and Roland Vollgraf. Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms. arXiv preprint arXiv:1708.07747, 2017.   \n[84] Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals. Understanding deep learning requires rethinking generalization. arXiv preprint arXiv:1611.03530, 2016.   \n[85] Ruqi Zhang, Chunyuan Li, Jianyi Zhang, Changyou Chen, and Andrew Gordon Wilson. Cyclical stochastic gradient mcmc for bayesian deep learning. arXiv preprint arXiv:1902.03932, 2019. ",
+        "bbox": [
+            173,
+            90,
+            828,
+            271
+        ],
+        "page_idx": 14
+    }
+]
\ No newline at end of file
diff --git a/parse/train/LAKplpLMbP8/LAKplpLMbP8_middle.json b/parse/train/LAKplpLMbP8/LAKplpLMbP8_middle.json
new file mode 100644
index 0000000000000000000000000000000000000000..a935f021b6d1534c6c6c7cd3c536886861250c0a
--- /dev/null
+++ b/parse/train/LAKplpLMbP8/LAKplpLMbP8_middle.json
@@ -0,0 +1,41100 @@
+{
+    "pdf_info": [
+        {
+            "preproc_blocks": [
+                {
+                    "type": "title",
+                    "bbox": [
+                        156,
+                        97,
+                        455,
+                        117
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                156,
+                                96,
+                                455,
+                                119
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        156,
+                                        96,
+                                        455,
+                                        119
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Repulsive Deep Ensembles are Bayesian",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        175,
+                        159,
+                        263,
+                        204
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                174,
+                                159,
+                                263,
+                                172
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        174,
+                                        159,
+                                        263,
+                                        172
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Francesco D’Angelo",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                192,
+                                169,
+                                245,
+                                182
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        192,
+                                        169,
+                                        245,
+                                        182
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ETH Zürich",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                177,
+                                180,
+                                260,
+                                193
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        177,
+                                        180,
+                                        260,
+                                        193
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Zürich, Switzerland",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                176,
+                                192,
+                                262,
+                                205
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        176,
+                                        192,
+                                        262,
+                                        205
+                                    ],
+                                    "score": 1.0,
+                                    "content": "dngfra@gmail.com",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 4.0
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        335,
+                        160,
+                        436,
+                        203
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                351,
+                                160,
+                                420,
+                                170
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        351,
+                                        160,
+                                        420,
+                                        170
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Vincent Fortuin",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                359,
+                                169,
+                                411,
+                                182
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        359,
+                                        169,
+                                        411,
+                                        182
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ETH Zürich",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                345,
+                                182,
+                                426,
+                                192
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        345,
+                                        182,
+                                        426,
+                                        192
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Zürich, Switzerland",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                335,
+                                193,
+                                436,
+                                203
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        335,
+                                        193,
+                                        436,
+                                        203
+                                    ],
+                                    "score": 1.0,
+                                    "content": "fortuin@inf.ethz.ch",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 5.0
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        283,
+                        232,
+                        328,
+                        244
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                282,
+                                232,
+                                330,
+                                245
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        282,
+                                        232,
+                                        330,
+                                        245
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Abstract",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        143,
+                        258,
+                        469,
+                        454
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                141,
+                                257,
+                                469,
+                                271
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        257,
+                                        469,
+                                        271
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Deep ensembles have recently gained popularity in the deep learning community",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                267,
+                                469,
+                                281
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        267,
+                                        469,
+                                        281
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for their conceptual simplicity and efficiency. However, maintaining functional",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                278,
+                                470,
+                                292
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        278,
+                                        470,
+                                        292
+                                    ],
+                                    "score": 1.0,
+                                    "content": "diversity between ensemble members that are independently trained with gradient",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                290,
+                                469,
+                                302
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        290,
+                                        469,
+                                        302
+                                    ],
+                                    "score": 1.0,
+                                    "content": "descent is challenging. This can lead to pathologies when adding more ensemble",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                302,
+                                469,
+                                313
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        302,
+                                        469,
+                                        313
+                                    ],
+                                    "score": 1.0,
+                                    "content": "members, such as a saturation of the ensemble performance, which converges to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                312,
+                                469,
+                                325
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        312,
+                                        469,
+                                        325
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the performance of a single model. Moreover, this does not only affect the quality",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                323,
+                                469,
+                                335
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        323,
+                                        469,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of its predictions, but even more so the uncertainty estimates of the ensemble, and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                334,
+                                469,
+                                346
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        334,
+                                        469,
+                                        346
+                                    ],
+                                    "score": 1.0,
+                                    "content": "thus its performance on out-of-distribution data. We hypothesize that this limitation",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                344,
+                                469,
+                                358
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        344,
+                                        469,
+                                        358
+                                    ],
+                                    "score": 1.0,
+                                    "content": "can be overcome by discouraging different ensemble members from collapsing to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                356,
+                                469,
+                                367
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        356,
+                                        469,
+                                        367
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the same function. To this end, we introduce a kernelized repulsive term in the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                366,
+                                470,
+                                379
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        366,
+                                        470,
+                                        379
+                                    ],
+                                    "score": 1.0,
+                                    "content": "update rule of the deep ensembles. We show that this simple modification not only",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                377,
+                                470,
+                                390
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        377,
+                                        470,
+                                        390
+                                    ],
+                                    "score": 1.0,
+                                    "content": "enforces and maintains diversity among the members but, even more importantly,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                388,
+                                470,
+                                401
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        388,
+                                        470,
+                                        401
+                                    ],
+                                    "score": 1.0,
+                                    "content": "transforms the maximum a posteriori inference into proper Bayesian inference.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                398,
+                                470,
+                                412
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        398,
+                                        470,
+                                        412
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Namely, we show that the training dynamics of our proposed repulsive ensembles",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                410,
+                                470,
+                                423
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        410,
+                                        470,
+                                        423
+                                    ],
+                                    "score": 1.0,
+                                    "content": "follow a Wasserstein gradient flow of the KL divergence to the true posterior.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                421,
+                                470,
+                                434
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        421,
+                                        470,
+                                        434
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We study repulsive terms in weight and function space and empirically compare",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                432,
+                                470,
+                                445
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        432,
+                                        470,
+                                        445
+                                    ],
+                                    "score": 1.0,
+                                    "content": "their performance to standard ensembles and Bayesian baselines on synthetic and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                443,
+                                254,
+                                455
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        443,
+                                        254,
+                                        455
+                                    ],
+                                    "score": 1.0,
+                                    "content": "real-world prediction tasks.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 18.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        475,
+                        190,
+                        488
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                473,
+                                192,
+                                490
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        473,
+                                        192,
+                                        490
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1 Introduction",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 28
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        500,
+                        505,
+                        621
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                500,
+                                505,
+                                513
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        500,
+                                        505,
+                                        513
+                                    ],
+                                    "score": 1.0,
+                                    "content": "There have been many recent advances on the theoretical properties of sampling algorithms for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                511,
+                                506,
+                                524
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        511,
+                                        506,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": "approximate Bayesian inference, which changed our interpretation and understanding of them.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                521,
+                                505,
+                                535
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        521,
+                                        505,
+                                        535
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Particularly worth mentioning is the work of Jordan et al. [38], who reinterpret Markov Chain Monte",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                532,
+                                505,
+                                547
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        532,
+                                        505,
+                                        547
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Carlo (MCMC) as a gradient flow of the KL divergence over the Wasserstein space of probability",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                543,
+                                506,
+                                557
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        543,
+                                        506,
+                                        557
+                                    ],
+                                    "score": 1.0,
+                                    "content": "measures. This new formulation allowed for a deeper understanding of approximate inference",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                554,
+                                505,
+                                568
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        554,
+                                        505,
+                                        568
+                                    ],
+                                    "score": 1.0,
+                                    "content": "methods but also inspired the inception of new and more efficient inference strategies. Following",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                565,
+                                505,
+                                578
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        566,
+                                        222,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": "this direction, Liu and Wang",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        222,
+                                        565,
+                                        240,
+                                        577
+                                    ],
+                                    "score": 0.4,
+                                    "content": "\\pmb { \\mathbb { B } } \\mathbf { \\mathbb { 1 } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        240,
+                                        566,
+                                        505,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": "recently proposed the Stein Variational Gradient Descent (SVGD)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                576,
+                                505,
+                                588
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        576,
+                                        505,
+                                        588
+                                    ],
+                                    "score": 1.0,
+                                    "content": "method to perform approximate Wasserstein gradient descent. Conceptually, this method, which",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                587,
+                                505,
+                                600
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        587,
+                                        505,
+                                        600
+                                    ],
+                                    "score": 1.0,
+                                    "content": "belongs to the family of particle-optimization variational inference (POVI), introduces a repulsive",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                598,
+                                505,
+                                612
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        598,
+                                        505,
+                                        612
+                                    ],
+                                    "score": 1.0,
+                                    "content": "force through a kernel acting in the parameter space to evolve a set of samples towards high-density",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                610,
+                                391,
+                                622
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        610,
+                                        391,
+                                        622
+                                    ],
+                                    "score": 1.0,
+                                    "content": "regions of the target distribution without collapsing to a point estimate.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 34
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        626,
+                        505,
+                        713
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                625,
+                                507,
+                                639
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        625,
+                                        507,
+                                        639
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Another method which has achieved great success recently are ensembles of neural networks (so-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                636,
+                                506,
+                                649
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        636,
+                                        430,
+                                        649
+                                    ],
+                                    "score": 1.0,
+                                    "content": "called deep ensembles), which work well both in terms of predictive performance",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        430,
+                                        636,
+                                        463,
+                                        648
+                                    ],
+                                    "score": 0.54,
+                                    "content": "\\pm 2 \\sqrt { 8 0 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        463,
+                                        636,
+                                        506,
+                                        649
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as well as",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                647,
+                                506,
+                                660
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        648,
+                                        196,
+                                        660
+                                    ],
+                                    "score": 1.0,
+                                    "content": "uncertainty estimation",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        197,
+                                        647,
+                                        214,
+                                        659
+                                    ],
+                                    "score": 0.62,
+                                    "content": "\\begin{array} { r l } {  { \\| 6 5 \\| } } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        215,
+                                        648,
+                                        506,
+                                        660
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and have also been proposed as a way to perform approximate inference",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                658,
+                                505,
+                                671
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        658,
+                                        505,
+                                        671
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in Bayesian neural networks [82, 36]. That being said, while they might allow for the averaging of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                669,
+                                506,
+                                681
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        669,
+                                        506,
+                                        681
+                                    ],
+                                    "score": 1.0,
+                                    "content": "predictions over several hypotheses, they do not offer any guarantees for the diversity between those",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                680,
+                                507,
+                                693
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        680,
+                                        507,
+                                        693
+                                    ],
+                                    "score": 1.0,
+                                    "content": "hypotheses nor do they provably converge to the true Bayesian posterior under any meaningful limit.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                691,
+                                506,
+                                703
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        691,
+                                        506,
+                                        703
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In this work, we show how the introduction of a repulsive term between the members in the ensemble,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                703,
+                                505,
+                                714
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        703,
+                                        505,
+                                        714
+                                    ],
+                                    "score": 1.0,
+                                    "content": "inspired by SVGD, not only naïvely guarantees the diversity among the members, avoiding their",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        }
+                    ],
+                    "index": 43.5
+                }
+            ],
+            "page_idx": 0,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        731,
+                        385,
+                        741
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                730,
+                                387,
+                                744
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        730,
+                                        387,
+                                        744
+                                    ],
+                                    "score": 1.0,
+                                    "content": "35th Conference on Neural Information Processing Systems (NeurIPS 2021).",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "title",
+                    "bbox": [
+                        156,
+                        97,
+                        455,
+                        117
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                156,
+                                96,
+                                455,
+                                119
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        156,
+                                        96,
+                                        455,
+                                        119
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Repulsive Deep Ensembles are Bayesian",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        175,
+                        159,
+                        263,
+                        204
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                174,
+                                159,
+                                263,
+                                172
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        174,
+                                        159,
+                                        263,
+                                        172
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Francesco D’Angelo",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                192,
+                                169,
+                                245,
+                                182
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        192,
+                                        169,
+                                        245,
+                                        182
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ETH Zürich",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                177,
+                                180,
+                                260,
+                                193
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        177,
+                                        180,
+                                        260,
+                                        193
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Zürich, Switzerland",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                176,
+                                192,
+                                262,
+                                205
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        176,
+                                        192,
+                                        262,
+                                        205
+                                    ],
+                                    "score": 1.0,
+                                    "content": "dngfra@gmail.com",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 4.0,
+                    "bbox_fs": [
+                        174,
+                        159,
+                        263,
+                        205
+                    ]
+                },
+                {
+                    "type": "list",
+                    "bbox": [
+                        335,
+                        160,
+                        436,
+                        203
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                351,
+                                160,
+                                420,
+                                170
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        351,
+                                        160,
+                                        420,
+                                        170
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Vincent Fortuin",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                359,
+                                169,
+                                411,
+                                182
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        359,
+                                        169,
+                                        411,
+                                        182
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ETH Zürich",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                345,
+                                182,
+                                426,
+                                192
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        345,
+                                        182,
+                                        426,
+                                        192
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Zürich, Switzerland",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                335,
+                                193,
+                                436,
+                                203
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        335,
+                                        193,
+                                        436,
+                                        203
+                                    ],
+                                    "score": 1.0,
+                                    "content": "fortuin@inf.ethz.ch",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8,
+                            "is_list_start_line": true
+                        }
+                    ],
+                    "index": 5.0,
+                    "bbox_fs": [
+                        335,
+                        160,
+                        436,
+                        203
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        283,
+                        232,
+                        328,
+                        244
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                282,
+                                232,
+                                330,
+                                245
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        282,
+                                        232,
+                                        330,
+                                        245
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Abstract",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        143,
+                        258,
+                        469,
+                        454
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                141,
+                                257,
+                                469,
+                                271
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        257,
+                                        469,
+                                        271
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Deep ensembles have recently gained popularity in the deep learning community",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                267,
+                                469,
+                                281
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        267,
+                                        469,
+                                        281
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for their conceptual simplicity and efficiency. However, maintaining functional",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                278,
+                                470,
+                                292
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        278,
+                                        470,
+                                        292
+                                    ],
+                                    "score": 1.0,
+                                    "content": "diversity between ensemble members that are independently trained with gradient",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                290,
+                                469,
+                                302
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        290,
+                                        469,
+                                        302
+                                    ],
+                                    "score": 1.0,
+                                    "content": "descent is challenging. This can lead to pathologies when adding more ensemble",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                302,
+                                469,
+                                313
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        302,
+                                        469,
+                                        313
+                                    ],
+                                    "score": 1.0,
+                                    "content": "members, such as a saturation of the ensemble performance, which converges to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                312,
+                                469,
+                                325
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        312,
+                                        469,
+                                        325
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the performance of a single model. Moreover, this does not only affect the quality",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                323,
+                                469,
+                                335
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        323,
+                                        469,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of its predictions, but even more so the uncertainty estimates of the ensemble, and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                334,
+                                469,
+                                346
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        334,
+                                        469,
+                                        346
+                                    ],
+                                    "score": 1.0,
+                                    "content": "thus its performance on out-of-distribution data. We hypothesize that this limitation",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                344,
+                                469,
+                                358
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        344,
+                                        469,
+                                        358
+                                    ],
+                                    "score": 1.0,
+                                    "content": "can be overcome by discouraging different ensemble members from collapsing to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                356,
+                                469,
+                                367
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        356,
+                                        469,
+                                        367
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the same function. To this end, we introduce a kernelized repulsive term in the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                366,
+                                470,
+                                379
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        366,
+                                        470,
+                                        379
+                                    ],
+                                    "score": 1.0,
+                                    "content": "update rule of the deep ensembles. We show that this simple modification not only",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                377,
+                                470,
+                                390
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        377,
+                                        470,
+                                        390
+                                    ],
+                                    "score": 1.0,
+                                    "content": "enforces and maintains diversity among the members but, even more importantly,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                388,
+                                470,
+                                401
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        388,
+                                        470,
+                                        401
+                                    ],
+                                    "score": 1.0,
+                                    "content": "transforms the maximum a posteriori inference into proper Bayesian inference.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                398,
+                                470,
+                                412
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        398,
+                                        470,
+                                        412
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Namely, we show that the training dynamics of our proposed repulsive ensembles",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                410,
+                                470,
+                                423
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        410,
+                                        470,
+                                        423
+                                    ],
+                                    "score": 1.0,
+                                    "content": "follow a Wasserstein gradient flow of the KL divergence to the true posterior.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                421,
+                                470,
+                                434
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        421,
+                                        470,
+                                        434
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We study repulsive terms in weight and function space and empirically compare",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                432,
+                                470,
+                                445
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        432,
+                                        470,
+                                        445
+                                    ],
+                                    "score": 1.0,
+                                    "content": "their performance to standard ensembles and Bayesian baselines on synthetic and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                443,
+                                254,
+                                455
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        443,
+                                        254,
+                                        455
+                                    ],
+                                    "score": 1.0,
+                                    "content": "real-world prediction tasks.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 18.5,
+                    "bbox_fs": [
+                        141,
+                        257,
+                        470,
+                        455
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        475,
+                        190,
+                        488
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                473,
+                                192,
+                                490
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        473,
+                                        192,
+                                        490
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1 Introduction",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 28
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        500,
+                        505,
+                        621
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                500,
+                                505,
+                                513
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        500,
+                                        505,
+                                        513
+                                    ],
+                                    "score": 1.0,
+                                    "content": "There have been many recent advances on the theoretical properties of sampling algorithms for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                511,
+                                506,
+                                524
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        511,
+                                        506,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": "approximate Bayesian inference, which changed our interpretation and understanding of them.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                521,
+                                505,
+                                535
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        521,
+                                        505,
+                                        535
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Particularly worth mentioning is the work of Jordan et al. [38], who reinterpret Markov Chain Monte",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                532,
+                                505,
+                                547
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        532,
+                                        505,
+                                        547
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Carlo (MCMC) as a gradient flow of the KL divergence over the Wasserstein space of probability",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                543,
+                                506,
+                                557
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        543,
+                                        506,
+                                        557
+                                    ],
+                                    "score": 1.0,
+                                    "content": "measures. This new formulation allowed for a deeper understanding of approximate inference",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                554,
+                                505,
+                                568
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        554,
+                                        505,
+                                        568
+                                    ],
+                                    "score": 1.0,
+                                    "content": "methods but also inspired the inception of new and more efficient inference strategies. Following",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                565,
+                                505,
+                                578
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        566,
+                                        222,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": "this direction, Liu and Wang",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        222,
+                                        565,
+                                        240,
+                                        577
+                                    ],
+                                    "score": 0.4,
+                                    "content": "\\pmb { \\mathbb { B } } \\mathbf { \\mathbb { 1 } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        240,
+                                        566,
+                                        505,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": "recently proposed the Stein Variational Gradient Descent (SVGD)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                576,
+                                505,
+                                588
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        576,
+                                        505,
+                                        588
+                                    ],
+                                    "score": 1.0,
+                                    "content": "method to perform approximate Wasserstein gradient descent. Conceptually, this method, which",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                587,
+                                505,
+                                600
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        587,
+                                        505,
+                                        600
+                                    ],
+                                    "score": 1.0,
+                                    "content": "belongs to the family of particle-optimization variational inference (POVI), introduces a repulsive",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                598,
+                                505,
+                                612
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        598,
+                                        505,
+                                        612
+                                    ],
+                                    "score": 1.0,
+                                    "content": "force through a kernel acting in the parameter space to evolve a set of samples towards high-density",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                610,
+                                391,
+                                622
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        610,
+                                        391,
+                                        622
+                                    ],
+                                    "score": 1.0,
+                                    "content": "regions of the target distribution without collapsing to a point estimate.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 34,
+                    "bbox_fs": [
+                        105,
+                        500,
+                        506,
+                        622
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        626,
+                        505,
+                        713
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                625,
+                                507,
+                                639
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        625,
+                                        507,
+                                        639
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Another method which has achieved great success recently are ensembles of neural networks (so-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                636,
+                                506,
+                                649
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        636,
+                                        430,
+                                        649
+                                    ],
+                                    "score": 1.0,
+                                    "content": "called deep ensembles), which work well both in terms of predictive performance",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        430,
+                                        636,
+                                        463,
+                                        648
+                                    ],
+                                    "score": 0.54,
+                                    "content": "\\pm 2 \\sqrt { 8 0 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        463,
+                                        636,
+                                        506,
+                                        649
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as well as",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                647,
+                                506,
+                                660
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        648,
+                                        196,
+                                        660
+                                    ],
+                                    "score": 1.0,
+                                    "content": "uncertainty estimation",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        197,
+                                        647,
+                                        214,
+                                        659
+                                    ],
+                                    "score": 0.62,
+                                    "content": "\\begin{array} { r l } {  { \\| 6 5 \\| } } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        215,
+                                        648,
+                                        506,
+                                        660
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and have also been proposed as a way to perform approximate inference",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                658,
+                                505,
+                                671
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        658,
+                                        505,
+                                        671
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in Bayesian neural networks [82, 36]. That being said, while they might allow for the averaging of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                669,
+                                506,
+                                681
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        669,
+                                        506,
+                                        681
+                                    ],
+                                    "score": 1.0,
+                                    "content": "predictions over several hypotheses, they do not offer any guarantees for the diversity between those",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                680,
+                                507,
+                                693
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        680,
+                                        507,
+                                        693
+                                    ],
+                                    "score": 1.0,
+                                    "content": "hypotheses nor do they provably converge to the true Bayesian posterior under any meaningful limit.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                691,
+                                506,
+                                703
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        691,
+                                        506,
+                                        703
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In this work, we show how the introduction of a repulsive term between the members in the ensemble,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                703,
+                                505,
+                                714
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        703,
+                                        505,
+                                        714
+                                    ],
+                                    "score": 1.0,
+                                    "content": "inspired by SVGD, not only naïvely guarantees the diversity among the members, avoiding their",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                259,
+                                505,
+                                272
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        259,
+                                        505,
+                                        272
+                                    ],
+                                    "score": 1.0,
+                                    "content": "collapse in parameter space, but also allows for a reformulation of the method as a gradient flow of",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                270,
+                                505,
+                                284
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        270,
+                                        505,
+                                        284
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the KL divergence in the Wasserstein space of distributions. It thus allows to endow deep ensembles",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                281,
+                                345,
+                                294
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        281,
+                                        345,
+                                        294
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with convergence guarantees to the true Bayesian posterior.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 43.5,
+                    "bbox_fs": [
+                        105,
+                        625,
+                        507,
+                        714
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "image",
+                    "bbox": [
+                        120,
+                        68,
+                        493,
+                        199
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                120,
+                                68,
+                                493,
+                                199
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        120,
+                                        68,
+                                        493,
+                                        199
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                120,
+                                                68,
+                                                493,
+                                                199
+                                            ],
+                                            "score": 0.971,
+                                            "type": "image",
+                                            "image_path": "c87b35667fe31cb24e44c323fe8bffeb4df13996d7df41a00bfd504161843062.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        120,
+                                        68,
+                                        493,
+                                        111.66666666666666
+                                    ],
+                                    "spans": [],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        120,
+                                        111.66666666666666,
+                                        493,
+                                        155.33333333333331
+                                    ],
+                                    "spans": [],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        120,
+                                        155.33333333333331,
+                                        493,
+                                        198.99999999999997
+                                    ],
+                                    "spans": [],
+                                    "index": 2
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                106,
+                                203,
+                                505,
+                                236
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        203,
+                                        505,
+                                        216
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                203,
+                                                505,
+                                                216
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 1: BNN 1D regression. The function-space methods (SVGD and WGD) approach the HMC",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        214,
+                                        505,
+                                        228
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                214,
+                                                505,
+                                                228
+                                            ],
+                                            "score": 1.0,
+                                            "content": "posterior more closely, while the standard deep ensembles and weight-space methods fail to properly",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        225,
+                                        371,
+                                        239
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                225,
+                                                371,
+                                                239
+                                            ],
+                                            "score": 1.0,
+                                            "content": "account for the uncertainty, especially the in-between uncertainty.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 5
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 2.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        259,
+                        503,
+                        293
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                259,
+                                505,
+                                272
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        259,
+                                        505,
+                                        272
+                                    ],
+                                    "score": 1.0,
+                                    "content": "collapse in parameter space, but also allows for a reformulation of the method as a gradient flow of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                270,
+                                505,
+                                284
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        270,
+                                        505,
+                                        284
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the KL divergence in the Wasserstein space of distributions. It thus allows to endow deep ensembles",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                281,
+                                345,
+                                294
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        281,
+                                        345,
+                                        294
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with convergence guarantees to the true Bayesian posterior.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        297,
+                        505,
+                        418
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                298,
+                                506,
+                                311
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        298,
+                                        506,
+                                        311
+                                    ],
+                                    "score": 1.0,
+                                    "content": "An additional problem is that BNN inference in weight space can lead to degenerate solutions, due to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                309,
+                                505,
+                                321
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        309,
+                                        505,
+                                        321
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the overparametrization of these models. That is, several samples could have very different weights",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                320,
+                                506,
+                                332
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        320,
+                                        506,
+                                        332
+                                    ],
+                                    "score": 1.0,
+                                    "content": "but map to the same function, thus giving a false sense of diversity in the ensemble. This property, that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                330,
+                                506,
+                                343
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        330,
+                                        381,
+                                        343
+                                    ],
+                                    "score": 1.0,
+                                    "content": "we will refer to as non-identifiability of neural networks (see Appendix",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        381,
+                                        330,
+                                        394,
+                                        343
+                                    ],
+                                    "score": 0.42,
+                                    "content": "\\boxed { \\mathrm { A } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        394,
+                                        330,
+                                        506,
+                                        343
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", can lead to redundancies in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                341,
+                                505,
+                                354
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        341,
+                                        505,
+                                        354
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the posterior distribution. It implies that methods like MCMC sampling, deep ensembles, and SVGD",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                353,
+                                506,
+                                365
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        353,
+                                        506,
+                                        365
+                                    ],
+                                    "score": 1.0,
+                                    "content": "waste computation in local modes that account for equivalent functions. Predictive distributions",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                363,
+                                506,
+                                376
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        363,
+                                        506,
+                                        376
+                                    ],
+                                    "score": 1.0,
+                                    "content": "approximated using samples from these modes do not improve over a simple point estimate and lead",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                374,
+                                506,
+                                386
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        374,
+                                        371,
+                                        386
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to a poor uncertainty estimation. Following this idea, Wang et al.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        371,
+                                        374,
+                                        389,
+                                        385
+                                    ],
+                                    "score": 0.79,
+                                    "content": "\\mathbb { \\left[ \\left] \\right. \\right]} 2 ",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        389,
+                                        374,
+                                        506,
+                                        386
+                                    ],
+                                    "score": 1.0,
+                                    "content": "introduced a new method to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                385,
+                                505,
+                                397
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        385,
+                                        505,
+                                        397
+                                    ],
+                                    "score": 1.0,
+                                    "content": "extend POVI methods to function space, overcoming this limitation. Here, we also study an update",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                396,
+                                505,
+                                409
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        396,
+                                        505,
+                                        409
+                                    ],
+                                    "score": 1.0,
+                                    "content": "rule that allows for an approximation of the gradient flow of the KL divergence in function space in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                407,
+                                246,
+                                419
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        407,
+                                        246,
+                                        419
+                                    ],
+                                    "score": 1.0,
+                                    "content": "our proposed repulsive ensembles.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        423,
+                        258,
+                        435
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                422,
+                                259,
+                                436
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        422,
+                                        259,
+                                        436
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We make the following contributions:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 20
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        133,
+                        444,
+                        505,
+                        559
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                132,
+                                443,
+                                505,
+                                457
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        132,
+                                        443,
+                                        505,
+                                        457
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• We derive several different repulsion terms that can be added as regularizers to the gradient",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                456,
+                                469,
+                                468
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        456,
+                                        469,
+                                        468
+                                    ],
+                                    "score": 1.0,
+                                    "content": "updates of deep ensembles to endow them with Bayesian convergence properties.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                132,
+                                470,
+                                505,
+                                484
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        132,
+                                        470,
+                                        505,
+                                        484
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• We show that these terms approximate Wasserstein gradient flows of the KL divergence and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                483,
+                                356,
+                                495
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        483,
+                                        356,
+                                        495
+                                    ],
+                                    "score": 1.0,
+                                    "content": "can be used both in weight space and function space.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                132,
+                                497,
+                                505,
+                                511
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        132,
+                                        497,
+                                        505,
+                                        511
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• We compare these proposed methods theoretically to standard deep ensembles and SVGD",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                509,
+                                303,
+                                522
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        509,
+                                        303,
+                                        522
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and highlight their different guarantees.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                132,
+                                525,
+                                505,
+                                538
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        132,
+                                        525,
+                                        505,
+                                        538
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• We assess all these methods on synthetic and real-world deep learning tasks and show",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                537,
+                                505,
+                                549
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        537,
+                                        505,
+                                        549
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that our proposed repulsive ensembles can achieve competitive performance and improved",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                548,
+                                235,
+                                560
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        548,
+                                        235,
+                                        560
+                                    ],
+                                    "score": 1.0,
+                                    "content": "uncertainty estimation.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 25
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        580,
+                        262,
+                        594
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                578,
+                                263,
+                                597
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        578,
+                                        263,
+                                        597
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2 Repulsive Deep Ensembles",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 30
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        605,
+                        506,
+                        694
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                605,
+                                507,
+                                618
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        605,
+                                        399,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In supervised deep learning, we typically consider a likelihood function",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        400,
+                                        606,
+                                        455,
+                                        618
+                                    ],
+                                    "score": 0.92,
+                                    "content": "p ( \\pmb { y } | f ( \\pmb { x } ; \\mathbf { w } ) )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        456,
+                                        605,
+                                        507,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(e.g., Gaus-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                617,
+                                505,
+                                629
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        617,
+                                        470,
+                                        629
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sian for regression or Categorical for classification) parameterized by a neural network",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        471,
+                                        617,
+                                        505,
+                                        629
+                                    ],
+                                    "score": 0.93,
+                                    "content": "f ( \\pmb { x } ; \\mathbf { w } )",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                626,
+                                508,
+                                642
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        626,
+                                        184,
+                                        642
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and training data",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        627,
+                                        270,
+                                        640
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\textit { D } = \\{ ( \\boldsymbol { \\mathbf { { x } } } _ { i } , \\boldsymbol { \\mathbf { { y } } } _ { i } ) \\} _ { i = 1 } ^ { n }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        270,
+                                        626,
+                                        296,
+                                        642
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        628,
+                                        333,
+                                        638
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\textbf { \\textit { x } } \\in \\textbf { \\textit { X } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        334,
+                                        626,
+                                        356,
+                                        642
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        356,
+                                        628,
+                                        392,
+                                        639
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\textbf { \\textit { y } } \\in \\textbf { \\textit { y } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        392,
+                                        626,
+                                        508,
+                                        642
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". In Bayesian neural net-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                637,
+                                506,
+                                651
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        637,
+                                        506,
+                                        651
+                                    ],
+                                    "score": 1.0,
+                                    "content": "works (BNNs), we are interested in the posterior distribution of all likely networks given by",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                649,
+                                507,
+                                663
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        649,
+                                        266,
+                                        662
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\begin{array} { r } { p ( \\mathbf { w } | \\mathcal { D } ) \\propto \\prod _ { i = 1 } ^ { n } p ( \\pmb { y } _ { i } | f ( \\pmb { x } _ { i } ; \\mathbf { w } ) ) p ( \\mathbf { w } ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        266,
+                                        649,
+                                        299,
+                                        663
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        299,
+                                        649,
+                                        321,
+                                        661
+                                    ],
+                                    "score": 0.91,
+                                    "content": "p ( \\mathbf { w } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        322,
+                                        649,
+                                        507,
+                                        663
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the prior distribution over weights. Cru-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                660,
+                                506,
+                                673
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        660,
+                                        303,
+                                        673
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cially, when making a prediction on a test point",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        662,
+                                        315,
+                                        671
+                                    ],
+                                    "score": 0.86,
+                                    "content": "\\mathbf { \\boldsymbol { x } } ^ { * }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        316,
+                                        660,
+                                        506,
+                                        673
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", in the Bayesian approach we do not only use",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                671,
+                                505,
+                                684
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        671,
+                                        183,
+                                        684
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a single parameter",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        183,
+                                        672,
+                                        193,
+                                        681
+                                    ],
+                                    "score": 0.76,
+                                    "content": "\\widehat { \\bf w }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        194,
+                                        671,
+                                        236,
+                                        684
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to predict",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        236,
+                                        671,
+                                        298,
+                                        683
+                                    ],
+                                    "score": 0.93,
+                                    "content": "{ \\pmb y } ^ { * } = f ( { \\pmb x } ^ { * } ; \\widehat { \\mathbf { w } } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        299,
+                                        671,
+                                        505,
+                                        684
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", but we marginalize over the whole posterior, thus",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                682,
+                                333,
+                                695
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        682,
+                                        333,
+                                        695
+                                    ],
+                                    "score": 1.0,
+                                    "content": "taking all possible explanations of the data into account:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        }
+                    ],
+                    "index": 34.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        210,
+                        700,
+                        400,
+                        726
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                210,
+                                700,
+                                400,
+                                726
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        210,
+                                        700,
+                                        400,
+                                        726
+                                    ],
+                                    "score": 0.94,
+                                    "content": "p ( \\pmb { y } ^ { * } | \\pmb { x } ^ { * } , \\mathcal { D } ) = \\int p ( \\pmb { y } ^ { * } | f ( \\pmb { x } ^ { * } ; \\mathbf { w } ) ) p ( \\mathbf { w } | \\mathcal { D } ) \\mathrm { d } \\mathbf { w }",
+                                    "type": "interline_equation",
+                                    "image_path": "ea58bf85c2893e1394390263ae7f97e3c6d3270c2715a883b91057d7c53c61ba.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 39,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                210,
+                                700,
+                                400,
+                                726
+                            ],
+                            "spans": [],
+                            "index": 39
+                        }
+                    ]
+                }
+            ],
+            "page_idx": 1,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        741,
+                        309,
+                        750
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                301,
+                                740,
+                                310,
+                                753
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        301,
+                                        740,
+                                        310,
+                                        753
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "image",
+                    "bbox": [
+                        120,
+                        68,
+                        493,
+                        199
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                120,
+                                68,
+                                493,
+                                199
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        120,
+                                        68,
+                                        493,
+                                        199
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                120,
+                                                68,
+                                                493,
+                                                199
+                                            ],
+                                            "score": 0.971,
+                                            "type": "image",
+                                            "image_path": "c87b35667fe31cb24e44c323fe8bffeb4df13996d7df41a00bfd504161843062.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        120,
+                                        68,
+                                        493,
+                                        111.66666666666666
+                                    ],
+                                    "spans": [],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        120,
+                                        111.66666666666666,
+                                        493,
+                                        155.33333333333331
+                                    ],
+                                    "spans": [],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        120,
+                                        155.33333333333331,
+                                        493,
+                                        198.99999999999997
+                                    ],
+                                    "spans": [],
+                                    "index": 2
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                106,
+                                203,
+                                505,
+                                236
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        203,
+                                        505,
+                                        216
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                203,
+                                                505,
+                                                216
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 1: BNN 1D regression. The function-space methods (SVGD and WGD) approach the HMC",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        214,
+                                        505,
+                                        228
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                214,
+                                                505,
+                                                228
+                                            ],
+                                            "score": 1.0,
+                                            "content": "posterior more closely, while the standard deep ensembles and weight-space methods fail to properly",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        225,
+                                        371,
+                                        239
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                225,
+                                                371,
+                                                239
+                                            ],
+                                            "score": 1.0,
+                                            "content": "account for the uncertainty, especially the in-between uncertainty.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 5
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 2.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        259,
+                        503,
+                        293
+                    ],
+                    "lines": [],
+                    "index": 7,
+                    "bbox_fs": [
+                        105,
+                        259,
+                        505,
+                        294
+                    ],
+                    "lines_deleted": true
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        297,
+                        505,
+                        418
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                298,
+                                506,
+                                311
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        298,
+                                        506,
+                                        311
+                                    ],
+                                    "score": 1.0,
+                                    "content": "An additional problem is that BNN inference in weight space can lead to degenerate solutions, due to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                309,
+                                505,
+                                321
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        309,
+                                        505,
+                                        321
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the overparametrization of these models. That is, several samples could have very different weights",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                320,
+                                506,
+                                332
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        320,
+                                        506,
+                                        332
+                                    ],
+                                    "score": 1.0,
+                                    "content": "but map to the same function, thus giving a false sense of diversity in the ensemble. This property, that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                330,
+                                506,
+                                343
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        330,
+                                        381,
+                                        343
+                                    ],
+                                    "score": 1.0,
+                                    "content": "we will refer to as non-identifiability of neural networks (see Appendix",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        381,
+                                        330,
+                                        394,
+                                        343
+                                    ],
+                                    "score": 0.42,
+                                    "content": "\\boxed { \\mathrm { A } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        394,
+                                        330,
+                                        506,
+                                        343
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", can lead to redundancies in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                341,
+                                505,
+                                354
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        341,
+                                        505,
+                                        354
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the posterior distribution. It implies that methods like MCMC sampling, deep ensembles, and SVGD",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                353,
+                                506,
+                                365
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        353,
+                                        506,
+                                        365
+                                    ],
+                                    "score": 1.0,
+                                    "content": "waste computation in local modes that account for equivalent functions. Predictive distributions",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                363,
+                                506,
+                                376
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        363,
+                                        506,
+                                        376
+                                    ],
+                                    "score": 1.0,
+                                    "content": "approximated using samples from these modes do not improve over a simple point estimate and lead",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                374,
+                                506,
+                                386
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        374,
+                                        371,
+                                        386
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to a poor uncertainty estimation. Following this idea, Wang et al.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        371,
+                                        374,
+                                        389,
+                                        385
+                                    ],
+                                    "score": 0.79,
+                                    "content": "\\mathbb { \\left[ \\left] \\right. \\right]} 2 ",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        389,
+                                        374,
+                                        506,
+                                        386
+                                    ],
+                                    "score": 1.0,
+                                    "content": "introduced a new method to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                385,
+                                505,
+                                397
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        385,
+                                        505,
+                                        397
+                                    ],
+                                    "score": 1.0,
+                                    "content": "extend POVI methods to function space, overcoming this limitation. Here, we also study an update",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                396,
+                                505,
+                                409
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        396,
+                                        505,
+                                        409
+                                    ],
+                                    "score": 1.0,
+                                    "content": "rule that allows for an approximation of the gradient flow of the KL divergence in function space in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                407,
+                                246,
+                                419
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        407,
+                                        246,
+                                        419
+                                    ],
+                                    "score": 1.0,
+                                    "content": "our proposed repulsive ensembles.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 14,
+                    "bbox_fs": [
+                        105,
+                        298,
+                        506,
+                        419
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        423,
+                        258,
+                        435
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                422,
+                                259,
+                                436
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        422,
+                                        259,
+                                        436
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We make the following contributions:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 20,
+                    "bbox_fs": [
+                        106,
+                        422,
+                        259,
+                        436
+                    ]
+                },
+                {
+                    "type": "list",
+                    "bbox": [
+                        133,
+                        444,
+                        505,
+                        559
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                132,
+                                443,
+                                505,
+                                457
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        132,
+                                        443,
+                                        505,
+                                        457
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• We derive several different repulsion terms that can be added as regularizers to the gradient",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                456,
+                                469,
+                                468
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        456,
+                                        469,
+                                        468
+                                    ],
+                                    "score": 1.0,
+                                    "content": "updates of deep ensembles to endow them with Bayesian convergence properties.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                132,
+                                470,
+                                505,
+                                484
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        132,
+                                        470,
+                                        505,
+                                        484
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• We show that these terms approximate Wasserstein gradient flows of the KL divergence and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                483,
+                                356,
+                                495
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        483,
+                                        356,
+                                        495
+                                    ],
+                                    "score": 1.0,
+                                    "content": "can be used both in weight space and function space.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                132,
+                                497,
+                                505,
+                                511
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        132,
+                                        497,
+                                        505,
+                                        511
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• We compare these proposed methods theoretically to standard deep ensembles and SVGD",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                509,
+                                303,
+                                522
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        509,
+                                        303,
+                                        522
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and highlight their different guarantees.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                132,
+                                525,
+                                505,
+                                538
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        132,
+                                        525,
+                                        505,
+                                        538
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• We assess all these methods on synthetic and real-world deep learning tasks and show",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                537,
+                                505,
+                                549
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        537,
+                                        505,
+                                        549
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that our proposed repulsive ensembles can achieve competitive performance and improved",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                548,
+                                235,
+                                560
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        548,
+                                        235,
+                                        560
+                                    ],
+                                    "score": 1.0,
+                                    "content": "uncertainty estimation.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29,
+                            "is_list_end_line": true
+                        }
+                    ],
+                    "index": 25,
+                    "bbox_fs": [
+                        132,
+                        443,
+                        505,
+                        560
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        580,
+                        262,
+                        594
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                578,
+                                263,
+                                597
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        578,
+                                        263,
+                                        597
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2 Repulsive Deep Ensembles",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 30
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        605,
+                        506,
+                        694
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                605,
+                                507,
+                                618
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        605,
+                                        399,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In supervised deep learning, we typically consider a likelihood function",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        400,
+                                        606,
+                                        455,
+                                        618
+                                    ],
+                                    "score": 0.92,
+                                    "content": "p ( \\pmb { y } | f ( \\pmb { x } ; \\mathbf { w } ) )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        456,
+                                        605,
+                                        507,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(e.g., Gaus-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                617,
+                                505,
+                                629
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        617,
+                                        470,
+                                        629
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sian for regression or Categorical for classification) parameterized by a neural network",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        471,
+                                        617,
+                                        505,
+                                        629
+                                    ],
+                                    "score": 0.93,
+                                    "content": "f ( \\pmb { x } ; \\mathbf { w } )",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                626,
+                                508,
+                                642
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        626,
+                                        184,
+                                        642
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and training data",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        627,
+                                        270,
+                                        640
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\textit { D } = \\{ ( \\boldsymbol { \\mathbf { { x } } } _ { i } , \\boldsymbol { \\mathbf { { y } } } _ { i } ) \\} _ { i = 1 } ^ { n }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        270,
+                                        626,
+                                        296,
+                                        642
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        628,
+                                        333,
+                                        638
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\textbf { \\textit { x } } \\in \\textbf { \\textit { X } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        334,
+                                        626,
+                                        356,
+                                        642
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        356,
+                                        628,
+                                        392,
+                                        639
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\textbf { \\textit { y } } \\in \\textbf { \\textit { y } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        392,
+                                        626,
+                                        508,
+                                        642
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". In Bayesian neural net-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                637,
+                                506,
+                                651
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        637,
+                                        506,
+                                        651
+                                    ],
+                                    "score": 1.0,
+                                    "content": "works (BNNs), we are interested in the posterior distribution of all likely networks given by",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                649,
+                                507,
+                                663
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        649,
+                                        266,
+                                        662
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\begin{array} { r } { p ( \\mathbf { w } | \\mathcal { D } ) \\propto \\prod _ { i = 1 } ^ { n } p ( \\pmb { y } _ { i } | f ( \\pmb { x } _ { i } ; \\mathbf { w } ) ) p ( \\mathbf { w } ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        266,
+                                        649,
+                                        299,
+                                        663
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        299,
+                                        649,
+                                        321,
+                                        661
+                                    ],
+                                    "score": 0.91,
+                                    "content": "p ( \\mathbf { w } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        322,
+                                        649,
+                                        507,
+                                        663
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the prior distribution over weights. Cru-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                660,
+                                506,
+                                673
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        660,
+                                        303,
+                                        673
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cially, when making a prediction on a test point",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        662,
+                                        315,
+                                        671
+                                    ],
+                                    "score": 0.86,
+                                    "content": "\\mathbf { \\boldsymbol { x } } ^ { * }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        316,
+                                        660,
+                                        506,
+                                        673
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", in the Bayesian approach we do not only use",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                671,
+                                505,
+                                684
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        671,
+                                        183,
+                                        684
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a single parameter",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        183,
+                                        672,
+                                        193,
+                                        681
+                                    ],
+                                    "score": 0.76,
+                                    "content": "\\widehat { \\bf w }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        194,
+                                        671,
+                                        236,
+                                        684
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to predict",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        236,
+                                        671,
+                                        298,
+                                        683
+                                    ],
+                                    "score": 0.93,
+                                    "content": "{ \\pmb y } ^ { * } = f ( { \\pmb x } ^ { * } ; \\widehat { \\mathbf { w } } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        299,
+                                        671,
+                                        505,
+                                        684
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", but we marginalize over the whole posterior, thus",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                682,
+                                333,
+                                695
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        682,
+                                        333,
+                                        695
+                                    ],
+                                    "score": 1.0,
+                                    "content": "taking all possible explanations of the data into account:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        }
+                    ],
+                    "index": 34.5,
+                    "bbox_fs": [
+                        104,
+                        605,
+                        508,
+                        695
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        210,
+                        700,
+                        400,
+                        726
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                210,
+                                700,
+                                400,
+                                726
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        210,
+                                        700,
+                                        400,
+                                        726
+                                    ],
+                                    "score": 0.94,
+                                    "content": "p ( \\pmb { y } ^ { * } | \\pmb { x } ^ { * } , \\mathcal { D } ) = \\int p ( \\pmb { y } ^ { * } | f ( \\pmb { x } ^ { * } ; \\mathbf { w } ) ) p ( \\mathbf { w } | \\mathcal { D } ) \\mathrm { d } \\mathbf { w }",
+                                    "type": "interline_equation",
+                                    "image_path": "ea58bf85c2893e1394390263ae7f97e3c6d3270c2715a883b91057d7c53c61ba.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 39,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                210,
+                                700,
+                                400,
+                                726
+                            ],
+                            "spans": [],
+                            "index": 39
+                        }
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        72,
+                        506,
+                        139
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                71,
+                                506,
+                                87
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        71,
+                                        506,
+                                        87
+                                    ],
+                                    "score": 1.0,
+                                    "content": "While approximating the posterior of Bayesian neural networks (or sampling from it) is a challenging",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                83,
+                                506,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        83,
+                                        506,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "task, performing maximum a posteriori (MAP) estimation, which corresponds to finding the mode of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                95,
+                                506,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        95,
+                                        506,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the posterior, is usually simple. Ensembles of neural networks use the non-convexity of the MAP",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                105,
+                                507,
+                                118
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        105,
+                                        293,
+                                        118
+                                    ],
+                                    "score": 1.0,
+                                    "content": "optimization problem to create a collection of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        294,
+                                        106,
+                                        304,
+                                        115
+                                    ],
+                                    "score": 0.83,
+                                    "content": "K",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        105,
+                                        507,
+                                        118
+                                    ],
+                                    "score": 1.0,
+                                    "content": "independent—and possibly different— solutions.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                114,
+                                507,
+                                131
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        114,
+                                        158,
+                                        131
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Considering",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        159,
+                                        118,
+                                        166,
+                                        126
+                                    ],
+                                    "score": 0.61,
+                                    "content": "n",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        166,
+                                        114,
+                                        339,
+                                        131
+                                    ],
+                                    "score": 1.0,
+                                    "content": "weight configurations of a neural network",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        339,
+                                        116,
+                                        375,
+                                        128
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\{ { \\bf w } _ { i } \\} _ { i = 1 } ^ { n }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        375,
+                                        114,
+                                        397,
+                                        131
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        397,
+                                        116,
+                                        434,
+                                        127
+                                    ],
+                                    "score": 0.92,
+                                    "content": "{ \\bf w } _ { i } \\in \\mathbb { R } ^ { d }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        434,
+                                        114,
+                                        507,
+                                        131
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the dynamics of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                127,
+                                487,
+                                140
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        127,
+                                        477,
+                                        140
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the ensemble under the gradient of the posterior lead to the following update rule at iteration",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        477,
+                                        128,
+                                        482,
+                                        137
+                                    ],
+                                    "score": 0.77,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        482,
+                                        127,
+                                        487,
+                                        140
+                                    ],
+                                    "score": 1.0,
+                                    "content": ":",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        }
+                    ],
+                    "index": 2.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        228,
+                        142,
+                        383,
+                        177
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                228,
+                                142,
+                                383,
+                                177
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        228,
+                                        142,
+                                        383,
+                                        177
+                                    ],
+                                    "score": 0.83,
+                                    "content": "\\begin{array} { r l } & { \\mathbf { w } _ { i } ^ { t + 1 }  \\mathbf { w } _ { i } ^ { t } + \\epsilon _ { t } \\phi ( \\mathbf { w } _ { i } ^ { t } ) } \\\\ { \\mathrm { w i t h } \\quad } & { \\phi ( \\mathbf { w } _ { i } ^ { t } ) = \\nabla _ { \\mathbf { w } _ { i } ^ { t } } \\log p ( \\mathbf { w } _ { i } ^ { t } | \\mathcal { D } ) , } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "dec175f126457d7570141af68aa834ee6aa688fa0490be6f7e2b319f4c374697.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                228,
+                                142,
+                                383,
+                                159.5
+                            ],
+                            "spans": [],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                228,
+                                159.5,
+                                383,
+                                177.0
+                            ],
+                            "spans": [],
+                            "index": 7
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        178,
+                        505,
+                        289
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                179,
+                                506,
+                                193
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        179,
+                                        162,
+                                        193
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with step size",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        163,
+                                        181,
+                                        171,
+                                        191
+                                    ],
+                                    "score": 0.82,
+                                    "content": "\\epsilon _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        172,
+                                        179,
+                                        506,
+                                        193
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Ensemble methods have a long history [e.g., 45, 26, 6] and were recently revisited",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                189,
+                                506,
+                                204
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        189,
+                                        188,
+                                        204
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for neural networks",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        188,
+                                        190,
+                                        206,
+                                        202
+                                    ],
+                                    "score": 0.78,
+                                    "content": "\\pm 2 \\|",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        206,
+                                        189,
+                                        506,
+                                        204
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and coined deep ensembles. The predictions of the different members are",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                202,
+                                505,
+                                213
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        202,
+                                        505,
+                                        213
+                                    ],
+                                    "score": 1.0,
+                                    "content": "combined to create a predictive distribution by using the solutions to compute the Bayesian model",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                211,
+                                506,
+                                226
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        211,
+                                        196,
+                                        226
+                                    ],
+                                    "score": 1.0,
+                                    "content": "average (BMA) in Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        197,
+                                        212,
+                                        209,
+                                        225
+                                    ],
+                                    "score": 0.69,
+                                    "content": "\\mathbb { D }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        209,
+                                        211,
+                                        270,
+                                        226
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Recent works",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        270,
+                                        212,
+                                        288,
+                                        223
+                                    ],
+                                    "score": 0.75,
+                                    "content": "\\mathbb { \\lVert \\rVert }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        288,
+                                        211,
+                                        506,
+                                        226
+                                    ],
+                                    "score": 1.0,
+                                    "content": "have shown that deep ensembles can outperform some",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                223,
+                                504,
+                                236
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        223,
+                                        486,
+                                        236
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of the Bayesian approaches for uncertainty estimation. Even more recently, Wilson and Izmailov",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        486,
+                                        223,
+                                        504,
+                                        235
+                                    ],
+                                    "score": 0.82,
+                                    "content": "\\pmb { \\Vert 8 2 \\Vert }",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                233,
+                                507,
+                                248
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        233,
+                                        507,
+                                        248
+                                    ],
+                                    "score": 1.0,
+                                    "content": "argued that deep ensembles can be considered a compelling approach to Bayesian model averaging.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                244,
+                                506,
+                                258
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        244,
+                                        506,
+                                        258
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Despite these ideas, the ability of deep ensembles to efficiently average over multiple hypotheses and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                255,
+                                505,
+                                268
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        255,
+                                        407,
+                                        268
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to explore the functional landscape of the posterior distribution studied in",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        407,
+                                        255,
+                                        425,
+                                        267
+                                    ],
+                                    "score": 0.77,
+                                    "content": "[ \\overline { { 1 8 } } ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        425,
+                                        255,
+                                        505,
+                                        268
+                                    ],
+                                    "score": 1.0,
+                                    "content": "does not guarantee",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                267,
+                                505,
+                                279
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        267,
+                                        457,
+                                        279
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sampling from the right distribution. Indeed, the additional Langevin noise introduced in",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        457,
+                                        267,
+                                        475,
+                                        278
+                                    ],
+                                    "score": 0.78,
+                                    "content": "\\mathbb { [ \\breve { ] { ] \\mathrm { ~ Z ~ Z ~ } ] } } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        475,
+                                        267,
+                                        505,
+                                        279
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", which",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                277,
+                                500,
+                                290
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        277,
+                                        500,
+                                        290
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is not considered in deep ensembles, is crucial to ensure samples from the true Bayesian posterior.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 12.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        294,
+                        506,
+                        404
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                294,
+                                506,
+                                307
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        294,
+                                        506,
+                                        307
+                                    ],
+                                    "score": 1.0,
+                                    "content": "From a practical standpoint, since the quality of an ensemble hinges on the diversity of its members,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                306,
+                                505,
+                                317
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        306,
+                                        505,
+                                        317
+                                    ],
+                                    "score": 1.0,
+                                    "content": "many methods were recently proposed to improve this diversity without compromising the individual",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                316,
+                                506,
+                                328
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        316,
+                                        506,
+                                        328
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accuracy. For instance, Wenzel et al. [80] propose hyper-deep ensembles that combine deep networks",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                326,
+                                506,
+                                339
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        326,
+                                        506,
+                                        339
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with different hyperparameters. Similarly, cyclical learning-rate schedules can explore several local",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                337,
+                                506,
+                                350
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        338,
+                                        244,
+                                        350
+                                    ],
+                                    "score": 1.0,
+                                    "content": "minima for the ensemble members",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        245,
+                                        337,
+                                        262,
+                                        349
+                                    ],
+                                    "score": 0.31,
+                                    "content": "\\pmb { \\mathbb { B 3 } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        263,
+                                        338,
+                                        386,
+                                        350
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Alternatively, Rame and Cord",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        386,
+                                        337,
+                                        404,
+                                        349
+                                    ],
+                                    "score": 0.69,
+                                    "content": " { \\mathbb { I } }  { \\mathbb { I } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        404,
+                                        338,
+                                        506,
+                                        350
+                                    ],
+                                    "score": 1.0,
+                                    "content": "proposed an information-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                348,
+                                506,
+                                361
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        348,
+                                        417,
+                                        361
+                                    ],
+                                    "score": 1.0,
+                                    "content": "theoretic framework to avoid redundancy in the members and Oswald et al.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        418,
+                                        348,
+                                        435,
+                                        360
+                                    ],
+                                    "score": 0.56,
+                                    "content": "\\overline { { \\| 6 3 \\| } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        436,
+                                        348,
+                                        506,
+                                        361
+                                    ],
+                                    "score": 1.0,
+                                    "content": "studied possible",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                360,
+                                505,
+                                372
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        360,
+                                        505,
+                                        372
+                                    ],
+                                    "score": 1.0,
+                                    "content": "interactions between members based on weight sharing. However, the absence of a constraint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                370,
+                                505,
+                                383
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        370,
+                                        505,
+                                        383
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that prevents particles from converging to the same mode limits the possibility of improvement by",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                381,
+                                506,
+                                394
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        381,
+                                        506,
+                                        394
+                                    ],
+                                    "score": 1.0,
+                                    "content": "introducing more ensemble members. This means that any hopes to converge to different modes must",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                392,
+                                187,
+                                406
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        392,
+                                        187,
+                                        406
+                                    ],
+                                    "score": 1.0,
+                                    "content": "exclusively rely on:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 22.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        129,
+                        412,
+                        439,
+                        454
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                130,
+                                412,
+                                285,
+                                424
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        130,
+                                        412,
+                                        285,
+                                        424
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1. the randomness of the initialization",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                426,
+                                397,
+                                440
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        426,
+                                        397,
+                                        440
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2. the noise in the estimation of the gradients due to minibatching",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                441,
+                                439,
+                                455
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        441,
+                                        439,
+                                        455
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3. the number of local optima that might be reached during gradient descent.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 29
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        461,
+                        506,
+                        539
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                461,
+                                505,
+                                475
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        461,
+                                        276,
+                                        475
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Moreover, the recent study of Geiger et al.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        277,
+                                        461,
+                                        295,
+                                        473
+                                    ],
+                                    "score": 0.57,
+                                    "content": "\\pmb { \\left. \\pmb { \\left. \\bar { 2 5 } \\right. } \\right. }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        295,
+                                        461,
+                                        505,
+                                        475
+                                    ],
+                                    "score": 1.0,
+                                    "content": "showed how the empirical test error of the ensemble",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                473,
+                                505,
+                                486
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        473,
+                                        505,
+                                        486
+                                    ],
+                                    "score": 1.0,
+                                    "content": "converges to the one of a single trained model when the number of parameters goes to infinity, leading",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                484,
+                                505,
+                                496
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        484,
+                                        505,
+                                        496
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to deterioration of the performance. In other words, the bigger the model, the harder it is to maintain",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                494,
+                                505,
+                                507
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        494,
+                                        505,
+                                        507
+                                    ],
+                                    "score": 1.0,
+                                    "content": "diversity in the ensemble and avoid collapse to the same solution. This is intuitively due to the fact",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                505,
+                                506,
+                                518
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        505,
+                                        506,
+                                        518
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that bigger models are less sensitive to the initialization. Namely, in order for them to get stuck in a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                516,
+                                507,
+                                529
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        516,
+                                        507,
+                                        529
+                                    ],
+                                    "score": 1.0,
+                                    "content": "local minimum, they must have second derivatives that are positive simultaneously in all directions.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                527,
+                                374,
+                                540
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        527,
+                                        374,
+                                        540
+                                    ],
+                                    "score": 1.0,
+                                    "content": "As the number of hidden units gets larger, this becomes less likely.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 34
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        551,
+                        263,
+                        564
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                549,
+                                264,
+                                567
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        549,
+                                        264,
+                                        567
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2.1 Repulsive force in weight space",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        }
+                    ],
+                    "index": 38
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        571,
+                        506,
+                        638
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                571,
+                                506,
+                                584
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        571,
+                                        506,
+                                        584
+                                    ],
+                                    "score": 1.0,
+                                    "content": "To overcome the aforementioned limitations of standard deep ensembles, we introduce, inspired",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                582,
+                                506,
+                                595
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        582,
+                                        150,
+                                        595
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by SVGD",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        150,
+                                        582,
+                                        168,
+                                        594
+                                    ],
+                                    "score": 0.48,
+                                    "content": "\\mathbb { \\left[ \\left[ 5 1 \\right] \\right] }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        168,
+                                        582,
+                                        506,
+                                        595
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", a deep ensemble with members that interact with each other through a repulsive",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                594,
+                                506,
+                                606
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        594,
+                                        506,
+                                        606
+                                    ],
+                                    "score": 1.0,
+                                    "content": "component. Using a kernel function to model this interaction, the single models repel each other",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                604,
+                                506,
+                                617
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        604,
+                                        506,
+                                        617
+                                    ],
+                                    "score": 1.0,
+                                    "content": "based on their position in the weight space, so that two members can never assume the same weights.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                613,
+                                506,
+                                629
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        613,
+                                        236,
+                                        629
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Considering a stationary kernel",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        237,
+                                        615,
+                                        329,
+                                        628
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\bar { k } ( \\cdot , \\cdot ) : \\mathbb { R } ^ { d } \\times \\mathbb { R } ^ { d } \\to \\mathbb { R }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        329,
+                                        613,
+                                        506,
+                                        629
+                                    ],
+                                    "score": 1.0,
+                                    "content": "acting in the parameter space of the neural",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                626,
+                                392,
+                                639
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        626,
+                                        210,
+                                        639
+                                    ],
+                                    "score": 1.0,
+                                    "content": "network, a repulsive term",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        210,
+                                        627,
+                                        220,
+                                        636
+                                    ],
+                                    "score": 0.82,
+                                    "content": "\\mathcal { R }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        221,
+                                        626,
+                                        392,
+                                        639
+                                    ],
+                                    "score": 1.0,
+                                    "content": "can be parameterized through its gradient:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        }
+                    ],
+                    "index": 41.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        183,
+                        642,
+                        428,
+                        670
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                183,
+                                642,
+                                428,
+                                670
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        183,
+                                        642,
+                                        428,
+                                        670
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\phi ( \\mathbf { w } _ { i } ^ { t } ) = \\nabla _ { \\mathbf { w } _ { i } ^ { t } } \\log p ( \\mathbf { w } _ { i } ^ { t } | \\mathcal { D } ) - \\mathcal { R } \\left( \\left\\{ \\nabla _ { \\mathbf { w } _ { i } ^ { t } } k ( \\mathbf { w } _ { i } ^ { t } , \\mathbf { w } _ { j } ^ { t } ) \\right\\} _ { j = 1 } ^ { n } \\right) .",
+                                    "type": "interline_equation",
+                                    "image_path": "52631e0ed6e1a61e9e013d38c7585cc4709cd85b719f28114ba1570f9f671c2a.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 46,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                183,
+                                642,
+                                428,
+                                651.3333333333334
+                            ],
+                            "spans": [],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                183,
+                                651.3333333333334,
+                                428,
+                                660.6666666666667
+                            ],
+                            "spans": [],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                183,
+                                660.6666666666667,
+                                428,
+                                670.0000000000001
+                            ],
+                            "spans": [],
+                            "index": 47
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        673,
+                        505,
+                        698
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                674,
+                                505,
+                                686
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        674,
+                                        505,
+                                        686
+                                    ],
+                                    "score": 1.0,
+                                    "content": "To get an intuition for the behavior of this repulsive term and its gradients, we can consider the RBF",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                684,
+                                475,
+                                698
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        684,
+                                        134,
+                                        698
+                                    ],
+                                    "score": 1.0,
+                                    "content": "kernel",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        134,
+                                        684,
+                                        286,
+                                        698
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\begin{array} { r } { k ( \\mathbf { w } _ { i } , \\mathbf { w } _ { j } ) = \\exp \\big ( - \\frac { 1 } { h } | | \\mathbf { w } _ { i } - \\mathbf { w } _ { j } | | ^ { 2 } \\big ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        287,
+                                        684,
+                                        356,
+                                        698
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with lengthscale",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        356,
+                                        687,
+                                        362,
+                                        695
+                                    ],
+                                    "score": 0.87,
+                                    "content": "h",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        363,
+                                        684,
+                                        475,
+                                        698
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and notice how its gradient",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        }
+                    ],
+                    "index": 48.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        219,
+                        702,
+                        391,
+                        726
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                219,
+                                702,
+                                391,
+                                726
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        219,
+                                        702,
+                                        391,
+                                        726
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\nabla _ { \\mathbf { w } _ { i } ^ { t } } k ( \\mathbf { w } _ { i } ^ { t } , \\mathbf { w } _ { j } ^ { t } ) = \\frac { 2 } { h } ( \\mathbf { w } _ { j } ^ { t } - \\mathbf { w } _ { i } ^ { t } ) k ( \\mathbf { w } _ { i } ^ { t } , \\mathbf { w } _ { j } ^ { t } )",
+                                    "type": "interline_equation",
+                                    "image_path": "f23cff6e6b3dc3c8e61b222583d646eef0fa3e0251332d45f77faee6e2130a87.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 50,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                219,
+                                702,
+                                391,
+                                726
+                            ],
+                            "spans": [],
+                            "index": 50
+                        }
+                    ]
+                }
+            ],
+            "page_idx": 2,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        741,
+                        309,
+                        750
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                301,
+                                740,
+                                310,
+                                752
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        301,
+                                        740,
+                                        310,
+                                        752
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        72,
+                        506,
+                        139
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                71,
+                                506,
+                                87
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        71,
+                                        506,
+                                        87
+                                    ],
+                                    "score": 1.0,
+                                    "content": "While approximating the posterior of Bayesian neural networks (or sampling from it) is a challenging",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                83,
+                                506,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        83,
+                                        506,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "task, performing maximum a posteriori (MAP) estimation, which corresponds to finding the mode of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                95,
+                                506,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        95,
+                                        506,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the posterior, is usually simple. Ensembles of neural networks use the non-convexity of the MAP",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                105,
+                                507,
+                                118
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        105,
+                                        293,
+                                        118
+                                    ],
+                                    "score": 1.0,
+                                    "content": "optimization problem to create a collection of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        294,
+                                        106,
+                                        304,
+                                        115
+                                    ],
+                                    "score": 0.83,
+                                    "content": "K",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        105,
+                                        507,
+                                        118
+                                    ],
+                                    "score": 1.0,
+                                    "content": "independent—and possibly different— solutions.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                114,
+                                507,
+                                131
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        114,
+                                        158,
+                                        131
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Considering",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        159,
+                                        118,
+                                        166,
+                                        126
+                                    ],
+                                    "score": 0.61,
+                                    "content": "n",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        166,
+                                        114,
+                                        339,
+                                        131
+                                    ],
+                                    "score": 1.0,
+                                    "content": "weight configurations of a neural network",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        339,
+                                        116,
+                                        375,
+                                        128
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\{ { \\bf w } _ { i } \\} _ { i = 1 } ^ { n }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        375,
+                                        114,
+                                        397,
+                                        131
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        397,
+                                        116,
+                                        434,
+                                        127
+                                    ],
+                                    "score": 0.92,
+                                    "content": "{ \\bf w } _ { i } \\in \\mathbb { R } ^ { d }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        434,
+                                        114,
+                                        507,
+                                        131
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the dynamics of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                127,
+                                487,
+                                140
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        127,
+                                        477,
+                                        140
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the ensemble under the gradient of the posterior lead to the following update rule at iteration",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        477,
+                                        128,
+                                        482,
+                                        137
+                                    ],
+                                    "score": 0.77,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        482,
+                                        127,
+                                        487,
+                                        140
+                                    ],
+                                    "score": 1.0,
+                                    "content": ":",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        }
+                    ],
+                    "index": 2.5,
+                    "bbox_fs": [
+                        104,
+                        71,
+                        507,
+                        140
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        228,
+                        142,
+                        383,
+                        177
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                228,
+                                142,
+                                383,
+                                177
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        228,
+                                        142,
+                                        383,
+                                        177
+                                    ],
+                                    "score": 0.83,
+                                    "content": "\\begin{array} { r l } & { \\mathbf { w } _ { i } ^ { t + 1 }  \\mathbf { w } _ { i } ^ { t } + \\epsilon _ { t } \\phi ( \\mathbf { w } _ { i } ^ { t } ) } \\\\ { \\mathrm { w i t h } \\quad } & { \\phi ( \\mathbf { w } _ { i } ^ { t } ) = \\nabla _ { \\mathbf { w } _ { i } ^ { t } } \\log p ( \\mathbf { w } _ { i } ^ { t } | \\mathcal { D } ) , } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "dec175f126457d7570141af68aa834ee6aa688fa0490be6f7e2b319f4c374697.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                228,
+                                142,
+                                383,
+                                159.5
+                            ],
+                            "spans": [],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                228,
+                                159.5,
+                                383,
+                                177.0
+                            ],
+                            "spans": [],
+                            "index": 7
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        178,
+                        505,
+                        289
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                179,
+                                506,
+                                193
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        179,
+                                        162,
+                                        193
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with step size",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        163,
+                                        181,
+                                        171,
+                                        191
+                                    ],
+                                    "score": 0.82,
+                                    "content": "\\epsilon _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        172,
+                                        179,
+                                        506,
+                                        193
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Ensemble methods have a long history [e.g., 45, 26, 6] and were recently revisited",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                189,
+                                506,
+                                204
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        189,
+                                        188,
+                                        204
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for neural networks",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        188,
+                                        190,
+                                        206,
+                                        202
+                                    ],
+                                    "score": 0.78,
+                                    "content": "\\pm 2 \\|",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        206,
+                                        189,
+                                        506,
+                                        204
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and coined deep ensembles. The predictions of the different members are",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                202,
+                                505,
+                                213
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        202,
+                                        505,
+                                        213
+                                    ],
+                                    "score": 1.0,
+                                    "content": "combined to create a predictive distribution by using the solutions to compute the Bayesian model",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                211,
+                                506,
+                                226
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        211,
+                                        196,
+                                        226
+                                    ],
+                                    "score": 1.0,
+                                    "content": "average (BMA) in Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        197,
+                                        212,
+                                        209,
+                                        225
+                                    ],
+                                    "score": 0.69,
+                                    "content": "\\mathbb { D }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        209,
+                                        211,
+                                        270,
+                                        226
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Recent works",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        270,
+                                        212,
+                                        288,
+                                        223
+                                    ],
+                                    "score": 0.75,
+                                    "content": "\\mathbb { \\lVert \\rVert }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        288,
+                                        211,
+                                        506,
+                                        226
+                                    ],
+                                    "score": 1.0,
+                                    "content": "have shown that deep ensembles can outperform some",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                223,
+                                504,
+                                236
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        223,
+                                        486,
+                                        236
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of the Bayesian approaches for uncertainty estimation. Even more recently, Wilson and Izmailov",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        486,
+                                        223,
+                                        504,
+                                        235
+                                    ],
+                                    "score": 0.82,
+                                    "content": "\\pmb { \\Vert 8 2 \\Vert }",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                233,
+                                507,
+                                248
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        233,
+                                        507,
+                                        248
+                                    ],
+                                    "score": 1.0,
+                                    "content": "argued that deep ensembles can be considered a compelling approach to Bayesian model averaging.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                244,
+                                506,
+                                258
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        244,
+                                        506,
+                                        258
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Despite these ideas, the ability of deep ensembles to efficiently average over multiple hypotheses and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                255,
+                                505,
+                                268
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        255,
+                                        407,
+                                        268
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to explore the functional landscape of the posterior distribution studied in",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        407,
+                                        255,
+                                        425,
+                                        267
+                                    ],
+                                    "score": 0.77,
+                                    "content": "[ \\overline { { 1 8 } } ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        425,
+                                        255,
+                                        505,
+                                        268
+                                    ],
+                                    "score": 1.0,
+                                    "content": "does not guarantee",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                267,
+                                505,
+                                279
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        267,
+                                        457,
+                                        279
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sampling from the right distribution. Indeed, the additional Langevin noise introduced in",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        457,
+                                        267,
+                                        475,
+                                        278
+                                    ],
+                                    "score": 0.78,
+                                    "content": "\\mathbb { [ \\breve { ] { ] \\mathrm { ~ Z ~ Z ~ } ] } } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        475,
+                                        267,
+                                        505,
+                                        279
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", which",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                277,
+                                500,
+                                290
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        277,
+                                        500,
+                                        290
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is not considered in deep ensembles, is crucial to ensure samples from the true Bayesian posterior.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 12.5,
+                    "bbox_fs": [
+                        105,
+                        179,
+                        507,
+                        290
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        294,
+                        506,
+                        404
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                294,
+                                506,
+                                307
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        294,
+                                        506,
+                                        307
+                                    ],
+                                    "score": 1.0,
+                                    "content": "From a practical standpoint, since the quality of an ensemble hinges on the diversity of its members,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                306,
+                                505,
+                                317
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        306,
+                                        505,
+                                        317
+                                    ],
+                                    "score": 1.0,
+                                    "content": "many methods were recently proposed to improve this diversity without compromising the individual",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                316,
+                                506,
+                                328
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        316,
+                                        506,
+                                        328
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accuracy. For instance, Wenzel et al. [80] propose hyper-deep ensembles that combine deep networks",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                326,
+                                506,
+                                339
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        326,
+                                        506,
+                                        339
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with different hyperparameters. Similarly, cyclical learning-rate schedules can explore several local",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                337,
+                                506,
+                                350
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        338,
+                                        244,
+                                        350
+                                    ],
+                                    "score": 1.0,
+                                    "content": "minima for the ensemble members",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        245,
+                                        337,
+                                        262,
+                                        349
+                                    ],
+                                    "score": 0.31,
+                                    "content": "\\pmb { \\mathbb { B 3 } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        263,
+                                        338,
+                                        386,
+                                        350
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Alternatively, Rame and Cord",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        386,
+                                        337,
+                                        404,
+                                        349
+                                    ],
+                                    "score": 0.69,
+                                    "content": " { \\mathbb { I } }  { \\mathbb { I } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        404,
+                                        338,
+                                        506,
+                                        350
+                                    ],
+                                    "score": 1.0,
+                                    "content": "proposed an information-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                348,
+                                506,
+                                361
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        348,
+                                        417,
+                                        361
+                                    ],
+                                    "score": 1.0,
+                                    "content": "theoretic framework to avoid redundancy in the members and Oswald et al.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        418,
+                                        348,
+                                        435,
+                                        360
+                                    ],
+                                    "score": 0.56,
+                                    "content": "\\overline { { \\| 6 3 \\| } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        436,
+                                        348,
+                                        506,
+                                        361
+                                    ],
+                                    "score": 1.0,
+                                    "content": "studied possible",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                360,
+                                505,
+                                372
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        360,
+                                        505,
+                                        372
+                                    ],
+                                    "score": 1.0,
+                                    "content": "interactions between members based on weight sharing. However, the absence of a constraint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                370,
+                                505,
+                                383
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        370,
+                                        505,
+                                        383
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that prevents particles from converging to the same mode limits the possibility of improvement by",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                381,
+                                506,
+                                394
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        381,
+                                        506,
+                                        394
+                                    ],
+                                    "score": 1.0,
+                                    "content": "introducing more ensemble members. This means that any hopes to converge to different modes must",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                392,
+                                187,
+                                406
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        392,
+                                        187,
+                                        406
+                                    ],
+                                    "score": 1.0,
+                                    "content": "exclusively rely on:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 22.5,
+                    "bbox_fs": [
+                        105,
+                        294,
+                        506,
+                        406
+                    ]
+                },
+                {
+                    "type": "index",
+                    "bbox": [
+                        129,
+                        412,
+                        439,
+                        454
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                130,
+                                412,
+                                285,
+                                424
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        130,
+                                        412,
+                                        285,
+                                        424
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1. the randomness of the initialization",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                426,
+                                397,
+                                440
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        426,
+                                        397,
+                                        440
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2. the noise in the estimation of the gradients due to minibatching",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                441,
+                                439,
+                                455
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        441,
+                                        439,
+                                        455
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3. the number of local optima that might be reached during gradient descent.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30,
+                            "is_list_start_line": true
+                        }
+                    ],
+                    "index": 29,
+                    "bbox_fs": [
+                        128,
+                        412,
+                        439,
+                        455
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        461,
+                        506,
+                        539
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                461,
+                                505,
+                                475
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        461,
+                                        276,
+                                        475
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Moreover, the recent study of Geiger et al.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        277,
+                                        461,
+                                        295,
+                                        473
+                                    ],
+                                    "score": 0.57,
+                                    "content": "\\pmb { \\left. \\pmb { \\left. \\bar { 2 5 } \\right. } \\right. }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        295,
+                                        461,
+                                        505,
+                                        475
+                                    ],
+                                    "score": 1.0,
+                                    "content": "showed how the empirical test error of the ensemble",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                473,
+                                505,
+                                486
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        473,
+                                        505,
+                                        486
+                                    ],
+                                    "score": 1.0,
+                                    "content": "converges to the one of a single trained model when the number of parameters goes to infinity, leading",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                484,
+                                505,
+                                496
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        484,
+                                        505,
+                                        496
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to deterioration of the performance. In other words, the bigger the model, the harder it is to maintain",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                494,
+                                505,
+                                507
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        494,
+                                        505,
+                                        507
+                                    ],
+                                    "score": 1.0,
+                                    "content": "diversity in the ensemble and avoid collapse to the same solution. This is intuitively due to the fact",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                505,
+                                506,
+                                518
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        505,
+                                        506,
+                                        518
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that bigger models are less sensitive to the initialization. Namely, in order for them to get stuck in a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                516,
+                                507,
+                                529
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        516,
+                                        507,
+                                        529
+                                    ],
+                                    "score": 1.0,
+                                    "content": "local minimum, they must have second derivatives that are positive simultaneously in all directions.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                527,
+                                374,
+                                540
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        527,
+                                        374,
+                                        540
+                                    ],
+                                    "score": 1.0,
+                                    "content": "As the number of hidden units gets larger, this becomes less likely.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 34,
+                    "bbox_fs": [
+                        105,
+                        461,
+                        507,
+                        540
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        551,
+                        263,
+                        564
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                549,
+                                264,
+                                567
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        549,
+                                        264,
+                                        567
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2.1 Repulsive force in weight space",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        }
+                    ],
+                    "index": 38
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        571,
+                        506,
+                        638
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                571,
+                                506,
+                                584
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        571,
+                                        506,
+                                        584
+                                    ],
+                                    "score": 1.0,
+                                    "content": "To overcome the aforementioned limitations of standard deep ensembles, we introduce, inspired",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                582,
+                                506,
+                                595
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        582,
+                                        150,
+                                        595
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by SVGD",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        150,
+                                        582,
+                                        168,
+                                        594
+                                    ],
+                                    "score": 0.48,
+                                    "content": "\\mathbb { \\left[ \\left[ 5 1 \\right] \\right] }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        168,
+                                        582,
+                                        506,
+                                        595
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", a deep ensemble with members that interact with each other through a repulsive",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                594,
+                                506,
+                                606
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        594,
+                                        506,
+                                        606
+                                    ],
+                                    "score": 1.0,
+                                    "content": "component. Using a kernel function to model this interaction, the single models repel each other",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                604,
+                                506,
+                                617
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        604,
+                                        506,
+                                        617
+                                    ],
+                                    "score": 1.0,
+                                    "content": "based on their position in the weight space, so that two members can never assume the same weights.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                613,
+                                506,
+                                629
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        613,
+                                        236,
+                                        629
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Considering a stationary kernel",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        237,
+                                        615,
+                                        329,
+                                        628
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\bar { k } ( \\cdot , \\cdot ) : \\mathbb { R } ^ { d } \\times \\mathbb { R } ^ { d } \\to \\mathbb { R }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        329,
+                                        613,
+                                        506,
+                                        629
+                                    ],
+                                    "score": 1.0,
+                                    "content": "acting in the parameter space of the neural",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                626,
+                                392,
+                                639
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        626,
+                                        210,
+                                        639
+                                    ],
+                                    "score": 1.0,
+                                    "content": "network, a repulsive term",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        210,
+                                        627,
+                                        220,
+                                        636
+                                    ],
+                                    "score": 0.82,
+                                    "content": "\\mathcal { R }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        221,
+                                        626,
+                                        392,
+                                        639
+                                    ],
+                                    "score": 1.0,
+                                    "content": "can be parameterized through its gradient:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        }
+                    ],
+                    "index": 41.5,
+                    "bbox_fs": [
+                        105,
+                        571,
+                        506,
+                        639
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        183,
+                        642,
+                        428,
+                        670
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                183,
+                                642,
+                                428,
+                                670
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        183,
+                                        642,
+                                        428,
+                                        670
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\phi ( \\mathbf { w } _ { i } ^ { t } ) = \\nabla _ { \\mathbf { w } _ { i } ^ { t } } \\log p ( \\mathbf { w } _ { i } ^ { t } | \\mathcal { D } ) - \\mathcal { R } \\left( \\left\\{ \\nabla _ { \\mathbf { w } _ { i } ^ { t } } k ( \\mathbf { w } _ { i } ^ { t } , \\mathbf { w } _ { j } ^ { t } ) \\right\\} _ { j = 1 } ^ { n } \\right) .",
+                                    "type": "interline_equation",
+                                    "image_path": "52631e0ed6e1a61e9e013d38c7585cc4709cd85b719f28114ba1570f9f671c2a.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 46,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                183,
+                                642,
+                                428,
+                                651.3333333333334
+                            ],
+                            "spans": [],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                183,
+                                651.3333333333334,
+                                428,
+                                660.6666666666667
+                            ],
+                            "spans": [],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                183,
+                                660.6666666666667,
+                                428,
+                                670.0000000000001
+                            ],
+                            "spans": [],
+                            "index": 47
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        673,
+                        505,
+                        698
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                674,
+                                505,
+                                686
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        674,
+                                        505,
+                                        686
+                                    ],
+                                    "score": 1.0,
+                                    "content": "To get an intuition for the behavior of this repulsive term and its gradients, we can consider the RBF",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                684,
+                                475,
+                                698
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        684,
+                                        134,
+                                        698
+                                    ],
+                                    "score": 1.0,
+                                    "content": "kernel",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        134,
+                                        684,
+                                        286,
+                                        698
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\begin{array} { r } { k ( \\mathbf { w } _ { i } , \\mathbf { w } _ { j } ) = \\exp \\big ( - \\frac { 1 } { h } | | \\mathbf { w } _ { i } - \\mathbf { w } _ { j } | | ^ { 2 } \\big ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        287,
+                                        684,
+                                        356,
+                                        698
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with lengthscale",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        356,
+                                        687,
+                                        362,
+                                        695
+                                    ],
+                                    "score": 0.87,
+                                    "content": "h",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        363,
+                                        684,
+                                        475,
+                                        698
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and notice how its gradient",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        }
+                    ],
+                    "index": 48.5,
+                    "bbox_fs": [
+                        105,
+                        674,
+                        505,
+                        698
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        219,
+                        702,
+                        391,
+                        726
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                219,
+                                702,
+                                391,
+                                726
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        219,
+                                        702,
+                                        391,
+                                        726
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\nabla _ { \\mathbf { w } _ { i } ^ { t } } k ( \\mathbf { w } _ { i } ^ { t } , \\mathbf { w } _ { j } ^ { t } ) = \\frac { 2 } { h } ( \\mathbf { w } _ { j } ^ { t } - \\mathbf { w } _ { i } ^ { t } ) k ( \\mathbf { w } _ { i } ^ { t } , \\mathbf { w } _ { j } ^ { t } )",
+                                    "type": "interline_equation",
+                                    "image_path": "f23cff6e6b3dc3c8e61b222583d646eef0fa3e0251332d45f77faee6e2130a87.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 50,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                219,
+                                702,
+                                391,
+                                726
+                            ],
+                            "spans": [],
+                            "index": 50
+                        }
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        72,
+                        506,
+                        141
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                72,
+                                506,
+                                86
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        72,
+                                        133,
+                                        86
+                                    ],
+                                    "score": 1.0,
+                                    "content": "drives",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        133,
+                                        74,
+                                        146,
+                                        84
+                                    ],
+                                    "score": 0.86,
+                                    "content": "\\mathbf { w } _ { i }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        147,
+                                        72,
+                                        298,
+                                        86
+                                    ],
+                                    "score": 1.0,
+                                    "content": "away from its neighboring members",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        298,
+                                        74,
+                                        312,
+                                        85
+                                    ],
+                                    "score": 0.88,
+                                    "content": "{ \\bf w } _ { j }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        312,
+                                        72,
+                                        506,
+                                        86
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", thus creating a repulsive effect. Naturally, not",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                83,
+                                505,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        83,
+                                        178,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "all the choices of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        178,
+                                        84,
+                                        188,
+                                        93
+                                    ],
+                                    "score": 0.83,
+                                    "content": "\\mathcal { R }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        189,
+                                        83,
+                                        505,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "induce this effect. One of the simplest formulations to obtain it is via a linear",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                101,
+                                90,
+                                509,
+                                113
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        101,
+                                        90,
+                                        387,
+                                        113
+                                    ],
+                                    "score": 1.0,
+                                    "content": "combination of the kernel gradients scaled by a positive factor, that is,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        388,
+                                        94,
+                                        484,
+                                        108
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\begin{array} { r } { \\beta \\sum _ { j = 1 } ^ { n } \\nabla _ { \\mathbf { w } _ { i } ^ { t } } k ( \\mathbf { w } _ { i } ^ { t } , \\mathbf { w } _ { j } ^ { t } ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        484,
+                                        90,
+                                        509,
+                                        113
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                106,
+                                505,
+                                121
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        107,
+                                        140,
+                                        119
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\beta \\in \\mathbb { R } _ { * } ^ { + }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        140,
+                                        106,
+                                        232,
+                                        121
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". We will see in Section",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        233,
+                                        106,
+                                        242,
+                                        121
+                                    ],
+                                    "score": 0.79,
+                                    "content": "\\begin{array} { l } { 3 } \\\\ { . } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        243,
+                                        106,
+                                        313,
+                                        121
+                                    ],
+                                    "score": 1.0,
+                                    "content": "how the choice of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        313,
+                                        108,
+                                        321,
+                                        119
+                                    ],
+                                    "score": 0.84,
+                                    "content": "\\beta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        321,
+                                        106,
+                                        505,
+                                        121
+                                    ],
+                                    "score": 1.0,
+                                    "content": "can be justified in order to obtain convergence",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                118,
+                                506,
+                                131
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        118,
+                                        420,
+                                        131
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to the Bayesian posterior together with alternative possible formulations of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        420,
+                                        119,
+                                        430,
+                                        128
+                                    ],
+                                    "score": 0.84,
+                                    "content": "\\mathcal { R }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        430,
+                                        118,
+                                        506,
+                                        131
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that preserve this",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                131,
+                                162,
+                                143
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        131,
+                                        162,
+                                        143
+                                    ],
+                                    "score": 1.0,
+                                    "content": "convergence.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        }
+                    ],
+                    "index": 2.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        153,
+                        270,
+                        165
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                152,
+                                271,
+                                168
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        152,
+                                        271,
+                                        168
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2.2 Repulsive force in function space",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        173,
+                        506,
+                        284
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                173,
+                                505,
+                                186
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        174,
+                                        410,
+                                        186
+                                    ],
+                                    "score": 1.0,
+                                    "content": "To overcome the aforementioned overparameterization issue, the update in Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        410,
+                                        173,
+                                        423,
+                                        186
+                                    ],
+                                    "score": 0.83,
+                                    "content": "\\textcircled { 3 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        423,
+                                        174,
+                                        505,
+                                        186
+                                    ],
+                                    "score": 1.0,
+                                    "content": "can be formulated in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                185,
+                                505,
+                                197
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        185,
+                                        277,
+                                        197
+                                    ],
+                                    "score": 1.0,
+                                    "content": "function space instead of weight space. Let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        277,
+                                        185,
+                                        348,
+                                        197
+                                    ],
+                                    "score": 0.93,
+                                    "content": "f : \\mathbf { w } \\mapsto f ( \\cdot ; \\mathbf { w } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        348,
+                                        185,
+                                        505,
+                                        197
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be the map that maps a configuration of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                196,
+                                505,
+                                209
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        196,
+                                        138,
+                                        209
+                                    ],
+                                    "score": 1.0,
+                                    "content": "weights",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        138,
+                                        196,
+                                        172,
+                                        207
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\mathbf { w } \\in \\mathbb { R } ^ { d }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        172,
+                                        196,
+                                        444,
+                                        209
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to the corresponding neural network regression function and denote as",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        445,
+                                        196,
+                                        505,
+                                        209
+                                    ],
+                                    "score": 0.92,
+                                    "content": "f _ { i } : = f ( \\cdot ; { \\mathbf w } _ { i } )",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                207,
+                                506,
+                                220
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        207,
+                                        311,
+                                        220
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the function with a certain configuration of weights",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        311,
+                                        209,
+                                        324,
+                                        219
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\mathbf { w } _ { i }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        324,
+                                        207,
+                                        415,
+                                        220
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". We can now consider",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        415,
+                                        210,
+                                        423,
+                                        218
+                                    ],
+                                    "score": 0.75,
+                                    "content": "n",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        423,
+                                        207,
+                                        506,
+                                        220
+                                    ],
+                                    "score": 1.0,
+                                    "content": "particles in function",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                216,
+                                508,
+                                233
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        216,
+                                        131,
+                                        233
+                                    ],
+                                    "score": 1.0,
+                                    "content": "space",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        132,
+                                        218,
+                                        164,
+                                        231
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\{ f _ { i } \\} _ { i = 1 } ^ { n }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        165,
+                                        216,
+                                        186,
+                                        233
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        187,
+                                        219,
+                                        215,
+                                        230
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\pmb { f } \\in \\mathcal { F }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        215,
+                                        216,
+                                        478,
+                                        233
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and model their interaction with a general positive definite kernel",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        479,
+                                        219,
+                                        503,
+                                        230
+                                    ],
+                                    "score": 0.91,
+                                    "content": "k ( \\cdot , \\cdot )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        503,
+                                        216,
+                                        508,
+                                        233
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                228,
+                                505,
+                                242
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        228,
+                                        309,
+                                        242
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We also consider the implicit functional likelihood",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        309,
+                                        230,
+                                        349,
+                                        241
+                                    ],
+                                    "score": 0.92,
+                                    "content": "p ( \\pmb { y } | \\pmb { x } , \\pmb { f } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        349,
+                                        228,
+                                        462,
+                                        242
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", determined by the measure",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        463,
+                                        230,
+                                        505,
+                                        241
+                                    ],
+                                    "score": 0.91,
+                                    "content": "p ( \\pmb { y } | \\pmb { x } , \\mathbf { w } )",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                238,
+                                507,
+                                254
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        238,
+                                        306,
+                                        254
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in the weight space, as well as the functional prior",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        241,
+                                        327,
+                                        252
+                                    ],
+                                    "score": 0.91,
+                                    "content": "p ( f )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        327,
+                                        238,
+                                        507,
+                                        254
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", which can either be defined separately (e.g.,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                250,
+                                506,
+                                266
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        250,
+                                        419,
+                                        266
+                                    ],
+                                    "score": 1.0,
+                                    "content": "using a GP) or modeled as a push-forward measure of the weight-space prior",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        419,
+                                        251,
+                                        441,
+                                        263
+                                    ],
+                                    "score": 0.91,
+                                    "content": "p ( \\mathbf { w } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        441,
+                                        250,
+                                        506,
+                                        266
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Together, they",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                261,
+                                506,
+                                275
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        261,
+                                        271,
+                                        275
+                                    ],
+                                    "score": 1.0,
+                                    "content": "determine the posterior in function space",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        271,
+                                        262,
+                                        302,
+                                        274
+                                    ],
+                                    "score": 0.92,
+                                    "content": "p ( \\pmb { f } | \\mathcal { D } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        261,
+                                        506,
+                                        275
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". The functional evolution of a particle can then be",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                272,
+                                151,
+                                285
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        272,
+                                        151,
+                                        285
+                                    ],
+                                    "score": 1.0,
+                                    "content": "written as:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 11.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        182,
+                        287,
+                        441,
+                        332
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                182,
+                                287,
+                                441,
+                                332
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        182,
+                                        287,
+                                        441,
+                                        332
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\begin{array} { r l } & { f _ { i } ^ { t + 1 } \\gets f _ { i } ^ { t } + \\epsilon _ { t } \\phi ( f _ { i } ^ { t } ) } \\\\ { \\mathrm { t h } \\quad } & { \\phi ( f _ { i } ^ { t } ) = \\nabla _ { f _ { i } ^ { t } } \\log p ( f _ { i } ^ { t } | \\mathcal { D } ) - \\mathcal { R } \\left( \\left\\{ \\nabla _ { f _ { i } ^ { t } } k ( f _ { i } ^ { t } , f _ { j } ^ { t } ) \\right\\} _ { j = 1 } ^ { n } \\right) . } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "6e9ccd562a52a4d7474eb2dbb571b766cb26754c555d1761309dd914491e04b8.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                182,
+                                287,
+                                441,
+                                302.0
+                            ],
+                            "spans": [],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                182,
+                                302.0,
+                                441,
+                                317.0
+                            ],
+                            "spans": [],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                182,
+                                317.0,
+                                441,
+                                332.0
+                            ],
+                            "spans": [],
+                            "index": 19
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        109,
+                        335,
+                        504,
+                        369
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                335,
+                                505,
+                                348
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        335,
+                                        505,
+                                        348
+                                    ],
+                                    "score": 1.0,
+                                    "content": "However, computing the update in function space is neither tractable nor practical, which is why two",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                108,
+                                347,
+                                505,
+                                358
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        108,
+                                        347,
+                                        505,
+                                        358
+                                    ],
+                                    "score": 1.0,
+                                    "content": "additional considerations are needed. The first one regards the infinite dimensionality of function",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                357,
+                                403,
+                                370
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        357,
+                                        403,
+                                        370
+                                    ],
+                                    "score": 1.0,
+                                    "content": "space, which we circumvent using a canonical projection into a subspace:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 21
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        371,
+                        503,
+                        396
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                369,
+                                506,
+                                385
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        369,
+                                        292,
+                                        385
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Definition 1 (Canonical projection). For any",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        293,
+                                        371,
+                                        323,
+                                        382
+                                    ],
+                                    "score": 0.88,
+                                    "content": "A \\subset { \\mathcal { X } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        323,
+                                        369,
+                                        368,
+                                        385
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", we define",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        368,
+                                        370,
+                                        434,
+                                        383
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\pi _ { A } : \\mathbb { R } ^ { \\mathcal { X } } \\to \\mathbb { R } ^ { A }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        434,
+                                        369,
+                                        506,
+                                        385
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as the canonical",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                381,
+                                302,
+                                397
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        381,
+                                        169,
+                                        397
+                                    ],
+                                    "score": 1.0,
+                                    "content": "projection onto",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        170,
+                                        383,
+                                        178,
+                                        393
+                                    ],
+                                    "score": 0.69,
+                                    "content": "A",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        178,
+                                        381,
+                                        212,
+                                        397
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", that is,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        212,
+                                        383,
+                                        297,
+                                        395
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\pi _ { A } ( f ) = \\{ f ( a ) \\} _ { a \\in A }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        297,
+                                        381,
+                                        302,
+                                        397
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 23.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        402,
+                        505,
+                        458
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                402,
+                                505,
+                                415
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        402,
+                                        505,
+                                        415
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In other words, the kernel will not be evaluated directly in function space, but on the projection",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                413,
+                                506,
+                                426
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        413,
+                                        182,
+                                        426
+                                    ],
+                                    "score": 0.91,
+                                    "content": "k \\big ( \\pi _ { B } ( f ) , \\pi _ { B } ( f ^ { \\prime } ) \\big )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        182,
+                                        413,
+                                        205,
+                                        426
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", with",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        206,
+                                        414,
+                                        215,
+                                        424
+                                    ],
+                                    "score": 0.81,
+                                    "content": "B",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        216,
+                                        413,
+                                        506,
+                                        426
+                                    ],
+                                    "score": 1.0,
+                                    "content": "being a subset of the input space given by a batch of training data points.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                424,
+                                506,
+                                438
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        424,
+                                        506,
+                                        438
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The second consideration is to project this update back into the parameter space and evolve a set of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                435,
+                                506,
+                                448
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        435,
+                                        506,
+                                        448
+                                    ],
+                                    "score": 1.0,
+                                    "content": "particles there, because ultimately we are interested in representing the functions by parameterized",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                445,
+                                477,
+                                459
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        445,
+                                        369,
+                                        459
+                                    ],
+                                    "score": 1.0,
+                                    "content": "neural networks. For this purpose, we can use the Jacobian of the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        369,
+                                        447,
+                                        374,
+                                        456
+                                    ],
+                                    "score": 0.76,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        374,
+                                        445,
+                                        477,
+                                        459
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-th particle as a projector:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 27
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        141,
+                        470,
+                        470,
+                        500
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                141,
+                                470,
+                                470,
+                                500
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        470,
+                                        470,
+                                        500
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\phi ( { \\mathbf w } _ { i } ^ { t } ) = \\left( \\frac { \\partial f _ { i } ^ { t } } { \\partial { \\mathbf w } _ { i } ^ { t } } \\right) ^ { \\top } \\left[ \\nabla _ { f _ { i } ^ { t } } \\log p ( f _ { i } ^ { t } | { \\mathcal D } ) - { \\mathcal R } \\left( \\left\\{ \\nabla _ { f _ { i } ^ { t } } k ( \\pi _ { B } ( f _ { i } ^ { t } ) , \\pi _ { B } ( f _ { j } ^ { t } ) ) \\right\\} _ { j = 1 } ^ { n } \\right) \\right] .",
+                                    "type": "interline_equation",
+                                    "image_path": "d7dea1ea5314c734775cfe499bded9ea6e655f30206ef90295c8a3d5d82d37d3.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 31,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                141,
+                                470,
+                                470,
+                                480.0
+                            ],
+                            "spans": [],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                480.0,
+                                470,
+                                490.0
+                            ],
+                            "spans": [],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                490.0,
+                                470,
+                                500.0
+                            ],
+                            "spans": [],
+                            "index": 32
+                        }
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        106,
+                        511,
+                        340,
+                        524
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                510,
+                                341,
+                                525
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        510,
+                                        341,
+                                        525
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2.3 Comparison to Stein variational gradient descent",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 33
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        530,
+                        487,
+                        543
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                530,
+                                488,
+                                545
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        530,
+                                        289,
+                                        545
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Note that our update is reminiscent of SVGD",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        290,
+                                        533,
+                                        306,
+                                        542
+                                    ],
+                                    "score": 0.34,
+                                    "content": "\\mathbb { \\left[ 5 1 \\right] }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        530,
+                                        488,
+                                        545
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", which in parameter space can be written as:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        }
+                    ],
+                    "index": 34
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        173,
+                        547,
+                        438,
+                        582
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                173,
+                                547,
+                                438,
+                                582
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        173,
+                                        547,
+                                        438,
+                                        582
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\phi ( \\mathbf { w } _ { i } ^ { t } ) = \\sum _ { j = 1 } ^ { n } k ( \\mathbf { w } _ { i } ^ { t } , \\mathbf { w } _ { j } ^ { t } ) \\nabla _ { \\mathbf { w } _ { i } ^ { t } } \\log p ( \\mathbf { w } _ { i } ^ { t } | \\mathcal { D } ) + \\sum _ { j = 1 } ^ { n } \\nabla _ { \\mathbf { w } _ { j } ^ { t } } k ( \\mathbf { w } _ { j } ^ { t } , \\mathbf { w } _ { i } ^ { t } ) .",
+                                    "type": "interline_equation",
+                                    "image_path": "ed4ba25f1f792a3ef21feee9794a7aaba9ed6181f2313384dd85bba5b6760967.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 36,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                173,
+                                547,
+                                438,
+                                558.6666666666666
+                            ],
+                            "spans": [],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                173,
+                                558.6666666666666,
+                                438,
+                                570.3333333333333
+                            ],
+                            "spans": [],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                173,
+                                570.3333333333333,
+                                438,
+                                581.9999999999999
+                            ],
+                            "spans": [],
+                            "index": 37
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        585,
+                        506,
+                        630
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                585,
+                                505,
+                                597
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        585,
+                                        505,
+                                        597
+                                    ],
+                                    "score": 1.0,
+                                    "content": "It is important to notice that here, the gradients are averaged across all the particles using the kernel",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                596,
+                                506,
+                                609
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        596,
+                                        506,
+                                        609
+                                    ],
+                                    "score": 1.0,
+                                    "content": "matrix. Interestingly, SVGD can be asymptotically interpreted as gradient flow of the KL divergence",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                606,
+                                506,
+                                620
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        606,
+                                        506,
+                                        620
+                                    ],
+                                    "score": 1.0,
+                                    "content": "under a new metric induced by the Stein operator [16, 50] (see Appendix D for more details). Moving",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                618,
+                                410,
+                                630
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        618,
+                                        295,
+                                        630
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the inference from parameter to function space",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        618,
+                                        313,
+                                        629
+                                    ],
+                                    "score": 0.43,
+                                    "content": "\\pmb { \\mathbb { Z } } 6 \\|",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        314,
+                                        618,
+                                        410,
+                                        630
+                                    ],
+                                    "score": 1.0,
+                                    "content": "leads to the update rule",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        }
+                    ],
+                    "index": 39.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        154,
+                        633,
+                        457,
+                        668
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                154,
+                                633,
+                                457,
+                                668
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        154,
+                                        633,
+                                        457,
+                                        668
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\phi ( \\mathbf { w } _ { i } ^ { t } ) = \\left( \\frac { \\partial f _ { i } ^ { t } } { \\partial \\mathbf { w } _ { i } ^ { t } } \\right) ^ { \\top } \\left( \\frac { 1 } { n } \\sum _ { j = 1 } ^ { n } k ( f _ { i } ^ { t } , f _ { j } ^ { t } ) \\nabla _ { f _ { j } ^ { t } } \\log p ( f _ { j } ^ { t } | \\mathcal { D } ) + \\nabla _ { f _ { j } ^ { t } } k ( f _ { i } ^ { t } , f _ { j } ^ { t } ) \\right) .",
+                                    "type": "interline_equation",
+                                    "image_path": "da910223233132ed75eba544433552d88de5b055ed7c20ab997ee811df84045c.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 43,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                154,
+                                633,
+                                457,
+                                644.6666666666666
+                            ],
+                            "spans": [],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                154,
+                                644.6666666666666,
+                                457,
+                                656.3333333333333
+                            ],
+                            "spans": [],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                154,
+                                656.3333333333333,
+                                457,
+                                667.9999999999999
+                            ],
+                            "spans": [],
+                            "index": 44
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        677,
+                        505,
+                        723
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                677,
+                                505,
+                                690
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        677,
+                                        505,
+                                        690
+                                    ],
+                                    "score": 1.0,
+                                    "content": "This way of averaging gradients using a kernel can be dangerous in high-dimensional settings, where",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                687,
+                                505,
+                                702
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        687,
+                                        434,
+                                        702
+                                    ],
+                                    "score": 1.0,
+                                    "content": "kernel methods often suffer from the curse of dimensionality. Moreover, in Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        434,
+                                        689,
+                                        447,
+                                        702
+                                    ],
+                                    "score": 0.79,
+                                    "content": "\\textcircled{6}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        447,
+                                        687,
+                                        505,
+                                        702
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the posterior",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                699,
+                                505,
+                                713
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        699,
+                                        505,
+                                        713
+                                    ],
+                                    "score": 1.0,
+                                    "content": "gradients of the particles are averaged using their similarity in weight space, which can be misleading",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                711,
+                                505,
+                                724
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        711,
+                                        289,
+                                        724
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in multi-modal posteriors. Worse yet, in Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        290,
+                                        711,
+                                        302,
+                                        723
+                                    ],
+                                    "score": 0.8,
+                                    "content": "\\textcircled{7}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        711,
+                                        505,
+                                        724
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the gradients are averaged in function space and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        }
+                    ],
+                    "index": 46.5
+                }
+            ],
+            "page_idx": 3,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        741,
+                        308,
+                        750
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                301,
+                                740,
+                                310,
+                                752
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        301,
+                                        740,
+                                        310,
+                                        752
+                                    ],
+                                    "score": 1.0,
+                                    "content": "",
+                                    "type": "text",
+                                    "height": 12,
+                                    "width": 9
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        72,
+                        506,
+                        141
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                72,
+                                506,
+                                86
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        72,
+                                        133,
+                                        86
+                                    ],
+                                    "score": 1.0,
+                                    "content": "drives",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        133,
+                                        74,
+                                        146,
+                                        84
+                                    ],
+                                    "score": 0.86,
+                                    "content": "\\mathbf { w } _ { i }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        147,
+                                        72,
+                                        298,
+                                        86
+                                    ],
+                                    "score": 1.0,
+                                    "content": "away from its neighboring members",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        298,
+                                        74,
+                                        312,
+                                        85
+                                    ],
+                                    "score": 0.88,
+                                    "content": "{ \\bf w } _ { j }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        312,
+                                        72,
+                                        506,
+                                        86
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", thus creating a repulsive effect. Naturally, not",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                83,
+                                505,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        83,
+                                        178,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "all the choices of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        178,
+                                        84,
+                                        188,
+                                        93
+                                    ],
+                                    "score": 0.83,
+                                    "content": "\\mathcal { R }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        189,
+                                        83,
+                                        505,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "induce this effect. One of the simplest formulations to obtain it is via a linear",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                101,
+                                90,
+                                509,
+                                113
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        101,
+                                        90,
+                                        387,
+                                        113
+                                    ],
+                                    "score": 1.0,
+                                    "content": "combination of the kernel gradients scaled by a positive factor, that is,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        388,
+                                        94,
+                                        484,
+                                        108
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\begin{array} { r } { \\beta \\sum _ { j = 1 } ^ { n } \\nabla _ { \\mathbf { w } _ { i } ^ { t } } k ( \\mathbf { w } _ { i } ^ { t } , \\mathbf { w } _ { j } ^ { t } ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        484,
+                                        90,
+                                        509,
+                                        113
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                106,
+                                505,
+                                121
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        107,
+                                        140,
+                                        119
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\beta \\in \\mathbb { R } _ { * } ^ { + }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        140,
+                                        106,
+                                        232,
+                                        121
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". We will see in Section",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        233,
+                                        106,
+                                        242,
+                                        121
+                                    ],
+                                    "score": 0.79,
+                                    "content": "\\begin{array} { l } { 3 } \\\\ { . } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        243,
+                                        106,
+                                        313,
+                                        121
+                                    ],
+                                    "score": 1.0,
+                                    "content": "how the choice of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        313,
+                                        108,
+                                        321,
+                                        119
+                                    ],
+                                    "score": 0.84,
+                                    "content": "\\beta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        321,
+                                        106,
+                                        505,
+                                        121
+                                    ],
+                                    "score": 1.0,
+                                    "content": "can be justified in order to obtain convergence",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                118,
+                                506,
+                                131
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        118,
+                                        420,
+                                        131
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to the Bayesian posterior together with alternative possible formulations of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        420,
+                                        119,
+                                        430,
+                                        128
+                                    ],
+                                    "score": 0.84,
+                                    "content": "\\mathcal { R }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        430,
+                                        118,
+                                        506,
+                                        131
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that preserve this",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                131,
+                                162,
+                                143
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        131,
+                                        162,
+                                        143
+                                    ],
+                                    "score": 1.0,
+                                    "content": "convergence.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        }
+                    ],
+                    "index": 2.5,
+                    "bbox_fs": [
+                        101,
+                        72,
+                        509,
+                        143
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        153,
+                        270,
+                        165
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                152,
+                                271,
+                                168
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        152,
+                                        271,
+                                        168
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2.2 Repulsive force in function space",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        173,
+                        506,
+                        284
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                173,
+                                505,
+                                186
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        174,
+                                        410,
+                                        186
+                                    ],
+                                    "score": 1.0,
+                                    "content": "To overcome the aforementioned overparameterization issue, the update in Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        410,
+                                        173,
+                                        423,
+                                        186
+                                    ],
+                                    "score": 0.83,
+                                    "content": "\\textcircled { 3 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        423,
+                                        174,
+                                        505,
+                                        186
+                                    ],
+                                    "score": 1.0,
+                                    "content": "can be formulated in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                185,
+                                505,
+                                197
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        185,
+                                        277,
+                                        197
+                                    ],
+                                    "score": 1.0,
+                                    "content": "function space instead of weight space. Let",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        277,
+                                        185,
+                                        348,
+                                        197
+                                    ],
+                                    "score": 0.93,
+                                    "content": "f : \\mathbf { w } \\mapsto f ( \\cdot ; \\mathbf { w } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        348,
+                                        185,
+                                        505,
+                                        197
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be the map that maps a configuration of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                196,
+                                505,
+                                209
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        196,
+                                        138,
+                                        209
+                                    ],
+                                    "score": 1.0,
+                                    "content": "weights",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        138,
+                                        196,
+                                        172,
+                                        207
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\mathbf { w } \\in \\mathbb { R } ^ { d }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        172,
+                                        196,
+                                        444,
+                                        209
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to the corresponding neural network regression function and denote as",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        445,
+                                        196,
+                                        505,
+                                        209
+                                    ],
+                                    "score": 0.92,
+                                    "content": "f _ { i } : = f ( \\cdot ; { \\mathbf w } _ { i } )",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                207,
+                                506,
+                                220
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        207,
+                                        311,
+                                        220
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the function with a certain configuration of weights",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        311,
+                                        209,
+                                        324,
+                                        219
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\mathbf { w } _ { i }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        324,
+                                        207,
+                                        415,
+                                        220
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". We can now consider",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        415,
+                                        210,
+                                        423,
+                                        218
+                                    ],
+                                    "score": 0.75,
+                                    "content": "n",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        423,
+                                        207,
+                                        506,
+                                        220
+                                    ],
+                                    "score": 1.0,
+                                    "content": "particles in function",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                216,
+                                508,
+                                233
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        216,
+                                        131,
+                                        233
+                                    ],
+                                    "score": 1.0,
+                                    "content": "space",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        132,
+                                        218,
+                                        164,
+                                        231
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\{ f _ { i } \\} _ { i = 1 } ^ { n }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        165,
+                                        216,
+                                        186,
+                                        233
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        187,
+                                        219,
+                                        215,
+                                        230
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\pmb { f } \\in \\mathcal { F }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        215,
+                                        216,
+                                        478,
+                                        233
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and model their interaction with a general positive definite kernel",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        479,
+                                        219,
+                                        503,
+                                        230
+                                    ],
+                                    "score": 0.91,
+                                    "content": "k ( \\cdot , \\cdot )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        503,
+                                        216,
+                                        508,
+                                        233
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                228,
+                                505,
+                                242
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        228,
+                                        309,
+                                        242
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We also consider the implicit functional likelihood",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        309,
+                                        230,
+                                        349,
+                                        241
+                                    ],
+                                    "score": 0.92,
+                                    "content": "p ( \\pmb { y } | \\pmb { x } , \\pmb { f } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        349,
+                                        228,
+                                        462,
+                                        242
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", determined by the measure",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        463,
+                                        230,
+                                        505,
+                                        241
+                                    ],
+                                    "score": 0.91,
+                                    "content": "p ( \\pmb { y } | \\pmb { x } , \\mathbf { w } )",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                238,
+                                507,
+                                254
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        238,
+                                        306,
+                                        254
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in the weight space, as well as the functional prior",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        241,
+                                        327,
+                                        252
+                                    ],
+                                    "score": 0.91,
+                                    "content": "p ( f )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        327,
+                                        238,
+                                        507,
+                                        254
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", which can either be defined separately (e.g.,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                250,
+                                506,
+                                266
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        250,
+                                        419,
+                                        266
+                                    ],
+                                    "score": 1.0,
+                                    "content": "using a GP) or modeled as a push-forward measure of the weight-space prior",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        419,
+                                        251,
+                                        441,
+                                        263
+                                    ],
+                                    "score": 0.91,
+                                    "content": "p ( \\mathbf { w } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        441,
+                                        250,
+                                        506,
+                                        266
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Together, they",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                261,
+                                506,
+                                275
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        261,
+                                        271,
+                                        275
+                                    ],
+                                    "score": 1.0,
+                                    "content": "determine the posterior in function space",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        271,
+                                        262,
+                                        302,
+                                        274
+                                    ],
+                                    "score": 0.92,
+                                    "content": "p ( \\pmb { f } | \\mathcal { D } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        261,
+                                        506,
+                                        275
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". The functional evolution of a particle can then be",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                272,
+                                151,
+                                285
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        272,
+                                        151,
+                                        285
+                                    ],
+                                    "score": 1.0,
+                                    "content": "written as:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 11.5,
+                    "bbox_fs": [
+                        104,
+                        173,
+                        508,
+                        285
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        182,
+                        287,
+                        441,
+                        332
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                182,
+                                287,
+                                441,
+                                332
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        182,
+                                        287,
+                                        441,
+                                        332
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\begin{array} { r l } & { f _ { i } ^ { t + 1 } \\gets f _ { i } ^ { t } + \\epsilon _ { t } \\phi ( f _ { i } ^ { t } ) } \\\\ { \\mathrm { t h } \\quad } & { \\phi ( f _ { i } ^ { t } ) = \\nabla _ { f _ { i } ^ { t } } \\log p ( f _ { i } ^ { t } | \\mathcal { D } ) - \\mathcal { R } \\left( \\left\\{ \\nabla _ { f _ { i } ^ { t } } k ( f _ { i } ^ { t } , f _ { j } ^ { t } ) \\right\\} _ { j = 1 } ^ { n } \\right) . } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "6e9ccd562a52a4d7474eb2dbb571b766cb26754c555d1761309dd914491e04b8.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                182,
+                                287,
+                                441,
+                                302.0
+                            ],
+                            "spans": [],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                182,
+                                302.0,
+                                441,
+                                317.0
+                            ],
+                            "spans": [],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                182,
+                                317.0,
+                                441,
+                                332.0
+                            ],
+                            "spans": [],
+                            "index": 19
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        109,
+                        335,
+                        504,
+                        369
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                335,
+                                505,
+                                348
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        335,
+                                        505,
+                                        348
+                                    ],
+                                    "score": 1.0,
+                                    "content": "However, computing the update in function space is neither tractable nor practical, which is why two",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                108,
+                                347,
+                                505,
+                                358
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        108,
+                                        347,
+                                        505,
+                                        358
+                                    ],
+                                    "score": 1.0,
+                                    "content": "additional considerations are needed. The first one regards the infinite dimensionality of function",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                357,
+                                403,
+                                370
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        357,
+                                        403,
+                                        370
+                                    ],
+                                    "score": 1.0,
+                                    "content": "space, which we circumvent using a canonical projection into a subspace:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 21,
+                    "bbox_fs": [
+                        107,
+                        335,
+                        505,
+                        370
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        371,
+                        503,
+                        396
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                369,
+                                506,
+                                385
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        369,
+                                        292,
+                                        385
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Definition 1 (Canonical projection). For any",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        293,
+                                        371,
+                                        323,
+                                        382
+                                    ],
+                                    "score": 0.88,
+                                    "content": "A \\subset { \\mathcal { X } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        323,
+                                        369,
+                                        368,
+                                        385
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", we define",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        368,
+                                        370,
+                                        434,
+                                        383
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\pi _ { A } : \\mathbb { R } ^ { \\mathcal { X } } \\to \\mathbb { R } ^ { A }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        434,
+                                        369,
+                                        506,
+                                        385
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as the canonical",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                381,
+                                302,
+                                397
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        381,
+                                        169,
+                                        397
+                                    ],
+                                    "score": 1.0,
+                                    "content": "projection onto",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        170,
+                                        383,
+                                        178,
+                                        393
+                                    ],
+                                    "score": 0.69,
+                                    "content": "A",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        178,
+                                        381,
+                                        212,
+                                        397
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", that is,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        212,
+                                        383,
+                                        297,
+                                        395
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\pi _ { A } ( f ) = \\{ f ( a ) \\} _ { a \\in A }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        297,
+                                        381,
+                                        302,
+                                        397
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 23.5,
+                    "bbox_fs": [
+                        105,
+                        369,
+                        506,
+                        397
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        402,
+                        505,
+                        458
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                402,
+                                505,
+                                415
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        402,
+                                        505,
+                                        415
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In other words, the kernel will not be evaluated directly in function space, but on the projection",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                413,
+                                506,
+                                426
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        413,
+                                        182,
+                                        426
+                                    ],
+                                    "score": 0.91,
+                                    "content": "k \\big ( \\pi _ { B } ( f ) , \\pi _ { B } ( f ^ { \\prime } ) \\big )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        182,
+                                        413,
+                                        205,
+                                        426
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", with",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        206,
+                                        414,
+                                        215,
+                                        424
+                                    ],
+                                    "score": 0.81,
+                                    "content": "B",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        216,
+                                        413,
+                                        506,
+                                        426
+                                    ],
+                                    "score": 1.0,
+                                    "content": "being a subset of the input space given by a batch of training data points.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                424,
+                                506,
+                                438
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        424,
+                                        506,
+                                        438
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The second consideration is to project this update back into the parameter space and evolve a set of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                435,
+                                506,
+                                448
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        435,
+                                        506,
+                                        448
+                                    ],
+                                    "score": 1.0,
+                                    "content": "particles there, because ultimately we are interested in representing the functions by parameterized",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                445,
+                                477,
+                                459
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        445,
+                                        369,
+                                        459
+                                    ],
+                                    "score": 1.0,
+                                    "content": "neural networks. For this purpose, we can use the Jacobian of the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        369,
+                                        447,
+                                        374,
+                                        456
+                                    ],
+                                    "score": 0.76,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        374,
+                                        445,
+                                        477,
+                                        459
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-th particle as a projector:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 27,
+                    "bbox_fs": [
+                        105,
+                        402,
+                        506,
+                        459
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        141,
+                        470,
+                        470,
+                        500
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                141,
+                                470,
+                                470,
+                                500
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        470,
+                                        470,
+                                        500
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\phi ( { \\mathbf w } _ { i } ^ { t } ) = \\left( \\frac { \\partial f _ { i } ^ { t } } { \\partial { \\mathbf w } _ { i } ^ { t } } \\right) ^ { \\top } \\left[ \\nabla _ { f _ { i } ^ { t } } \\log p ( f _ { i } ^ { t } | { \\mathcal D } ) - { \\mathcal R } \\left( \\left\\{ \\nabla _ { f _ { i } ^ { t } } k ( \\pi _ { B } ( f _ { i } ^ { t } ) , \\pi _ { B } ( f _ { j } ^ { t } ) ) \\right\\} _ { j = 1 } ^ { n } \\right) \\right] .",
+                                    "type": "interline_equation",
+                                    "image_path": "d7dea1ea5314c734775cfe499bded9ea6e655f30206ef90295c8a3d5d82d37d3.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 31,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                141,
+                                470,
+                                470,
+                                480.0
+                            ],
+                            "spans": [],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                480.0,
+                                470,
+                                490.0
+                            ],
+                            "spans": [],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                490.0,
+                                470,
+                                500.0
+                            ],
+                            "spans": [],
+                            "index": 32
+                        }
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        106,
+                        511,
+                        340,
+                        524
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                510,
+                                341,
+                                525
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        510,
+                                        341,
+                                        525
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2.3 Comparison to Stein variational gradient descent",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 33
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        530,
+                        487,
+                        543
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                530,
+                                488,
+                                545
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        530,
+                                        289,
+                                        545
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Note that our update is reminiscent of SVGD",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        290,
+                                        533,
+                                        306,
+                                        542
+                                    ],
+                                    "score": 0.34,
+                                    "content": "\\mathbb { \\left[ 5 1 \\right] }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        530,
+                                        488,
+                                        545
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", which in parameter space can be written as:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        }
+                    ],
+                    "index": 34,
+                    "bbox_fs": [
+                        105,
+                        530,
+                        488,
+                        545
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        173,
+                        547,
+                        438,
+                        582
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                173,
+                                547,
+                                438,
+                                582
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        173,
+                                        547,
+                                        438,
+                                        582
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\phi ( \\mathbf { w } _ { i } ^ { t } ) = \\sum _ { j = 1 } ^ { n } k ( \\mathbf { w } _ { i } ^ { t } , \\mathbf { w } _ { j } ^ { t } ) \\nabla _ { \\mathbf { w } _ { i } ^ { t } } \\log p ( \\mathbf { w } _ { i } ^ { t } | \\mathcal { D } ) + \\sum _ { j = 1 } ^ { n } \\nabla _ { \\mathbf { w } _ { j } ^ { t } } k ( \\mathbf { w } _ { j } ^ { t } , \\mathbf { w } _ { i } ^ { t } ) .",
+                                    "type": "interline_equation",
+                                    "image_path": "ed4ba25f1f792a3ef21feee9794a7aaba9ed6181f2313384dd85bba5b6760967.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 36,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                173,
+                                547,
+                                438,
+                                558.6666666666666
+                            ],
+                            "spans": [],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                173,
+                                558.6666666666666,
+                                438,
+                                570.3333333333333
+                            ],
+                            "spans": [],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                173,
+                                570.3333333333333,
+                                438,
+                                581.9999999999999
+                            ],
+                            "spans": [],
+                            "index": 37
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        585,
+                        506,
+                        630
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                585,
+                                505,
+                                597
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        585,
+                                        505,
+                                        597
+                                    ],
+                                    "score": 1.0,
+                                    "content": "It is important to notice that here, the gradients are averaged across all the particles using the kernel",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                596,
+                                506,
+                                609
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        596,
+                                        506,
+                                        609
+                                    ],
+                                    "score": 1.0,
+                                    "content": "matrix. Interestingly, SVGD can be asymptotically interpreted as gradient flow of the KL divergence",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                606,
+                                506,
+                                620
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        606,
+                                        506,
+                                        620
+                                    ],
+                                    "score": 1.0,
+                                    "content": "under a new metric induced by the Stein operator [16, 50] (see Appendix D for more details). Moving",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                618,
+                                410,
+                                630
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        618,
+                                        295,
+                                        630
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the inference from parameter to function space",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        618,
+                                        313,
+                                        629
+                                    ],
+                                    "score": 0.43,
+                                    "content": "\\pmb { \\mathbb { Z } } 6 \\|",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        314,
+                                        618,
+                                        410,
+                                        630
+                                    ],
+                                    "score": 1.0,
+                                    "content": "leads to the update rule",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        }
+                    ],
+                    "index": 39.5,
+                    "bbox_fs": [
+                        105,
+                        585,
+                        506,
+                        630
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        154,
+                        633,
+                        457,
+                        668
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                154,
+                                633,
+                                457,
+                                668
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        154,
+                                        633,
+                                        457,
+                                        668
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\phi ( \\mathbf { w } _ { i } ^ { t } ) = \\left( \\frac { \\partial f _ { i } ^ { t } } { \\partial \\mathbf { w } _ { i } ^ { t } } \\right) ^ { \\top } \\left( \\frac { 1 } { n } \\sum _ { j = 1 } ^ { n } k ( f _ { i } ^ { t } , f _ { j } ^ { t } ) \\nabla _ { f _ { j } ^ { t } } \\log p ( f _ { j } ^ { t } | \\mathcal { D } ) + \\nabla _ { f _ { j } ^ { t } } k ( f _ { i } ^ { t } , f _ { j } ^ { t } ) \\right) .",
+                                    "type": "interline_equation",
+                                    "image_path": "da910223233132ed75eba544433552d88de5b055ed7c20ab997ee811df84045c.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 43,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                154,
+                                633,
+                                457,
+                                644.6666666666666
+                            ],
+                            "spans": [],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                154,
+                                644.6666666666666,
+                                457,
+                                656.3333333333333
+                            ],
+                            "spans": [],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                154,
+                                656.3333333333333,
+                                457,
+                                667.9999999999999
+                            ],
+                            "spans": [],
+                            "index": 44
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        677,
+                        505,
+                        723
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                677,
+                                505,
+                                690
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        677,
+                                        505,
+                                        690
+                                    ],
+                                    "score": 1.0,
+                                    "content": "This way of averaging gradients using a kernel can be dangerous in high-dimensional settings, where",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                687,
+                                505,
+                                702
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        687,
+                                        434,
+                                        702
+                                    ],
+                                    "score": 1.0,
+                                    "content": "kernel methods often suffer from the curse of dimensionality. Moreover, in Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        434,
+                                        689,
+                                        447,
+                                        702
+                                    ],
+                                    "score": 0.79,
+                                    "content": "\\textcircled{6}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        447,
+                                        687,
+                                        505,
+                                        702
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the posterior",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                699,
+                                505,
+                                713
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        699,
+                                        505,
+                                        713
+                                    ],
+                                    "score": 1.0,
+                                    "content": "gradients of the particles are averaged using their similarity in weight space, which can be misleading",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                711,
+                                505,
+                                724
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        711,
+                                        289,
+                                        724
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in multi-modal posteriors. Worse yet, in Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        290,
+                                        711,
+                                        302,
+                                        723
+                                    ],
+                                    "score": 0.8,
+                                    "content": "\\textcircled{7}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        711,
+                                        505,
+                                        724
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the gradients are averaged in function space and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                72,
+                                506,
+                                85
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        72,
+                                        293,
+                                        85
+                                    ],
+                                    "score": 1.0,
+                                    "content": "are then projected back using exclusively the",
+                                    "type": "text",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        294,
+                                        74,
+                                        298,
+                                        83
+                                    ],
+                                    "score": 0.72,
+                                    "content": "i",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        299,
+                                        72,
+                                        506,
+                                        85
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-th Jacobian, which can be harmful given that it is",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                83,
+                                506,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        83,
+                                        506,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "not guaranteed that distances between functions evaluated on a subset of their input space resemble",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                94,
+                                506,
+                                108
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        94,
+                                        506,
+                                        108
+                                    ],
+                                    "score": 1.0,
+                                    "content": "their true distance. Our proposed method, on the other hand, does not employ any averaging of the",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                106,
+                                469,
+                                118
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        106,
+                                        469,
+                                        118
+                                    ],
+                                    "score": 1.0,
+                                    "content": "posterior gradients and thus comes closest to the true particle gradients in deep ensembles.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 46.5,
+                    "bbox_fs": [
+                        105,
+                        677,
+                        505,
+                        724
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        72,
+                        505,
+                        117
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                72,
+                                506,
+                                85
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        72,
+                                        293,
+                                        85
+                                    ],
+                                    "score": 1.0,
+                                    "content": "are then projected back using exclusively the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        294,
+                                        74,
+                                        298,
+                                        83
+                                    ],
+                                    "score": 0.72,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        299,
+                                        72,
+                                        506,
+                                        85
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-th Jacobian, which can be harmful given that it is",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                83,
+                                506,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        83,
+                                        506,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "not guaranteed that distances between functions evaluated on a subset of their input space resemble",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                94,
+                                506,
+                                108
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        94,
+                                        506,
+                                        108
+                                    ],
+                                    "score": 1.0,
+                                    "content": "their true distance. Our proposed method, on the other hand, does not employ any averaging of the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                106,
+                                469,
+                                118
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        106,
+                                        469,
+                                        118
+                                    ],
+                                    "score": 1.0,
+                                    "content": "posterior gradients and thus comes closest to the true particle gradients in deep ensembles.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 1.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        131,
+                        326,
+                        145
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                130,
+                                327,
+                                149
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        130,
+                                        327,
+                                        149
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3 Repulsive deep ensembles are Bayesian",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        155,
+                        506,
+                        200
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                155,
+                                506,
+                                169
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        155,
+                                        506,
+                                        169
+                                    ],
+                                    "score": 1.0,
+                                    "content": "So far, we represented the repulsive force as a general function of the gradients of a kernel. In this",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                166,
+                                505,
+                                179
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        166,
+                                        505,
+                                        179
+                                    ],
+                                    "score": 1.0,
+                                    "content": "section, we show how to determine the explicit form of the repulsive term, such that the resulting",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                178,
+                                505,
+                                190
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        178,
+                                        505,
+                                        190
+                                    ],
+                                    "score": 1.0,
+                                    "content": "update rule is equivalent to the discretization of the gradient flow dynamics of the KL divergence in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                188,
+                                507,
+                                201
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        188,
+                                        507,
+                                        201
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Wasserstein space. We begin by introducing the concepts of particle approximation and gradient flow.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 6.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        212,
+                        229,
+                        224
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                210,
+                                230,
+                                227
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        210,
+                                        230,
+                                        227
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3.1 Particle approximation",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        232,
+                        504,
+                        255
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                232,
+                                505,
+                                246
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        232,
+                                        505,
+                                        246
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A particle-based approximation of a target measure depends on a set of weighted samples",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                242,
+                                367,
+                                257
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        243,
+                                        162,
+                                        256
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\{ ( \\bar { x _ { i } } , w _ { i } ) \\} _ { i = 1 } ^ { n }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        163,
+                                        242,
+                                        367,
+                                        257
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", for which an empirical measure can be defined as",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 10.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        253,
+                        258,
+                        358,
+                        290
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                253,
+                                258,
+                                358,
+                                290
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        253,
+                                        258,
+                                        358,
+                                        290
+                                    ],
+                                    "score": 0.95,
+                                    "content": "\\rho ( x ) = \\sum _ { i = 1 } ^ { n } w _ { i } \\delta ( x - x _ { i } ) ,",
+                                    "type": "interline_equation",
+                                    "image_path": "b51a8eebc42b5a02f34979b6c46328fac936b6561c35ce4b3a464937651a8dd3.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                253,
+                                258,
+                                358,
+                                274.0
+                            ],
+                            "spans": [],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                253,
+                                274.0,
+                                358,
+                                290.0
+                            ],
+                            "spans": [],
+                            "index": 13
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        293,
+                        505,
+                        338
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                102,
+                                287,
+                                509,
+                                311
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        102,
+                                        287,
+                                        133,
+                                        311
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        134,
+                                        293,
+                                        150,
+                                        306
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\delta ( \\cdot )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        150,
+                                        287,
+                                        326,
+                                        311
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the Dirac delta function and the weights",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        326,
+                                        295,
+                                        338,
+                                        304
+                                    ],
+                                    "score": 0.86,
+                                    "content": "w _ { i }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        338,
+                                        287,
+                                        368,
+                                        311
+                                    ],
+                                    "score": 1.0,
+                                    "content": "satisfy",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        369,
+                                        293,
+                                        413,
+                                        305
+                                    ],
+                                    "score": 0.92,
+                                    "content": "w _ { i } \\in [ 0 , 1 ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        413,
+                                        287,
+                                        431,
+                                        311
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        432,
+                                        293,
+                                        487,
+                                        306
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\textstyle \\sum _ { i = 1 } ^ { n } w _ { i } = 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        488,
+                                        287,
+                                        509,
+                                        311
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". To",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                304,
+                                506,
+                                316
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        304,
+                                        241,
+                                        316
+                                    ],
+                                    "score": 1.0,
+                                    "content": "approximate a target distribution",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        241,
+                                        305,
+                                        261,
+                                        316
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\pi ( x )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        262,
+                                        304,
+                                        506,
+                                        316
+                                    ],
+                                    "score": 1.0,
+                                    "content": "using the empirical measure, the particles and their weights",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                315,
+                                505,
+                                328
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        315,
+                                        484,
+                                        328
+                                    ],
+                                    "score": 1.0,
+                                    "content": "need to be selected in a principled manner that minimizes some measure of distance between",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        484,
+                                        316,
+                                        505,
+                                        327
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\pi ( x )",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                326,
+                                488,
+                                339
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        326,
+                                        123,
+                                        339
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        124,
+                                        326,
+                                        143,
+                                        338
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\rho ( x )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        144,
+                                        326,
+                                        198,
+                                        339
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(e.g., a set of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        199,
+                                        327,
+                                        208,
+                                        336
+                                    ],
+                                    "score": 0.85,
+                                    "content": "N",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        209,
+                                        326,
+                                        298,
+                                        339
+                                    ],
+                                    "score": 1.0,
+                                    "content": "samples with weights",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        299,
+                                        326,
+                                        342,
+                                        338
+                                    ],
+                                    "score": 0.92,
+                                    "content": "w _ { i } = 1 / N",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        342,
+                                        326,
+                                        488,
+                                        339
+                                    ],
+                                    "score": 1.0,
+                                    "content": "obtained using an MCMC method).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 15.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        350,
+                        273,
+                        362
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                348,
+                                275,
+                                364
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        348,
+                                        275,
+                                        364
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3.2 Gradient flow in parameter space",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        369,
+                        505,
+                        414
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                369,
+                                506,
+                                383
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        369,
+                                        207,
+                                        383
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Given a smooth function",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        207,
+                                        369,
+                                        257,
+                                        380
+                                    ],
+                                    "score": 0.9,
+                                    "content": "J : \\mathbb { R } ^ { d }  \\mathbb { R }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        257,
+                                        369,
+                                        506,
+                                        383
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in Euclidean space, we can minimize it by creating a path that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                380,
+                                506,
+                                394
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        380,
+                                        373,
+                                        394
+                                    ],
+                                    "score": 1.0,
+                                    "content": "follows its negative gradient starting from some initial conditions",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        373,
+                                        383,
+                                        384,
+                                        393
+                                    ],
+                                    "score": 0.86,
+                                    "content": "x _ { 0 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        385,
+                                        380,
+                                        432,
+                                        394
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". The curve",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        432,
+                                        381,
+                                        450,
+                                        393
+                                    ],
+                                    "score": 0.91,
+                                    "content": "x ( t )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        451,
+                                        380,
+                                        506,
+                                        394
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with starting",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                392,
+                                506,
+                                404
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        392,
+                                        130,
+                                        404
+                                    ],
+                                    "score": 1.0,
+                                    "content": "point",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        130,
+                                        393,
+                                        142,
+                                        403
+                                    ],
+                                    "score": 0.85,
+                                    "content": "x _ { 0 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        142,
+                                        392,
+                                        506,
+                                        404
+                                    ],
+                                    "score": 1.0,
+                                    "content": "described by that path is called gradient flow. The dynamics and evolution in time of a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                403,
+                                481,
+                                415
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        403,
+                                        481,
+                                        415
+                                    ],
+                                    "score": 1.0,
+                                    "content": "considered point in the space under this minimization problem can be described as the ODE1",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 20.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        271,
+                        417,
+                        340,
+                        441
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                271,
+                                417,
+                                340,
+                                441
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        271,
+                                        417,
+                                        340,
+                                        441
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\frac { d \\boldsymbol { x } } { d t } = - \\boldsymbol { \\nabla } J ( \\boldsymbol { x } ) .",
+                                    "type": "interline_equation",
+                                    "image_path": "4af9c8caebc8dd0f4bb240ad868ba49b8044f29f61003074e861ae4833cdfbee.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 23,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                271,
+                                417,
+                                340,
+                                441
+                            ],
+                            "spans": [],
+                            "index": 23
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        442,
+                        505,
+                        475
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                442,
+                                504,
+                                455
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        442,
+                                        504,
+                                        455
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We can extend this concept to the space of probability distributions (Wasserstein gradient flow) [3].",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                453,
+                                505,
+                                466
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        453,
+                                        311,
+                                        466
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Let us consider the space of probability measures",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        311,
+                                        453,
+                                        343,
+                                        466
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\mathcal { P } _ { 2 } ( \\mathcal { M } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        343,
+                                        453,
+                                        505,
+                                        466
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", that is, the set of probability measures",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                464,
+                                333,
+                                476
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        464,
+                                        316,
+                                        476
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with finite second moments defined on the manifold",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        316,
+                                        466,
+                                        329,
+                                        474
+                                    ],
+                                    "score": 0.83,
+                                    "content": "\\mathcal { M }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        329,
+                                        464,
+                                        333,
+                                        476
+                                    ],
+                                    "score": 1.0,
+                                    "content": ":",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 25
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        159,
+                        476,
+                        451,
+                        504
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                159,
+                                476,
+                                451,
+                                504
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        159,
+                                        476,
+                                        451,
+                                        504
+                                    ],
+                                    "score": 0.96,
+                                    "content": "\\mathcal { P } _ { 2 } ( \\mathcal { M } ) = \\left\\{ \\varphi : \\mathcal { M } \\to [ 0 , \\infty ) \\bigg | \\int _ { \\mathcal { M } } \\mathrm { d } \\varphi = 1 , ~ \\int _ { \\mathcal { M } } | x | ^ { 2 } \\varphi ( x ) \\mathrm { d } x < + \\infty \\right\\} .",
+                                    "type": "interline_equation",
+                                    "image_path": "c1e5d77c719b4d2fa7a0247805d6e0144779c241f5db03b43a6f1d113276ff19.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 28,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                159,
+                                476,
+                                451,
+                                485.3333333333333
+                            ],
+                            "spans": [],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                159,
+                                485.3333333333333,
+                                451,
+                                494.66666666666663
+                            ],
+                            "spans": [],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                159,
+                                494.66666666666663,
+                                451,
+                                503.99999999999994
+                            ],
+                            "spans": [],
+                            "index": 29
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        109,
+                        506,
+                        502,
+                        529
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                505,
+                                504,
+                                519
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        505,
+                                        137,
+                                        519
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Taking",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        138,
+                                        506,
+                                        170,
+                                        518
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\Pi ( \\mu , \\nu )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        171,
+                                        505,
+                                        405,
+                                        519
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as the set of joint probability measures with marginals",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        406,
+                                        508,
+                                        423,
+                                        518
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\mu , \\nu",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        423,
+                                        505,
+                                        504,
+                                        519
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", we can define the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                516,
+                                282,
+                                530
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        516,
+                                        235,
+                                        530
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Wasserstein metric on the space",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        236,
+                                        517,
+                                        268,
+                                        529
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\mathcal { P } _ { 2 } ( \\mathcal { M } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        268,
+                                        516,
+                                        282,
+                                        530
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        }
+                    ],
+                    "index": 30.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        217,
+                        531,
+                        393,
+                        557
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                217,
+                                531,
+                                393,
+                                557
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        217,
+                                        531,
+                                        393,
+                                        557
+                                    ],
+                                    "score": 0.94,
+                                    "content": "W _ { 2 } ^ { 2 } ( \\mu , \\nu ) = \\operatorname* { i n f } _ { \\pi \\in \\Pi ( \\mu , \\nu ) } \\int | x - y | ^ { 2 } { \\mathrm { d } } \\pi ( x , y ) .",
+                                    "type": "interline_equation",
+                                    "image_path": "22875a9421a3c955c184f36bee03fad9988e4e0d847133375befe3e5951b4f25.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 32,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                217,
+                                531,
+                                393,
+                                557
+                            ],
+                            "spans": [],
+                            "index": 32
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        560,
+                        504,
+                        583
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                559,
+                                505,
+                                574
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        559,
+                                        323,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Considering the optimization problem of a functional",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        324,
+                                        560,
+                                        393,
+                                        573
+                                    ],
+                                    "score": 0.92,
+                                    "content": "J : \\mathcal { P } _ { 2 } ( \\mathcal { M } )  \\mathbb { R }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        393,
+                                        559,
+                                        443,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", such as the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        443,
+                                        561,
+                                        458,
+                                        571
+                                    ],
+                                    "score": 0.39,
+                                    "content": "\\mathrm { K L }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        458,
+                                        559,
+                                        505,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": "divergence",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                571,
+                                409,
+                                585
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        571,
+                                        276,
+                                        584
+                                    ],
+                                    "score": 1.0,
+                                    "content": "between the particle approximation in Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        276,
+                                        571,
+                                        289,
+                                        585
+                                    ],
+                                    "score": 0.83,
+                                    "content": "\\textcircled { 8 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        571,
+                                        385,
+                                        584
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and the target posterior",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        385,
+                                        572,
+                                        405,
+                                        583
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\pi ( x )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        405,
+                                        571,
+                                        409,
+                                        584
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        }
+                    ],
+                    "index": 33.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        187,
+                        586,
+                        423,
+                        612
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                187,
+                                586,
+                                423,
+                                612
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        187,
+                                        586,
+                                        423,
+                                        612
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\operatorname* { i n f } _ { \\rho \\in \\mathcal { P } _ { 2 } ( \\mathcal { M } ) } D _ { K L } ( \\rho , \\pi ) = \\int _ { \\mathcal { M } } ( \\log \\rho ( x ) - \\log \\pi ( x ) ) \\rho ( x ) \\mathrm { d } x ,",
+                                    "type": "interline_equation",
+                                    "image_path": "202eca2cfd27979881321c7e7947951e3cc456330188130d02fcab3cc4c0abde.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 35,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                187,
+                                586,
+                                423,
+                                612
+                            ],
+                            "spans": [],
+                            "index": 35
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        614,
+                        505,
+                        637
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                613,
+                                505,
+                                626
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        613,
+                                        252,
+                                        626
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the evolution in time of the measure",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        252,
+                                        616,
+                                        259,
+                                        626
+                                    ],
+                                    "score": 0.8,
+                                    "content": "\\rho",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        259,
+                                        613,
+                                        505,
+                                        626
+                                    ],
+                                    "score": 1.0,
+                                    "content": "under the equivalent of the gradient, the Wasserstein gradient",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                623,
+                                331,
+                                638
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        623,
+                                        331,
+                                        638
+                                    ],
+                                    "score": 1.0,
+                                    "content": "flow, is described by the Liouville equation2 [38, 3, 64]:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 36.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        208,
+                        639,
+                        402,
+                        695
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                208,
+                                639,
+                                402,
+                                695
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        208,
+                                        639,
+                                        402,
+                                        695
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { l } { \\displaystyle \\frac { \\partial \\rho ( \\boldsymbol { x } ) } { \\partial t } = \\nabla \\cdot \\left( \\rho ( \\boldsymbol { x } ) \\nabla \\frac { \\delta } { \\delta \\rho } D _ { K L } ( \\rho , \\pi ) \\right) } \\\\ { \\displaystyle = \\nabla \\cdot \\left( \\rho ( \\boldsymbol { x } ) \\nabla \\big ( \\log \\rho ( \\boldsymbol { x } ) - \\log \\pi ( \\boldsymbol { x } ) \\big ) \\right) , } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "319c5dba11def8b47c62bbed7e518cec22d2bb6447df21ccd8c8f0ceacda0468.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 39.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                208,
+                                639,
+                                402,
+                                653.0
+                            ],
+                            "spans": [],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                208,
+                                653.0,
+                                402,
+                                667.0
+                            ],
+                            "spans": [],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                208,
+                                667.0,
+                                402,
+                                681.0
+                            ],
+                            "spans": [],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                208,
+                                681.0,
+                                402,
+                                695.0
+                            ],
+                            "spans": [],
+                            "index": 41
+                        }
+                    ]
+                }
+            ],
+            "page_idx": 4,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        741,
+                        309,
+                        750
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                301,
+                                740,
+                                310,
+                                753
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        301,
+                                        740,
+                                        310,
+                                        753
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        118,
+                        700,
+                        381,
+                        722
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                119,
+                                698,
+                                381,
+                                713
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        119,
+                                        698,
+                                        381,
+                                        713
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1 Together with the initial condition, this is know as the Cauchy problem.",
+                                    "type": "text"
+                                }
+                            ]
+                        },
+                        {
+                            "bbox": [
+                                118,
+                                709,
+                                266,
+                                724
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        118,
+                                        709,
+                                        266,
+                                        724
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2 Also referred to as continuity equation.",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        72,
+                        505,
+                        117
+                    ],
+                    "lines": [],
+                    "index": 1.5,
+                    "bbox_fs": [
+                        105,
+                        72,
+                        506,
+                        118
+                    ],
+                    "lines_deleted": true
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        131,
+                        326,
+                        145
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                130,
+                                327,
+                                149
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        130,
+                                        327,
+                                        149
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3 Repulsive deep ensembles are Bayesian",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        155,
+                        506,
+                        200
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                155,
+                                506,
+                                169
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        155,
+                                        506,
+                                        169
+                                    ],
+                                    "score": 1.0,
+                                    "content": "So far, we represented the repulsive force as a general function of the gradients of a kernel. In this",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                166,
+                                505,
+                                179
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        166,
+                                        505,
+                                        179
+                                    ],
+                                    "score": 1.0,
+                                    "content": "section, we show how to determine the explicit form of the repulsive term, such that the resulting",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                178,
+                                505,
+                                190
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        178,
+                                        505,
+                                        190
+                                    ],
+                                    "score": 1.0,
+                                    "content": "update rule is equivalent to the discretization of the gradient flow dynamics of the KL divergence in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                188,
+                                507,
+                                201
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        188,
+                                        507,
+                                        201
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Wasserstein space. We begin by introducing the concepts of particle approximation and gradient flow.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 6.5,
+                    "bbox_fs": [
+                        105,
+                        155,
+                        507,
+                        201
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        212,
+                        229,
+                        224
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                210,
+                                230,
+                                227
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        210,
+                                        230,
+                                        227
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3.1 Particle approximation",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        232,
+                        504,
+                        255
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                232,
+                                505,
+                                246
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        232,
+                                        505,
+                                        246
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A particle-based approximation of a target measure depends on a set of weighted samples",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                242,
+                                367,
+                                257
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        243,
+                                        162,
+                                        256
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\{ ( \\bar { x _ { i } } , w _ { i } ) \\} _ { i = 1 } ^ { n }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        163,
+                                        242,
+                                        367,
+                                        257
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", for which an empirical measure can be defined as",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 10.5,
+                    "bbox_fs": [
+                        105,
+                        232,
+                        505,
+                        257
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        253,
+                        258,
+                        358,
+                        290
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                253,
+                                258,
+                                358,
+                                290
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        253,
+                                        258,
+                                        358,
+                                        290
+                                    ],
+                                    "score": 0.95,
+                                    "content": "\\rho ( x ) = \\sum _ { i = 1 } ^ { n } w _ { i } \\delta ( x - x _ { i } ) ,",
+                                    "type": "interline_equation",
+                                    "image_path": "b51a8eebc42b5a02f34979b6c46328fac936b6561c35ce4b3a464937651a8dd3.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                253,
+                                258,
+                                358,
+                                274.0
+                            ],
+                            "spans": [],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                253,
+                                274.0,
+                                358,
+                                290.0
+                            ],
+                            "spans": [],
+                            "index": 13
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        293,
+                        505,
+                        338
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                102,
+                                287,
+                                509,
+                                311
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        102,
+                                        287,
+                                        133,
+                                        311
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        134,
+                                        293,
+                                        150,
+                                        306
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\delta ( \\cdot )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        150,
+                                        287,
+                                        326,
+                                        311
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the Dirac delta function and the weights",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        326,
+                                        295,
+                                        338,
+                                        304
+                                    ],
+                                    "score": 0.86,
+                                    "content": "w _ { i }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        338,
+                                        287,
+                                        368,
+                                        311
+                                    ],
+                                    "score": 1.0,
+                                    "content": "satisfy",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        369,
+                                        293,
+                                        413,
+                                        305
+                                    ],
+                                    "score": 0.92,
+                                    "content": "w _ { i } \\in [ 0 , 1 ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        413,
+                                        287,
+                                        431,
+                                        311
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        432,
+                                        293,
+                                        487,
+                                        306
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\textstyle \\sum _ { i = 1 } ^ { n } w _ { i } = 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        488,
+                                        287,
+                                        509,
+                                        311
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". To",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                304,
+                                506,
+                                316
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        304,
+                                        241,
+                                        316
+                                    ],
+                                    "score": 1.0,
+                                    "content": "approximate a target distribution",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        241,
+                                        305,
+                                        261,
+                                        316
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\pi ( x )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        262,
+                                        304,
+                                        506,
+                                        316
+                                    ],
+                                    "score": 1.0,
+                                    "content": "using the empirical measure, the particles and their weights",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                315,
+                                505,
+                                328
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        315,
+                                        484,
+                                        328
+                                    ],
+                                    "score": 1.0,
+                                    "content": "need to be selected in a principled manner that minimizes some measure of distance between",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        484,
+                                        316,
+                                        505,
+                                        327
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\pi ( x )",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                326,
+                                488,
+                                339
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        326,
+                                        123,
+                                        339
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        124,
+                                        326,
+                                        143,
+                                        338
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\rho ( x )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        144,
+                                        326,
+                                        198,
+                                        339
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(e.g., a set of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        199,
+                                        327,
+                                        208,
+                                        336
+                                    ],
+                                    "score": 0.85,
+                                    "content": "N",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        209,
+                                        326,
+                                        298,
+                                        339
+                                    ],
+                                    "score": 1.0,
+                                    "content": "samples with weights",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        299,
+                                        326,
+                                        342,
+                                        338
+                                    ],
+                                    "score": 0.92,
+                                    "content": "w _ { i } = 1 / N",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        342,
+                                        326,
+                                        488,
+                                        339
+                                    ],
+                                    "score": 1.0,
+                                    "content": "obtained using an MCMC method).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 15.5,
+                    "bbox_fs": [
+                        102,
+                        287,
+                        509,
+                        339
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        350,
+                        273,
+                        362
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                348,
+                                275,
+                                364
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        348,
+                                        275,
+                                        364
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3.2 Gradient flow in parameter space",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        369,
+                        505,
+                        414
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                369,
+                                506,
+                                383
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        369,
+                                        207,
+                                        383
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Given a smooth function",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        207,
+                                        369,
+                                        257,
+                                        380
+                                    ],
+                                    "score": 0.9,
+                                    "content": "J : \\mathbb { R } ^ { d }  \\mathbb { R }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        257,
+                                        369,
+                                        506,
+                                        383
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in Euclidean space, we can minimize it by creating a path that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                380,
+                                506,
+                                394
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        380,
+                                        373,
+                                        394
+                                    ],
+                                    "score": 1.0,
+                                    "content": "follows its negative gradient starting from some initial conditions",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        373,
+                                        383,
+                                        384,
+                                        393
+                                    ],
+                                    "score": 0.86,
+                                    "content": "x _ { 0 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        385,
+                                        380,
+                                        432,
+                                        394
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". The curve",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        432,
+                                        381,
+                                        450,
+                                        393
+                                    ],
+                                    "score": 0.91,
+                                    "content": "x ( t )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        451,
+                                        380,
+                                        506,
+                                        394
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with starting",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                392,
+                                506,
+                                404
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        392,
+                                        130,
+                                        404
+                                    ],
+                                    "score": 1.0,
+                                    "content": "point",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        130,
+                                        393,
+                                        142,
+                                        403
+                                    ],
+                                    "score": 0.85,
+                                    "content": "x _ { 0 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        142,
+                                        392,
+                                        506,
+                                        404
+                                    ],
+                                    "score": 1.0,
+                                    "content": "described by that path is called gradient flow. The dynamics and evolution in time of a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                403,
+                                481,
+                                415
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        403,
+                                        481,
+                                        415
+                                    ],
+                                    "score": 1.0,
+                                    "content": "considered point in the space under this minimization problem can be described as the ODE1",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 20.5,
+                    "bbox_fs": [
+                        105,
+                        369,
+                        506,
+                        415
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        271,
+                        417,
+                        340,
+                        441
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                271,
+                                417,
+                                340,
+                                441
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        271,
+                                        417,
+                                        340,
+                                        441
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\frac { d \\boldsymbol { x } } { d t } = - \\boldsymbol { \\nabla } J ( \\boldsymbol { x } ) .",
+                                    "type": "interline_equation",
+                                    "image_path": "4af9c8caebc8dd0f4bb240ad868ba49b8044f29f61003074e861ae4833cdfbee.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 23,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                271,
+                                417,
+                                340,
+                                441
+                            ],
+                            "spans": [],
+                            "index": 23
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        442,
+                        505,
+                        475
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                442,
+                                504,
+                                455
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        442,
+                                        504,
+                                        455
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We can extend this concept to the space of probability distributions (Wasserstein gradient flow) [3].",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                453,
+                                505,
+                                466
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        453,
+                                        311,
+                                        466
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Let us consider the space of probability measures",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        311,
+                                        453,
+                                        343,
+                                        466
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\mathcal { P } _ { 2 } ( \\mathcal { M } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        343,
+                                        453,
+                                        505,
+                                        466
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", that is, the set of probability measures",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                464,
+                                333,
+                                476
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        464,
+                                        316,
+                                        476
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with finite second moments defined on the manifold",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        316,
+                                        466,
+                                        329,
+                                        474
+                                    ],
+                                    "score": 0.83,
+                                    "content": "\\mathcal { M }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        329,
+                                        464,
+                                        333,
+                                        476
+                                    ],
+                                    "score": 1.0,
+                                    "content": ":",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 25,
+                    "bbox_fs": [
+                        105,
+                        442,
+                        505,
+                        476
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        159,
+                        476,
+                        451,
+                        504
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                159,
+                                476,
+                                451,
+                                504
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        159,
+                                        476,
+                                        451,
+                                        504
+                                    ],
+                                    "score": 0.96,
+                                    "content": "\\mathcal { P } _ { 2 } ( \\mathcal { M } ) = \\left\\{ \\varphi : \\mathcal { M } \\to [ 0 , \\infty ) \\bigg | \\int _ { \\mathcal { M } } \\mathrm { d } \\varphi = 1 , ~ \\int _ { \\mathcal { M } } | x | ^ { 2 } \\varphi ( x ) \\mathrm { d } x < + \\infty \\right\\} .",
+                                    "type": "interline_equation",
+                                    "image_path": "c1e5d77c719b4d2fa7a0247805d6e0144779c241f5db03b43a6f1d113276ff19.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 28,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                159,
+                                476,
+                                451,
+                                485.3333333333333
+                            ],
+                            "spans": [],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                159,
+                                485.3333333333333,
+                                451,
+                                494.66666666666663
+                            ],
+                            "spans": [],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                159,
+                                494.66666666666663,
+                                451,
+                                503.99999999999994
+                            ],
+                            "spans": [],
+                            "index": 29
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        109,
+                        506,
+                        502,
+                        529
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                505,
+                                504,
+                                519
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        505,
+                                        137,
+                                        519
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Taking",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        138,
+                                        506,
+                                        170,
+                                        518
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\Pi ( \\mu , \\nu )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        171,
+                                        505,
+                                        405,
+                                        519
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as the set of joint probability measures with marginals",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        406,
+                                        508,
+                                        423,
+                                        518
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\mu , \\nu",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        423,
+                                        505,
+                                        504,
+                                        519
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", we can define the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                516,
+                                282,
+                                530
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        516,
+                                        235,
+                                        530
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Wasserstein metric on the space",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        236,
+                                        517,
+                                        268,
+                                        529
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\mathcal { P } _ { 2 } ( \\mathcal { M } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        268,
+                                        516,
+                                        282,
+                                        530
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        }
+                    ],
+                    "index": 30.5,
+                    "bbox_fs": [
+                        107,
+                        505,
+                        504,
+                        530
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        217,
+                        531,
+                        393,
+                        557
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                217,
+                                531,
+                                393,
+                                557
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        217,
+                                        531,
+                                        393,
+                                        557
+                                    ],
+                                    "score": 0.94,
+                                    "content": "W _ { 2 } ^ { 2 } ( \\mu , \\nu ) = \\operatorname* { i n f } _ { \\pi \\in \\Pi ( \\mu , \\nu ) } \\int | x - y | ^ { 2 } { \\mathrm { d } } \\pi ( x , y ) .",
+                                    "type": "interline_equation",
+                                    "image_path": "22875a9421a3c955c184f36bee03fad9988e4e0d847133375befe3e5951b4f25.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 32,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                217,
+                                531,
+                                393,
+                                557
+                            ],
+                            "spans": [],
+                            "index": 32
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        560,
+                        504,
+                        583
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                559,
+                                505,
+                                574
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        559,
+                                        323,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Considering the optimization problem of a functional",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        324,
+                                        560,
+                                        393,
+                                        573
+                                    ],
+                                    "score": 0.92,
+                                    "content": "J : \\mathcal { P } _ { 2 } ( \\mathcal { M } )  \\mathbb { R }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        393,
+                                        559,
+                                        443,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", such as the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        443,
+                                        561,
+                                        458,
+                                        571
+                                    ],
+                                    "score": 0.39,
+                                    "content": "\\mathrm { K L }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        458,
+                                        559,
+                                        505,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": "divergence",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                571,
+                                409,
+                                585
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        571,
+                                        276,
+                                        584
+                                    ],
+                                    "score": 1.0,
+                                    "content": "between the particle approximation in Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        276,
+                                        571,
+                                        289,
+                                        585
+                                    ],
+                                    "score": 0.83,
+                                    "content": "\\textcircled { 8 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        571,
+                                        385,
+                                        584
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and the target posterior",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        385,
+                                        572,
+                                        405,
+                                        583
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\pi ( x )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        405,
+                                        571,
+                                        409,
+                                        584
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        }
+                    ],
+                    "index": 33.5,
+                    "bbox_fs": [
+                        106,
+                        559,
+                        505,
+                        585
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        187,
+                        586,
+                        423,
+                        612
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                187,
+                                586,
+                                423,
+                                612
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        187,
+                                        586,
+                                        423,
+                                        612
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\operatorname* { i n f } _ { \\rho \\in \\mathcal { P } _ { 2 } ( \\mathcal { M } ) } D _ { K L } ( \\rho , \\pi ) = \\int _ { \\mathcal { M } } ( \\log \\rho ( x ) - \\log \\pi ( x ) ) \\rho ( x ) \\mathrm { d } x ,",
+                                    "type": "interline_equation",
+                                    "image_path": "202eca2cfd27979881321c7e7947951e3cc456330188130d02fcab3cc4c0abde.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 35,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                187,
+                                586,
+                                423,
+                                612
+                            ],
+                            "spans": [],
+                            "index": 35
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        614,
+                        505,
+                        637
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                613,
+                                505,
+                                626
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        613,
+                                        252,
+                                        626
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the evolution in time of the measure",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        252,
+                                        616,
+                                        259,
+                                        626
+                                    ],
+                                    "score": 0.8,
+                                    "content": "\\rho",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        259,
+                                        613,
+                                        505,
+                                        626
+                                    ],
+                                    "score": 1.0,
+                                    "content": "under the equivalent of the gradient, the Wasserstein gradient",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                623,
+                                331,
+                                638
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        623,
+                                        331,
+                                        638
+                                    ],
+                                    "score": 1.0,
+                                    "content": "flow, is described by the Liouville equation2 [38, 3, 64]:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 36.5,
+                    "bbox_fs": [
+                        105,
+                        613,
+                        505,
+                        638
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        208,
+                        639,
+                        402,
+                        695
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                208,
+                                639,
+                                402,
+                                695
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        208,
+                                        639,
+                                        402,
+                                        695
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\begin{array} { l } { \\displaystyle \\frac { \\partial \\rho ( \\boldsymbol { x } ) } { \\partial t } = \\nabla \\cdot \\left( \\rho ( \\boldsymbol { x } ) \\nabla \\frac { \\delta } { \\delta \\rho } D _ { K L } ( \\rho , \\pi ) \\right) } \\\\ { \\displaystyle = \\nabla \\cdot \\left( \\rho ( \\boldsymbol { x } ) \\nabla \\big ( \\log \\rho ( \\boldsymbol { x } ) - \\log \\pi ( \\boldsymbol { x } ) \\big ) \\right) , } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "319c5dba11def8b47c62bbed7e518cec22d2bb6447df21ccd8c8f0ceacda0468.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 39.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                208,
+                                639,
+                                402,
+                                653.0
+                            ],
+                            "spans": [],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                208,
+                                653.0,
+                                402,
+                                667.0
+                            ],
+                            "spans": [],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                208,
+                                667.0,
+                                402,
+                                681.0
+                            ],
+                            "spans": [],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                208,
+                                681.0,
+                                402,
+                                695.0
+                            ],
+                            "spans": [],
+                            "index": 41
+                        }
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        71,
+                        506,
+                        108
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                70,
+                                496,
+                                87
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        70,
+                                        135,
+                                        86
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        135,
+                                        72,
+                                        289,
+                                        86
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\nabla _ { \\delta \\rho } ^ { \\delta } D _ { K L } ( \\rho , \\pi ) \\ = : \\ \\nabla _ { \\mathcal { W } _ { 2 } } D _ { K L } ( \\rho , \\pi )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        70,
+                                        484,
+                                        86
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the Wasserstein gradient and the operator",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        485,
+                                        72,
+                                        496,
+                                        87
+                                    ],
+                                    "score": 0.7,
+                                    "content": "\\frac { \\delta } { \\delta \\rho }",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                85,
+                                506,
+                                99
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        86,
+                                        167,
+                                        98
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\mathcal { P } _ { 2 } ( \\mathcal { M } ) \\stackrel { \\cdot } {  } \\mathbb { R }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        167,
+                                        86,
+                                        453,
+                                        98
+                                    ],
+                                    "score": 1.0,
+                                    "content": "represents the functional derivative or first variation (see Appendix",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        454,
+                                        85,
+                                        465,
+                                        99
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\boxed { \\mathsf { C } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        466,
+                                        86,
+                                        506,
+                                        98
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for more",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                96,
+                                491,
+                                110
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        96,
+                                        491,
+                                        110
+                                    ],
+                                    "score": 1.0,
+                                    "content": "details). In the particular case of the KL functional, we can recover the Fokker-Planck equation,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        213,
+                        109,
+                        396,
+                        150
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                213,
+                                109,
+                                396,
+                                150
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        213,
+                                        109,
+                                        396,
+                                        150
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\begin{array} { r l r } & { } & { \\frac { \\partial \\rho ( x ) } { \\partial t } = \\nabla \\cdot \\left( \\rho ( x ) \\nabla ( \\log \\rho ( x ) - \\log \\pi ( x ) ) \\right) } \\\\ & { } & { = - \\nabla \\cdot \\left( \\rho ( x ) \\nabla \\log \\pi ( x ) \\right) + \\nabla ^ { 2 } \\rho ( x ) , } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "bc5069e97a8be7662b9fea29c7dc30021ca7cea5d088b0d8d45da5c537562e37.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                213,
+                                109,
+                                396,
+                                122.66666666666667
+                            ],
+                            "spans": [],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                213,
+                                122.66666666666667,
+                                396,
+                                136.33333333333334
+                            ],
+                            "spans": [],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                213,
+                                136.33333333333334,
+                                396,
+                                150.0
+                            ],
+                            "spans": [],
+                            "index": 5
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        150,
+                        504,
+                        172
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                149,
+                                505,
+                                162
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        149,
+                                        335,
+                                        162
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that admits as unique stationary distribution the posterior",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        335,
+                                        150,
+                                        356,
+                                        162
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\pi ( x )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        356,
+                                        149,
+                                        505,
+                                        162
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". The deterministic particle dynamics",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                159,
+                                459,
+                                173
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        159,
+                                        129,
+                                        173
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ODE",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        130,
+                                        160,
+                                        142,
+                                        172
+                                    ],
+                                    "score": 0.61,
+                                    "content": "\\left[ \\left[ 2 \\right] \\right]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        143,
+                                        159,
+                                        199,
+                                        173
+                                    ],
+                                    "score": 1.0,
+                                    "content": "related to Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        200,
+                                        160,
+                                        217,
+                                        173
+                                    ],
+                                    "score": 0.58,
+                                    "content": "\\mathbb { ( 1 1 ) }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        217,
+                                        159,
+                                        459,
+                                        173
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", namely mean-field Wasserstein dynamics, is then given by:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 6.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        236,
+                        173,
+                        375,
+                        196
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                236,
+                                173,
+                                375,
+                                196
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        236,
+                                        173,
+                                        375,
+                                        196
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\frac { d x } { d t } = - \\nabla \\big ( \\log \\rho ( x ) - \\log \\pi ( x ) \\big ) .",
+                                    "type": "interline_equation",
+                                    "image_path": "dd2081dc85db6793f99ac9a48cbba2bf3fdd0b388e3458acd6fdadb5a243ac7b.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                236,
+                                173,
+                                375,
+                                196
+                            ],
+                            "spans": [],
+                            "index": 8
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        201,
+                        504,
+                        225
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                200,
+                                506,
+                                216
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        200,
+                                        354,
+                                        216
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Considering a discretization of Eq. (12) for a particle system",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        354,
+                                        202,
+                                        384,
+                                        215
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\{ x \\} _ { i = 1 } ^ { n }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        384,
+                                        200,
+                                        461,
+                                        216
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and small stepsize",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        461,
+                                        205,
+                                        470,
+                                        213
+                                    ],
+                                    "score": 0.83,
+                                    "content": "\\epsilon _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        470,
+                                        200,
+                                        506,
+                                        216
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", we can",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                209,
+                                186,
+                                227
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        209,
+                                        153,
+                                        227
+                                    ],
+                                    "score": 1.0,
+                                    "content": "rewrite Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        213,
+                                        171,
+                                        226
+                                    ],
+                                    "score": 0.7,
+                                    "content": "\\mathbb { \\underline { { ( 1 2 ) } } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        171,
+                                        209,
+                                        186,
+                                        227
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 9.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        213,
+                        223,
+                        397,
+                        238
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                213,
+                                223,
+                                397,
+                                238
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        213,
+                                        223,
+                                        397,
+                                        238
+                                    ],
+                                    "score": 0.91,
+                                    "content": "x _ { i } ^ { t + 1 } = x _ { i } ^ { t } + \\epsilon _ { t } \\bigl ( \\nabla \\log \\pi ( x _ { i } ^ { t } ) - \\nabla \\log \\rho ( x _ { i } ^ { t } ) \\bigr ) .",
+                                    "type": "interline_equation",
+                                    "image_path": "8a84c16f9a2296b238e38136d0db6478f4239c987d86ac3eef254ae1bde2a3a0.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                213,
+                                223,
+                                397,
+                                238
+                            ],
+                            "spans": [],
+                            "index": 11
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        237,
+                        506,
+                        335
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                236,
+                                507,
+                                250
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        236,
+                                        414,
+                                        250
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Unfortunately, we do not have access to the analytical form of the gradient",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        414,
+                                        237,
+                                        444,
+                                        248
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\nabla \\log \\rho",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        445,
+                                        236,
+                                        507,
+                                        250
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", so an approx-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                249,
+                                505,
+                                259
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        249,
+                                        505,
+                                        259
+                                    ],
+                                    "score": 1.0,
+                                    "content": "imation is needed. At this point, it is crucial to observe the similarity between the discretization",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                258,
+                                506,
+                                272
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        258,
+                                        270,
+                                        272
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of the Wasserstein gradient flow in Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        270,
+                                        258,
+                                        288,
+                                        272
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\textcircled { 1 3 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        288,
+                                        258,
+                                        420,
+                                        272
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and the repulsive update in Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        420,
+                                        258,
+                                        434,
+                                        271
+                                    ],
+                                    "score": 0.87,
+                                    "content": "( 3 )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        434,
+                                        258,
+                                        506,
+                                        272
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to notice how, if",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                269,
+                                505,
+                                282
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        269,
+                                        505,
+                                        282
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the kernelized repulsion is an approximation of the gradient of the empirical particle measure, the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                280,
+                                507,
+                                293
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        280,
+                                        507,
+                                        293
+                                    ],
+                                    "score": 1.0,
+                                    "content": "update rule minimizes the KL divergence between the particle measure and the target posterior.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                291,
+                                505,
+                                304
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        291,
+                                        505,
+                                        304
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Different sample-based approximations of the gradient that use a kernel function have been recently",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                302,
+                                505,
+                                315
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        302,
+                                        492,
+                                        315
+                                    ],
+                                    "score": 1.0,
+                                    "content": "studied. The simplest one is given by the kernel density estimation (KDE) (details in Appendix",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        492,
+                                        302,
+                                        505,
+                                        315
+                                    ],
+                                    "score": 0.68,
+                                    "content": "\\dot { \\mathrm { ~ E ~ } } )",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                311,
+                                507,
+                                328
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        313,
+                                        210,
+                                        326
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\begin{array} { r } { \\tilde { \\rho } _ { t } ( x ) = \\frac { 1 } { n } \\sum _ { i = 1 } ^ { n } \\dot { k } ( x , x _ { t } ^ { i } ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        210,
+                                        311,
+                                        241,
+                                        328
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        241,
+                                        313,
+                                        333,
+                                        325
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\boldsymbol { k } ( \\cdot , \\cdot ) : \\mathbb { R } ^ { d } \\times \\mathbb { R } ^ { d }  \\dot { \\mathbb { R } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        333,
+                                        311,
+                                        507,
+                                        328
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and the gradient of its log density is given",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                323,
+                                141,
+                                338
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        323,
+                                        119,
+                                        338
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        119,
+                                        325,
+                                        137,
+                                        336
+                                    ],
+                                    "score": 0.75,
+                                    "content": "\\mathbb { \\ m }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        137,
+                                        324,
+                                        141,
+                                        337
+                                    ],
+                                    "score": 1.0,
+                                    "content": ":",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        231,
+                        334,
+                        380,
+                        365
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                231,
+                                334,
+                                380,
+                                365
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        231,
+                                        334,
+                                        380,
+                                        365
+                                    ],
+                                    "score": 0.95,
+                                    "content": "\\nabla \\log \\rho ( x _ { i } ^ { t } ) \\approx \\frac { \\sum _ { j = 1 } ^ { n } \\nabla _ { x _ { i } ^ { t } } k ( x _ { i } ^ { t } , x _ { j } ^ { t } ) } { \\sum _ { j = 1 } ^ { n } k ( x _ { i } ^ { t } , x _ { j } ^ { t } ) } .",
+                                    "type": "interline_equation",
+                                    "image_path": "690e51dceea0054b390381bde15c30e9e687f9c712f52307c2e07985d9200e39.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                231,
+                                334,
+                                380,
+                                349.5
+                            ],
+                            "spans": [],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                231,
+                                349.5,
+                                380,
+                                365.0
+                            ],
+                            "spans": [],
+                            "index": 22
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        363,
+                        299,
+                        375
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                362,
+                                300,
+                                377
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        362,
+                                        236,
+                                        377
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Using this approximation in Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        237,
+                                        363,
+                                        254,
+                                        376
+                                    ],
+                                    "score": 0.82,
+                                    "content": "( 1 3 )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        255,
+                                        362,
+                                        300,
+                                        377
+                                    ],
+                                    "score": 1.0,
+                                    "content": "we obtain:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 23
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        193,
+                        375,
+                        417,
+                        406
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                193,
+                                375,
+                                417,
+                                406
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        193,
+                                        375,
+                                        417,
+                                        406
+                                    ],
+                                    "score": 0.93,
+                                    "content": "x _ { i } ^ { t + 1 } = x _ { i } ^ { t } + \\epsilon _ { t } \\Bigg ( \\nabla \\log \\pi ( x _ { i } ^ { t } ) - \\frac { \\sum _ { j = 1 } ^ { n } \\nabla _ { x _ { i } ^ { t } } k ( x _ { i } ^ { t } , x _ { j } ^ { t } ) } { \\sum _ { j = 1 } ^ { n } k ( x _ { i } ^ { t } , x _ { j } ^ { t } ) } \\Bigg ) ,",
+                                    "type": "interline_equation",
+                                    "image_path": "371ffb0715cb9a3b57e74ec4c78b9d2ce1313431a8e5f80ccc30135a0cfa4053.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 24.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                193,
+                                375,
+                                417,
+                                390.5
+                            ],
+                            "spans": [],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                193,
+                                390.5,
+                                417,
+                                406.0
+                            ],
+                            "spans": [],
+                            "index": 25
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        406,
+                        505,
+                        471
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                405,
+                                505,
+                                419
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        405,
+                                        278,
+                                        419
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where, if we substitute the posterior for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        279,
+                                        409,
+                                        286,
+                                        416
+                                    ],
+                                    "score": 0.77,
+                                    "content": "\\pi",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        286,
+                                        405,
+                                        505,
+                                        419
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", we obtain an expression for the repulsive force in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                415,
+                                506,
+                                432
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        415,
+                                        123,
+                                        432
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        123,
+                                        417,
+                                        135,
+                                        430
+                                    ],
+                                    "score": 0.84,
+                                    "content": "\\textcircled{3}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        136,
+                                        415,
+                                        314,
+                                        432
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". This shows that if the repulsive term in Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        314,
+                                        417,
+                                        327,
+                                        430
+                                    ],
+                                    "score": 0.88,
+                                    "content": "( 3 )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        327,
+                                        415,
+                                        483,
+                                        432
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the normalized sum of the gradients",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        484,
+                                        417,
+                                        506,
+                                        428
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\mathcal { R } =",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                425,
+                                510,
+                                455
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        428,
+                                        288,
+                                        450
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { r } { \\left( \\bar { \\sum _ { j = 1 } ^ { n } } k ( \\mathbf { w } _ { i } ^ { t } , \\mathbf { w } _ { j } ^ { t } ) \\right) ^ { - 1 } \\sum _ { j = 1 } ^ { n } \\nabla _ { \\mathbf { w } _ { i } ^ { t } } k ( \\mathbf { w } _ { i } ^ { t } , \\mathbf { w } _ { j } ^ { t } ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        288,
+                                        425,
+                                        510,
+                                        455
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", we do not only encourage diversity of the ensemble",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                447,
+                                504,
+                                460
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        447,
+                                        426,
+                                        460
+                                    ],
+                                    "score": 1.0,
+                                    "content": "members and thus avoid collapse, but surprisingly—in the asymptotic limit of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        459,
+                                        447,
+                                        504,
+                                        460
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", where the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                458,
+                                429,
+                                472
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        458,
+                                        223,
+                                        472
+                                    ],
+                                    "score": 1.0,
+                                    "content": "KDE approximation is exact",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        223,
+                                        459,
+                                        240,
+                                        470
+                                    ],
+                                    "score": 0.77,
+                                    "content": "\\left[ \\left[ 6 6 \\right] \\right]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        240,
+                                        458,
+                                        429,
+                                        472
+                                    ],
+                                    "score": 1.0,
+                                    "content": "—also converge to the true Bayesian posterior!",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 28
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        474,
+                        506,
+                        552
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                474,
+                                507,
+                                488
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        474,
+                                        507,
+                                        488
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Nevertheless, approximating the gradient of the empirical measure with the KDE can lead to subop-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                486,
+                                506,
+                                498
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        486,
+                                        333,
+                                        498
+                                    ],
+                                    "score": 1.0,
+                                    "content": "timal performance, as already studied by Li and Turner",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        333,
+                                        486,
+                                        351,
+                                        497
+                                    ],
+                                    "score": 0.84,
+                                    "content": "[ \\overline { { | 4 6 | } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        351,
+                                        486,
+                                        506,
+                                        498
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". They instead introduced a new Stein",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                497,
+                                505,
+                                510
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        497,
+                                        505,
+                                        510
+                                    ],
+                                    "score": 1.0,
+                                    "content": "gradient estimator (SGE) that offers better performance, while maintaining the same computational",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                508,
+                                506,
+                                520
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        508,
+                                        245,
+                                        520
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cost. Even more recently, Shi et al.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        245,
+                                        508,
+                                        263,
+                                        519
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\mathbb { \\left. \\boldsymbol { \\mathfrak { G } } \\boldsymbol { \\mathfrak { A } } \\right. }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        263,
+                                        508,
+                                        506,
+                                        520
+                                    ],
+                                    "score": 1.0,
+                                    "content": "introduced a spectral method for gradient estimation (SSGE),",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                519,
+                                506,
+                                532
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        519,
+                                        506,
+                                        532
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that also allows for a simple estimation on out-of-sample points. These two estimators can be used in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                529,
+                                506,
+                                544
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        529,
+                                        122,
+                                        544
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        123,
+                                        529,
+                                        140,
+                                        543
+                                    ],
+                                    "score": 0.77,
+                                    "content": "\\textcircled { 1 3 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        140,
+                                        529,
+                                        506,
+                                        544
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", to formulate the following update rules with two alternative repulsive forces. The one using",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                541,
+                                315,
+                                552
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        541,
+                                        315,
+                                        552
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the Stein estimator, that we will call SGE-WGD, is:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 34
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        165,
+                        552,
+                        444,
+                        585
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                165,
+                                552,
+                                444,
+                                585
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        165,
+                                        552,
+                                        444,
+                                        585
+                                    ],
+                                    "score": 0.94,
+                                    "content": "x _ { i } ^ { t + 1 } = x _ { i } ^ { t } + \\epsilon _ { t } \\bigg ( \\nabla \\log \\pi ( x _ { i } ^ { t } ) + \\sum _ { j = 1 } ^ { n } ( K + \\eta \\mathbb { I } ) _ { i j } ^ { - 1 } \\sum _ { k = 1 } ^ { n } \\nabla _ { x _ { k } ^ { t } } k ( x _ { k } ^ { t } , x _ { j } ^ { t } ) \\bigg ) ,",
+                                    "type": "interline_equation",
+                                    "image_path": "fc8beab1c532557f6b4c53d364e88ab075d4917c7571f2c182526373978fd6c4.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 39,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                165,
+                                552,
+                                444,
+                                563.0
+                            ],
+                            "spans": [],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                165,
+                                563.0,
+                                444,
+                                574.0
+                            ],
+                            "spans": [],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                165,
+                                574.0,
+                                444,
+                                585.0
+                            ],
+                            "spans": [],
+                            "index": 40
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        586,
+                        505,
+                        641
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                585,
+                                506,
+                                598
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        585,
+                                        133,
+                                        598
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        133,
+                                        586,
+                                        144,
+                                        596
+                                    ],
+                                    "score": 0.83,
+                                    "content": "K",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        144,
+                                        585,
+                                        253,
+                                        598
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the kernel Gram matrix,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        253,
+                                        588,
+                                        260,
+                                        597
+                                    ],
+                                    "score": 0.82,
+                                    "content": "\\eta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        260,
+                                        585,
+                                        506,
+                                        598
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a small constant, and I the identity matrix. We can notice an",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                596,
+                                506,
+                                609
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        596,
+                                        506,
+                                        609
+                                    ],
+                                    "score": 1.0,
+                                    "content": "important difference between KDE and SGE, in that the former is only considering the interaction of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                608,
+                                505,
+                                620
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        608,
+                                        121,
+                                        620
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        121,
+                                        609,
+                                        126,
+                                        618
+                                    ],
+                                    "score": 0.81,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        126,
+                                        608,
+                                        505,
+                                        620
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-th particle being updated with all the others, while the latter is simultaneously considering also",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                618,
+                                506,
+                                631
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        618,
+                                        506,
+                                        631
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the interactions between the remaining particles. The spectral method, that we will call SSGE-WGD,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                630,
+                                245,
+                                641
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        630,
+                                        245,
+                                        641
+                                    ],
+                                    "score": 1.0,
+                                    "content": "leads to the following update rule:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        }
+                    ],
+                    "index": 43
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        121,
+                        641,
+                        473,
+                        676
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                121,
+                                641,
+                                473,
+                                676
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        121,
+                                        641,
+                                        473,
+                                        676
+                                    ],
+                                    "score": 0.94,
+                                    "content": "x _ { t + 1 } ^ { i } = x _ { t } ^ { i } + \\epsilon _ { t } \\bigg ( \\nabla \\log \\pi ( x _ { t } ^ { i } ) + \\sum _ { j = 1 } ^ { J } \\frac { 1 } { \\lambda _ { j } ^ { 2 } } \\sum _ { m = 1 } ^ { n } \\sum _ { k = 1 } ^ { n } u _ { j k } \\nabla _ { x _ { m } } k ( x _ { m } ^ { t } , x _ { k } ^ { t } ) \\cdot \\sum _ { l = 1 } ^ { n } u _ { j l } k ( x _ { i } ^ { t } , x _ { l } ^ { t } ) \\bigg )",
+                                    "type": "interline_equation",
+                                    "image_path": "22b05cdc924e14a9f81460eed44ce5ae2949169ff1032670bb23204d0bc3d3f9.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 47,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                121,
+                                641,
+                                473,
+                                652.6666666666666
+                            ],
+                            "spans": [],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                121,
+                                652.6666666666666,
+                                473,
+                                664.3333333333333
+                            ],
+                            "spans": [],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                121,
+                                664.3333333333333,
+                                473,
+                                675.9999999999999
+                            ],
+                            "spans": [],
+                            "index": 48
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        677,
+                        505,
+                        723
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                676,
+                                505,
+                                690
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        676,
+                                        134,
+                                        690
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        135,
+                                        677,
+                                        146,
+                                        689
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\lambda _ { j }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        146,
+                                        676,
+                                        174,
+                                        690
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        174,
+                                        678,
+                                        180,
+                                        689
+                                    ],
+                                    "score": 0.82,
+                                    "content": "j",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        180,
+                                        676,
+                                        345,
+                                        690
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-th eigenvalue of the kernel matrix and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        346,
+                                        679,
+                                        361,
+                                        689
+                                    ],
+                                    "score": 0.83,
+                                    "content": "u _ { j k }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        361,
+                                        676,
+                                        389,
+                                        690
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        390,
+                                        677,
+                                        396,
+                                        687
+                                    ],
+                                    "score": 0.82,
+                                    "content": "k",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        397,
+                                        676,
+                                        486,
+                                        690
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-th component of the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        487,
+                                        678,
+                                        492,
+                                        689
+                                    ],
+                                    "score": 0.82,
+                                    "content": "j",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        493,
+                                        676,
+                                        505,
+                                        690
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-th",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                687,
+                                506,
+                                703
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        687,
+                                        378,
+                                        703
+                                    ],
+                                    "score": 1.0,
+                                    "content": "eigenvector. Computationally, both SSGE and SGE have a cost of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        378,
+                                        688,
+                                        442,
+                                        701
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\mathcal { O } ( M ^ { 3 } + M ^ { 2 } d )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        442,
+                                        687,
+                                        466,
+                                        703
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", with",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        467,
+                                        690,
+                                        478,
+                                        699
+                                    ],
+                                    "score": 0.82,
+                                    "content": "M",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        479,
+                                        687,
+                                        506,
+                                        703
+                                    ],
+                                    "score": 1.0,
+                                    "content": "being",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                700,
+                                505,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        700,
+                                        213,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the number of points and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        214,
+                                        700,
+                                        220,
+                                        710
+                                    ],
+                                    "score": 0.82,
+                                    "content": "d",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        220,
+                                        700,
+                                        505,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "their dimensionality. SSGE has an additional cost for predictions of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 51
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                711,
+                                324,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        711,
+                                        165,
+                                        723
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\mathcal { O } ( M ( d + J ) )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        165,
+                                        711,
+                                        196,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        197,
+                                        711,
+                                        204,
+                                        721
+                                    ],
+                                    "score": 0.83,
+                                    "content": "J",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        205,
+                                        711,
+                                        324,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the number of eigenvalues.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 52
+                        }
+                    ],
+                    "index": 50.5
+                }
+            ],
+            "page_idx": 5,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        741,
+                        309,
+                        750
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                302,
+                                741,
+                                310,
+                                752
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        302,
+                                        741,
+                                        310,
+                                        752
+                                    ],
+                                    "score": 1.0,
+                                    "content": "6",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        71,
+                        506,
+                        108
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                70,
+                                496,
+                                87
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        70,
+                                        135,
+                                        86
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        135,
+                                        72,
+                                        289,
+                                        86
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\nabla _ { \\delta \\rho } ^ { \\delta } D _ { K L } ( \\rho , \\pi ) \\ = : \\ \\nabla _ { \\mathcal { W } _ { 2 } } D _ { K L } ( \\rho , \\pi )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        70,
+                                        484,
+                                        86
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the Wasserstein gradient and the operator",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        485,
+                                        72,
+                                        496,
+                                        87
+                                    ],
+                                    "score": 0.7,
+                                    "content": "\\frac { \\delta } { \\delta \\rho }",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                85,
+                                506,
+                                99
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        86,
+                                        167,
+                                        98
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\mathcal { P } _ { 2 } ( \\mathcal { M } ) \\stackrel { \\cdot } {  } \\mathbb { R }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        167,
+                                        86,
+                                        453,
+                                        98
+                                    ],
+                                    "score": 1.0,
+                                    "content": "represents the functional derivative or first variation (see Appendix",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        454,
+                                        85,
+                                        465,
+                                        99
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\boxed { \\mathsf { C } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        466,
+                                        86,
+                                        506,
+                                        98
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for more",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                96,
+                                491,
+                                110
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        96,
+                                        491,
+                                        110
+                                    ],
+                                    "score": 1.0,
+                                    "content": "details). In the particular case of the KL functional, we can recover the Fokker-Planck equation,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1,
+                    "bbox_fs": [
+                        104,
+                        70,
+                        506,
+                        110
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        213,
+                        109,
+                        396,
+                        150
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                213,
+                                109,
+                                396,
+                                150
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        213,
+                                        109,
+                                        396,
+                                        150
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\begin{array} { r l r } & { } & { \\frac { \\partial \\rho ( x ) } { \\partial t } = \\nabla \\cdot \\left( \\rho ( x ) \\nabla ( \\log \\rho ( x ) - \\log \\pi ( x ) ) \\right) } \\\\ & { } & { = - \\nabla \\cdot \\left( \\rho ( x ) \\nabla \\log \\pi ( x ) \\right) + \\nabla ^ { 2 } \\rho ( x ) , } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "bc5069e97a8be7662b9fea29c7dc30021ca7cea5d088b0d8d45da5c537562e37.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                213,
+                                109,
+                                396,
+                                122.66666666666667
+                            ],
+                            "spans": [],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                213,
+                                122.66666666666667,
+                                396,
+                                136.33333333333334
+                            ],
+                            "spans": [],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                213,
+                                136.33333333333334,
+                                396,
+                                150.0
+                            ],
+                            "spans": [],
+                            "index": 5
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        150,
+                        504,
+                        172
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                149,
+                                505,
+                                162
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        149,
+                                        335,
+                                        162
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that admits as unique stationary distribution the posterior",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        335,
+                                        150,
+                                        356,
+                                        162
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\pi ( x )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        356,
+                                        149,
+                                        505,
+                                        162
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". The deterministic particle dynamics",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                159,
+                                459,
+                                173
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        159,
+                                        129,
+                                        173
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ODE",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        130,
+                                        160,
+                                        142,
+                                        172
+                                    ],
+                                    "score": 0.61,
+                                    "content": "\\left[ \\left[ 2 \\right] \\right]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        143,
+                                        159,
+                                        199,
+                                        173
+                                    ],
+                                    "score": 1.0,
+                                    "content": "related to Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        200,
+                                        160,
+                                        217,
+                                        173
+                                    ],
+                                    "score": 0.58,
+                                    "content": "\\mathbb { ( 1 1 ) }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        217,
+                                        159,
+                                        459,
+                                        173
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", namely mean-field Wasserstein dynamics, is then given by:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 6.5,
+                    "bbox_fs": [
+                        105,
+                        149,
+                        505,
+                        173
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        236,
+                        173,
+                        375,
+                        196
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                236,
+                                173,
+                                375,
+                                196
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        236,
+                                        173,
+                                        375,
+                                        196
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\frac { d x } { d t } = - \\nabla \\big ( \\log \\rho ( x ) - \\log \\pi ( x ) \\big ) .",
+                                    "type": "interline_equation",
+                                    "image_path": "dd2081dc85db6793f99ac9a48cbba2bf3fdd0b388e3458acd6fdadb5a243ac7b.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                236,
+                                173,
+                                375,
+                                196
+                            ],
+                            "spans": [],
+                            "index": 8
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        201,
+                        504,
+                        225
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                200,
+                                506,
+                                216
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        200,
+                                        354,
+                                        216
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Considering a discretization of Eq. (12) for a particle system",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        354,
+                                        202,
+                                        384,
+                                        215
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\{ x \\} _ { i = 1 } ^ { n }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        384,
+                                        200,
+                                        461,
+                                        216
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and small stepsize",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        461,
+                                        205,
+                                        470,
+                                        213
+                                    ],
+                                    "score": 0.83,
+                                    "content": "\\epsilon _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        470,
+                                        200,
+                                        506,
+                                        216
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", we can",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                209,
+                                186,
+                                227
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        209,
+                                        153,
+                                        227
+                                    ],
+                                    "score": 1.0,
+                                    "content": "rewrite Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        213,
+                                        171,
+                                        226
+                                    ],
+                                    "score": 0.7,
+                                    "content": "\\mathbb { \\underline { { ( 1 2 ) } } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        171,
+                                        209,
+                                        186,
+                                        227
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 9.5,
+                    "bbox_fs": [
+                        104,
+                        200,
+                        506,
+                        227
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        213,
+                        223,
+                        397,
+                        238
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                213,
+                                223,
+                                397,
+                                238
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        213,
+                                        223,
+                                        397,
+                                        238
+                                    ],
+                                    "score": 0.91,
+                                    "content": "x _ { i } ^ { t + 1 } = x _ { i } ^ { t } + \\epsilon _ { t } \\bigl ( \\nabla \\log \\pi ( x _ { i } ^ { t } ) - \\nabla \\log \\rho ( x _ { i } ^ { t } ) \\bigr ) .",
+                                    "type": "interline_equation",
+                                    "image_path": "8a84c16f9a2296b238e38136d0db6478f4239c987d86ac3eef254ae1bde2a3a0.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                213,
+                                223,
+                                397,
+                                238
+                            ],
+                            "spans": [],
+                            "index": 11
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        237,
+                        506,
+                        335
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                236,
+                                507,
+                                250
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        236,
+                                        414,
+                                        250
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Unfortunately, we do not have access to the analytical form of the gradient",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        414,
+                                        237,
+                                        444,
+                                        248
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\nabla \\log \\rho",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        445,
+                                        236,
+                                        507,
+                                        250
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", so an approx-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                249,
+                                505,
+                                259
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        249,
+                                        505,
+                                        259
+                                    ],
+                                    "score": 1.0,
+                                    "content": "imation is needed. At this point, it is crucial to observe the similarity between the discretization",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                258,
+                                506,
+                                272
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        258,
+                                        270,
+                                        272
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of the Wasserstein gradient flow in Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        270,
+                                        258,
+                                        288,
+                                        272
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\textcircled { 1 3 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        288,
+                                        258,
+                                        420,
+                                        272
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and the repulsive update in Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        420,
+                                        258,
+                                        434,
+                                        271
+                                    ],
+                                    "score": 0.87,
+                                    "content": "( 3 )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        434,
+                                        258,
+                                        506,
+                                        272
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to notice how, if",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                269,
+                                505,
+                                282
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        269,
+                                        505,
+                                        282
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the kernelized repulsion is an approximation of the gradient of the empirical particle measure, the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                280,
+                                507,
+                                293
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        280,
+                                        507,
+                                        293
+                                    ],
+                                    "score": 1.0,
+                                    "content": "update rule minimizes the KL divergence between the particle measure and the target posterior.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                291,
+                                505,
+                                304
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        291,
+                                        505,
+                                        304
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Different sample-based approximations of the gradient that use a kernel function have been recently",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                302,
+                                505,
+                                315
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        302,
+                                        492,
+                                        315
+                                    ],
+                                    "score": 1.0,
+                                    "content": "studied. The simplest one is given by the kernel density estimation (KDE) (details in Appendix",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        492,
+                                        302,
+                                        505,
+                                        315
+                                    ],
+                                    "score": 0.68,
+                                    "content": "\\dot { \\mathrm { ~ E ~ } } )",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                311,
+                                507,
+                                328
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        313,
+                                        210,
+                                        326
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\begin{array} { r } { \\tilde { \\rho } _ { t } ( x ) = \\frac { 1 } { n } \\sum _ { i = 1 } ^ { n } \\dot { k } ( x , x _ { t } ^ { i } ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        210,
+                                        311,
+                                        241,
+                                        328
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        241,
+                                        313,
+                                        333,
+                                        325
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\boldsymbol { k } ( \\cdot , \\cdot ) : \\mathbb { R } ^ { d } \\times \\mathbb { R } ^ { d }  \\dot { \\mathbb { R } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        333,
+                                        311,
+                                        507,
+                                        328
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and the gradient of its log density is given",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                323,
+                                141,
+                                338
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        323,
+                                        119,
+                                        338
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        119,
+                                        325,
+                                        137,
+                                        336
+                                    ],
+                                    "score": 0.75,
+                                    "content": "\\mathbb { \\ m }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        137,
+                                        324,
+                                        141,
+                                        337
+                                    ],
+                                    "score": 1.0,
+                                    "content": ":",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 16,
+                    "bbox_fs": [
+                        105,
+                        236,
+                        507,
+                        338
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        231,
+                        334,
+                        380,
+                        365
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                231,
+                                334,
+                                380,
+                                365
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        231,
+                                        334,
+                                        380,
+                                        365
+                                    ],
+                                    "score": 0.95,
+                                    "content": "\\nabla \\log \\rho ( x _ { i } ^ { t } ) \\approx \\frac { \\sum _ { j = 1 } ^ { n } \\nabla _ { x _ { i } ^ { t } } k ( x _ { i } ^ { t } , x _ { j } ^ { t } ) } { \\sum _ { j = 1 } ^ { n } k ( x _ { i } ^ { t } , x _ { j } ^ { t } ) } .",
+                                    "type": "interline_equation",
+                                    "image_path": "690e51dceea0054b390381bde15c30e9e687f9c712f52307c2e07985d9200e39.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                231,
+                                334,
+                                380,
+                                349.5
+                            ],
+                            "spans": [],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                231,
+                                349.5,
+                                380,
+                                365.0
+                            ],
+                            "spans": [],
+                            "index": 22
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        363,
+                        299,
+                        375
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                362,
+                                300,
+                                377
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        362,
+                                        236,
+                                        377
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Using this approximation in Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        237,
+                                        363,
+                                        254,
+                                        376
+                                    ],
+                                    "score": 0.82,
+                                    "content": "( 1 3 )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        255,
+                                        362,
+                                        300,
+                                        377
+                                    ],
+                                    "score": 1.0,
+                                    "content": "we obtain:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 23,
+                    "bbox_fs": [
+                        106,
+                        362,
+                        300,
+                        377
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        193,
+                        375,
+                        417,
+                        406
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                193,
+                                375,
+                                417,
+                                406
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        193,
+                                        375,
+                                        417,
+                                        406
+                                    ],
+                                    "score": 0.93,
+                                    "content": "x _ { i } ^ { t + 1 } = x _ { i } ^ { t } + \\epsilon _ { t } \\Bigg ( \\nabla \\log \\pi ( x _ { i } ^ { t } ) - \\frac { \\sum _ { j = 1 } ^ { n } \\nabla _ { x _ { i } ^ { t } } k ( x _ { i } ^ { t } , x _ { j } ^ { t } ) } { \\sum _ { j = 1 } ^ { n } k ( x _ { i } ^ { t } , x _ { j } ^ { t } ) } \\Bigg ) ,",
+                                    "type": "interline_equation",
+                                    "image_path": "371ffb0715cb9a3b57e74ec4c78b9d2ce1313431a8e5f80ccc30135a0cfa4053.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 24.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                193,
+                                375,
+                                417,
+                                390.5
+                            ],
+                            "spans": [],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                193,
+                                390.5,
+                                417,
+                                406.0
+                            ],
+                            "spans": [],
+                            "index": 25
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        406,
+                        505,
+                        471
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                405,
+                                505,
+                                419
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        405,
+                                        278,
+                                        419
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where, if we substitute the posterior for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        279,
+                                        409,
+                                        286,
+                                        416
+                                    ],
+                                    "score": 0.77,
+                                    "content": "\\pi",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        286,
+                                        405,
+                                        505,
+                                        419
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", we obtain an expression for the repulsive force in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                415,
+                                506,
+                                432
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        415,
+                                        123,
+                                        432
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        123,
+                                        417,
+                                        135,
+                                        430
+                                    ],
+                                    "score": 0.84,
+                                    "content": "\\textcircled{3}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        136,
+                                        415,
+                                        314,
+                                        432
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". This shows that if the repulsive term in Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        314,
+                                        417,
+                                        327,
+                                        430
+                                    ],
+                                    "score": 0.88,
+                                    "content": "( 3 )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        327,
+                                        415,
+                                        483,
+                                        432
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the normalized sum of the gradients",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        484,
+                                        417,
+                                        506,
+                                        428
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\mathcal { R } =",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                425,
+                                510,
+                                455
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        428,
+                                        288,
+                                        450
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { r } { \\left( \\bar { \\sum _ { j = 1 } ^ { n } } k ( \\mathbf { w } _ { i } ^ { t } , \\mathbf { w } _ { j } ^ { t } ) \\right) ^ { - 1 } \\sum _ { j = 1 } ^ { n } \\nabla _ { \\mathbf { w } _ { i } ^ { t } } k ( \\mathbf { w } _ { i } ^ { t } , \\mathbf { w } _ { j } ^ { t } ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        288,
+                                        425,
+                                        510,
+                                        455
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", we do not only encourage diversity of the ensemble",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                447,
+                                504,
+                                460
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        447,
+                                        426,
+                                        460
+                                    ],
+                                    "score": 1.0,
+                                    "content": "members and thus avoid collapse, but surprisingly—in the asymptotic limit of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        459,
+                                        447,
+                                        504,
+                                        460
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", where the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                458,
+                                429,
+                                472
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        458,
+                                        223,
+                                        472
+                                    ],
+                                    "score": 1.0,
+                                    "content": "KDE approximation is exact",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        223,
+                                        459,
+                                        240,
+                                        470
+                                    ],
+                                    "score": 0.77,
+                                    "content": "\\left[ \\left[ 6 6 \\right] \\right]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        240,
+                                        458,
+                                        429,
+                                        472
+                                    ],
+                                    "score": 1.0,
+                                    "content": "—also converge to the true Bayesian posterior!",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 28,
+                    "bbox_fs": [
+                        105,
+                        405,
+                        510,
+                        472
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        474,
+                        506,
+                        552
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                474,
+                                507,
+                                488
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        474,
+                                        507,
+                                        488
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Nevertheless, approximating the gradient of the empirical measure with the KDE can lead to subop-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                486,
+                                506,
+                                498
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        486,
+                                        333,
+                                        498
+                                    ],
+                                    "score": 1.0,
+                                    "content": "timal performance, as already studied by Li and Turner",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        333,
+                                        486,
+                                        351,
+                                        497
+                                    ],
+                                    "score": 0.84,
+                                    "content": "[ \\overline { { | 4 6 | } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        351,
+                                        486,
+                                        506,
+                                        498
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". They instead introduced a new Stein",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                497,
+                                505,
+                                510
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        497,
+                                        505,
+                                        510
+                                    ],
+                                    "score": 1.0,
+                                    "content": "gradient estimator (SGE) that offers better performance, while maintaining the same computational",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                508,
+                                506,
+                                520
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        508,
+                                        245,
+                                        520
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cost. Even more recently, Shi et al.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        245,
+                                        508,
+                                        263,
+                                        519
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\mathbb { \\left. \\boldsymbol { \\mathfrak { G } } \\boldsymbol { \\mathfrak { A } } \\right. }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        263,
+                                        508,
+                                        506,
+                                        520
+                                    ],
+                                    "score": 1.0,
+                                    "content": "introduced a spectral method for gradient estimation (SSGE),",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                519,
+                                506,
+                                532
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        519,
+                                        506,
+                                        532
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that also allows for a simple estimation on out-of-sample points. These two estimators can be used in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                529,
+                                506,
+                                544
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        529,
+                                        122,
+                                        544
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        123,
+                                        529,
+                                        140,
+                                        543
+                                    ],
+                                    "score": 0.77,
+                                    "content": "\\textcircled { 1 3 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        140,
+                                        529,
+                                        506,
+                                        544
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", to formulate the following update rules with two alternative repulsive forces. The one using",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                541,
+                                315,
+                                552
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        541,
+                                        315,
+                                        552
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the Stein estimator, that we will call SGE-WGD, is:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 34,
+                    "bbox_fs": [
+                        105,
+                        474,
+                        507,
+                        552
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        165,
+                        552,
+                        444,
+                        585
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                165,
+                                552,
+                                444,
+                                585
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        165,
+                                        552,
+                                        444,
+                                        585
+                                    ],
+                                    "score": 0.94,
+                                    "content": "x _ { i } ^ { t + 1 } = x _ { i } ^ { t } + \\epsilon _ { t } \\bigg ( \\nabla \\log \\pi ( x _ { i } ^ { t } ) + \\sum _ { j = 1 } ^ { n } ( K + \\eta \\mathbb { I } ) _ { i j } ^ { - 1 } \\sum _ { k = 1 } ^ { n } \\nabla _ { x _ { k } ^ { t } } k ( x _ { k } ^ { t } , x _ { j } ^ { t } ) \\bigg ) ,",
+                                    "type": "interline_equation",
+                                    "image_path": "fc8beab1c532557f6b4c53d364e88ab075d4917c7571f2c182526373978fd6c4.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 39,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                165,
+                                552,
+                                444,
+                                563.0
+                            ],
+                            "spans": [],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                165,
+                                563.0,
+                                444,
+                                574.0
+                            ],
+                            "spans": [],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                165,
+                                574.0,
+                                444,
+                                585.0
+                            ],
+                            "spans": [],
+                            "index": 40
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        586,
+                        505,
+                        641
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                585,
+                                506,
+                                598
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        585,
+                                        133,
+                                        598
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        133,
+                                        586,
+                                        144,
+                                        596
+                                    ],
+                                    "score": 0.83,
+                                    "content": "K",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        144,
+                                        585,
+                                        253,
+                                        598
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the kernel Gram matrix,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        253,
+                                        588,
+                                        260,
+                                        597
+                                    ],
+                                    "score": 0.82,
+                                    "content": "\\eta",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        260,
+                                        585,
+                                        506,
+                                        598
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a small constant, and I the identity matrix. We can notice an",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                596,
+                                506,
+                                609
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        596,
+                                        506,
+                                        609
+                                    ],
+                                    "score": 1.0,
+                                    "content": "important difference between KDE and SGE, in that the former is only considering the interaction of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                608,
+                                505,
+                                620
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        608,
+                                        121,
+                                        620
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        121,
+                                        609,
+                                        126,
+                                        618
+                                    ],
+                                    "score": 0.81,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        126,
+                                        608,
+                                        505,
+                                        620
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-th particle being updated with all the others, while the latter is simultaneously considering also",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                618,
+                                506,
+                                631
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        618,
+                                        506,
+                                        631
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the interactions between the remaining particles. The spectral method, that we will call SSGE-WGD,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                630,
+                                245,
+                                641
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        630,
+                                        245,
+                                        641
+                                    ],
+                                    "score": 1.0,
+                                    "content": "leads to the following update rule:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        }
+                    ],
+                    "index": 43,
+                    "bbox_fs": [
+                        105,
+                        585,
+                        506,
+                        641
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        121,
+                        641,
+                        473,
+                        676
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                121,
+                                641,
+                                473,
+                                676
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        121,
+                                        641,
+                                        473,
+                                        676
+                                    ],
+                                    "score": 0.94,
+                                    "content": "x _ { t + 1 } ^ { i } = x _ { t } ^ { i } + \\epsilon _ { t } \\bigg ( \\nabla \\log \\pi ( x _ { t } ^ { i } ) + \\sum _ { j = 1 } ^ { J } \\frac { 1 } { \\lambda _ { j } ^ { 2 } } \\sum _ { m = 1 } ^ { n } \\sum _ { k = 1 } ^ { n } u _ { j k } \\nabla _ { x _ { m } } k ( x _ { m } ^ { t } , x _ { k } ^ { t } ) \\cdot \\sum _ { l = 1 } ^ { n } u _ { j l } k ( x _ { i } ^ { t } , x _ { l } ^ { t } ) \\bigg )",
+                                    "type": "interline_equation",
+                                    "image_path": "22b05cdc924e14a9f81460eed44ce5ae2949169ff1032670bb23204d0bc3d3f9.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 47,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                121,
+                                641,
+                                473,
+                                652.6666666666666
+                            ],
+                            "spans": [],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                121,
+                                652.6666666666666,
+                                473,
+                                664.3333333333333
+                            ],
+                            "spans": [],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                121,
+                                664.3333333333333,
+                                473,
+                                675.9999999999999
+                            ],
+                            "spans": [],
+                            "index": 48
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        677,
+                        505,
+                        723
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                676,
+                                505,
+                                690
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        676,
+                                        134,
+                                        690
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        135,
+                                        677,
+                                        146,
+                                        689
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\lambda _ { j }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        146,
+                                        676,
+                                        174,
+                                        690
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        174,
+                                        678,
+                                        180,
+                                        689
+                                    ],
+                                    "score": 0.82,
+                                    "content": "j",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        180,
+                                        676,
+                                        345,
+                                        690
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-th eigenvalue of the kernel matrix and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        346,
+                                        679,
+                                        361,
+                                        689
+                                    ],
+                                    "score": 0.83,
+                                    "content": "u _ { j k }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        361,
+                                        676,
+                                        389,
+                                        690
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        390,
+                                        677,
+                                        396,
+                                        687
+                                    ],
+                                    "score": 0.82,
+                                    "content": "k",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        397,
+                                        676,
+                                        486,
+                                        690
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-th component of the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        487,
+                                        678,
+                                        492,
+                                        689
+                                    ],
+                                    "score": 0.82,
+                                    "content": "j",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        493,
+                                        676,
+                                        505,
+                                        690
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-th",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                687,
+                                506,
+                                703
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        687,
+                                        378,
+                                        703
+                                    ],
+                                    "score": 1.0,
+                                    "content": "eigenvector. Computationally, both SSGE and SGE have a cost of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        378,
+                                        688,
+                                        442,
+                                        701
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\mathcal { O } ( M ^ { 3 } + M ^ { 2 } d )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        442,
+                                        687,
+                                        466,
+                                        703
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", with",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        467,
+                                        690,
+                                        478,
+                                        699
+                                    ],
+                                    "score": 0.82,
+                                    "content": "M",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        479,
+                                        687,
+                                        506,
+                                        703
+                                    ],
+                                    "score": 1.0,
+                                    "content": "being",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                700,
+                                505,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        700,
+                                        213,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the number of points and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        214,
+                                        700,
+                                        220,
+                                        710
+                                    ],
+                                    "score": 0.82,
+                                    "content": "d",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        220,
+                                        700,
+                                        505,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "their dimensionality. SSGE has an additional cost for predictions of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 51
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                711,
+                                324,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        711,
+                                        165,
+                                        723
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\mathcal { O } ( M ( d + J ) )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        165,
+                                        711,
+                                        196,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        197,
+                                        711,
+                                        204,
+                                        721
+                                    ],
+                                    "score": 0.83,
+                                    "content": "J",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        205,
+                                        711,
+                                        324,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the number of eigenvalues.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 52
+                        }
+                    ],
+                    "index": 50.5,
+                    "bbox_fs": [
+                        105,
+                        676,
+                        506,
+                        723
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "image",
+                    "bbox": [
+                        111,
+                        68,
+                        502,
+                        168
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                111,
+                                68,
+                                502,
+                                168
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        68,
+                                        502,
+                                        168
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                111,
+                                                68,
+                                                502,
+                                                168
+                                            ],
+                                            "score": 0.966,
+                                            "type": "image",
+                                            "image_path": "909c60e208223cd54336af828c72fc5777f5cbee78dd1b5dffc27345c64eca36.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        68,
+                                        502,
+                                        101.33333333333334
+                                    ],
+                                    "spans": [],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        111,
+                                        101.33333333333334,
+                                        502,
+                                        134.66666666666669
+                                    ],
+                                    "spans": [],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        111,
+                                        134.66666666666669,
+                                        502,
+                                        168.00000000000003
+                                    ],
+                                    "spans": [],
+                                    "index": 2
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                106,
+                                172,
+                                506,
+                                206
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        172,
+                                        507,
+                                        185
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                172,
+                                                507,
+                                                185
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 2: Single Gaussian. We show samples from SVGD, KDE-WGD, SGE-WGD, and SSGE-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        182,
+                                        505,
+                                        196
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                182,
+                                                505,
+                                                196
+                                            ],
+                                            "score": 1.0,
+                                            "content": "WGD (from left to right). The upper and right plots show the empirical one-dimensional marginal",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        194,
+                                        435,
+                                        207
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                194,
+                                                435,
+                                                207
+                                            ],
+                                            "score": 1.0,
+                                            "content": "distributions obtained using KDE on the samples (red) and on the particles (blue).",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 5
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 2.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        228,
+                        263,
+                        240
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                227,
+                                265,
+                                243
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        227,
+                                        265,
+                                        243
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3.3 Gradient flow in function space",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        249,
+                        504,
+                        273
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                248,
+                                505,
+                                262
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        248,
+                                        410,
+                                        262
+                                    ],
+                                    "score": 1.0,
+                                    "content": "To theoretically justify the update rule introduced in function space in Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        410,
+                                        249,
+                                        423,
+                                        262
+                                    ],
+                                    "score": 0.54,
+                                    "content": "\\textcircled{5}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        423,
+                                        248,
+                                        505,
+                                        262
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", we can rewrite the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                260,
+                                394,
+                                273
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        261,
+                                        292,
+                                        273
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Liouville equation for the gradient flow in Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        293,
+                                        260,
+                                        310,
+                                        273
+                                    ],
+                                    "score": 0.79,
+                                    "content": "\\textcircled { 1 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        311,
+                                        261,
+                                        394,
+                                        273
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in function space as",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 7.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        206,
+                        279,
+                        406,
+                        335
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                206,
+                                279,
+                                406,
+                                335
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        206,
+                                        279,
+                                        406,
+                                        335
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { l } { \\displaystyle \\frac { \\partial \\rho ( { \\pmb f } ) } { \\partial t } = \\nabla \\cdot \\left( \\rho ( { \\pmb f } ) \\nabla \\frac { \\delta } { \\delta \\rho } D _ { K L } ( \\rho , \\pi ) \\right) } \\\\ { \\displaystyle = \\nabla \\cdot \\left( \\rho ( { \\pmb f } ) \\nabla \\big ( \\log \\rho ( { \\pmb f } ) - \\log \\pi ( { \\pmb f } ) \\big ) \\right) . } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "5c17155651b4b8a9222af9e3b20c3d19517ca6b37f38c6cba7442ed799860e6c.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                206,
+                                279,
+                                406,
+                                293.0
+                            ],
+                            "spans": [],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                206,
+                                293.0,
+                                406,
+                                307.0
+                            ],
+                            "spans": [],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                206,
+                                307.0,
+                                406,
+                                321.0
+                            ],
+                            "spans": [],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                206,
+                                321.0,
+                                406,
+                                335.0
+                            ],
+                            "spans": [],
+                            "index": 12
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        340,
+                        355,
+                        352
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                340,
+                                355,
+                                353
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        340,
+                                        355,
+                                        353
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Following this update, the mean field functional dynamics are",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        234,
+                        358,
+                        377,
+                        383
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                234,
+                                358,
+                                377,
+                                383
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        234,
+                                        358,
+                                        377,
+                                        383
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\frac { d \\pmb f } { d t } = - \\nabla \\big ( \\log \\rho ( \\pmb f ) - \\log \\pi ( \\pmb f ) \\big ) .",
+                                    "type": "interline_equation",
+                                    "image_path": "6ec49c1866059fd222d901856c6fd87a5e5117e19a3da56886cb693721fd87d0.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                234,
+                                358,
+                                377,
+                                383
+                            ],
+                            "spans": [],
+                            "index": 14
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        388,
+                        505,
+                        412
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                387,
+                                505,
+                                402
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        387,
+                                        505,
+                                        402
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Using the same KDE approximation as above, we can obtain a discretized evolution in function space",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                398,
+                                361,
+                                414
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        398,
+                                        334,
+                                        414
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and with it an explicit form for the repulsive force in Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        334,
+                                        399,
+                                        347,
+                                        413
+                                    ],
+                                    "score": 0.86,
+                                    "content": "\\textcircled{4}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        348,
+                                        398,
+                                        361,
+                                        414
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 15.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        188,
+                        417,
+                        423,
+                        450
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                188,
+                                417,
+                                423,
+                                450
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        188,
+                                        417,
+                                        423,
+                                        450
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\pmb { f } _ { t + 1 } ^ { i } = \\pmb { f } _ { t } ^ { i } + \\epsilon _ { t } \\bigg ( \\nabla _ { \\pmb { f } } \\log \\pi ( \\pmb { f } _ { t } ^ { i } ) - \\frac { \\sum _ { j = 1 } ^ { n } \\nabla _ { \\pmb { f } _ { i } ^ { t } } k ( \\pmb { f } _ { i } ^ { t } , \\pmb { f } _ { j } ^ { t } ) } { \\sum _ { j = 1 } ^ { n } k ( \\pmb { f } _ { i } ^ { t } , \\pmb { f } _ { j } ^ { t } ) } \\bigg ) .",
+                                    "type": "interline_equation",
+                                    "image_path": "413dc39054cf2ffe58aac203b1f546f1178b0fd741a1e970d847b042475c73d1.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                188,
+                                417,
+                                423,
+                                433.5
+                            ],
+                            "spans": [],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                188,
+                                433.5,
+                                423,
+                                450.0
+                            ],
+                            "spans": [],
+                            "index": 18
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        455,
+                        506,
+                        555
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                456,
+                                506,
+                                468
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        456,
+                                        506,
+                                        468
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The update rules using the SGE and SSGE approximations follow as for the parametric case. It is im-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                466,
+                                506,
+                                479
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        466,
+                                        416,
+                                        479
+                                    ],
+                                    "score": 1.0,
+                                    "content": "portant to notice that this update rule requires the function space prior gradient:",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        417,
+                                        466,
+                                        506,
+                                        479
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\nabla _ { f _ { j } } \\log { p ( f _ { j } | x , y ) } =",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                476,
+                                507,
+                                493
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        478,
+                                        252,
+                                        491
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\nabla _ { f _ { j } } \\log p ( \\pmb { y } | \\pmb { x } , \\pmb { f _ { j } } ) + \\nabla _ { f _ { j } } \\log p ( \\pmb { f _ { j } } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        252,
+                                        476,
+                                        507,
+                                        493
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". If one wants to use an implicit prior defined in weight space,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                489,
+                                506,
+                                501
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        489,
+                                        506,
+                                        501
+                                    ],
+                                    "score": 1.0,
+                                    "content": "an additional estimator is needed due to its analytical intractability. We again adopted the SSGE,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                499,
+                                506,
+                                513
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        499,
+                                        204,
+                                        513
+                                    ],
+                                    "score": 1.0,
+                                    "content": "introduced by Shi et al.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        204,
+                                        500,
+                                        222,
+                                        511
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\mathbb { \\lVert \\boldsymbol { 6 9 } \\rVert }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        222,
+                                        499,
+                                        464,
+                                        513
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", which was already used for a similar purpose in Sun et al.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        465,
+                                        500,
+                                        482,
+                                        511
+                                    ],
+                                    "score": 0.77,
+                                    "content": "\\pmb { \\mathbb { Z } 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        482,
+                                        499,
+                                        506,
+                                        513
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". It is",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                510,
+                                505,
+                                524
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        510,
+                                        303,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": "also interesting to note that the update rule in Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        510,
+                                        321,
+                                        524
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\textcircled { 1 2 0 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        322,
+                                        510,
+                                        505,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": "readily allows for the use of alternative priors",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                522,
+                                506,
+                                535
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        522,
+                                        506,
+                                        535
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that have an analytical form, such as Gaussian processes. This is an important feature of our method",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                533,
+                                506,
+                                546
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        533,
+                                        506,
+                                        546
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that allows for an explicit encoding of function space properties that can be useful for example in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                543,
+                                353,
+                                555
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        543,
+                                        334,
+                                        555
+                                    ],
+                                    "score": 1.0,
+                                    "content": "achieving better out of distribution detection capabilities",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        334,
+                                        543,
+                                        352,
+                                        555
+                                    ],
+                                    "score": 0.49,
+                                    "content": "\\checkmark",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        352,
+                                        543,
+                                        353,
+                                        555
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 23
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        569,
+                        232,
+                        581
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                569,
+                                233,
+                                583
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        569,
+                                        233,
+                                        583
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3.4 The choice of the kernel",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 28
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        590,
+                        505,
+                        722
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                590,
+                                506,
+                                604
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        590,
+                                        506,
+                                        604
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A repulsive effect can always be created in the ensemble by means of the gradient of any kernel",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                600,
+                                506,
+                                615
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        600,
+                                        506,
+                                        615
+                                    ],
+                                    "score": 1.0,
+                                    "content": "function that is measuring the similarity between two members. Nevertheless, it is important to keep",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                612,
+                                506,
+                                625
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        612,
+                                        506,
+                                        625
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in mind that to ensure the asymptotic convergence to the Bayesian posterior, the repulsive component",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                623,
+                                506,
+                                637
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        623,
+                                        320,
+                                        637
+                                    ],
+                                    "score": 1.0,
+                                    "content": "must be a consistent estimator of the gradient in Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        320,
+                                        623,
+                                        338,
+                                        636
+                                    ],
+                                    "score": 0.52,
+                                    "content": "( 1 3 )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        338,
+                                        623,
+                                        424,
+                                        637
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", as shown in Section",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        424,
+                                        623,
+                                        432,
+                                        636
+                                    ],
+                                    "score": 0.68,
+                                    "content": "\\checkmark",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        432,
+                                        623,
+                                        506,
+                                        637
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Therefore, some",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                634,
+                                506,
+                                646
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        634,
+                                        506,
+                                        646
+                                    ],
+                                    "score": 1.0,
+                                    "content": "important constraints over the kernel choice are needed. In particular, the SGE and SSGE need a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                645,
+                                506,
+                                657
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        645,
+                                        338,
+                                        657
+                                    ],
+                                    "score": 1.0,
+                                    "content": "kernel function belonging to the Stein class (see Shi et al.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        338,
+                                        645,
+                                        356,
+                                        657
+                                    ],
+                                    "score": 0.64,
+                                    "content": "\\dot { \\overline { { \\vert 6 9 \\vert } } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        356,
+                                        645,
+                                        506,
+                                        657
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for more details). On the other hand,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                655,
+                                506,
+                                669
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        655,
+                                        506,
+                                        669
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for the KDE, any symmetric probability density function can be used. On this subject, the work of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                667,
+                                505,
+                                679
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        667,
+                                        505,
+                                        679
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Aggarwal et al. [1] has shown how the Manhattan distance metric (L1 norm) might be preferable",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                677,
+                                505,
+                                691
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        677,
+                                        505,
+                                        691
+                                    ],
+                                    "score": 1.0,
+                                    "content": "over the Euclidean distance metric (L2 norm) for high-dimensional settings. We performed some",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                687,
+                                506,
+                                702
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        687,
+                                        506,
+                                        702
+                                    ],
+                                    "score": 1.0,
+                                    "content": "additional experiments using the L1 norm (Laplace kernel) for the KDE but we could not observe",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                700,
+                                505,
+                                713
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        700,
+                                        505,
+                                        713
+                                    ],
+                                    "score": 1.0,
+                                    "content": "any substantial difference compared to using the L2 norm. Further investigations regarding this",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                711,
+                                260,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        711,
+                                        260,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "hypothesis are left for future research.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        }
+                    ],
+                    "index": 34.5
+                }
+            ],
+            "page_idx": 6,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        741,
+                        309,
+                        750
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                302,
+                                741,
+                                309,
+                                752
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        302,
+                                        741,
+                                        309,
+                                        752
+                                    ],
+                                    "score": 1.0,
+                                    "content": "7",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "image",
+                    "bbox": [
+                        111,
+                        68,
+                        502,
+                        168
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                111,
+                                68,
+                                502,
+                                168
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        68,
+                                        502,
+                                        168
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                111,
+                                                68,
+                                                502,
+                                                168
+                                            ],
+                                            "score": 0.966,
+                                            "type": "image",
+                                            "image_path": "909c60e208223cd54336af828c72fc5777f5cbee78dd1b5dffc27345c64eca36.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        68,
+                                        502,
+                                        101.33333333333334
+                                    ],
+                                    "spans": [],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        111,
+                                        101.33333333333334,
+                                        502,
+                                        134.66666666666669
+                                    ],
+                                    "spans": [],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        111,
+                                        134.66666666666669,
+                                        502,
+                                        168.00000000000003
+                                    ],
+                                    "spans": [],
+                                    "index": 2
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                106,
+                                172,
+                                506,
+                                206
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        172,
+                                        507,
+                                        185
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                172,
+                                                507,
+                                                185
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 2: Single Gaussian. We show samples from SVGD, KDE-WGD, SGE-WGD, and SSGE-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        182,
+                                        505,
+                                        196
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                182,
+                                                505,
+                                                196
+                                            ],
+                                            "score": 1.0,
+                                            "content": "WGD (from left to right). The upper and right plots show the empirical one-dimensional marginal",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        194,
+                                        435,
+                                        207
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                194,
+                                                435,
+                                                207
+                                            ],
+                                            "score": 1.0,
+                                            "content": "distributions obtained using KDE on the samples (red) and on the particles (blue).",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 5
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 2.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        228,
+                        263,
+                        240
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                227,
+                                265,
+                                243
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        227,
+                                        265,
+                                        243
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3.3 Gradient flow in function space",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        249,
+                        504,
+                        273
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                248,
+                                505,
+                                262
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        248,
+                                        410,
+                                        262
+                                    ],
+                                    "score": 1.0,
+                                    "content": "To theoretically justify the update rule introduced in function space in Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        410,
+                                        249,
+                                        423,
+                                        262
+                                    ],
+                                    "score": 0.54,
+                                    "content": "\\textcircled{5}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        423,
+                                        248,
+                                        505,
+                                        262
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", we can rewrite the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                260,
+                                394,
+                                273
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        261,
+                                        292,
+                                        273
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Liouville equation for the gradient flow in Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        293,
+                                        260,
+                                        310,
+                                        273
+                                    ],
+                                    "score": 0.79,
+                                    "content": "\\textcircled { 1 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        311,
+                                        261,
+                                        394,
+                                        273
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in function space as",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 7.5,
+                    "bbox_fs": [
+                        105,
+                        248,
+                        505,
+                        273
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        206,
+                        279,
+                        406,
+                        335
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                206,
+                                279,
+                                406,
+                                335
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        206,
+                                        279,
+                                        406,
+                                        335
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\begin{array} { l } { \\displaystyle \\frac { \\partial \\rho ( { \\pmb f } ) } { \\partial t } = \\nabla \\cdot \\left( \\rho ( { \\pmb f } ) \\nabla \\frac { \\delta } { \\delta \\rho } D _ { K L } ( \\rho , \\pi ) \\right) } \\\\ { \\displaystyle = \\nabla \\cdot \\left( \\rho ( { \\pmb f } ) \\nabla \\big ( \\log \\rho ( { \\pmb f } ) - \\log \\pi ( { \\pmb f } ) \\big ) \\right) . } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "5c17155651b4b8a9222af9e3b20c3d19517ca6b37f38c6cba7442ed799860e6c.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                206,
+                                279,
+                                406,
+                                293.0
+                            ],
+                            "spans": [],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                206,
+                                293.0,
+                                406,
+                                307.0
+                            ],
+                            "spans": [],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                206,
+                                307.0,
+                                406,
+                                321.0
+                            ],
+                            "spans": [],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                206,
+                                321.0,
+                                406,
+                                335.0
+                            ],
+                            "spans": [],
+                            "index": 12
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        340,
+                        355,
+                        352
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                340,
+                                355,
+                                353
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        340,
+                                        355,
+                                        353
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Following this update, the mean field functional dynamics are",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 13,
+                    "bbox_fs": [
+                        106,
+                        340,
+                        355,
+                        353
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        234,
+                        358,
+                        377,
+                        383
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                234,
+                                358,
+                                377,
+                                383
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        234,
+                                        358,
+                                        377,
+                                        383
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\frac { d \\pmb f } { d t } = - \\nabla \\big ( \\log \\rho ( \\pmb f ) - \\log \\pi ( \\pmb f ) \\big ) .",
+                                    "type": "interline_equation",
+                                    "image_path": "6ec49c1866059fd222d901856c6fd87a5e5117e19a3da56886cb693721fd87d0.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                234,
+                                358,
+                                377,
+                                383
+                            ],
+                            "spans": [],
+                            "index": 14
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        388,
+                        505,
+                        412
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                387,
+                                505,
+                                402
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        387,
+                                        505,
+                                        402
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Using the same KDE approximation as above, we can obtain a discretized evolution in function space",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                398,
+                                361,
+                                414
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        398,
+                                        334,
+                                        414
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and with it an explicit form for the repulsive force in Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        334,
+                                        399,
+                                        347,
+                                        413
+                                    ],
+                                    "score": 0.86,
+                                    "content": "\\textcircled{4}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        348,
+                                        398,
+                                        361,
+                                        414
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 15.5,
+                    "bbox_fs": [
+                        105,
+                        387,
+                        505,
+                        414
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        188,
+                        417,
+                        423,
+                        450
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                188,
+                                417,
+                                423,
+                                450
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        188,
+                                        417,
+                                        423,
+                                        450
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\pmb { f } _ { t + 1 } ^ { i } = \\pmb { f } _ { t } ^ { i } + \\epsilon _ { t } \\bigg ( \\nabla _ { \\pmb { f } } \\log \\pi ( \\pmb { f } _ { t } ^ { i } ) - \\frac { \\sum _ { j = 1 } ^ { n } \\nabla _ { \\pmb { f } _ { i } ^ { t } } k ( \\pmb { f } _ { i } ^ { t } , \\pmb { f } _ { j } ^ { t } ) } { \\sum _ { j = 1 } ^ { n } k ( \\pmb { f } _ { i } ^ { t } , \\pmb { f } _ { j } ^ { t } ) } \\bigg ) .",
+                                    "type": "interline_equation",
+                                    "image_path": "413dc39054cf2ffe58aac203b1f546f1178b0fd741a1e970d847b042475c73d1.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                188,
+                                417,
+                                423,
+                                433.5
+                            ],
+                            "spans": [],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                188,
+                                433.5,
+                                423,
+                                450.0
+                            ],
+                            "spans": [],
+                            "index": 18
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        455,
+                        506,
+                        555
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                456,
+                                506,
+                                468
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        456,
+                                        506,
+                                        468
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The update rules using the SGE and SSGE approximations follow as for the parametric case. It is im-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                466,
+                                506,
+                                479
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        466,
+                                        416,
+                                        479
+                                    ],
+                                    "score": 1.0,
+                                    "content": "portant to notice that this update rule requires the function space prior gradient:",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        417,
+                                        466,
+                                        506,
+                                        479
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\nabla _ { f _ { j } } \\log { p ( f _ { j } | x , y ) } =",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                476,
+                                507,
+                                493
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        478,
+                                        252,
+                                        491
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\nabla _ { f _ { j } } \\log p ( \\pmb { y } | \\pmb { x } , \\pmb { f _ { j } } ) + \\nabla _ { f _ { j } } \\log p ( \\pmb { f _ { j } } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        252,
+                                        476,
+                                        507,
+                                        493
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". If one wants to use an implicit prior defined in weight space,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                489,
+                                506,
+                                501
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        489,
+                                        506,
+                                        501
+                                    ],
+                                    "score": 1.0,
+                                    "content": "an additional estimator is needed due to its analytical intractability. We again adopted the SSGE,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                499,
+                                506,
+                                513
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        499,
+                                        204,
+                                        513
+                                    ],
+                                    "score": 1.0,
+                                    "content": "introduced by Shi et al.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        204,
+                                        500,
+                                        222,
+                                        511
+                                    ],
+                                    "score": 0.85,
+                                    "content": "\\mathbb { \\lVert \\boldsymbol { 6 9 } \\rVert }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        222,
+                                        499,
+                                        464,
+                                        513
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", which was already used for a similar purpose in Sun et al.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        465,
+                                        500,
+                                        482,
+                                        511
+                                    ],
+                                    "score": 0.77,
+                                    "content": "\\pmb { \\mathbb { Z } 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        482,
+                                        499,
+                                        506,
+                                        513
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". It is",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                510,
+                                505,
+                                524
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        510,
+                                        303,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": "also interesting to note that the update rule in Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        510,
+                                        321,
+                                        524
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\textcircled { 1 2 0 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        322,
+                                        510,
+                                        505,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": "readily allows for the use of alternative priors",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                522,
+                                506,
+                                535
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        522,
+                                        506,
+                                        535
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that have an analytical form, such as Gaussian processes. This is an important feature of our method",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                533,
+                                506,
+                                546
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        533,
+                                        506,
+                                        546
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that allows for an explicit encoding of function space properties that can be useful for example in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                543,
+                                353,
+                                555
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        543,
+                                        334,
+                                        555
+                                    ],
+                                    "score": 1.0,
+                                    "content": "achieving better out of distribution detection capabilities",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        334,
+                                        543,
+                                        352,
+                                        555
+                                    ],
+                                    "score": 0.49,
+                                    "content": "\\checkmark",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        352,
+                                        543,
+                                        353,
+                                        555
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 23,
+                    "bbox_fs": [
+                        105,
+                        456,
+                        507,
+                        555
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        569,
+                        232,
+                        581
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                569,
+                                233,
+                                583
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        569,
+                                        233,
+                                        583
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3.4 The choice of the kernel",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 28
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        590,
+                        505,
+                        722
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                590,
+                                506,
+                                604
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        590,
+                                        506,
+                                        604
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A repulsive effect can always be created in the ensemble by means of the gradient of any kernel",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                600,
+                                506,
+                                615
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        600,
+                                        506,
+                                        615
+                                    ],
+                                    "score": 1.0,
+                                    "content": "function that is measuring the similarity between two members. Nevertheless, it is important to keep",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                612,
+                                506,
+                                625
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        612,
+                                        506,
+                                        625
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in mind that to ensure the asymptotic convergence to the Bayesian posterior, the repulsive component",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                623,
+                                506,
+                                637
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        623,
+                                        320,
+                                        637
+                                    ],
+                                    "score": 1.0,
+                                    "content": "must be a consistent estimator of the gradient in Eq.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        320,
+                                        623,
+                                        338,
+                                        636
+                                    ],
+                                    "score": 0.52,
+                                    "content": "( 1 3 )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        338,
+                                        623,
+                                        424,
+                                        637
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", as shown in Section",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        424,
+                                        623,
+                                        432,
+                                        636
+                                    ],
+                                    "score": 0.68,
+                                    "content": "\\checkmark",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        432,
+                                        623,
+                                        506,
+                                        637
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Therefore, some",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                634,
+                                506,
+                                646
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        634,
+                                        506,
+                                        646
+                                    ],
+                                    "score": 1.0,
+                                    "content": "important constraints over the kernel choice are needed. In particular, the SGE and SSGE need a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                645,
+                                506,
+                                657
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        645,
+                                        338,
+                                        657
+                                    ],
+                                    "score": 1.0,
+                                    "content": "kernel function belonging to the Stein class (see Shi et al.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        338,
+                                        645,
+                                        356,
+                                        657
+                                    ],
+                                    "score": 0.64,
+                                    "content": "\\dot { \\overline { { \\vert 6 9 \\vert } } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        356,
+                                        645,
+                                        506,
+                                        657
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for more details). On the other hand,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                655,
+                                506,
+                                669
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        655,
+                                        506,
+                                        669
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for the KDE, any symmetric probability density function can be used. On this subject, the work of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                667,
+                                505,
+                                679
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        667,
+                                        505,
+                                        679
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Aggarwal et al. [1] has shown how the Manhattan distance metric (L1 norm) might be preferable",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                677,
+                                505,
+                                691
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        677,
+                                        505,
+                                        691
+                                    ],
+                                    "score": 1.0,
+                                    "content": "over the Euclidean distance metric (L2 norm) for high-dimensional settings. We performed some",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                687,
+                                506,
+                                702
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        687,
+                                        506,
+                                        702
+                                    ],
+                                    "score": 1.0,
+                                    "content": "additional experiments using the L1 norm (Laplace kernel) for the KDE but we could not observe",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                700,
+                                505,
+                                713
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        700,
+                                        505,
+                                        713
+                                    ],
+                                    "score": 1.0,
+                                    "content": "any substantial difference compared to using the L2 norm. Further investigations regarding this",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                711,
+                                260,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        711,
+                                        260,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "hypothesis are left for future research.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        }
+                    ],
+                    "index": 34.5,
+                    "bbox_fs": [
+                        105,
+                        590,
+                        506,
+                        722
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "image",
+                    "bbox": [
+                        120,
+                        74,
+                        509,
+                        232
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                120,
+                                74,
+                                509,
+                                232
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        120,
+                                        74,
+                                        509,
+                                        232
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                120,
+                                                74,
+                                                509,
+                                                232
+                                            ],
+                                            "score": 0.974,
+                                            "type": "image",
+                                            "image_path": "094ed7ba5611118de5688c3ddd1545168ced55dff3ababfdac0ee5e88615b714.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        120,
+                                        74,
+                                        509,
+                                        126.66666666666666
+                                    ],
+                                    "spans": [],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        120,
+                                        126.66666666666666,
+                                        509,
+                                        179.33333333333331
+                                    ],
+                                    "spans": [],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        120,
+                                        179.33333333333331,
+                                        509,
+                                        231.99999999999997
+                                    ],
+                                    "spans": [],
+                                    "index": 2
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                108,
+                                242,
+                                507,
+                                275
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        241,
+                                        505,
+                                        255
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                241,
+                                                505,
+                                                255
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 3: BNN 2D classification. We show the entropy of the predictive posteriors. Again, the",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        252,
+                                        505,
+                                        267
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                252,
+                                                505,
+                                                267
+                                            ],
+                                            "score": 1.0,
+                                            "content": "function-space methods capture the uncertainty better than the weight-space ones, thus approaching",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        107,
+                                        264,
+                                        244,
+                                        276
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                107,
+                                                264,
+                                                244,
+                                                276
+                                            ],
+                                            "score": 1.0,
+                                            "content": "the gold-standard HMC posterior.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 5
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 2.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        296,
+                        191,
+                        310
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                294,
+                                193,
+                                313
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        294,
+                                        193,
+                                        313
+                                    ],
+                                    "score": 1.0,
+                                    "content": "4 Experiments",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        321,
+                        505,
+                        475
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                322,
+                                504,
+                                334
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        322,
+                                        504,
+                                        334
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In this section, we compare the different proposed WGD methods with deep ensembles and SVGD",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                333,
+                                507,
+                                345
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        333,
+                                        507,
+                                        345
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on synthetic sampling, regression, and classification tasks and real-world image classification tasks.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                343,
+                                504,
+                                356
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        343,
+                                        475,
+                                        356
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We use an RBF kernel (except where otherwise specified) with the popular median heuristic",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        476,
+                                        343,
+                                        493,
+                                        355
+                                    ],
+                                    "score": 0.64,
+                                    "content": "\\mathbb { \\left[ \\left[ 5 1 \\right] \\right] }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        494,
+                                        343,
+                                        504,
+                                        356
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                354,
+                                506,
+                                367
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        354,
+                                        506,
+                                        367
+                                    ],
+                                    "score": 1.0,
+                                    "content": "choose the kernel bandwidth. In our experiments, an adaptive bandwidth leads to better performance",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                365,
+                                506,
+                                378
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        365,
+                                        506,
+                                        378
+                                    ],
+                                    "score": 1.0,
+                                    "content": "than fixing and tuning a single constant value for the entire evolution of the particles. We also",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                377,
+                                505,
+                                388
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        377,
+                                        505,
+                                        388
+                                    ],
+                                    "score": 1.0,
+                                    "content": "quantitatively assess the uncertainty estimation of the methods in terms of calibration and OOD",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                387,
+                                506,
+                                400
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        387,
+                                        506,
+                                        400
+                                    ],
+                                    "score": 1.0,
+                                    "content": "detection. In our experiments, we report the test accuracy, negative log-likelihood (NLL), and the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                398,
+                                506,
+                                411
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        398,
+                                        506,
+                                        411
+                                    ],
+                                    "score": 1.0,
+                                    "content": "expected calibration error (ECE) [58]. To assert the robustness on out-of-distribution (OOD) data,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                409,
+                                506,
+                                421
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        409,
+                                        408,
+                                        421
+                                    ],
+                                    "score": 1.0,
+                                    "content": "we report the ratio between predictive entropy on OOD and test data points",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        408,
+                                        409,
+                                        445,
+                                        421
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( H _ { o } / H _ { t } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        446,
+                                        409,
+                                        506,
+                                        421
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and the OOD",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                420,
+                                505,
+                                433
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        420,
+                                        312,
+                                        433
+                                    ],
+                                    "score": 1.0,
+                                    "content": "detection area under the ROC curve AUROC(H)",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        312,
+                                        420,
+                                        330,
+                                        432
+                                    ],
+                                    "score": 0.47,
+                                    "content": "\\mathbb { H }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        331,
+                                        420,
+                                        505,
+                                        433
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Moreover, to assess the diversity of the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                430,
+                                505,
+                                444
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        430,
+                                        505,
+                                        444
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ensemble generated by the different methods in function space, we measure the functional diversity",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                442,
+                                505,
+                                455
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        442,
+                                        329,
+                                        455
+                                    ],
+                                    "score": 1.0,
+                                    "content": "using the model disagreement (MD) (details in Appendix",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        329,
+                                        442,
+                                        341,
+                                        455
+                                    ],
+                                    "score": 0.43,
+                                    "content": "\\bar { \\bigtriangledown } \\bar { \\bigtriangledown }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        342,
+                                        442,
+                                        505,
+                                        455
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". In particular, we report the ratio between",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                453,
+                                505,
+                                466
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        453,
+                                        365,
+                                        466
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the average model disagreement on the OOD and test data points",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        366,
+                                        453,
+                                        423,
+                                        465
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( M D _ { o } / M D _ { t } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        423,
+                                        453,
+                                        505,
+                                        466
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and additionally the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                463,
+                                438,
+                                477
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        463,
+                                        438,
+                                        477
+                                    ],
+                                    "score": 1.0,
+                                    "content": "OOD detection AUROC(MD) computed using this measure instead of the entropy.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 13.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        488,
+                        505,
+                        554
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                487,
+                                506,
+                                500
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        487,
+                                        506,
+                                        500
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sampling from synthetic distributions As a sanity check, we first assessed the ability of our",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                498,
+                                505,
+                                511
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        498,
+                                        505,
+                                        511
+                                    ],
+                                    "score": 1.0,
+                                    "content": "different approximations for Wasserstein gradient descent (using KDE, SGE, and SSGE) to sample",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                509,
+                                505,
+                                522
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        509,
+                                        321,
+                                        522
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from a two-dimensional Gaussian distribution (Figure",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        321,
+                                        509,
+                                        332,
+                                        522
+                                    ],
+                                    "score": 0.66,
+                                    "content": "^ { 2 ) }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        333,
+                                        509,
+                                        505,
+                                        522
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". We see that our SGE-WGD, SSGE-WGD",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                520,
+                                505,
+                                533
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        520,
+                                        505,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and the SVGD fit the target almost perfectly. We also tested the different methods in a more complex",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                530,
+                                507,
+                                544
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        530,
+                                        251,
+                                        544
+                                    ],
+                                    "score": 1.0,
+                                    "content": "two-dimensional Funnel distribution",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        251,
+                                        531,
+                                        269,
+                                        543
+                                    ],
+                                    "score": 0.82,
+                                    "content": "\\mathbb { \\left[ \\left[ 5 9 \\right] \\right] }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        269,
+                                        530,
+                                        395,
+                                        544
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and present the results in Figure",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        395,
+                                        531,
+                                        411,
+                                        544
+                                    ],
+                                    "score": 0.36,
+                                    "content": "\\mathrm { F . l }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        411,
+                                        530,
+                                        507,
+                                        544
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in the Appendix. There,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                541,
+                                276,
+                                555
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        541,
+                                        276,
+                                        555
+                                    ],
+                                    "score": 1.0,
+                                    "content": "SGE-WGD and SVGD also perform best.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 23.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        566,
+                        505,
+                        654
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                566,
+                                506,
+                                579
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        566,
+                                        506,
+                                        579
+                                    ],
+                                    "score": 1.0,
+                                    "content": "BNN 1D regression We then assessed the different methods in fitting a BNN posterior on a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                577,
+                                502,
+                                591
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        577,
+                                        502,
+                                        591
+                                    ],
+                                    "score": 1.0,
+                                    "content": "synthetically generated one-dimensional regression task. The results are reported in Figure 1",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                588,
+                                505,
+                                601
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        589,
+                                        257,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": "consisting of the mean prediction and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        258,
+                                        588,
+                                        291,
+                                        600
+                                    ],
+                                    "score": 0.66,
+                                    "content": "\\pm 1 , 2 , 3",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        291,
+                                        589,
+                                        505,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": "standard deviations of the predictive distribution. We",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                600,
+                                505,
+                                612
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        600,
+                                        505,
+                                        612
+                                    ],
+                                    "score": 1.0,
+                                    "content": "can see that all methods performing inference in the weight space (DE, w-SVGD, WGD) are unable",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                611,
+                                505,
+                                623
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        611,
+                                        505,
+                                        623
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to capture the epistemic uncertainty between the two clusters of training data points. Conversely, the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                621,
+                                505,
+                                633
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        621,
+                                        505,
+                                        633
+                                    ],
+                                    "score": 1.0,
+                                    "content": "functional methods (f-SVGD, fWGD) are perfectly able to infer the diversity of the hypotheses in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                631,
+                                505,
+                                645
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        631,
+                                        505,
+                                        645
+                                    ],
+                                    "score": 1.0,
+                                    "content": "this region due to the lack of training evidence. They thereby achieve a predictive posterior that very",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                642,
+                                407,
+                                657
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        642,
+                                        407,
+                                        657
+                                    ],
+                                    "score": 1.0,
+                                    "content": "closely resembles the one obtained with the gold-standard HMC sampling.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        }
+                    ],
+                    "index": 30.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        667,
+                        505,
+                        722
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                666,
+                                505,
+                                680
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        666,
+                                        505,
+                                        680
+                                    ],
+                                    "score": 1.0,
+                                    "content": "BNN 2D classification Next, we investigated the predictive performance and quality of uncertainty",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                677,
+                                505,
+                                690
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        677,
+                                        505,
+                                        690
+                                    ],
+                                    "score": 1.0,
+                                    "content": "estimation of the methods in a two-dimensional synthetic classification setting. The results are",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                688,
+                                506,
+                                703
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        688,
+                                        182,
+                                        703
+                                    ],
+                                    "score": 1.0,
+                                    "content": "displayed in Figure",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        182,
+                                        688,
+                                        193,
+                                        702
+                                    ],
+                                    "score": 0.31,
+                                    "content": "\\textcircled { 3 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        193,
+                                        688,
+                                        506,
+                                        703
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We can clearly observe that the weight-space methods are overconfident and do",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                700,
+                                506,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        700,
+                                        506,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "not capture the uncertainty well. Moreover, all the functions seems to collapse to the optimal classifier.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                711,
+                                505,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        711,
+                                        505,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "These methods thus only account for uncertainty close to the decision boundaries and to the origin",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 37
+                }
+            ],
+            "page_idx": 7,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        742,
+                        308,
+                        750
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                302,
+                                741,
+                                309,
+                                752
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        302,
+                                        741,
+                                        309,
+                                        752
+                                    ],
+                                    "score": 1.0,
+                                    "content": "8",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "image",
+                    "bbox": [
+                        120,
+                        74,
+                        509,
+                        232
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                120,
+                                74,
+                                509,
+                                232
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        120,
+                                        74,
+                                        509,
+                                        232
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                120,
+                                                74,
+                                                509,
+                                                232
+                                            ],
+                                            "score": 0.974,
+                                            "type": "image",
+                                            "image_path": "094ed7ba5611118de5688c3ddd1545168ced55dff3ababfdac0ee5e88615b714.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        120,
+                                        74,
+                                        509,
+                                        126.66666666666666
+                                    ],
+                                    "spans": [],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        120,
+                                        126.66666666666666,
+                                        509,
+                                        179.33333333333331
+                                    ],
+                                    "spans": [],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        120,
+                                        179.33333333333331,
+                                        509,
+                                        231.99999999999997
+                                    ],
+                                    "spans": [],
+                                    "index": 2
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                108,
+                                242,
+                                507,
+                                275
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        241,
+                                        505,
+                                        255
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                241,
+                                                505,
+                                                255
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 3: BNN 2D classification. We show the entropy of the predictive posteriors. Again, the",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        252,
+                                        505,
+                                        267
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                252,
+                                                505,
+                                                267
+                                            ],
+                                            "score": 1.0,
+                                            "content": "function-space methods capture the uncertainty better than the weight-space ones, thus approaching",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        107,
+                                        264,
+                                        244,
+                                        276
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                107,
+                                                264,
+                                                244,
+                                                276
+                                            ],
+                                            "score": 1.0,
+                                            "content": "the gold-standard HMC posterior.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 5
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 2.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        296,
+                        191,
+                        310
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                294,
+                                193,
+                                313
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        294,
+                                        193,
+                                        313
+                                    ],
+                                    "score": 1.0,
+                                    "content": "4 Experiments",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        321,
+                        505,
+                        475
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                322,
+                                504,
+                                334
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        322,
+                                        504,
+                                        334
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In this section, we compare the different proposed WGD methods with deep ensembles and SVGD",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                333,
+                                507,
+                                345
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        333,
+                                        507,
+                                        345
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on synthetic sampling, regression, and classification tasks and real-world image classification tasks.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                343,
+                                504,
+                                356
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        343,
+                                        475,
+                                        356
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We use an RBF kernel (except where otherwise specified) with the popular median heuristic",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        476,
+                                        343,
+                                        493,
+                                        355
+                                    ],
+                                    "score": 0.64,
+                                    "content": "\\mathbb { \\left[ \\left[ 5 1 \\right] \\right] }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        494,
+                                        343,
+                                        504,
+                                        356
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                354,
+                                506,
+                                367
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        354,
+                                        506,
+                                        367
+                                    ],
+                                    "score": 1.0,
+                                    "content": "choose the kernel bandwidth. In our experiments, an adaptive bandwidth leads to better performance",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                365,
+                                506,
+                                378
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        365,
+                                        506,
+                                        378
+                                    ],
+                                    "score": 1.0,
+                                    "content": "than fixing and tuning a single constant value for the entire evolution of the particles. We also",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                377,
+                                505,
+                                388
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        377,
+                                        505,
+                                        388
+                                    ],
+                                    "score": 1.0,
+                                    "content": "quantitatively assess the uncertainty estimation of the methods in terms of calibration and OOD",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                387,
+                                506,
+                                400
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        387,
+                                        506,
+                                        400
+                                    ],
+                                    "score": 1.0,
+                                    "content": "detection. In our experiments, we report the test accuracy, negative log-likelihood (NLL), and the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                398,
+                                506,
+                                411
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        398,
+                                        506,
+                                        411
+                                    ],
+                                    "score": 1.0,
+                                    "content": "expected calibration error (ECE) [58]. To assert the robustness on out-of-distribution (OOD) data,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                409,
+                                506,
+                                421
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        409,
+                                        408,
+                                        421
+                                    ],
+                                    "score": 1.0,
+                                    "content": "we report the ratio between predictive entropy on OOD and test data points",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        408,
+                                        409,
+                                        445,
+                                        421
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( H _ { o } / H _ { t } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        446,
+                                        409,
+                                        506,
+                                        421
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and the OOD",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                420,
+                                505,
+                                433
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        420,
+                                        312,
+                                        433
+                                    ],
+                                    "score": 1.0,
+                                    "content": "detection area under the ROC curve AUROC(H)",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        312,
+                                        420,
+                                        330,
+                                        432
+                                    ],
+                                    "score": 0.47,
+                                    "content": "\\mathbb { H }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        331,
+                                        420,
+                                        505,
+                                        433
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Moreover, to assess the diversity of the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                430,
+                                505,
+                                444
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        430,
+                                        505,
+                                        444
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ensemble generated by the different methods in function space, we measure the functional diversity",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                442,
+                                505,
+                                455
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        442,
+                                        329,
+                                        455
+                                    ],
+                                    "score": 1.0,
+                                    "content": "using the model disagreement (MD) (details in Appendix",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        329,
+                                        442,
+                                        341,
+                                        455
+                                    ],
+                                    "score": 0.43,
+                                    "content": "\\bar { \\bigtriangledown } \\bar { \\bigtriangledown }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        342,
+                                        442,
+                                        505,
+                                        455
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". In particular, we report the ratio between",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                453,
+                                505,
+                                466
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        453,
+                                        365,
+                                        466
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the average model disagreement on the OOD and test data points",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        366,
+                                        453,
+                                        423,
+                                        465
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( M D _ { o } / M D _ { t } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        423,
+                                        453,
+                                        505,
+                                        466
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and additionally the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                463,
+                                438,
+                                477
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        463,
+                                        438,
+                                        477
+                                    ],
+                                    "score": 1.0,
+                                    "content": "OOD detection AUROC(MD) computed using this measure instead of the entropy.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 13.5,
+                    "bbox_fs": [
+                        105,
+                        322,
+                        507,
+                        477
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        488,
+                        505,
+                        554
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                487,
+                                506,
+                                500
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        487,
+                                        506,
+                                        500
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sampling from synthetic distributions As a sanity check, we first assessed the ability of our",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                498,
+                                505,
+                                511
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        498,
+                                        505,
+                                        511
+                                    ],
+                                    "score": 1.0,
+                                    "content": "different approximations for Wasserstein gradient descent (using KDE, SGE, and SSGE) to sample",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                509,
+                                505,
+                                522
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        509,
+                                        321,
+                                        522
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from a two-dimensional Gaussian distribution (Figure",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        321,
+                                        509,
+                                        332,
+                                        522
+                                    ],
+                                    "score": 0.66,
+                                    "content": "^ { 2 ) }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        333,
+                                        509,
+                                        505,
+                                        522
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". We see that our SGE-WGD, SSGE-WGD",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                520,
+                                505,
+                                533
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        520,
+                                        505,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and the SVGD fit the target almost perfectly. We also tested the different methods in a more complex",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                530,
+                                507,
+                                544
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        530,
+                                        251,
+                                        544
+                                    ],
+                                    "score": 1.0,
+                                    "content": "two-dimensional Funnel distribution",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        251,
+                                        531,
+                                        269,
+                                        543
+                                    ],
+                                    "score": 0.82,
+                                    "content": "\\mathbb { \\left[ \\left[ 5 9 \\right] \\right] }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        269,
+                                        530,
+                                        395,
+                                        544
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and present the results in Figure",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        395,
+                                        531,
+                                        411,
+                                        544
+                                    ],
+                                    "score": 0.36,
+                                    "content": "\\mathrm { F . l }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        411,
+                                        530,
+                                        507,
+                                        544
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in the Appendix. There,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                541,
+                                276,
+                                555
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        541,
+                                        276,
+                                        555
+                                    ],
+                                    "score": 1.0,
+                                    "content": "SGE-WGD and SVGD also perform best.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 23.5,
+                    "bbox_fs": [
+                        105,
+                        487,
+                        507,
+                        555
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        566,
+                        505,
+                        654
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                566,
+                                506,
+                                579
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        566,
+                                        506,
+                                        579
+                                    ],
+                                    "score": 1.0,
+                                    "content": "BNN 1D regression We then assessed the different methods in fitting a BNN posterior on a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                577,
+                                502,
+                                591
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        577,
+                                        502,
+                                        591
+                                    ],
+                                    "score": 1.0,
+                                    "content": "synthetically generated one-dimensional regression task. The results are reported in Figure 1",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                588,
+                                505,
+                                601
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        589,
+                                        257,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": "consisting of the mean prediction and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        258,
+                                        588,
+                                        291,
+                                        600
+                                    ],
+                                    "score": 0.66,
+                                    "content": "\\pm 1 , 2 , 3",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        291,
+                                        589,
+                                        505,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": "standard deviations of the predictive distribution. We",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                600,
+                                505,
+                                612
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        600,
+                                        505,
+                                        612
+                                    ],
+                                    "score": 1.0,
+                                    "content": "can see that all methods performing inference in the weight space (DE, w-SVGD, WGD) are unable",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                611,
+                                505,
+                                623
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        611,
+                                        505,
+                                        623
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to capture the epistemic uncertainty between the two clusters of training data points. Conversely, the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                621,
+                                505,
+                                633
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        621,
+                                        505,
+                                        633
+                                    ],
+                                    "score": 1.0,
+                                    "content": "functional methods (f-SVGD, fWGD) are perfectly able to infer the diversity of the hypotheses in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                631,
+                                505,
+                                645
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        631,
+                                        505,
+                                        645
+                                    ],
+                                    "score": 1.0,
+                                    "content": "this region due to the lack of training evidence. They thereby achieve a predictive posterior that very",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                642,
+                                407,
+                                657
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        642,
+                                        407,
+                                        657
+                                    ],
+                                    "score": 1.0,
+                                    "content": "closely resembles the one obtained with the gold-standard HMC sampling.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        }
+                    ],
+                    "index": 30.5,
+                    "bbox_fs": [
+                        105,
+                        566,
+                        506,
+                        657
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        667,
+                        505,
+                        722
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                666,
+                                505,
+                                680
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        666,
+                                        505,
+                                        680
+                                    ],
+                                    "score": 1.0,
+                                    "content": "BNN 2D classification Next, we investigated the predictive performance and quality of uncertainty",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                677,
+                                505,
+                                690
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        677,
+                                        505,
+                                        690
+                                    ],
+                                    "score": 1.0,
+                                    "content": "estimation of the methods in a two-dimensional synthetic classification setting. The results are",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                688,
+                                506,
+                                703
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        688,
+                                        182,
+                                        703
+                                    ],
+                                    "score": 1.0,
+                                    "content": "displayed in Figure",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        182,
+                                        688,
+                                        193,
+                                        702
+                                    ],
+                                    "score": 0.31,
+                                    "content": "\\textcircled { 3 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        193,
+                                        688,
+                                        506,
+                                        703
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We can clearly observe that the weight-space methods are overconfident and do",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                700,
+                                506,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        700,
+                                        506,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "not capture the uncertainty well. Moreover, all the functions seems to collapse to the optimal classifier.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                711,
+                                505,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        711,
+                                        505,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "These methods thus only account for uncertainty close to the decision boundaries and to the origin",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                334,
+                                506,
+                                347
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        334,
+                                        506,
+                                        347
+                                    ],
+                                    "score": 1.0,
+                                    "content": "region, for which the uncertainty is purely aleatoric. In this setting, f-SVGD suffers from similar",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                346,
+                                506,
+                                359
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        346,
+                                        506,
+                                        359
+                                    ],
+                                    "score": 1.0,
+                                    "content": "issues as the weight space methods, being overconfident away from the training data. Conversely,",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                357,
+                                505,
+                                369
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        357,
+                                        505,
+                                        369
+                                    ],
+                                    "score": 1.0,
+                                    "content": "our fWGD methods are confident (low entropy) around the data but not out-of-distribution, thus",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                367,
+                                506,
+                                380
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        367,
+                                        506,
+                                        380
+                                    ],
+                                    "score": 1.0,
+                                    "content": "representing the epistemic uncertainty better. This suggests that the functional diversity captured",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                378,
+                                505,
+                                392
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        378,
+                                        406,
+                                        392
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by this method naturally leads to a distance-aware uncertainty estimation",
+                                    "type": "text",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        407,
+                                        378,
+                                        439,
+                                        390
+                                    ],
+                                    "score": 0.56,
+                                    "content": "\\mathbb { H 9 } \\mathbb { L O }",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        440,
+                                        378,
+                                        505,
+                                        392
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", a property that",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                389,
+                                506,
+                                402
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        389,
+                                        506,
+                                        402
+                                    ],
+                                    "score": 1.0,
+                                    "content": "translates into confident predictions only in the proximity of the training data, allowing for a principled",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                400,
+                                172,
+                                412
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        400,
+                                        172,
+                                        412
+                                    ],
+                                    "score": 1.0,
+                                    "content": "OOD detection.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 37,
+                    "bbox_fs": [
+                        105,
+                        666,
+                        506,
+                        723
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "table",
+                    "bbox": [
+                        107,
+                        143,
+                        505,
+                        312
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                106,
+                                69,
+                                505,
+                                136
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        69,
+                                        505,
+                                        83
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                69,
+                                                288,
+                                                83
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 1: BNN image classification. AUROC",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
+                                                288,
+                                                70,
+                                                302,
+                                                81
+                                            ],
+                                            "score": 0.29,
+                                            "content": "\\mathbf { ( H ) }",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
+                                                302,
+                                                69,
+                                                505,
+                                                83
+                                            ],
+                                            "score": 1.0,
+                                            "content": "is the AUROC computed using the entropy whereas",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        81,
+                                        505,
+                                        95
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                81,
+                                                346,
+                                                95
+                                            ],
+                                            "score": 1.0,
+                                            "content": "AUROC(MD) is computed using the model disagreement.",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
+                                                347,
+                                                81,
+                                                380,
+                                                93
+                                            ],
+                                            "score": 0.93,
+                                            "content": "\\mathbf { H _ { o } / H _ { t } }",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
+                                                380,
+                                                81,
+                                                505,
+                                                95
+                                            ],
+                                            "score": 1.0,
+                                            "content": "is the ratio of the entropies on",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        92,
+                                        505,
+                                        104
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                93,
+                                                257,
+                                                104
+                                            ],
+                                            "score": 1.0,
+                                            "content": "OOD and test points respectively and",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
+                                                257,
+                                                92,
+                                                312,
+                                                104
+                                            ],
+                                            "score": 0.9,
+                                            "content": "\\mathbf { M D _ { o } / M D _ { t } }",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
+                                                312,
+                                                93,
+                                                505,
+                                                104
+                                            ],
+                                            "score": 1.0,
+                                            "content": "is the ratio for model disagreement. We see that",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 2
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        103,
+                                        505,
+                                        116
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                103,
+                                                505,
+                                                116
+                                            ],
+                                            "score": 1.0,
+                                            "content": "the best accuracy is achieved by our WGD methods, while our fWGD methods yield the best OOD",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        113,
+                                        506,
+                                        128
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                113,
+                                                506,
+                                                128
+                                            ],
+                                            "score": 1.0,
+                                            "content": "detection and funtional diversity. All our proposed methods improve over standard deep ensembles in",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        124,
+                                        395,
+                                        139
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                124,
+                                                395,
+                                                139
+                                            ],
+                                            "score": 1.0,
+                                            "content": "terms of accuracy and diversity, highlighting the effect of our repulsion.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 5
+                                }
+                            ],
+                            "index": 2.5
+                        },
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                107,
+                                143,
+                                505,
+                                312
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        143,
+                                        505,
+                                        312
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                107,
+                                                143,
+                                                505,
+                                                312
+                                            ],
+                                            "score": 0.985,
+                                            "html": "<table><tr><td rowspan=\"11\">Prroiiiie</td><td></td><td>AUROC(H)</td><td>AUROC(MD)</td><td>Accuracy</td><td>H/Ht</td><td>MD/MDt</td><td>ECE</td><td>NLL</td></tr><tr><td>Deep ensemble 4</td><td>0.958±0.001</td><td>0.975±0.001</td><td>91.122±0.013</td><td>6.257±0.005</td><td>6.394±0.001</td><td>0.012±0.001</td><td>0.129±0.001</td></tr><tr><td>SVGD [51</td><td>0.960±0.001</td><td>0.973±0.001</td><td>91.134±0.024</td><td>6.315±0.019</td><td>6.395±0.018</td><td>0.014±0.001</td><td>0.127±0.001</td></tr><tr><td>f-SVGD [76</td><td>0.956±0.001</td><td>0.975±0.001</td><td>89.884±0.015</td><td>5.652±0.009</td><td>6.531±0.005</td><td>0.013±0.001</td><td>0.150±0.001</td></tr><tr><td>hyper-DE [80]</td><td>0.968±0.001</td><td>0.981±0.001</td><td>91.160±0.007</td><td>6.682±0.065</td><td>7.059±0.152</td><td>0.014±0.001</td><td>0.128±0.001</td></tr><tr><td>kde-WGD (ours)</td><td>0.960±0.001</td><td>0.970±0.001</td><td>91.238±0.019</td><td>6.587±0.019</td><td>6.379±0.018</td><td>0.014±0.001</td><td>0.128±0.001</td></tr><tr><td>sge-WGD (ours)</td><td>0.960±0.001</td><td>0.970±0.001</td><td>91.312±0.016</td><td>6.562±0.007</td><td>6.363±0.009</td><td>0.012±0.001</td><td>0.128±0.001</td></tr><tr><td>ssge-WGD (ours)</td><td>0.968±0.001</td><td>0.979±0.001</td><td>91.198±0.024</td><td>6.522±0.009</td><td>6.610±0.012</td><td>0.012±0.001</td><td>0.130±0.001</td></tr><tr><td>kde-fWGD (ours)</td><td>0.971±0.001</td><td>0.980±0.001</td><td>91.260±0.011</td><td>7.079±0.016</td><td>6.887±0.015</td><td>0.015±0.001</td><td>0.125±0.001</td></tr><tr><td>sge-fWGD (ours)</td><td>0.969±0.001</td><td>0.978±0.001</td><td>91.192±0.013</td><td>7.076±0.004</td><td>6.900±0.005</td><td>0.015±0.001</td><td>0.125±0.001</td></tr><tr><td>ssge-fWGD (ours)</td><td>0.971±0.001</td><td>0.980±0.001</td><td>91.240±0.022</td><td>7.129±0.006</td><td>6.951±0.005</td><td>0.016±0.001</td><td>0.124±0.001</td></tr><tr><td rowspan=\"11\">CITIIIO</td><td>Deep ensemble 42</td><td>0.843±0.004</td><td>0.736±0.005</td><td>85,552±0.076</td><td>2.244±0.006</td><td>1.667±0.008</td><td>0.049±0.001</td><td>0.277±0.001</td></tr><tr><td>SVGD [51</td><td>0.825±0.001</td><td>0.710±0.002</td><td>85.142±0.017</td><td>2.106±0.003</td><td>1.567±0.004</td><td>0.052±0.001</td><td>0.287±0.001</td></tr><tr><td>fSVGD 回</td><td>0.783±0.001</td><td>0.712±0.001</td><td>84.510±0.031</td><td>1.968±0.004</td><td>1.624±0.003</td><td>0.049±0.001</td><td>0.292±0.001</td></tr><tr><td>hyper-DE [80]</td><td>0.789±0.001</td><td>0.743±0.001</td><td>84.743±0.011</td><td>1.951±0.010</td><td>1.690±0.015</td><td>0.046±0.001</td><td>0.288±0.001</td></tr><tr><td>kde-WGD (ours)</td><td>0.838±0.001</td><td>0.735±0.004</td><td>85.904±0.030</td><td>2.205±0.003</td><td>1.661±0.008</td><td>0.053±0.001</td><td>0.276±0.001</td></tr><tr><td>sge-WGD (ours)</td><td>0.837±0.003</td><td>0.725±0.004</td><td>85.792±0.035</td><td>2.214±0.010</td><td>1.634±0.004</td><td>0.051±0.001</td><td>0.275±0.001</td></tr><tr><td>ssge-WGD (ours)</td><td>0.832±0.003</td><td>0.731±0.005</td><td>85.638±0.038</td><td>2.182±0.015</td><td>1.655±0.001</td><td>0.049±0.001</td><td>0.276±0.001</td></tr><tr><td>kde-fWGD (ours)</td><td>0.791±0.002</td><td>0.758±0.002</td><td>84.888±0.030</td><td>1.970±0.004</td><td>1.749±0.005</td><td>0.044±0.001</td><td>0.282±0.001</td></tr><tr><td>sge-fWGD (ours)</td><td>0.795±0.001</td><td>0.754±0.002</td><td>84.766±0.060</td><td>1.984±0.003</td><td>1.729±0.002</td><td>0.047±0.001</td><td>0.288±0.001</td></tr><tr><td>ssge-fWGD (ours)</td><td>0.792±0.002</td><td>0.752±0.002</td><td>84.762±0.034</td><td>1.970±0.006</td><td>1.723±0.005</td><td>0.046±0.001</td><td>0.286±0.001</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "c10e7e6db9d6afe7b283337a217b0daf6bdc8ff99b073aef9c58623cfb518d7c.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 7,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        143,
+                                        505,
+                                        199.33333333333334
+                                    ],
+                                    "spans": [],
+                                    "index": 6
+                                },
+                                {
+                                    "bbox": [
+                                        107,
+                                        199.33333333333334,
+                                        505,
+                                        255.66666666666669
+                                    ],
+                                    "spans": [],
+                                    "index": 7
+                                },
+                                {
+                                    "bbox": [
+                                        107,
+                                        255.66666666666669,
+                                        505,
+                                        312.0
+                                    ],
+                                    "spans": [],
+                                    "index": 8
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4.75
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        334,
+                        505,
+                        411
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                334,
+                                506,
+                                347
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        334,
+                                        506,
+                                        347
+                                    ],
+                                    "score": 1.0,
+                                    "content": "region, for which the uncertainty is purely aleatoric. In this setting, f-SVGD suffers from similar",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                346,
+                                506,
+                                359
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        346,
+                                        506,
+                                        359
+                                    ],
+                                    "score": 1.0,
+                                    "content": "issues as the weight space methods, being overconfident away from the training data. Conversely,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                357,
+                                505,
+                                369
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        357,
+                                        505,
+                                        369
+                                    ],
+                                    "score": 1.0,
+                                    "content": "our fWGD methods are confident (low entropy) around the data but not out-of-distribution, thus",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                367,
+                                506,
+                                380
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        367,
+                                        506,
+                                        380
+                                    ],
+                                    "score": 1.0,
+                                    "content": "representing the epistemic uncertainty better. This suggests that the functional diversity captured",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                378,
+                                505,
+                                392
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        378,
+                                        406,
+                                        392
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by this method naturally leads to a distance-aware uncertainty estimation",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        407,
+                                        378,
+                                        439,
+                                        390
+                                    ],
+                                    "score": 0.56,
+                                    "content": "\\mathbb { H 9 } \\mathbb { L O }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        440,
+                                        378,
+                                        505,
+                                        392
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", a property that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                389,
+                                506,
+                                402
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        389,
+                                        506,
+                                        402
+                                    ],
+                                    "score": 1.0,
+                                    "content": "translates into confident predictions only in the proximity of the training data, allowing for a principled",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                400,
+                                172,
+                                412
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        400,
+                                        172,
+                                        412
+                                    ],
+                                    "score": 1.0,
+                                    "content": "OOD detection.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        425,
+                        505,
+                        578
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                424,
+                                505,
+                                437
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        424,
+                                        505,
+                                        437
+                                    ],
+                                    "score": 1.0,
+                                    "content": "FashionMNIST classification Moving on to real-world data, we used an image classification",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                435,
+                                506,
+                                448
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        435,
+                                        271,
+                                        448
+                                    ],
+                                    "score": 1.0,
+                                    "content": "setting using the FashionMNIST dataset",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        271,
+                                        435,
+                                        289,
+                                        447
+                                    ],
+                                    "score": 0.78,
+                                    "content": "\\dot { \\left[ \\left| 8 3 \\right| \\right] }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        435,
+                                        434,
+                                        448
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for training and the MNIST dataset",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        434,
+                                        435,
+                                        452,
+                                        447
+                                    ],
+                                    "score": 0.78,
+                                    "content": "\\bar { \\mathbb { E } 3 } \\mathbb { I }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        452,
+                                        435,
+                                        506,
+                                        448
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as an out-of-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                447,
+                                505,
+                                460
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        447,
+                                        340,
+                                        459
+                                    ],
+                                    "score": 1.0,
+                                    "content": "distribution (OOD) task. The results are reported in Table",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        340,
+                                        447,
+                                        350,
+                                        460
+                                    ],
+                                    "score": 0.55,
+                                    "content": "^ 1 { } _ { . }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        350,
+                                        447,
+                                        505,
+                                        459
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(top). We can see that all our methods",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                457,
+                                506,
+                                470
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        457,
+                                        506,
+                                        470
+                                    ],
+                                    "score": 1.0,
+                                    "content": "improve upon standard deep ensembles and SVGD, highlighting the effectiveness of our proposed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                469,
+                                506,
+                                481
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        469,
+                                        506,
+                                        481
+                                    ],
+                                    "score": 1.0,
+                                    "content": "repulsion terms when training neural network ensembles. In particular, the sge-WGD offers the best",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                479,
+                                505,
+                                492
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        479,
+                                        505,
+                                        492
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accuracy, whereas the methods in function space all offer a better OOD detection. This is probably",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                490,
+                                505,
+                                503
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        490,
+                                        505,
+                                        503
+                                    ],
+                                    "score": 1.0,
+                                    "content": "due to the fact that these methods achieve a higher entropy ratio and functional diversity measured",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                502,
+                                505,
+                                514
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        502,
+                                        505,
+                                        514
+                                    ],
+                                    "score": 1.0,
+                                    "content": "via the model disagreement when compared to their weight-space counterparts. Interestingly, they",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                511,
+                                505,
+                                525
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        511,
+                                        505,
+                                        525
+                                    ],
+                                    "score": 1.0,
+                                    "content": "also reach the lowest NLL values. We can also notice how the model disagreement (MD) not only",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                523,
+                                506,
+                                536
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        523,
+                                        506,
+                                        536
+                                    ],
+                                    "score": 1.0,
+                                    "content": "serves its purpose as a metric for the functional heterogeneity of the ensemble but also allows for a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                533,
+                                505,
+                                547
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        533,
+                                        505,
+                                        547
+                                    ],
+                                    "score": 1.0,
+                                    "content": "better OOD detection in comparison to the entropy. To the best of our knowledge, this insight has",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                543,
+                                505,
+                                559
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        543,
+                                        403,
+                                        559
+                                    ],
+                                    "score": 1.0,
+                                    "content": "not been described before, although it has been used in continual learning",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        404,
+                                        545,
+                                        421,
+                                        556
+                                    ],
+                                    "score": 0.27,
+                                    "content": "\\pmb { \\mathbb { B } } \\mathbf { \\mathbb { 1 } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        421,
+                                        543,
+                                        505,
+                                        559
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Interestingly, using",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                555,
+                                505,
+                                569
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        555,
+                                        257,
+                                        569
+                                    ],
+                                    "score": 1.0,
+                                    "content": "this metric, the hyper-deep ensemble",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        257,
+                                        555,
+                                        275,
+                                        567
+                                    ],
+                                    "score": 0.44,
+                                    "content": "[ \\textcircled { 8 0 } ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        275,
+                                        555,
+                                        505,
+                                        569
+                                    ],
+                                    "score": 1.0,
+                                    "content": "shows OOD detection performance comparable with our",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                568,
+                                258,
+                                579
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        568,
+                                        258,
+                                        579
+                                    ],
+                                    "score": 1.0,
+                                    "content": "repulsive ensemble in function space.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 22.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        591,
+                        505,
+                        657
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                591,
+                                505,
+                                604
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        591,
+                                        371,
+                                        604
+                                    ],
+                                    "score": 1.0,
+                                    "content": "CIFAR classification Finally, we use a ResNet32 architecture",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        371,
+                                        591,
+                                        389,
+                                        603
+                                    ],
+                                    "score": 0.4,
+                                    "content": "\\mathbb { \\left| \\left[ 2 9 \\right] \\right| }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        389,
+                                        591,
+                                        505,
+                                        604
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on CIFAR-10 [41] with the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                602,
+                                506,
+                                615
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        602,
+                                        165,
+                                        615
+                                    ],
+                                    "score": 1.0,
+                                    "content": "SVHN dataset",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        165,
+                                        602,
+                                        183,
+                                        614
+                                    ],
+                                    "score": 0.46,
+                                    "content": "\\mathbb { \\left[ 6 1 \\right] }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        183,
+                                        602,
+                                        506,
+                                        615
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as OOD data. The results are reported in Table 1 (bottom). We can see that in this",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                614,
+                                505,
+                                625
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        614,
+                                        505,
+                                        625
+                                    ],
+                                    "score": 1.0,
+                                    "content": "case, the weight-space methods achieve better performance in accuracy and OOD detection using the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                624,
+                                505,
+                                637
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        624,
+                                        505,
+                                        637
+                                    ],
+                                    "score": 1.0,
+                                    "content": "entropy than the ones in function space. Nevertheless, all our repulsive ensembles improve functional",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                634,
+                                506,
+                                648
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        634,
+                                        506,
+                                        648
+                                    ],
+                                    "score": 1.0,
+                                    "content": "diversity, accuracy, and OOD detection when compared to standard SVGD, whereas the standard",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                645,
+                                374,
+                                659
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        645,
+                                        374,
+                                        659
+                                    ],
+                                    "score": 1.0,
+                                    "content": "deep ensemble achieves the best OOD detection using the entropy.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        }
+                    ],
+                    "index": 32.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        673,
+                        197,
+                        687
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                673,
+                                198,
+                                689
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        673,
+                                        198,
+                                        689
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5 Related Work",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 36
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        699,
+                        503,
+                        722
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                698,
+                                505,
+                                713
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        698,
+                                        505,
+                                        713
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The theoretical and empirical properties of SVGD have been well studied [40, 48, 13] and it can",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                709,
+                                505,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        709,
+                                        505,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "also be seen as a Wasserstein gradient flow of the KL divergence in the Stein geometry [16, 50]",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        }
+                    ],
+                    "index": 37.5
+                }
+            ],
+            "page_idx": 8,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        741,
+                        308,
+                        750
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                302,
+                                741,
+                                309,
+                                752
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        302,
+                                        741,
+                                        309,
+                                        752
+                                    ],
+                                    "score": 1.0,
+                                    "content": "9",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "table",
+                    "bbox": [
+                        107,
+                        143,
+                        505,
+                        312
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                106,
+                                69,
+                                505,
+                                136
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        69,
+                                        505,
+                                        83
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                69,
+                                                288,
+                                                83
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 1: BNN image classification. AUROC",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
+                                                288,
+                                                70,
+                                                302,
+                                                81
+                                            ],
+                                            "score": 0.29,
+                                            "content": "\\mathbf { ( H ) }",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
+                                                302,
+                                                69,
+                                                505,
+                                                83
+                                            ],
+                                            "score": 1.0,
+                                            "content": "is the AUROC computed using the entropy whereas",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        81,
+                                        505,
+                                        95
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                81,
+                                                346,
+                                                95
+                                            ],
+                                            "score": 1.0,
+                                            "content": "AUROC(MD) is computed using the model disagreement.",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
+                                                347,
+                                                81,
+                                                380,
+                                                93
+                                            ],
+                                            "score": 0.93,
+                                            "content": "\\mathbf { H _ { o } / H _ { t } }",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
+                                                380,
+                                                81,
+                                                505,
+                                                95
+                                            ],
+                                            "score": 1.0,
+                                            "content": "is the ratio of the entropies on",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        92,
+                                        505,
+                                        104
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                93,
+                                                257,
+                                                104
+                                            ],
+                                            "score": 1.0,
+                                            "content": "OOD and test points respectively and",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
+                                                257,
+                                                92,
+                                                312,
+                                                104
+                                            ],
+                                            "score": 0.9,
+                                            "content": "\\mathbf { M D _ { o } / M D _ { t } }",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
+                                                312,
+                                                93,
+                                                505,
+                                                104
+                                            ],
+                                            "score": 1.0,
+                                            "content": "is the ratio for model disagreement. We see that",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 2
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        103,
+                                        505,
+                                        116
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                103,
+                                                505,
+                                                116
+                                            ],
+                                            "score": 1.0,
+                                            "content": "the best accuracy is achieved by our WGD methods, while our fWGD methods yield the best OOD",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        113,
+                                        506,
+                                        128
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                113,
+                                                506,
+                                                128
+                                            ],
+                                            "score": 1.0,
+                                            "content": "detection and funtional diversity. All our proposed methods improve over standard deep ensembles in",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        124,
+                                        395,
+                                        139
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                124,
+                                                395,
+                                                139
+                                            ],
+                                            "score": 1.0,
+                                            "content": "terms of accuracy and diversity, highlighting the effect of our repulsion.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 5
+                                }
+                            ],
+                            "index": 2.5
+                        },
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                107,
+                                143,
+                                505,
+                                312
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        143,
+                                        505,
+                                        312
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                107,
+                                                143,
+                                                505,
+                                                312
+                                            ],
+                                            "score": 0.985,
+                                            "html": "<table><tr><td rowspan=\"11\">Prroiiiie</td><td></td><td>AUROC(H)</td><td>AUROC(MD)</td><td>Accuracy</td><td>H/Ht</td><td>MD/MDt</td><td>ECE</td><td>NLL</td></tr><tr><td>Deep ensemble 4</td><td>0.958±0.001</td><td>0.975±0.001</td><td>91.122±0.013</td><td>6.257±0.005</td><td>6.394±0.001</td><td>0.012±0.001</td><td>0.129±0.001</td></tr><tr><td>SVGD [51</td><td>0.960±0.001</td><td>0.973±0.001</td><td>91.134±0.024</td><td>6.315±0.019</td><td>6.395±0.018</td><td>0.014±0.001</td><td>0.127±0.001</td></tr><tr><td>f-SVGD [76</td><td>0.956±0.001</td><td>0.975±0.001</td><td>89.884±0.015</td><td>5.652±0.009</td><td>6.531±0.005</td><td>0.013±0.001</td><td>0.150±0.001</td></tr><tr><td>hyper-DE [80]</td><td>0.968±0.001</td><td>0.981±0.001</td><td>91.160±0.007</td><td>6.682±0.065</td><td>7.059±0.152</td><td>0.014±0.001</td><td>0.128±0.001</td></tr><tr><td>kde-WGD (ours)</td><td>0.960±0.001</td><td>0.970±0.001</td><td>91.238±0.019</td><td>6.587±0.019</td><td>6.379±0.018</td><td>0.014±0.001</td><td>0.128±0.001</td></tr><tr><td>sge-WGD (ours)</td><td>0.960±0.001</td><td>0.970±0.001</td><td>91.312±0.016</td><td>6.562±0.007</td><td>6.363±0.009</td><td>0.012±0.001</td><td>0.128±0.001</td></tr><tr><td>ssge-WGD (ours)</td><td>0.968±0.001</td><td>0.979±0.001</td><td>91.198±0.024</td><td>6.522±0.009</td><td>6.610±0.012</td><td>0.012±0.001</td><td>0.130±0.001</td></tr><tr><td>kde-fWGD (ours)</td><td>0.971±0.001</td><td>0.980±0.001</td><td>91.260±0.011</td><td>7.079±0.016</td><td>6.887±0.015</td><td>0.015±0.001</td><td>0.125±0.001</td></tr><tr><td>sge-fWGD (ours)</td><td>0.969±0.001</td><td>0.978±0.001</td><td>91.192±0.013</td><td>7.076±0.004</td><td>6.900±0.005</td><td>0.015±0.001</td><td>0.125±0.001</td></tr><tr><td>ssge-fWGD (ours)</td><td>0.971±0.001</td><td>0.980±0.001</td><td>91.240±0.022</td><td>7.129±0.006</td><td>6.951±0.005</td><td>0.016±0.001</td><td>0.124±0.001</td></tr><tr><td rowspan=\"11\">CITIIIO</td><td>Deep ensemble 42</td><td>0.843±0.004</td><td>0.736±0.005</td><td>85,552±0.076</td><td>2.244±0.006</td><td>1.667±0.008</td><td>0.049±0.001</td><td>0.277±0.001</td></tr><tr><td>SVGD [51</td><td>0.825±0.001</td><td>0.710±0.002</td><td>85.142±0.017</td><td>2.106±0.003</td><td>1.567±0.004</td><td>0.052±0.001</td><td>0.287±0.001</td></tr><tr><td>fSVGD 回</td><td>0.783±0.001</td><td>0.712±0.001</td><td>84.510±0.031</td><td>1.968±0.004</td><td>1.624±0.003</td><td>0.049±0.001</td><td>0.292±0.001</td></tr><tr><td>hyper-DE [80]</td><td>0.789±0.001</td><td>0.743±0.001</td><td>84.743±0.011</td><td>1.951±0.010</td><td>1.690±0.015</td><td>0.046±0.001</td><td>0.288±0.001</td></tr><tr><td>kde-WGD (ours)</td><td>0.838±0.001</td><td>0.735±0.004</td><td>85.904±0.030</td><td>2.205±0.003</td><td>1.661±0.008</td><td>0.053±0.001</td><td>0.276±0.001</td></tr><tr><td>sge-WGD (ours)</td><td>0.837±0.003</td><td>0.725±0.004</td><td>85.792±0.035</td><td>2.214±0.010</td><td>1.634±0.004</td><td>0.051±0.001</td><td>0.275±0.001</td></tr><tr><td>ssge-WGD (ours)</td><td>0.832±0.003</td><td>0.731±0.005</td><td>85.638±0.038</td><td>2.182±0.015</td><td>1.655±0.001</td><td>0.049±0.001</td><td>0.276±0.001</td></tr><tr><td>kde-fWGD (ours)</td><td>0.791±0.002</td><td>0.758±0.002</td><td>84.888±0.030</td><td>1.970±0.004</td><td>1.749±0.005</td><td>0.044±0.001</td><td>0.282±0.001</td></tr><tr><td>sge-fWGD (ours)</td><td>0.795±0.001</td><td>0.754±0.002</td><td>84.766±0.060</td><td>1.984±0.003</td><td>1.729±0.002</td><td>0.047±0.001</td><td>0.288±0.001</td></tr><tr><td>ssge-fWGD (ours)</td><td>0.792±0.002</td><td>0.752±0.002</td><td>84.762±0.034</td><td>1.970±0.006</td><td>1.723±0.005</td><td>0.046±0.001</td><td>0.286±0.001</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "c10e7e6db9d6afe7b283337a217b0daf6bdc8ff99b073aef9c58623cfb518d7c.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 7,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        143,
+                                        505,
+                                        199.33333333333334
+                                    ],
+                                    "spans": [],
+                                    "index": 6
+                                },
+                                {
+                                    "bbox": [
+                                        107,
+                                        199.33333333333334,
+                                        505,
+                                        255.66666666666669
+                                    ],
+                                    "spans": [],
+                                    "index": 7
+                                },
+                                {
+                                    "bbox": [
+                                        107,
+                                        255.66666666666669,
+                                        505,
+                                        312.0
+                                    ],
+                                    "spans": [],
+                                    "index": 8
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4.75
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        334,
+                        505,
+                        411
+                    ],
+                    "lines": [],
+                    "index": 12,
+                    "bbox_fs": [
+                        104,
+                        334,
+                        506,
+                        412
+                    ],
+                    "lines_deleted": true
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        425,
+                        505,
+                        578
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                424,
+                                505,
+                                437
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        424,
+                                        505,
+                                        437
+                                    ],
+                                    "score": 1.0,
+                                    "content": "FashionMNIST classification Moving on to real-world data, we used an image classification",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                435,
+                                506,
+                                448
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        435,
+                                        271,
+                                        448
+                                    ],
+                                    "score": 1.0,
+                                    "content": "setting using the FashionMNIST dataset",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        271,
+                                        435,
+                                        289,
+                                        447
+                                    ],
+                                    "score": 0.78,
+                                    "content": "\\dot { \\left[ \\left| 8 3 \\right| \\right] }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        435,
+                                        434,
+                                        448
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for training and the MNIST dataset",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        434,
+                                        435,
+                                        452,
+                                        447
+                                    ],
+                                    "score": 0.78,
+                                    "content": "\\bar { \\mathbb { E } 3 } \\mathbb { I }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        452,
+                                        435,
+                                        506,
+                                        448
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as an out-of-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                447,
+                                505,
+                                460
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        447,
+                                        340,
+                                        459
+                                    ],
+                                    "score": 1.0,
+                                    "content": "distribution (OOD) task. The results are reported in Table",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        340,
+                                        447,
+                                        350,
+                                        460
+                                    ],
+                                    "score": 0.55,
+                                    "content": "^ 1 { } _ { . }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        350,
+                                        447,
+                                        505,
+                                        459
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(top). We can see that all our methods",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                457,
+                                506,
+                                470
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        457,
+                                        506,
+                                        470
+                                    ],
+                                    "score": 1.0,
+                                    "content": "improve upon standard deep ensembles and SVGD, highlighting the effectiveness of our proposed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                469,
+                                506,
+                                481
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        469,
+                                        506,
+                                        481
+                                    ],
+                                    "score": 1.0,
+                                    "content": "repulsion terms when training neural network ensembles. In particular, the sge-WGD offers the best",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                479,
+                                505,
+                                492
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        479,
+                                        505,
+                                        492
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accuracy, whereas the methods in function space all offer a better OOD detection. This is probably",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                490,
+                                505,
+                                503
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        490,
+                                        505,
+                                        503
+                                    ],
+                                    "score": 1.0,
+                                    "content": "due to the fact that these methods achieve a higher entropy ratio and functional diversity measured",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                502,
+                                505,
+                                514
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        502,
+                                        505,
+                                        514
+                                    ],
+                                    "score": 1.0,
+                                    "content": "via the model disagreement when compared to their weight-space counterparts. Interestingly, they",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                511,
+                                505,
+                                525
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        511,
+                                        505,
+                                        525
+                                    ],
+                                    "score": 1.0,
+                                    "content": "also reach the lowest NLL values. We can also notice how the model disagreement (MD) not only",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                523,
+                                506,
+                                536
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        523,
+                                        506,
+                                        536
+                                    ],
+                                    "score": 1.0,
+                                    "content": "serves its purpose as a metric for the functional heterogeneity of the ensemble but also allows for a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                533,
+                                505,
+                                547
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        533,
+                                        505,
+                                        547
+                                    ],
+                                    "score": 1.0,
+                                    "content": "better OOD detection in comparison to the entropy. To the best of our knowledge, this insight has",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                543,
+                                505,
+                                559
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        543,
+                                        403,
+                                        559
+                                    ],
+                                    "score": 1.0,
+                                    "content": "not been described before, although it has been used in continual learning",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        404,
+                                        545,
+                                        421,
+                                        556
+                                    ],
+                                    "score": 0.27,
+                                    "content": "\\pmb { \\mathbb { B } } \\mathbf { \\mathbb { 1 } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        421,
+                                        543,
+                                        505,
+                                        559
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Interestingly, using",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                555,
+                                505,
+                                569
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        555,
+                                        257,
+                                        569
+                                    ],
+                                    "score": 1.0,
+                                    "content": "this metric, the hyper-deep ensemble",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        257,
+                                        555,
+                                        275,
+                                        567
+                                    ],
+                                    "score": 0.44,
+                                    "content": "[ \\textcircled { 8 0 } ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        275,
+                                        555,
+                                        505,
+                                        569
+                                    ],
+                                    "score": 1.0,
+                                    "content": "shows OOD detection performance comparable with our",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                568,
+                                258,
+                                579
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        568,
+                                        258,
+                                        579
+                                    ],
+                                    "score": 1.0,
+                                    "content": "repulsive ensemble in function space.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 22.5,
+                    "bbox_fs": [
+                        104,
+                        424,
+                        506,
+                        579
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        591,
+                        505,
+                        657
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                591,
+                                505,
+                                604
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        591,
+                                        371,
+                                        604
+                                    ],
+                                    "score": 1.0,
+                                    "content": "CIFAR classification Finally, we use a ResNet32 architecture",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        371,
+                                        591,
+                                        389,
+                                        603
+                                    ],
+                                    "score": 0.4,
+                                    "content": "\\mathbb { \\left| \\left[ 2 9 \\right] \\right| }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        389,
+                                        591,
+                                        505,
+                                        604
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on CIFAR-10 [41] with the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                602,
+                                506,
+                                615
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        602,
+                                        165,
+                                        615
+                                    ],
+                                    "score": 1.0,
+                                    "content": "SVHN dataset",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        165,
+                                        602,
+                                        183,
+                                        614
+                                    ],
+                                    "score": 0.46,
+                                    "content": "\\mathbb { \\left[ 6 1 \\right] }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        183,
+                                        602,
+                                        506,
+                                        615
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as OOD data. The results are reported in Table 1 (bottom). We can see that in this",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                614,
+                                505,
+                                625
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        614,
+                                        505,
+                                        625
+                                    ],
+                                    "score": 1.0,
+                                    "content": "case, the weight-space methods achieve better performance in accuracy and OOD detection using the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                624,
+                                505,
+                                637
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        624,
+                                        505,
+                                        637
+                                    ],
+                                    "score": 1.0,
+                                    "content": "entropy than the ones in function space. Nevertheless, all our repulsive ensembles improve functional",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                634,
+                                506,
+                                648
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        634,
+                                        506,
+                                        648
+                                    ],
+                                    "score": 1.0,
+                                    "content": "diversity, accuracy, and OOD detection when compared to standard SVGD, whereas the standard",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                645,
+                                374,
+                                659
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        645,
+                                        374,
+                                        659
+                                    ],
+                                    "score": 1.0,
+                                    "content": "deep ensemble achieves the best OOD detection using the entropy.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        }
+                    ],
+                    "index": 32.5,
+                    "bbox_fs": [
+                        105,
+                        591,
+                        506,
+                        659
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        673,
+                        197,
+                        687
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                673,
+                                198,
+                                689
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        673,
+                                        198,
+                                        689
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5 Related Work",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 36
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        699,
+                        503,
+                        722
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                698,
+                                505,
+                                713
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        698,
+                                        505,
+                                        713
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The theoretical and empirical properties of SVGD have been well studied [40, 48, 13] and it can",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                709,
+                                505,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        709,
+                                        505,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "also be seen as a Wasserstein gradient flow of the KL divergence in the Stein geometry [16, 50]",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                72,
+                                506,
+                                86
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        72,
+                                        506,
+                                        86
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(see Appendix D for more details). Interestingly, a gradient flow interpretation is also possible for",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                83,
+                                505,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        83,
+                                        294,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(stochastic gradient) MCMC-type algorithms",
+                                    "type": "text",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        294,
+                                        83,
+                                        312,
+                                        95
+                                    ],
+                                    "score": 0.35,
+                                    "content": "\\dot { \\left. \\overline { { 4 8 } } \\right. }",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        312,
+                                        83,
+                                        505,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", which can be unified under a general particle",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                94,
+                                505,
+                                107
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        94,
+                                        505,
+                                        107
+                                    ],
+                                    "score": 1.0,
+                                    "content": "inference framework [10]. Moreover, our Wasserstein gradient descent using the SGE approximation",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                105,
+                                505,
+                                118
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        105,
+                                        505,
+                                        118
+                                    ],
+                                    "score": 1.0,
+                                    "content": "can also be derived using an alternative formulation as a gradient flow with smoothed test functions",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                116,
+                                505,
+                                128
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        116,
+                                        372,
+                                        128
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[48]. A projected version of WGD has been studied in Wang et al.",
+                                    "type": "text",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        372,
+                                        116,
+                                        390,
+                                        128
+                                    ],
+                                    "score": 0.71,
+                                    "content": "\\mathbb { \\left. \\overline { { \\boldsymbol { \\mathscr { Q } } \\boldsymbol { \\cdot } \\boldsymbol { \\cdot } } } \\right. }",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        390,
+                                        116,
+                                        505,
+                                        128
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", which could also be readily",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                127,
+                                506,
+                                140
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        127,
+                                        421,
+                                        140
+                                    ],
+                                    "score": 1.0,
+                                    "content": "applied in our framework. Besides particle methods, Bayesian neural networks",
+                                    "type": "text",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        421,
+                                        127,
+                                        454,
+                                        138
+                                    ],
+                                    "score": 0.35,
+                                    "content": "\\pm \\pm \\infty",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        455,
+                                        127,
+                                        506,
+                                        140
+                                    ],
+                                    "score": 1.0,
+                                    "content": "have gained",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                137,
+                                506,
+                                150
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        137,
+                                        506,
+                                        150
+                                    ],
+                                    "score": 1.0,
+                                    "content": "popularity recently [79, 22, 19, 36], using modern MCMC [59, 79, 22, 24, 21] and variational",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                149,
+                                505,
+                                161
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        149,
+                                        505,
+                                        161
+                                    ],
+                                    "score": 1.0,
+                                    "content": "inference techniques [5, 72, 17, 34]. On the other hand, ensemble methods have also been extensively",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                159,
+                                504,
+                                172
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        159,
+                                        504,
+                                        172
+                                    ],
+                                    "score": 1.0,
+                                    "content": "studied [42, 18, 82, 23, 80, 32, 85, 78].Moreover, repulsive interactions between the members have",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                170,
+                                505,
+                                183
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        170,
+                                        505,
+                                        183
+                                    ],
+                                    "score": 1.0,
+                                    "content": "also been studied in Wabartha et al. [74]. Moreover, providing Bayesian interpretations for deep",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                181,
+                                505,
+                                194
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        181,
+                                        475,
+                                        194
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ensembles has been previously attempted through the lenses of stationary SGD distributions",
+                                    "type": "text",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        475,
+                                        181,
+                                        502,
+                                        193
+                                    ],
+                                    "score": 0.47,
+                                    "content": "[ \\sqrt { 5 6 } , \\sqrt ] { 8 } ]",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        503,
+                                        181,
+                                        505,
+                                        194
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                191,
+                                506,
+                                206
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        191,
+                                        220,
+                                        206
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ensembles of linear models",
+                                    "type": "text",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        221,
+                                        192,
+                                        238,
+                                        204
+                                    ],
+                                    "score": 0.39,
+                                    "content": "\\dot { \\bigtriangledown } 5 7 \\big |",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        239,
+                                        191,
+                                        359,
+                                        206
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", additional random functions",
+                                    "type": "text",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        360,
+                                        192,
+                                        407,
+                                        204
+                                    ],
+                                    "score": 0.64,
+                                    "content": "\\boxed { 6 2 } , \\boxed { 1 2 } , \\boxed { 2 7 }",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        408,
+                                        191,
+                                        506,
+                                        206
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", approximate inference",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                203,
+                                505,
+                                216
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        203,
+                                        124,
+                                        215
+                                    ],
+                                    "score": 0.48,
+                                    "content": "\\lVert 8 2 \\rVert",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        125,
+                                        203,
+                                        420,
+                                        216
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", Stein variational inference [15], and marginal likelihood lower bounds",
+                                    "type": "text",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        420,
+                                        203,
+                                        438,
+                                        215
+                                    ],
+                                    "score": 0.8,
+                                    "content": "\\bar { \\| 5 3 \\| }",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        438,
+                                        203,
+                                        505,
+                                        216
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and ensembles",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                214,
+                                505,
+                                227
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        214,
+                                        505,
+                                        227
+                                    ],
+                                    "score": 1.0,
+                                    "content": "have also been shown to provide good approximations to the true BNN posterior in some settings",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                225,
+                                506,
+                                237
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        225,
+                                        124,
+                                        237
+                                    ],
+                                    "score": 0.31,
+                                    "content": "\\left[ \\left[ 3 6 \\right] \\right]",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        124,
+                                        225,
+                                        454,
+                                        237
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Furthermore, variational inference in function space has recently gained attention",
+                                    "type": "text",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        455,
+                                        225,
+                                        473,
+                                        237
+                                    ],
+                                    "score": 0.83,
+                                    "content": "\\mathbb { \\ m }",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        473,
+                                        225,
+                                        506,
+                                        237
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and the",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                236,
+                                378,
+                                248
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        236,
+                                        378,
+                                        248
+                                    ],
+                                    "score": 1.0,
+                                    "content": "limitations of the KL divergence have been studied in Burt et al. [7].",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 37.5,
+                    "bbox_fs": [
+                        105,
+                        698,
+                        505,
+                        723
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        72,
+                        505,
+                        248
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                72,
+                                506,
+                                86
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        72,
+                                        506,
+                                        86
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(see Appendix D for more details). Interestingly, a gradient flow interpretation is also possible for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                83,
+                                505,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        83,
+                                        294,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(stochastic gradient) MCMC-type algorithms",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        294,
+                                        83,
+                                        312,
+                                        95
+                                    ],
+                                    "score": 0.35,
+                                    "content": "\\dot { \\left. \\overline { { 4 8 } } \\right. }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        312,
+                                        83,
+                                        505,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", which can be unified under a general particle",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                94,
+                                505,
+                                107
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        94,
+                                        505,
+                                        107
+                                    ],
+                                    "score": 1.0,
+                                    "content": "inference framework [10]. Moreover, our Wasserstein gradient descent using the SGE approximation",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                105,
+                                505,
+                                118
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        105,
+                                        505,
+                                        118
+                                    ],
+                                    "score": 1.0,
+                                    "content": "can also be derived using an alternative formulation as a gradient flow with smoothed test functions",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                116,
+                                505,
+                                128
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        116,
+                                        372,
+                                        128
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[48]. A projected version of WGD has been studied in Wang et al.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        372,
+                                        116,
+                                        390,
+                                        128
+                                    ],
+                                    "score": 0.71,
+                                    "content": "\\mathbb { \\left. \\overline { { \\boldsymbol { \\mathscr { Q } } \\boldsymbol { \\cdot } \\boldsymbol { \\cdot } } } \\right. }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        390,
+                                        116,
+                                        505,
+                                        128
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", which could also be readily",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                127,
+                                506,
+                                140
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        127,
+                                        421,
+                                        140
+                                    ],
+                                    "score": 1.0,
+                                    "content": "applied in our framework. Besides particle methods, Bayesian neural networks",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        421,
+                                        127,
+                                        454,
+                                        138
+                                    ],
+                                    "score": 0.35,
+                                    "content": "\\pm \\pm \\infty",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        455,
+                                        127,
+                                        506,
+                                        140
+                                    ],
+                                    "score": 1.0,
+                                    "content": "have gained",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                137,
+                                506,
+                                150
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        137,
+                                        506,
+                                        150
+                                    ],
+                                    "score": 1.0,
+                                    "content": "popularity recently [79, 22, 19, 36], using modern MCMC [59, 79, 22, 24, 21] and variational",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                149,
+                                505,
+                                161
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        149,
+                                        505,
+                                        161
+                                    ],
+                                    "score": 1.0,
+                                    "content": "inference techniques [5, 72, 17, 34]. On the other hand, ensemble methods have also been extensively",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                159,
+                                504,
+                                172
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        159,
+                                        504,
+                                        172
+                                    ],
+                                    "score": 1.0,
+                                    "content": "studied [42, 18, 82, 23, 80, 32, 85, 78].Moreover, repulsive interactions between the members have",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                170,
+                                505,
+                                183
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        170,
+                                        505,
+                                        183
+                                    ],
+                                    "score": 1.0,
+                                    "content": "also been studied in Wabartha et al. [74]. Moreover, providing Bayesian interpretations for deep",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                181,
+                                505,
+                                194
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        181,
+                                        475,
+                                        194
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ensembles has been previously attempted through the lenses of stationary SGD distributions",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        475,
+                                        181,
+                                        502,
+                                        193
+                                    ],
+                                    "score": 0.47,
+                                    "content": "[ \\sqrt { 5 6 } , \\sqrt ] { 8 } ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        503,
+                                        181,
+                                        505,
+                                        194
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                191,
+                                506,
+                                206
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        191,
+                                        220,
+                                        206
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ensembles of linear models",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        221,
+                                        192,
+                                        238,
+                                        204
+                                    ],
+                                    "score": 0.39,
+                                    "content": "\\dot { \\bigtriangledown } 5 7 \\big |",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        239,
+                                        191,
+                                        359,
+                                        206
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", additional random functions",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        360,
+                                        192,
+                                        407,
+                                        204
+                                    ],
+                                    "score": 0.64,
+                                    "content": "\\boxed { 6 2 } , \\boxed { 1 2 } , \\boxed { 2 7 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        408,
+                                        191,
+                                        506,
+                                        206
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", approximate inference",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                203,
+                                505,
+                                216
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        203,
+                                        124,
+                                        215
+                                    ],
+                                    "score": 0.48,
+                                    "content": "\\lVert 8 2 \\rVert",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        125,
+                                        203,
+                                        420,
+                                        216
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", Stein variational inference [15], and marginal likelihood lower bounds",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        420,
+                                        203,
+                                        438,
+                                        215
+                                    ],
+                                    "score": 0.8,
+                                    "content": "\\bar { \\| 5 3 \\| }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        438,
+                                        203,
+                                        505,
+                                        216
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and ensembles",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                214,
+                                505,
+                                227
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        214,
+                                        505,
+                                        227
+                                    ],
+                                    "score": 1.0,
+                                    "content": "have also been shown to provide good approximations to the true BNN posterior in some settings",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                225,
+                                506,
+                                237
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        225,
+                                        124,
+                                        237
+                                    ],
+                                    "score": 0.31,
+                                    "content": "\\left[ \\left[ 3 6 \\right] \\right]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        124,
+                                        225,
+                                        454,
+                                        237
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Furthermore, variational inference in function space has recently gained attention",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        455,
+                                        225,
+                                        473,
+                                        237
+                                    ],
+                                    "score": 0.83,
+                                    "content": "\\mathbb { \\ m }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        473,
+                                        225,
+                                        506,
+                                        237
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                236,
+                                378,
+                                248
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        236,
+                                        378,
+                                        248
+                                    ],
+                                    "score": 1.0,
+                                    "content": "limitations of the KL divergence have been studied in Burt et al. [7].",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 7.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        262,
+                        183,
+                        276
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                261,
+                                185,
+                                278
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        261,
+                                        185,
+                                        278
+                                    ],
+                                    "score": 1.0,
+                                    "content": "6 Conclusion",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        286,
+                        505,
+                        374
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                285,
+                                506,
+                                299
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        285,
+                                        506,
+                                        299
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We have presented a simple and principled way to improve upon standard deep ensemble methods.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                298,
+                                504,
+                                308
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        298,
+                                        504,
+                                        308
+                                    ],
+                                    "score": 1.0,
+                                    "content": "To this end, we have shown that the introduction of a kernelized repulsion between members of the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                308,
+                                506,
+                                321
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        308,
+                                        506,
+                                        321
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ensemble not only improves the accuracy of the predictions but—even more importantly—can be seen",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                318,
+                                505,
+                                332
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        318,
+                                        505,
+                                        332
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as Wasserstein gradient descent on the KL divergence, thus transforming the MAP inference of deep",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                330,
+                                505,
+                                342
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        330,
+                                        505,
+                                        342
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ensembles into proper Bayesian inference. Moreover, we have shown that incorporating functional",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                341,
+                                505,
+                                354
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        341,
+                                        505,
+                                        354
+                                    ],
+                                    "score": 1.0,
+                                    "content": "repulsion between ensemble members can improve the quality of the estimated uncertainties on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                352,
+                                505,
+                                364
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        352,
+                                        505,
+                                        364
+                                    ],
+                                    "score": 1.0,
+                                    "content": "simple synthetic examples and OOD detection on real-world data and can approach the true Bayesian",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                363,
+                                200,
+                                376
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        363,
+                                        200,
+                                        376
+                                    ],
+                                    "score": 1.0,
+                                    "content": "posterior more closely.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 20.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        379,
+                        505,
+                        434
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                379,
+                                505,
+                                391
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        379,
+                                        505,
+                                        391
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In future work, it will be interesting to study the impact of the Jacobian in the fWGD update and its",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                390,
+                                505,
+                                402
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        390,
+                                        505,
+                                        402
+                                    ],
+                                    "score": 1.0,
+                                    "content": "implications on the Liouville equation in more detail, also compared to other neural network Jacobian",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                400,
+                                505,
+                                414
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        400,
+                                        270,
+                                        414
+                                    ],
+                                    "score": 1.0,
+                                    "content": "methods, such as neural tangent kernels",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        271,
+                                        400,
+                                        289,
+                                        412
+                                    ],
+                                    "score": 0.59,
+                                    "content": "\\pmb { \\Vert 3 7 } \\Vert",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        400,
+                                        485,
+                                        414
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and generalized Gauss-Newton approximations",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        485,
+                                        400,
+                                        503,
+                                        412
+                                    ],
+                                    "score": 0.26,
+                                    "content": "\\boldsymbol { \\left[ \\left[ 3 5 \\right] \\right] }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        503,
+                                        400,
+                                        505,
+                                        414
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                411,
+                                506,
+                                425
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        411,
+                                        506,
+                                        425
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Moreover, it would be interesting to derive explicit convergence bounds for our proposed method and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                423,
+                                318,
+                                434
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        423,
+                                        318,
+                                        434
+                                    ],
+                                    "score": 1.0,
+                                    "content": "compare them to the existing bounds for SVGD [40].",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 27
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        446,
+                        186,
+                        458
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                444,
+                                187,
+                                460
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        444,
+                                        187,
+                                        460
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Acknowledgments",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 30
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        466,
+                        505,
+                        532
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                466,
+                                505,
+                                479
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        466,
+                                        505,
+                                        479
+                                    ],
+                                    "score": 1.0,
+                                    "content": "VF would like to acknowledge financial support from the Strategic Focus Area “Personalized Health",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                477,
+                                504,
+                                489
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        477,
+                                        504,
+                                        489
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and Related Technologies” of the ETH Domain through the grant #2017-110 and from the Swiss",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                487,
+                                505,
+                                501
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        487,
+                                        505,
+                                        501
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Data Science Center through a PhD fellowship. We thank Florian Wenzel, Alexander Immer, Andrew",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                499,
+                                506,
+                                511
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        499,
+                                        506,
+                                        511
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Gordon Wilson, Pavel Izmailov, Christian Henning, and Johannes von Oswald for helpful discussions.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                509,
+                                506,
+                                523
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        509,
+                                        506,
+                                        523
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We also thank Dr. Sheldon Cooper, Dr. Leonard Hofstadter and Penny Hofstadter for their support",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                521,
+                                170,
+                                533
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        521,
+                                        170,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and inspiration.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 33.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        547,
+                        163,
+                        560
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                546,
+                                165,
+                                562
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        546,
+                                        165,
+                                        562
+                                    ],
+                                    "score": 1.0,
+                                    "content": "References",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 37
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        110,
+                        565,
+                        506,
+                        722
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                110,
+                                565,
+                                506,
+                                578
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        565,
+                                        506,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[1] Charu C Aggarwal, Alexander Hinneburg, and Daniel A Keim. On the surprising behavior of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                576,
+                                506,
+                                589
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        576,
+                                        506,
+                                        589
+                                    ],
+                                    "score": 1.0,
+                                    "content": "distance metrics in high dimensional space. In International conference on database theory,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                588,
+                                257,
+                                600
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        588,
+                                        257,
+                                        600
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pages 420–434. Springer, 2001.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                110,
+                                604,
+                                506,
+                                618
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        604,
+                                        506,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[2] Luigi Ambrosio and Gianluca Crippa. Continuity equations and ode flows with non-smooth",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                615,
+                                506,
+                                628
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        615,
+                                        506,
+                                        628
+                                    ],
+                                    "score": 1.0,
+                                    "content": "velocity. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 144(6):",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                627,
+                                201,
+                                639
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        627,
+                                        201,
+                                        639
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1191–1244, 2014.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                111,
+                                644,
+                                505,
+                                657
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        644,
+                                        505,
+                                        657
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[3] Luigi Ambrosio, Nicola Gigli, and Giuseppe Savaré. Gradient flows: in metric spaces and in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                655,
+                                441,
+                                667
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        655,
+                                        441,
+                                        667
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the space of probability measures. Springer Science & Business Media, 2008.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                111,
+                                672,
+                                505,
+                                685
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        672,
+                                        505,
+                                        685
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[4] Vijay Badrinarayanan, Bamdev Mishra, and Roberto Cipolla. Symmetry-invariant optimization",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                682,
+                                364,
+                                695
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        682,
+                                        364,
+                                        695
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in deep networks. arXiv preprint arXiv:1511.01754, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                110,
+                                699,
+                                505,
+                                714
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        699,
+                                        505,
+                                        714
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[5] Charles Blundell, Julien Cornebise, Koray Kavukcuoglu, and Daan Wierstra. Weight uncertainty",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                711,
+                                371,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        711,
+                                        371,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in neural networks. arXiv preprint arXiv:1505.05424, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        }
+                    ],
+                    "index": 43.5
+                }
+            ],
+            "page_idx": 9,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        741,
+                        311,
+                        750
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                740,
+                                313,
+                                754
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        740,
+                                        313,
+                                        754
+                                    ],
+                                    "score": 1.0,
+                                    "content": "10",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        72,
+                        505,
+                        248
+                    ],
+                    "lines": [],
+                    "index": 7.5,
+                    "bbox_fs": [
+                        105,
+                        72,
+                        506,
+                        248
+                    ],
+                    "lines_deleted": true
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        262,
+                        183,
+                        276
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                261,
+                                185,
+                                278
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        261,
+                                        185,
+                                        278
+                                    ],
+                                    "score": 1.0,
+                                    "content": "6 Conclusion",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        286,
+                        505,
+                        374
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                285,
+                                506,
+                                299
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        285,
+                                        506,
+                                        299
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We have presented a simple and principled way to improve upon standard deep ensemble methods.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                298,
+                                504,
+                                308
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        298,
+                                        504,
+                                        308
+                                    ],
+                                    "score": 1.0,
+                                    "content": "To this end, we have shown that the introduction of a kernelized repulsion between members of the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                308,
+                                506,
+                                321
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        308,
+                                        506,
+                                        321
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ensemble not only improves the accuracy of the predictions but—even more importantly—can be seen",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                318,
+                                505,
+                                332
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        318,
+                                        505,
+                                        332
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as Wasserstein gradient descent on the KL divergence, thus transforming the MAP inference of deep",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                330,
+                                505,
+                                342
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        330,
+                                        505,
+                                        342
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ensembles into proper Bayesian inference. Moreover, we have shown that incorporating functional",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                341,
+                                505,
+                                354
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        341,
+                                        505,
+                                        354
+                                    ],
+                                    "score": 1.0,
+                                    "content": "repulsion between ensemble members can improve the quality of the estimated uncertainties on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                352,
+                                505,
+                                364
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        352,
+                                        505,
+                                        364
+                                    ],
+                                    "score": 1.0,
+                                    "content": "simple synthetic examples and OOD detection on real-world data and can approach the true Bayesian",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                363,
+                                200,
+                                376
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        363,
+                                        200,
+                                        376
+                                    ],
+                                    "score": 1.0,
+                                    "content": "posterior more closely.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 20.5,
+                    "bbox_fs": [
+                        105,
+                        285,
+                        506,
+                        376
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        379,
+                        505,
+                        434
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                379,
+                                505,
+                                391
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        379,
+                                        505,
+                                        391
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In future work, it will be interesting to study the impact of the Jacobian in the fWGD update and its",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                390,
+                                505,
+                                402
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        390,
+                                        505,
+                                        402
+                                    ],
+                                    "score": 1.0,
+                                    "content": "implications on the Liouville equation in more detail, also compared to other neural network Jacobian",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                400,
+                                505,
+                                414
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        400,
+                                        270,
+                                        414
+                                    ],
+                                    "score": 1.0,
+                                    "content": "methods, such as neural tangent kernels",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        271,
+                                        400,
+                                        289,
+                                        412
+                                    ],
+                                    "score": 0.59,
+                                    "content": "\\pmb { \\Vert 3 7 } \\Vert",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        400,
+                                        485,
+                                        414
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and generalized Gauss-Newton approximations",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        485,
+                                        400,
+                                        503,
+                                        412
+                                    ],
+                                    "score": 0.26,
+                                    "content": "\\boldsymbol { \\left[ \\left[ 3 5 \\right] \\right] }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        503,
+                                        400,
+                                        505,
+                                        414
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                411,
+                                506,
+                                425
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        411,
+                                        506,
+                                        425
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Moreover, it would be interesting to derive explicit convergence bounds for our proposed method and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                423,
+                                318,
+                                434
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        423,
+                                        318,
+                                        434
+                                    ],
+                                    "score": 1.0,
+                                    "content": "compare them to the existing bounds for SVGD [40].",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 27,
+                    "bbox_fs": [
+                        105,
+                        379,
+                        506,
+                        434
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        446,
+                        186,
+                        458
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                444,
+                                187,
+                                460
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        444,
+                                        187,
+                                        460
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Acknowledgments",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 30
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        466,
+                        505,
+                        532
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                466,
+                                505,
+                                479
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        466,
+                                        505,
+                                        479
+                                    ],
+                                    "score": 1.0,
+                                    "content": "VF would like to acknowledge financial support from the Strategic Focus Area “Personalized Health",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                477,
+                                504,
+                                489
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        477,
+                                        504,
+                                        489
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and Related Technologies” of the ETH Domain through the grant #2017-110 and from the Swiss",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                487,
+                                505,
+                                501
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        487,
+                                        505,
+                                        501
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Data Science Center through a PhD fellowship. We thank Florian Wenzel, Alexander Immer, Andrew",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                499,
+                                506,
+                                511
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        499,
+                                        506,
+                                        511
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Gordon Wilson, Pavel Izmailov, Christian Henning, and Johannes von Oswald for helpful discussions.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                509,
+                                506,
+                                523
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        509,
+                                        506,
+                                        523
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We also thank Dr. Sheldon Cooper, Dr. Leonard Hofstadter and Penny Hofstadter for their support",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                521,
+                                170,
+                                533
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        521,
+                                        170,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and inspiration.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 33.5,
+                    "bbox_fs": [
+                        105,
+                        466,
+                        506,
+                        533
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        547,
+                        163,
+                        560
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                546,
+                                165,
+                                562
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        546,
+                                        165,
+                                        562
+                                    ],
+                                    "score": 1.0,
+                                    "content": "References",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 37
+                },
+                {
+                    "type": "list",
+                    "bbox": [
+                        110,
+                        565,
+                        506,
+                        722
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                110,
+                                565,
+                                506,
+                                578
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        565,
+                                        506,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[1] Charu C Aggarwal, Alexander Hinneburg, and Daniel A Keim. On the surprising behavior of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                576,
+                                506,
+                                589
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        576,
+                                        506,
+                                        589
+                                    ],
+                                    "score": 1.0,
+                                    "content": "distance metrics in high dimensional space. In International conference on database theory,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                588,
+                                257,
+                                600
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        588,
+                                        257,
+                                        600
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pages 420–434. Springer, 2001.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                110,
+                                604,
+                                506,
+                                618
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        604,
+                                        506,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[2] Luigi Ambrosio and Gianluca Crippa. Continuity equations and ode flows with non-smooth",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                615,
+                                506,
+                                628
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        615,
+                                        506,
+                                        628
+                                    ],
+                                    "score": 1.0,
+                                    "content": "velocity. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 144(6):",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                627,
+                                201,
+                                639
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        627,
+                                        201,
+                                        639
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1191–1244, 2014.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                111,
+                                644,
+                                505,
+                                657
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        644,
+                                        505,
+                                        657
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[3] Luigi Ambrosio, Nicola Gigli, and Giuseppe Savaré. Gradient flows: in metric spaces and in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                655,
+                                441,
+                                667
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        655,
+                                        441,
+                                        667
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the space of probability measures. Springer Science & Business Media, 2008.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                111,
+                                672,
+                                505,
+                                685
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        672,
+                                        505,
+                                        685
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[4] Vijay Badrinarayanan, Bamdev Mishra, and Roberto Cipolla. Symmetry-invariant optimization",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                682,
+                                364,
+                                695
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        682,
+                                        364,
+                                        695
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in deep networks. arXiv preprint arXiv:1511.01754, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                110,
+                                699,
+                                505,
+                                714
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        699,
+                                        505,
+                                        714
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[5] Charles Blundell, Julien Cornebise, Koray Kavukcuoglu, and Daan Wierstra. Weight uncertainty",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                711,
+                                371,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        711,
+                                        371,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in neural networks. arXiv preprint arXiv:1505.05424, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49,
+                            "is_list_end_line": true
+                        }
+                    ],
+                    "index": 43.5,
+                    "bbox_fs": [
+                        110,
+                        565,
+                        506,
+                        723
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        110,
+                        72,
+                        433,
+                        85
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                111,
+                                72,
+                                433,
+                                86
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        72,
+                                        433,
+                                        86
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[6] Leo Breiman. Bagging predictors. Machine learning, 24(2):123–140, 1996.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        109,
+                        91,
+                        504,
+                        115
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                110,
+                                91,
+                                506,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        91,
+                                        506,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[7] David R Burt, Sebastian W Ober, Adrià Garriga-Alonso, and Mark van der Wilk. Understanding",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                102,
+                                449,
+                                115
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        102,
+                                        449,
+                                        115
+                                    ],
+                                    "score": 1.0,
+                                    "content": "variational inference in function-space. arXiv preprint arXiv:2011.09421, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        109,
+                        121,
+                        504,
+                        155
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                110,
+                                121,
+                                506,
+                                135
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        121,
+                                        506,
+                                        135
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[8] Pratik Chaudhari and Stefano Soatto. Stochastic gradient descent performs variational inference,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                132,
+                                505,
+                                146
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        132,
+                                        505,
+                                        146
+                                    ],
+                                    "score": 1.0,
+                                    "content": "converges to limit cycles for deep networks. In 2018 Information Theory and Applications",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                144,
+                                297,
+                                156
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        144,
+                                        297,
+                                        156
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Workshop (ITA), pages 1–10. IEEE, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        109,
+                        162,
+                        505,
+                        186
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                111,
+                                162,
+                                505,
+                                175
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        162,
+                                        505,
+                                        175
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[9] An Mei Chen, Haw-minn Lu, and Robert Hecht-Nielsen. On the geometry of feedforward",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                173,
+                                420,
+                                186
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        173,
+                                        420,
+                                        186
+                                    ],
+                                    "score": 1.0,
+                                    "content": "neural network error surfaces. Neural computation, 5(6):910–927, 1993.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 6.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        192,
+                        505,
+                        226
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                191,
+                                506,
+                                205
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        191,
+                                        506,
+                                        205
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[10] Changyou Chen, Ruiyi Zhang, Wenlin Wang, Bai Li, and Liqun Chen. A unified particle-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                203,
+                                506,
+                                216
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        203,
+                                        506,
+                                        216
+                                    ],
+                                    "score": 1.0,
+                                    "content": "optimization framework for scalable bayesian sampling. arXiv preprint arXiv:1805.11659,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                213,
+                                154,
+                                227
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        213,
+                                        154,
+                                        227
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        233,
+                        505,
+                        256
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                233,
+                                505,
+                                246
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        233,
+                                        505,
+                                        246
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[11] Jiefeng Chen, Xi Wu, Yingyu Liang, Somesh Jha, et al. Robust out-of-distribution detection in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                244,
+                                360,
+                                257
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        244,
+                                        360,
+                                        257
+                                    ],
+                                    "score": 1.0,
+                                    "content": "neural networks. arXiv preprint arXiv:2003.09711, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "index": 11.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        263,
+                        504,
+                        297
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                263,
+                                506,
+                                276
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        263,
+                                        506,
+                                        276
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[12] Kamil Ciosek, Vincent Fortuin, Ryota Tomioka, Katja Hofmann, and Richard Turner. Conserva-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                273,
+                                505,
+                                288
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        273,
+                                        505,
+                                        288
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tive uncertainty estimation by fitting prior networks. In International Conference on Learning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                285,
+                                222,
+                                298
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        285,
+                                        222,
+                                        298
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Representations, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        303,
+                        503,
+                        327
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                304,
+                                505,
+                                317
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        304,
+                                        505,
+                                        317
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[13] Francesco D’Angelo and Vincent Fortuin. Annealed stein variational gradient descent. arXiv",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                316,
+                                266,
+                                327
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        316,
+                                        266,
+                                        327
+                                    ],
+                                    "score": 1.0,
+                                    "content": "preprint arXiv:2101.09815, 2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 16.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        334,
+                        503,
+                        357
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                334,
+                                505,
+                                347
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        334,
+                                        505,
+                                        347
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[14] Francesco D’Angelo and Christian Henning. Uncertainty-based out-of-distribution detection",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                345,
+                                448,
+                                358
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        345,
+                                        448,
+                                        358
+                                    ],
+                                    "score": 1.0,
+                                    "content": "requires suitable function space priors. arXiv preprint arXiv:2110.06020, 2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 18.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        363,
+                        504,
+                        387
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                363,
+                                506,
+                                377
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        363,
+                                        506,
+                                        377
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[15] Francesco D’Angelo, Vincent Fortuin, and Florian Wenzel. On stein variational neural network",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                376,
+                                338,
+                                387
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        376,
+                                        338,
+                                        387
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ensembles. arXiv preprint arXiv:2106.10760, 2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 20.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        393,
+                        504,
+                        417
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                394,
+                                505,
+                                407
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        394,
+                                        505,
+                                        407
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[16] A Duncan, Nikolas Nuesken, and Lukasz Szpruch. On the geometry of stein variational gradient",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                405,
+                                326,
+                                417
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        405,
+                                        326,
+                                        417
+                                    ],
+                                    "score": 1.0,
+                                    "content": "descent. arXiv preprint arXiv:1912.00894, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 22.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        424,
+                        504,
+                        458
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                423,
+                                505,
+                                438
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        423,
+                                        505,
+                                        438
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[17] Michael W Dusenberry, Ghassen Jerfel, Yeming Wen, Yi-an Ma, Jasper Snoek, Katherine",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                435,
+                                505,
+                                448
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        435,
+                                        505,
+                                        448
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Heller, Balaji Lakshminarayanan, and Dustin Tran. Efficient and scalable bayesian neural nets",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                446,
+                                371,
+                                458
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        446,
+                                        371,
+                                        458
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with rank-1 factors. arXiv preprint arXiv:2005.07186, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        465,
+                        504,
+                        488
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                464,
+                                505,
+                                479
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        464,
+                                        505,
+                                        479
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[18] Stanislav Fort, Huiyi Hu, and Balaji Lakshminarayanan. Deep ensembles: A loss landscape",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                477,
+                                341,
+                                488
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        477,
+                                        341,
+                                        488
+                                    ],
+                                    "score": 1.0,
+                                    "content": "perspective. arXiv preprint arXiv:1912.02757, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 27.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        495,
+                        504,
+                        518
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                494,
+                                506,
+                                508
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        494,
+                                        506,
+                                        508
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[19] Vincent Fortuin. Priors in bayesian deep learning: A review. arXiv preprint arXiv:2105.06868,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                505,
+                                155,
+                                519
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        505,
+                                        155,
+                                        519
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 29.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        524,
+                        506,
+                        569
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                524,
+                                507,
+                                538
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        524,
+                                        507,
+                                        538
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[20] Vincent Fortuin, Mark Collier, Florian Wenzel, James Allingham, Jeremiah Liu, Dustin Tran,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                534,
+                                506,
+                                550
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        534,
+                                        506,
+                                        550
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Balaji Lakshminarayanan, Jesse Berent, Rodolphe Jenatton, and Effrosyni Kokiopoulou. Deep",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                546,
+                                506,
+                                560
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        546,
+                                        506,
+                                        560
+                                    ],
+                                    "score": 1.0,
+                                    "content": "classifiers with label noise modeling and distance awareness. arXiv preprint arXiv:2110.02609,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                557,
+                                155,
+                                570
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        557,
+                                        155,
+                                        570
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        }
+                    ],
+                    "index": 32.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        576,
+                        504,
+                        611
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                576,
+                                506,
+                                590
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        576,
+                                        506,
+                                        590
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[21] Vincent Fortuin, Adrià Garriga-Alonso, Mark van der Wilk, and Laurence Aitchison. Bnnpriors:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                587,
+                                505,
+                                601
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        587,
+                                        505,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A library for bayesian neural network inference with different prior distributions. Software",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                599,
+                                246,
+                                612
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        599,
+                                        246,
+                                        612
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Impacts, page 100079, 2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 36
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        617,
+                        504,
+                        651
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                617,
+                                506,
+                                630
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        617,
+                                        506,
+                                        630
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[22] Vincent Fortuin, Adrià Garriga-Alonso, Florian Wenzel, Gunnar Rätsch, Richard Turner, Mark",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                628,
+                                506,
+                                642
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        628,
+                                        506,
+                                        642
+                                    ],
+                                    "score": 1.0,
+                                    "content": "van der Wilk, and Laurence Aitchison. Bayesian neural network priors revisited. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                640,
+                                231,
+                                651
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        640,
+                                        231,
+                                        651
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:2102.06571, 2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        }
+                    ],
+                    "index": 39
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        658,
+                        503,
+                        693
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                658,
+                                505,
+                                671
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        658,
+                                        505,
+                                        671
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[23] Timur Garipov, Pavel Izmailov, Dmitrii Podoprikhin, Dmitry Vetrov, and Andrew Gordon",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                668,
+                                505,
+                                683
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        668,
+                                        505,
+                                        683
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Wilson. Loss surfaces, mode connectivity, and fast ensembling of dnns. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                681,
+                                231,
+                                693
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        681,
+                                        231,
+                                        693
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1802.10026, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        }
+                    ],
+                    "index": 42
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        699,
+                        502,
+                        722
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                699,
+                                504,
+                                713
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        699,
+                                        504,
+                                        713
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[24] Adrià Garriga-Alonso and Vincent Fortuin. Exact langevin dynamics with stochastic gradients.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                711,
+                                291,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        711,
+                                        291,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv preprint arXiv:2102.01691, 2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        }
+                    ],
+                    "index": 44.5
+                }
+            ],
+            "page_idx": 10,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        741,
+                        310,
+                        750
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                740,
+                                312,
+                                755
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        740,
+                                        312,
+                                        755
+                                    ],
+                                    "score": 1.0,
+                                    "content": "",
+                                    "type": "text",
+                                    "height": 15,
+                                    "width": 13
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        110,
+                        72,
+                        433,
+                        85
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                111,
+                                72,
+                                433,
+                                86
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        72,
+                                        433,
+                                        86
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[6] Leo Breiman. Bagging predictors. Machine learning, 24(2):123–140, 1996.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        }
+                    ],
+                    "index": 0,
+                    "bbox_fs": [
+                        111,
+                        72,
+                        433,
+                        86
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        109,
+                        91,
+                        504,
+                        115
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                110,
+                                91,
+                                506,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        91,
+                                        506,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[7] David R Burt, Sebastian W Ober, Adrià Garriga-Alonso, and Mark van der Wilk. Understanding",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                102,
+                                449,
+                                115
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        102,
+                                        449,
+                                        115
+                                    ],
+                                    "score": 1.0,
+                                    "content": "variational inference in function-space. arXiv preprint arXiv:2011.09421, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1.5,
+                    "bbox_fs": [
+                        110,
+                        91,
+                        506,
+                        115
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        109,
+                        121,
+                        504,
+                        155
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                110,
+                                121,
+                                506,
+                                135
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        121,
+                                        506,
+                                        135
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[8] Pratik Chaudhari and Stefano Soatto. Stochastic gradient descent performs variational inference,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                132,
+                                505,
+                                146
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        132,
+                                        505,
+                                        146
+                                    ],
+                                    "score": 1.0,
+                                    "content": "converges to limit cycles for deep networks. In 2018 Information Theory and Applications",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                144,
+                                297,
+                                156
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        144,
+                                        297,
+                                        156
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Workshop (ITA), pages 1–10. IEEE, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        }
+                    ],
+                    "index": 4,
+                    "bbox_fs": [
+                        110,
+                        121,
+                        506,
+                        156
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        109,
+                        162,
+                        505,
+                        186
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                111,
+                                162,
+                                505,
+                                175
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        162,
+                                        505,
+                                        175
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[9] An Mei Chen, Haw-minn Lu, and Robert Hecht-Nielsen. On the geometry of feedforward",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                173,
+                                420,
+                                186
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        173,
+                                        420,
+                                        186
+                                    ],
+                                    "score": 1.0,
+                                    "content": "neural network error surfaces. Neural computation, 5(6):910–927, 1993.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 6.5,
+                    "bbox_fs": [
+                        111,
+                        162,
+                        505,
+                        186
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        192,
+                        505,
+                        226
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                191,
+                                506,
+                                205
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        191,
+                                        506,
+                                        205
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[10] Changyou Chen, Ruiyi Zhang, Wenlin Wang, Bai Li, and Liqun Chen. A unified particle-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                203,
+                                506,
+                                216
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        203,
+                                        506,
+                                        216
+                                    ],
+                                    "score": 1.0,
+                                    "content": "optimization framework for scalable bayesian sampling. arXiv preprint arXiv:1805.11659,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                213,
+                                154,
+                                227
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        213,
+                                        154,
+                                        227
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 9,
+                    "bbox_fs": [
+                        105,
+                        191,
+                        506,
+                        227
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        233,
+                        505,
+                        256
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                233,
+                                505,
+                                246
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        233,
+                                        505,
+                                        246
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[11] Jiefeng Chen, Xi Wu, Yingyu Liang, Somesh Jha, et al. Robust out-of-distribution detection in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                244,
+                                360,
+                                257
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        244,
+                                        360,
+                                        257
+                                    ],
+                                    "score": 1.0,
+                                    "content": "neural networks. arXiv preprint arXiv:2003.09711, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "index": 11.5,
+                    "bbox_fs": [
+                        105,
+                        233,
+                        505,
+                        257
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        263,
+                        504,
+                        297
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                263,
+                                506,
+                                276
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        263,
+                                        506,
+                                        276
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[12] Kamil Ciosek, Vincent Fortuin, Ryota Tomioka, Katja Hofmann, and Richard Turner. Conserva-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                273,
+                                505,
+                                288
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        273,
+                                        505,
+                                        288
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tive uncertainty estimation by fitting prior networks. In International Conference on Learning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                285,
+                                222,
+                                298
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        285,
+                                        222,
+                                        298
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Representations, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 14,
+                    "bbox_fs": [
+                        105,
+                        263,
+                        506,
+                        298
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        303,
+                        503,
+                        327
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                304,
+                                505,
+                                317
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        304,
+                                        505,
+                                        317
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[13] Francesco D’Angelo and Vincent Fortuin. Annealed stein variational gradient descent. arXiv",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                316,
+                                266,
+                                327
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        316,
+                                        266,
+                                        327
+                                    ],
+                                    "score": 1.0,
+                                    "content": "preprint arXiv:2101.09815, 2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 16.5,
+                    "bbox_fs": [
+                        106,
+                        304,
+                        505,
+                        327
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        334,
+                        503,
+                        357
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                334,
+                                505,
+                                347
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        334,
+                                        505,
+                                        347
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[14] Francesco D’Angelo and Christian Henning. Uncertainty-based out-of-distribution detection",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                345,
+                                448,
+                                358
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        345,
+                                        448,
+                                        358
+                                    ],
+                                    "score": 1.0,
+                                    "content": "requires suitable function space priors. arXiv preprint arXiv:2110.06020, 2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 18.5,
+                    "bbox_fs": [
+                        106,
+                        334,
+                        505,
+                        358
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        363,
+                        504,
+                        387
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                363,
+                                506,
+                                377
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        363,
+                                        506,
+                                        377
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[15] Francesco D’Angelo, Vincent Fortuin, and Florian Wenzel. On stein variational neural network",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                376,
+                                338,
+                                387
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        376,
+                                        338,
+                                        387
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ensembles. arXiv preprint arXiv:2106.10760, 2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 20.5,
+                    "bbox_fs": [
+                        105,
+                        363,
+                        506,
+                        387
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        393,
+                        504,
+                        417
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                394,
+                                505,
+                                407
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        394,
+                                        505,
+                                        407
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[16] A Duncan, Nikolas Nuesken, and Lukasz Szpruch. On the geometry of stein variational gradient",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                405,
+                                326,
+                                417
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        405,
+                                        326,
+                                        417
+                                    ],
+                                    "score": 1.0,
+                                    "content": "descent. arXiv preprint arXiv:1912.00894, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 22.5,
+                    "bbox_fs": [
+                        106,
+                        394,
+                        505,
+                        417
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        424,
+                        504,
+                        458
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                423,
+                                505,
+                                438
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        423,
+                                        505,
+                                        438
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[17] Michael W Dusenberry, Ghassen Jerfel, Yeming Wen, Yi-an Ma, Jasper Snoek, Katherine",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                435,
+                                505,
+                                448
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        435,
+                                        505,
+                                        448
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Heller, Balaji Lakshminarayanan, and Dustin Tran. Efficient and scalable bayesian neural nets",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                446,
+                                371,
+                                458
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        446,
+                                        371,
+                                        458
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with rank-1 factors. arXiv preprint arXiv:2005.07186, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 25,
+                    "bbox_fs": [
+                        105,
+                        423,
+                        505,
+                        458
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        465,
+                        504,
+                        488
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                464,
+                                505,
+                                479
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        464,
+                                        505,
+                                        479
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[18] Stanislav Fort, Huiyi Hu, and Balaji Lakshminarayanan. Deep ensembles: A loss landscape",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                477,
+                                341,
+                                488
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        477,
+                                        341,
+                                        488
+                                    ],
+                                    "score": 1.0,
+                                    "content": "perspective. arXiv preprint arXiv:1912.02757, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 27.5,
+                    "bbox_fs": [
+                        105,
+                        464,
+                        505,
+                        488
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        495,
+                        504,
+                        518
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                494,
+                                506,
+                                508
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        494,
+                                        506,
+                                        508
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[19] Vincent Fortuin. Priors in bayesian deep learning: A review. arXiv preprint arXiv:2105.06868,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                505,
+                                155,
+                                519
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        505,
+                                        155,
+                                        519
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 29.5,
+                    "bbox_fs": [
+                        106,
+                        494,
+                        506,
+                        519
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        524,
+                        506,
+                        569
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                524,
+                                507,
+                                538
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        524,
+                                        507,
+                                        538
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[20] Vincent Fortuin, Mark Collier, Florian Wenzel, James Allingham, Jeremiah Liu, Dustin Tran,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                534,
+                                506,
+                                550
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        534,
+                                        506,
+                                        550
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Balaji Lakshminarayanan, Jesse Berent, Rodolphe Jenatton, and Effrosyni Kokiopoulou. Deep",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                546,
+                                506,
+                                560
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        546,
+                                        506,
+                                        560
+                                    ],
+                                    "score": 1.0,
+                                    "content": "classifiers with label noise modeling and distance awareness. arXiv preprint arXiv:2110.02609,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                557,
+                                155,
+                                570
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        557,
+                                        155,
+                                        570
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        }
+                    ],
+                    "index": 32.5,
+                    "bbox_fs": [
+                        105,
+                        524,
+                        507,
+                        570
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        576,
+                        504,
+                        611
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                576,
+                                506,
+                                590
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        576,
+                                        506,
+                                        590
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[21] Vincent Fortuin, Adrià Garriga-Alonso, Mark van der Wilk, and Laurence Aitchison. Bnnpriors:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                587,
+                                505,
+                                601
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        587,
+                                        505,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A library for bayesian neural network inference with different prior distributions. Software",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                599,
+                                246,
+                                612
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        599,
+                                        246,
+                                        612
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Impacts, page 100079, 2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 36,
+                    "bbox_fs": [
+                        106,
+                        576,
+                        506,
+                        612
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        617,
+                        504,
+                        651
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                617,
+                                506,
+                                630
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        617,
+                                        506,
+                                        630
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[22] Vincent Fortuin, Adrià Garriga-Alonso, Florian Wenzel, Gunnar Rätsch, Richard Turner, Mark",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                628,
+                                506,
+                                642
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        628,
+                                        506,
+                                        642
+                                    ],
+                                    "score": 1.0,
+                                    "content": "van der Wilk, and Laurence Aitchison. Bayesian neural network priors revisited. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                640,
+                                231,
+                                651
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        640,
+                                        231,
+                                        651
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:2102.06571, 2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        }
+                    ],
+                    "index": 39,
+                    "bbox_fs": [
+                        105,
+                        617,
+                        506,
+                        651
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        658,
+                        503,
+                        693
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                658,
+                                505,
+                                671
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        658,
+                                        505,
+                                        671
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[23] Timur Garipov, Pavel Izmailov, Dmitrii Podoprikhin, Dmitry Vetrov, and Andrew Gordon",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                668,
+                                505,
+                                683
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        668,
+                                        505,
+                                        683
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Wilson. Loss surfaces, mode connectivity, and fast ensembling of dnns. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                681,
+                                231,
+                                693
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        681,
+                                        231,
+                                        693
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1802.10026, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        }
+                    ],
+                    "index": 42,
+                    "bbox_fs": [
+                        105,
+                        658,
+                        505,
+                        693
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        699,
+                        502,
+                        722
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                699,
+                                504,
+                                713
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        699,
+                                        504,
+                                        713
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[24] Adrià Garriga-Alonso and Vincent Fortuin. Exact langevin dynamics with stochastic gradients.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                711,
+                                291,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        711,
+                                        291,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv preprint arXiv:2102.01691, 2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        }
+                    ],
+                    "index": 44.5,
+                    "bbox_fs": [
+                        105,
+                        699,
+                        504,
+                        723
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        103,
+                        34,
+                        507,
+                        725
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                72,
+                                506,
+                                86
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        72,
+                                        506,
+                                        86
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[25] Mario Geiger, Arthur Jacot, Stefano Spigler, Franck Gabriel, Levent Sagun, Stéphane d’Ascoli,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                83,
+                                506,
+                                97
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        83,
+                                        506,
+                                        97
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Giulio Biroli, Clément Hongler, and Matthieu Wyart. Scaling description of generalization",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                95,
+                                506,
+                                109
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        95,
+                                        506,
+                                        109
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with number of parameters in deep learning. Journal of Statistical Mechanics: Theory and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                105,
+                                273,
+                                119
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        105,
+                                        273,
+                                        119
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Experiment, 2020(2):023401, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                125,
+                                506,
+                                137
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        125,
+                                        506,
+                                        137
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[26] L. K. Hansen and P. Salamon. Neural network ensembles. IEEE Trans. Pattern Anal. Mach.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                135,
+                                506,
+                                147
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        135,
+                                        506,
+                                        147
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Intell., 12(10):993–1001, October 1990. ISSN 0162-8828. doi: 10.1109/34.58871. URL",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                146,
+                                300,
+                                160
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        146,
+                                        300,
+                                        160
+                                    ],
+                                    "score": 1.0,
+                                    "content": "https://doi.org/10.1109/34.58871.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                165,
+                                506,
+                                179
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        165,
+                                        506,
+                                        179
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[27] Bobby He, Balaji Lakshminarayanan, and Yee Whye Teh. Bayesian deep ensembles via the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                176,
+                                381,
+                                189
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        176,
+                                        381,
+                                        189
+                                    ],
+                                    "score": 1.0,
+                                    "content": "neural tangent kernel. arXiv preprint arXiv:2007.05864, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                194,
+                                507,
+                                209
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        194,
+                                        507,
+                                        209
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[28] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Delving deep into rectifiers:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                207,
+                                505,
+                                219
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        207,
+                                        505,
+                                        219
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Surpassing human-level performance on imagenet classification. In Proceedings of the IEEE",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                216,
+                                410,
+                                230
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        216,
+                                        410,
+                                        230
+                                    ],
+                                    "score": 1.0,
+                                    "content": "international conference on computer vision, pages 1026–1034, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                235,
+                                506,
+                                250
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        235,
+                                        506,
+                                        250
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[29] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                247,
+                                506,
+                                259
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        247,
+                                        506,
+                                        259
+                                    ],
+                                    "score": 1.0,
+                                    "content": "recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                257,
+                                218,
+                                270
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        257,
+                                        218,
+                                        270
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pages 770–778, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                275,
+                                506,
+                                290
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        275,
+                                        506,
+                                        290
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[30] Robert Hecht-Nielsen. On the algebraic structure of feedforward network weight spaces. In",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                288,
+                                376,
+                                302
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        288,
+                                        376,
+                                        302
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Advanced Neural Computers, pages 129–135. Elsevier, 1990.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                306,
+                                506,
+                                318
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        306,
+                                        506,
+                                        318
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[31] Christian Henning, Maria R Cervera, Francesco D’Angelo, Johannes von Oswald, Regina",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                318,
+                                506,
+                                330
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        318,
+                                        506,
+                                        330
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Traber, Benjamin Ehret, Seijin Kobayashi, João Sacramento, and Benjamin F Grewe. Posterior",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                327,
+                                433,
+                                342
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        327,
+                                        433,
+                                        342
+                                    ],
+                                    "score": 1.0,
+                                    "content": "meta-replay for continual learning. arXiv preprint arXiv:2103.01133, 2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                347,
+                                507,
+                                361
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        347,
+                                        507,
+                                        361
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[32] Gao Huang, Yixuan Li, Geoff Pleiss, Zhuang Liu, John E Hopcroft, and Kilian Q Weinberger.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                358,
+                                472,
+                                372
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        358,
+                                        472,
+                                        372
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Snapshot ensembles: Train 1, get m for free. arXiv preprint arXiv:1704.00109, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                376,
+                                507,
+                                390
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        376,
+                                        507,
+                                        390
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[33] Gao Huang, Yixuan Li, Geoff Pleiss, Zhuang Liu, John E. Hopcroft, and Kilian Q. Weinberger.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                388,
+                                507,
+                                403
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        388,
+                                        507,
+                                        403
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Snapshot ensembles: Train 1, get M for free. CoRR, abs/1704.00109, 2017. URL http:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                398,
+                                268,
+                                412
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        398,
+                                        268,
+                                        412
+                                    ],
+                                    "score": 1.0,
+                                    "content": "//arxiv.org/abs/1704.00109.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                417,
+                                506,
+                                432
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        417,
+                                        506,
+                                        432
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[34] Alexander Immer, Matthias Bauer, Vincent Fortuin, Gunnar Rätsch, and Mohammad Emtiyaz",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                428,
+                                504,
+                                441
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        428,
+                                        504,
+                                        441
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Khan. Scalable marginal likelihood estimation for model selection in deep learning. arXiv",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                439,
+                                267,
+                                452
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        439,
+                                        267,
+                                        452
+                                    ],
+                                    "score": 1.0,
+                                    "content": "preprint arXiv:2104.04975, 2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                458,
+                                506,
+                                472
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        458,
+                                        506,
+                                        472
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[35] Alexander Immer, Maciej Korzepa, and Matthias Bauer. Improving predictions of bayesian",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                469,
+                                506,
+                                483
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        469,
+                                        506,
+                                        483
+                                    ],
+                                    "score": 1.0,
+                                    "content": "neural nets via local linearization. In International Conference on Artificial Intelligence and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                480,
+                                292,
+                                494
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        480,
+                                        292,
+                                        494
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Statistics, pages 703–711. PMLR, 2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                500,
+                                506,
+                                511
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        500,
+                                        506,
+                                        511
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[36] Pavel Izmailov, Sharad Vikram, Matthew D Hoffman, and Andrew Gordon Wilson. What are",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                509,
+                                480,
+                                523
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        509,
+                                        480,
+                                        523
+                                    ],
+                                    "score": 1.0,
+                                    "content": "bayesian neural network posteriors really like? arXiv preprint arXiv:2104.14421, 2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                528,
+                                506,
+                                543
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        528,
+                                        506,
+                                        543
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[37] Arthur Jacot, Franck Gabriel, and Clément Hongler. Neural tangent kernel: convergence and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                540,
+                                506,
+                                553
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        540,
+                                        506,
+                                        553
+                                    ],
+                                    "score": 1.0,
+                                    "content": "generalization in neural networks. In Proceedings of the 32nd International Conference on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                550,
+                                390,
+                                565
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        550,
+                                        390,
+                                        565
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Neural Information Processing Systems, pages 8580–8589, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                568,
+                                507,
+                                583
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        568,
+                                        507,
+                                        583
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[38] Richard Jordan, David Kinderlehrer, and Felix Otto. The variational formulation of the fokker–",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                580,
+                                435,
+                                594
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        580,
+                                        435,
+                                        594
+                                    ],
+                                    "score": 1.0,
+                                    "content": "planck equation. SIAM journal on mathematical analysis, 29(1):1–17, 1998.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                599,
+                                506,
+                                613
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        599,
+                                        506,
+                                        613
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[39] Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                611,
+                                226,
+                                623
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        611,
+                                        226,
+                                        623
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1412.6980, 2014.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                629,
+                                506,
+                                643
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        629,
+                                        506,
+                                        643
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[40] Anna Korba, Adil Salim, Michael Arbel, Giulia Luise, and Arthur Gretton. A non-asymptotic",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                639,
+                                506,
+                                655
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        639,
+                                        506,
+                                        655
+                                    ],
+                                    "score": 1.0,
+                                    "content": "analysis for stein variational gradient descent. Advances in Neural Information Processing",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                651,
+                                205,
+                                664
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        651,
+                                        205,
+                                        664
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Systems, 33, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                669,
+                                465,
+                                683
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        669,
+                                        465,
+                                        683
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[41] Alex Krizhevsky et al. Learning multiple layers of features from tiny images. 2009.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                688,
+                                506,
+                                702
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        688,
+                                        506,
+                                        702
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[42] Balaji Lakshminarayanan, Alexander Pritzel, and Charles Blundell. Simple and scalable",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                699,
+                                506,
+                                714
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        699,
+                                        506,
+                                        714
+                                    ],
+                                    "score": 1.0,
+                                    "content": "predictive uncertainty estimation using deep ensembles. In Advances in neural information",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                125,
+                                711,
+                                309,
+                                724
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        125,
+                                        711,
+                                        309,
+                                        724
+                                    ],
+                                    "score": 1.0,
+                                    "content": "processing systems, pages 6402–6413, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        }
+                    ],
+                    "index": 23
+                }
+            ],
+            "page_idx": 11,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        741,
+                        311,
+                        750
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                740,
+                                313,
+                                754
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        740,
+                                        313,
+                                        754
+                                    ],
+                                    "score": 1.0,
+                                    "content": "12",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "list",
+                    "bbox": [
+                        103,
+                        34,
+                        507,
+                        725
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                72,
+                                506,
+                                86
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        72,
+                                        506,
+                                        86
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[25] Mario Geiger, Arthur Jacot, Stefano Spigler, Franck Gabriel, Levent Sagun, Stéphane d’Ascoli,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                83,
+                                506,
+                                97
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        83,
+                                        506,
+                                        97
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Giulio Biroli, Clément Hongler, and Matthieu Wyart. Scaling description of generalization",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                95,
+                                506,
+                                109
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        95,
+                                        506,
+                                        109
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with number of parameters in deep learning. Journal of Statistical Mechanics: Theory and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                105,
+                                273,
+                                119
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        105,
+                                        273,
+                                        119
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Experiment, 2020(2):023401, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                125,
+                                506,
+                                137
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        125,
+                                        506,
+                                        137
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[26] L. K. Hansen and P. Salamon. Neural network ensembles. IEEE Trans. Pattern Anal. Mach.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                135,
+                                506,
+                                147
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        135,
+                                        506,
+                                        147
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Intell., 12(10):993–1001, October 1990. ISSN 0162-8828. doi: 10.1109/34.58871. URL",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                146,
+                                300,
+                                160
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        146,
+                                        300,
+                                        160
+                                    ],
+                                    "score": 1.0,
+                                    "content": "https://doi.org/10.1109/34.58871.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                165,
+                                506,
+                                179
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        165,
+                                        506,
+                                        179
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[27] Bobby He, Balaji Lakshminarayanan, and Yee Whye Teh. Bayesian deep ensembles via the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                176,
+                                381,
+                                189
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        176,
+                                        381,
+                                        189
+                                    ],
+                                    "score": 1.0,
+                                    "content": "neural tangent kernel. arXiv preprint arXiv:2007.05864, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                194,
+                                507,
+                                209
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        194,
+                                        507,
+                                        209
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[28] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Delving deep into rectifiers:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                207,
+                                505,
+                                219
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        207,
+                                        505,
+                                        219
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Surpassing human-level performance on imagenet classification. In Proceedings of the IEEE",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                216,
+                                410,
+                                230
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        216,
+                                        410,
+                                        230
+                                    ],
+                                    "score": 1.0,
+                                    "content": "international conference on computer vision, pages 1026–1034, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                235,
+                                506,
+                                250
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        235,
+                                        506,
+                                        250
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[29] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                247,
+                                506,
+                                259
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        247,
+                                        506,
+                                        259
+                                    ],
+                                    "score": 1.0,
+                                    "content": "recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                257,
+                                218,
+                                270
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        257,
+                                        218,
+                                        270
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pages 770–778, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                275,
+                                506,
+                                290
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        275,
+                                        506,
+                                        290
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[30] Robert Hecht-Nielsen. On the algebraic structure of feedforward network weight spaces. In",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                288,
+                                376,
+                                302
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        288,
+                                        376,
+                                        302
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Advanced Neural Computers, pages 129–135. Elsevier, 1990.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                306,
+                                506,
+                                318
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        306,
+                                        506,
+                                        318
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[31] Christian Henning, Maria R Cervera, Francesco D’Angelo, Johannes von Oswald, Regina",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                318,
+                                506,
+                                330
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        318,
+                                        506,
+                                        330
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Traber, Benjamin Ehret, Seijin Kobayashi, João Sacramento, and Benjamin F Grewe. Posterior",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                327,
+                                433,
+                                342
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        327,
+                                        433,
+                                        342
+                                    ],
+                                    "score": 1.0,
+                                    "content": "meta-replay for continual learning. arXiv preprint arXiv:2103.01133, 2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                347,
+                                507,
+                                361
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        347,
+                                        507,
+                                        361
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[32] Gao Huang, Yixuan Li, Geoff Pleiss, Zhuang Liu, John E Hopcroft, and Kilian Q Weinberger.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                358,
+                                472,
+                                372
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        358,
+                                        472,
+                                        372
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Snapshot ensembles: Train 1, get m for free. arXiv preprint arXiv:1704.00109, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                376,
+                                507,
+                                390
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        376,
+                                        507,
+                                        390
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[33] Gao Huang, Yixuan Li, Geoff Pleiss, Zhuang Liu, John E. Hopcroft, and Kilian Q. Weinberger.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                388,
+                                507,
+                                403
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        388,
+                                        507,
+                                        403
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Snapshot ensembles: Train 1, get M for free. CoRR, abs/1704.00109, 2017. URL http:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                398,
+                                268,
+                                412
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        398,
+                                        268,
+                                        412
+                                    ],
+                                    "score": 1.0,
+                                    "content": "//arxiv.org/abs/1704.00109.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                417,
+                                506,
+                                432
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        417,
+                                        506,
+                                        432
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[34] Alexander Immer, Matthias Bauer, Vincent Fortuin, Gunnar Rätsch, and Mohammad Emtiyaz",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                428,
+                                504,
+                                441
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        428,
+                                        504,
+                                        441
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Khan. Scalable marginal likelihood estimation for model selection in deep learning. arXiv",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                439,
+                                267,
+                                452
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        439,
+                                        267,
+                                        452
+                                    ],
+                                    "score": 1.0,
+                                    "content": "preprint arXiv:2104.04975, 2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                458,
+                                506,
+                                472
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        458,
+                                        506,
+                                        472
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[35] Alexander Immer, Maciej Korzepa, and Matthias Bauer. Improving predictions of bayesian",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                469,
+                                506,
+                                483
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        469,
+                                        506,
+                                        483
+                                    ],
+                                    "score": 1.0,
+                                    "content": "neural nets via local linearization. In International Conference on Artificial Intelligence and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                480,
+                                292,
+                                494
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        480,
+                                        292,
+                                        494
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Statistics, pages 703–711. PMLR, 2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                500,
+                                506,
+                                511
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        500,
+                                        506,
+                                        511
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[36] Pavel Izmailov, Sharad Vikram, Matthew D Hoffman, and Andrew Gordon Wilson. What are",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                509,
+                                480,
+                                523
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        509,
+                                        480,
+                                        523
+                                    ],
+                                    "score": 1.0,
+                                    "content": "bayesian neural network posteriors really like? arXiv preprint arXiv:2104.14421, 2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                528,
+                                506,
+                                543
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        528,
+                                        506,
+                                        543
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[37] Arthur Jacot, Franck Gabriel, and Clément Hongler. Neural tangent kernel: convergence and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                540,
+                                506,
+                                553
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        540,
+                                        506,
+                                        553
+                                    ],
+                                    "score": 1.0,
+                                    "content": "generalization in neural networks. In Proceedings of the 32nd International Conference on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                550,
+                                390,
+                                565
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        550,
+                                        390,
+                                        565
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Neural Information Processing Systems, pages 8580–8589, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                568,
+                                507,
+                                583
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        568,
+                                        507,
+                                        583
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[38] Richard Jordan, David Kinderlehrer, and Felix Otto. The variational formulation of the fokker–",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                580,
+                                435,
+                                594
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        580,
+                                        435,
+                                        594
+                                    ],
+                                    "score": 1.0,
+                                    "content": "planck equation. SIAM journal on mathematical analysis, 29(1):1–17, 1998.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                599,
+                                506,
+                                613
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        599,
+                                        506,
+                                        613
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[39] Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                611,
+                                226,
+                                623
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        611,
+                                        226,
+                                        623
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1412.6980, 2014.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                629,
+                                506,
+                                643
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        629,
+                                        506,
+                                        643
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[40] Anna Korba, Adil Salim, Michael Arbel, Giulia Luise, and Arthur Gretton. A non-asymptotic",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                639,
+                                506,
+                                655
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        639,
+                                        506,
+                                        655
+                                    ],
+                                    "score": 1.0,
+                                    "content": "analysis for stein variational gradient descent. Advances in Neural Information Processing",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                651,
+                                205,
+                                664
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        651,
+                                        205,
+                                        664
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Systems, 33, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                669,
+                                465,
+                                683
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        669,
+                                        465,
+                                        683
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[41] Alex Krizhevsky et al. Learning multiple layers of features from tiny images. 2009.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43,
+                            "is_list_start_line": true,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                688,
+                                506,
+                                702
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        688,
+                                        506,
+                                        702
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[42] Balaji Lakshminarayanan, Alexander Pritzel, and Charles Blundell. Simple and scalable",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                699,
+                                506,
+                                714
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        699,
+                                        506,
+                                        714
+                                    ],
+                                    "score": 1.0,
+                                    "content": "predictive uncertainty estimation using deep ensembles. In Advances in neural information",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                125,
+                                711,
+                                309,
+                                724
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        125,
+                                        711,
+                                        309,
+                                        724
+                                    ],
+                                    "score": 1.0,
+                                    "content": "processing systems, pages 6402–6413, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                73,
+                                506,
+                                85
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        73,
+                                        506,
+                                        85
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[43] Yann LeCun. The mnist database of handwritten digits. http://yann. lecun. com/exdb/mnist/,",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 0,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                81,
+                                154,
+                                99
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        81,
+                                        154,
+                                        99
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1998.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 1,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                102,
+                                507,
+                                116
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        102,
+                                        507,
+                                        116
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[44] Jaehoon Lee, Yasaman Bahri, Roman Novak, Samuel S Schoenholz, Jeffrey Pennington,",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 2,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                113,
+                                506,
+                                127
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        113,
+                                        506,
+                                        127
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and Jascha Sohl-Dickstein. Deep neural networks as gaussian processes. arXiv preprint",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                123,
+                                232,
+                                137
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        123,
+                                        232,
+                                        137
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1711.00165, 2017.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 4,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                141,
+                                505,
+                                156
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        141,
+                                        505,
+                                        156
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[45] E. Levin, N. Tishby, and S. A. Solla. A statistical approach to learning and generalization in",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 5,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                154,
+                                474,
+                                167
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        154,
+                                        474,
+                                        167
+                                    ],
+                                    "score": 1.0,
+                                    "content": "layered neural networks. Proc. of the IEEE – Special issue on Neural Networks, 1990.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 6,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                172,
+                                506,
+                                186
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        172,
+                                        506,
+                                        186
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[46] Yingzhen Li and Richard E Turner. Gradient estimators for implicit models. arXiv preprint",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 7,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                183,
+                                231,
+                                197
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        183,
+                                        231,
+                                        197
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1705.07107, 2017.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 8,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                201,
+                                507,
+                                216
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        201,
+                                        507,
+                                        216
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[47] Shiyu Liang, Yixuan Li, and Rayadurgam Srikant. Enhancing the reliability of out-of-",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 9,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                213,
+                                483,
+                                225
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        213,
+                                        483,
+                                        225
+                                    ],
+                                    "score": 1.0,
+                                    "content": "distribution image detection in neural networks. arXiv preprint arXiv:1706.02690, 2017.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 10,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                231,
+                                506,
+                                245
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        231,
+                                        506,
+                                        245
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[48] Chang Liu, Jingwei Zhuo, Pengyu Cheng, Ruiyi Zhang, and Jun Zhu. Understanding and",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 11,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                125,
+                                241,
+                                507,
+                                257
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        125,
+                                        241,
+                                        507,
+                                        257
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accelerating particle-based variational inference. In International Conference on Machine",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                253,
+                                302,
+                                267
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        253,
+                                        302,
+                                        267
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Learning, pages 4082–4092. PMLR, 2019.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 13,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                272,
+                                505,
+                                284
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        272,
+                                        505,
+                                        284
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[49] Jeremiah Zhe Liu, Zi Lin, Shreyas Padhy, Dustin Tran, Tania Bedrax-Weiss, and Balaji Laksh-",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 14,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                282,
+                                506,
+                                297
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        282,
+                                        506,
+                                        297
+                                    ],
+                                    "score": 1.0,
+                                    "content": "minarayanan. Simple and principled uncertainty estimation with deterministic deep learning via",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                293,
+                                372,
+                                307
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        293,
+                                        372,
+                                        307
+                                    ],
+                                    "score": 1.0,
+                                    "content": "distance awareness. arXiv preprint arXiv:2006.10108, 2020.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 16,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                313,
+                                505,
+                                325
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        313,
+                                        505,
+                                        325
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[50] Qiang Liu. Stein variational gradient descent as gradient flow. In Advances in neural information",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 17,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                125,
+                                324,
+                                310,
+                                337
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        125,
+                                        324,
+                                        310,
+                                        337
+                                    ],
+                                    "score": 1.0,
+                                    "content": "processing systems, pages 3115–3123, 2017.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 18,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                341,
+                                507,
+                                356
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        341,
+                                        507,
+                                        356
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[51] Qiang Liu and Dilin Wang. Stein variational gradient descent: A general purpose bayesian",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 19,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                353,
+                                506,
+                                367
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        353,
+                                        506,
+                                        367
+                                    ],
+                                    "score": 1.0,
+                                    "content": "inference algorithm. In Advances in neural information processing systems, pages 2378–2386,",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                362,
+                                155,
+                                378
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        362,
+                                        155,
+                                        378
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2016.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 21,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                382,
+                                506,
+                                396
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        382,
+                                        506,
+                                        396
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[52] Qiang Liu, Jason Lee, and Michael Jordan. A kernelized stein discrepancy for goodness-of-fit",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 22,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                393,
+                                473,
+                                407
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        393,
+                                        473,
+                                        407
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tests. In International conference on machine learning, pages 276–284. PMLR, 2016.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 23,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                412,
+                                506,
+                                426
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        412,
+                                        506,
+                                        426
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[53] Clare Lyle, Lisa Schut, Robin Ru, Yarin Gal, and Mark van der Wilk. A bayesian perspective",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 24,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                422,
+                                507,
+                                437
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        422,
+                                        507,
+                                        437
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on training speed and model selection. Advances in Neural Information Processing Systems, 33,",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                433,
+                                155,
+                                448
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        433,
+                                        155,
+                                        448
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2020.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 26,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                453,
+                                505,
+                                465
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        453,
+                                        505,
+                                        465
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[54] David JC MacKay. A practical bayesian framework for backpropagation networks. Neural",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 27,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                464,
+                                268,
+                                477
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        464,
+                                        268,
+                                        477
+                                    ],
+                                    "score": 1.0,
+                                    "content": "computation, 4(3):448–472, 1992.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 28,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                482,
+                                505,
+                                496
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        482,
+                                        505,
+                                        496
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[55] Andrey Malinin, Bruno Mlodozeniec, and Mark Gales. Ensemble distribution distillation. arXiv",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 29,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                125,
+                                493,
+                                266,
+                                506
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        125,
+                                        493,
+                                        266,
+                                        506
+                                    ],
+                                    "score": 1.0,
+                                    "content": "preprint arXiv:1905.00076, 2019.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 30,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                510,
+                                507,
+                                526
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        510,
+                                        507,
+                                        526
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[56] Stephan Mandt, Matthew D Hoffman, and David M Blei. Stochastic gradient descent as",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 31,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                523,
+                                424,
+                                537
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        523,
+                                        424,
+                                        537
+                                    ],
+                                    "score": 1.0,
+                                    "content": "approximate bayesian inference. arXiv preprint arXiv:1704.04289, 2017.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 32,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                541,
+                                507,
+                                555
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        541,
+                                        507,
+                                        555
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[57] Alexander G de G Matthews, Jiri Hron, Richard E Turner, and Zoubin Ghahramani. Sample-",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 33,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                552,
+                                506,
+                                566
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        552,
+                                        506,
+                                        566
+                                    ],
+                                    "score": 1.0,
+                                    "content": "then-optimize posterior sampling for bayesian linear models. In NeurIPS Workshop on Advances",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                564,
+                                298,
+                                576
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        564,
+                                        298,
+                                        576
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in Approximate Bayesian Inference, 2017.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 35,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                581,
+                                506,
+                                595
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        581,
+                                        506,
+                                        595
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[58] Mahdi Pakdaman Naeini, Gregory Cooper, and Milos Hauskrecht. Obtaining well calibrated",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 36,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                591,
+                                505,
+                                606
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        591,
+                                        505,
+                                        606
+                                    ],
+                                    "score": 1.0,
+                                    "content": "probabilities using bayesian binning. In Proceedings of the AAAI Conference on Artificial",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                603,
+                                253,
+                                617
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        603,
+                                        253,
+                                        617
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Intelligence, volume 29, 2015.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 38,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                622,
+                                383,
+                                635
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        622,
+                                        383,
+                                        635
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[59] Radford M Neal. Bayesian learning for neural networks. 1995.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 39,
+                            "is_list_start_line": true,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                640,
+                                507,
+                                654
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        640,
+                                        507,
+                                        654
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[60] Radford M Neal. Bayesian learning for neural networks, volume 118. Springer Science &",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 40,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                652,
+                                221,
+                                664
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        652,
+                                        221,
+                                        664
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Business Media, 2012.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 41,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                670,
+                                507,
+                                684
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        670,
+                                        507,
+                                        684
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[61] Yuval Netzer, Tao Wang, Adam Coates, Alessandro Bissacco, Bo Wu, and Andrew Y Ng.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 42,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                682,
+                                429,
+                                694
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        682,
+                                        429,
+                                        694
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Reading digits in natural images with unsupervised feature learning. 2011.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 43,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                699,
+                                506,
+                                714
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        699,
+                                        506,
+                                        714
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[62] Ian Osband, Benjamin Van Roy, Daniel J Russo, Zheng Wen, et al. Deep exploration via",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 44,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                711,
+                                416,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        711,
+                                        416,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "randomized value functions. J. Mach. Learn. Res., 20(124):1–62, 2019.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 45,
+                            "is_list_end_line": true
+                        }
+                    ],
+                    "index": 23,
+                    "bbox_fs": [
+                        104,
+                        72,
+                        507,
+                        724
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        45,
+                        507,
+                        728
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                73,
+                                506,
+                                85
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        73,
+                                        506,
+                                        85
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[43] Yann LeCun. The mnist database of handwritten digits. http://yann. lecun. com/exdb/mnist/,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                81,
+                                154,
+                                99
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        81,
+                                        154,
+                                        99
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1998.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                102,
+                                507,
+                                116
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        102,
+                                        507,
+                                        116
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[44] Jaehoon Lee, Yasaman Bahri, Roman Novak, Samuel S Schoenholz, Jeffrey Pennington,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                113,
+                                506,
+                                127
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        113,
+                                        506,
+                                        127
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and Jascha Sohl-Dickstein. Deep neural networks as gaussian processes. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                123,
+                                232,
+                                137
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        123,
+                                        232,
+                                        137
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1711.00165, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                141,
+                                505,
+                                156
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        141,
+                                        505,
+                                        156
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[45] E. Levin, N. Tishby, and S. A. Solla. A statistical approach to learning and generalization in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                154,
+                                474,
+                                167
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        154,
+                                        474,
+                                        167
+                                    ],
+                                    "score": 1.0,
+                                    "content": "layered neural networks. Proc. of the IEEE – Special issue on Neural Networks, 1990.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                172,
+                                506,
+                                186
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        172,
+                                        506,
+                                        186
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[46] Yingzhen Li and Richard E Turner. Gradient estimators for implicit models. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                183,
+                                231,
+                                197
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        183,
+                                        231,
+                                        197
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1705.07107, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                201,
+                                507,
+                                216
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        201,
+                                        507,
+                                        216
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[47] Shiyu Liang, Yixuan Li, and Rayadurgam Srikant. Enhancing the reliability of out-of-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                213,
+                                483,
+                                225
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        213,
+                                        483,
+                                        225
+                                    ],
+                                    "score": 1.0,
+                                    "content": "distribution image detection in neural networks. arXiv preprint arXiv:1706.02690, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                231,
+                                506,
+                                245
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        231,
+                                        506,
+                                        245
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[48] Chang Liu, Jingwei Zhuo, Pengyu Cheng, Ruiyi Zhang, and Jun Zhu. Understanding and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                125,
+                                241,
+                                507,
+                                257
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        125,
+                                        241,
+                                        507,
+                                        257
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accelerating particle-based variational inference. In International Conference on Machine",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                253,
+                                302,
+                                267
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        253,
+                                        302,
+                                        267
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Learning, pages 4082–4092. PMLR, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                272,
+                                505,
+                                284
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        272,
+                                        505,
+                                        284
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[49] Jeremiah Zhe Liu, Zi Lin, Shreyas Padhy, Dustin Tran, Tania Bedrax-Weiss, and Balaji Laksh-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                282,
+                                506,
+                                297
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        282,
+                                        506,
+                                        297
+                                    ],
+                                    "score": 1.0,
+                                    "content": "minarayanan. Simple and principled uncertainty estimation with deterministic deep learning via",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                293,
+                                372,
+                                307
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        293,
+                                        372,
+                                        307
+                                    ],
+                                    "score": 1.0,
+                                    "content": "distance awareness. arXiv preprint arXiv:2006.10108, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                313,
+                                505,
+                                325
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        313,
+                                        505,
+                                        325
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[50] Qiang Liu. Stein variational gradient descent as gradient flow. In Advances in neural information",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                125,
+                                324,
+                                310,
+                                337
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        125,
+                                        324,
+                                        310,
+                                        337
+                                    ],
+                                    "score": 1.0,
+                                    "content": "processing systems, pages 3115–3123, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                341,
+                                507,
+                                356
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        341,
+                                        507,
+                                        356
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[51] Qiang Liu and Dilin Wang. Stein variational gradient descent: A general purpose bayesian",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                353,
+                                506,
+                                367
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        353,
+                                        506,
+                                        367
+                                    ],
+                                    "score": 1.0,
+                                    "content": "inference algorithm. In Advances in neural information processing systems, pages 2378–2386,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                362,
+                                155,
+                                378
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        362,
+                                        155,
+                                        378
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                382,
+                                506,
+                                396
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        382,
+                                        506,
+                                        396
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[52] Qiang Liu, Jason Lee, and Michael Jordan. A kernelized stein discrepancy for goodness-of-fit",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                393,
+                                473,
+                                407
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        393,
+                                        473,
+                                        407
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tests. In International conference on machine learning, pages 276–284. PMLR, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                412,
+                                506,
+                                426
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        412,
+                                        506,
+                                        426
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[53] Clare Lyle, Lisa Schut, Robin Ru, Yarin Gal, and Mark van der Wilk. A bayesian perspective",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                422,
+                                507,
+                                437
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        422,
+                                        507,
+                                        437
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on training speed and model selection. Advances in Neural Information Processing Systems, 33,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                433,
+                                155,
+                                448
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        433,
+                                        155,
+                                        448
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                453,
+                                505,
+                                465
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        453,
+                                        505,
+                                        465
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[54] David JC MacKay. A practical bayesian framework for backpropagation networks. Neural",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                464,
+                                268,
+                                477
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        464,
+                                        268,
+                                        477
+                                    ],
+                                    "score": 1.0,
+                                    "content": "computation, 4(3):448–472, 1992.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                482,
+                                505,
+                                496
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        482,
+                                        505,
+                                        496
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[55] Andrey Malinin, Bruno Mlodozeniec, and Mark Gales. Ensemble distribution distillation. arXiv",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                125,
+                                493,
+                                266,
+                                506
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        125,
+                                        493,
+                                        266,
+                                        506
+                                    ],
+                                    "score": 1.0,
+                                    "content": "preprint arXiv:1905.00076, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                510,
+                                507,
+                                526
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        510,
+                                        507,
+                                        526
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[56] Stephan Mandt, Matthew D Hoffman, and David M Blei. Stochastic gradient descent as",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                523,
+                                424,
+                                537
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        523,
+                                        424,
+                                        537
+                                    ],
+                                    "score": 1.0,
+                                    "content": "approximate bayesian inference. arXiv preprint arXiv:1704.04289, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                541,
+                                507,
+                                555
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        541,
+                                        507,
+                                        555
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[57] Alexander G de G Matthews, Jiri Hron, Richard E Turner, and Zoubin Ghahramani. Sample-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                552,
+                                506,
+                                566
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        552,
+                                        506,
+                                        566
+                                    ],
+                                    "score": 1.0,
+                                    "content": "then-optimize posterior sampling for bayesian linear models. In NeurIPS Workshop on Advances",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                564,
+                                298,
+                                576
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        564,
+                                        298,
+                                        576
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in Approximate Bayesian Inference, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                581,
+                                506,
+                                595
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        581,
+                                        506,
+                                        595
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[58] Mahdi Pakdaman Naeini, Gregory Cooper, and Milos Hauskrecht. Obtaining well calibrated",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                591,
+                                505,
+                                606
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        591,
+                                        505,
+                                        606
+                                    ],
+                                    "score": 1.0,
+                                    "content": "probabilities using bayesian binning. In Proceedings of the AAAI Conference on Artificial",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                603,
+                                253,
+                                617
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        603,
+                                        253,
+                                        617
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Intelligence, volume 29, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                622,
+                                383,
+                                635
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        622,
+                                        383,
+                                        635
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[59] Radford M Neal. Bayesian learning for neural networks. 1995.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                640,
+                                507,
+                                654
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        640,
+                                        507,
+                                        654
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[60] Radford M Neal. Bayesian learning for neural networks, volume 118. Springer Science &",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                652,
+                                221,
+                                664
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        652,
+                                        221,
+                                        664
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Business Media, 2012.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                670,
+                                507,
+                                684
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        670,
+                                        507,
+                                        684
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[61] Yuval Netzer, Tao Wang, Adam Coates, Alessandro Bissacco, Bo Wu, and Andrew Y Ng.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                682,
+                                429,
+                                694
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        682,
+                                        429,
+                                        694
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Reading digits in natural images with unsupervised feature learning. 2011.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                699,
+                                506,
+                                714
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        699,
+                                        506,
+                                        714
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[62] Ian Osband, Benjamin Van Roy, Daniel J Russo, Zheng Wen, et al. Deep exploration via",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                711,
+                                416,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        711,
+                                        416,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "randomized value functions. J. Mach. Learn. Res., 20(124):1–62, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        }
+                    ],
+                    "index": 22.5
+                }
+            ],
+            "page_idx": 12,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        741,
+                        311,
+                        750
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                740,
+                                313,
+                                754
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        740,
+                                        313,
+                                        754
+                                    ],
+                                    "score": 1.0,
+                                    "content": "13",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "list",
+                    "bbox": [
+                        105,
+                        45,
+                        507,
+                        728
+                    ],
+                    "lines": [],
+                    "index": 22.5,
+                    "bbox_fs": [
+                        104,
+                        73,
+                        507,
+                        723
+                    ],
+                    "lines_deleted": true
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        72,
+                        506,
+                        118
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                72,
+                                506,
+                                86
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        72,
+                                        506,
+                                        86
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[63] Johannes Von Oswald, Seijin Kobayashi, Joao Sacramento, Alexander Meulemans, Christian",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                83,
+                                506,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        83,
+                                        506,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Henning, and Benjamin F Grewe. Neural networks with late-phase weights. In International",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                94,
+                                506,
+                                107
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        94,
+                                        506,
+                                        107
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Conference on Learning Representations, 2021. URL https://openreview.net/forum?",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                106,
+                                205,
+                                118
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        106,
+                                        205,
+                                        118
+                                    ],
+                                    "score": 1.0,
+                                    "content": "id=C0qJUx5dxFb.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 1.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        123,
+                        505,
+                        146
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                122,
+                                506,
+                                136
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        122,
+                                        506,
+                                        136
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[64] Felix Otto. The geometry of dissipative evolution equations: the porous medium equation.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                131,
+                                155,
+                                147
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        131,
+                                        155,
+                                        147
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2001.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        }
+                    ],
+                    "index": 4.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        153,
+                        505,
+                        197
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                152,
+                                506,
+                                165
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        152,
+                                        506,
+                                        165
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[65] Yaniv Ovadia, Emily Fertig, Jie Ren, Zachary Nado, David Sculley, Sebastian Nowozin, Joshua",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                163,
+                                506,
+                                176
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        163,
+                                        506,
+                                        176
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Dillon, Balaji Lakshminarayanan, and Jasper Snoek. Can you trust your model’s uncertainty?",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                175,
+                                505,
+                                188
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        175,
+                                        505,
+                                        188
+                                    ],
+                                    "score": 1.0,
+                                    "content": "evaluating predictive uncertainty under dataset shift. In Advances in Neural Information",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                186,
+                                321,
+                                197
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        186,
+                                        321,
+                                        197
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Processing Systems, pages 13991–14002, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 7.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        203,
+                        504,
+                        226
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                202,
+                                506,
+                                217
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        202,
+                                        506,
+                                        217
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[66] Emanuel Parzen. On estimation of a probability density function and mode. The annals of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                214,
+                                325,
+                                227
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        214,
+                                        325,
+                                        227
+                                    ],
+                                    "score": 1.0,
+                                    "content": "mathematical statistics, 33(3):1065–1076, 1962.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 10.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        232,
+                        504,
+                        255
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                232,
+                                505,
+                                245
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        232,
+                                        505,
+                                        245
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[67] Alexandre Rame and Matthieu Cord. Dice: Diversity in deep ensembles via conditional",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                243,
+                                433,
+                                256
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        243,
+                                        433,
+                                        256
+                                    ],
+                                    "score": 1.0,
+                                    "content": "redundancy adversarial estimation. arXiv preprint arXiv:2101.05544, 2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 12.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        261,
+                        504,
+                        285
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                261,
+                                505,
+                                274
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        261,
+                                        505,
+                                        274
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[68] Geoffrey Roeder, Luke Metz, and Diederik P Kingma. On linear identifiability of learned",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                273,
+                                357,
+                                285
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        273,
+                                        357,
+                                        285
+                                    ],
+                                    "score": 1.0,
+                                    "content": "representations. arXiv preprint arXiv:2007.00810, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 14.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        290,
+                        505,
+                        324
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                290,
+                                505,
+                                304
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        290,
+                                        505,
+                                        304
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[69] Jiaxin Shi, Shengyang Sun, and Jun Zhu. A spectral approach to gradient estimation for implicit",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                302,
+                                506,
+                                314
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        302,
+                                        506,
+                                        314
+                                    ],
+                                    "score": 1.0,
+                                    "content": "distributions. In International Conference on Machine Learning, pages 4644–4653. PMLR,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                312,
+                                154,
+                                325
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        312,
+                                        154,
+                                        325
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        330,
+                        504,
+                        354
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                331,
+                                505,
+                                344
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        331,
+                                        505,
+                                        344
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[70] Radhey S Singh. Improvement on some known nonparametric uniformly consistent estimators",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                341,
+                                425,
+                                354
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        341,
+                                        425,
+                                        354
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of derivatives of a density. The Annals of Statistics, pages 394–399, 1977.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 19.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        360,
+                        504,
+                        383
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                359,
+                                505,
+                                374
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        359,
+                                        505,
+                                        374
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[71] Shengyang Sun, Guodong Zhang, Jiaxin Shi, and Roger Grosse. Functional variational bayesian",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                371,
+                                361,
+                                383
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        371,
+                                        361,
+                                        383
+                                    ],
+                                    "score": 1.0,
+                                    "content": "neural networks. arXiv preprint arXiv:1903.05779, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 21.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        389,
+                        506,
+                        433
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                389,
+                                506,
+                                401
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        389,
+                                        506,
+                                        401
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[72] Jakub Swiatkowski, Kevin Roth, Bastiaan S Veeling, Linh Tran, Joshua V Dillon, Stephan",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                400,
+                                505,
+                                412
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        400,
+                                        505,
+                                        412
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Mandt, Jasper Snoek, Tim Salimans, Rodolphe Jenatton, and Sebastian Nowozin. The k-tied",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                411,
+                                506,
+                                424
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        411,
+                                        506,
+                                        424
+                                    ],
+                                    "score": 1.0,
+                                    "content": "normal distribution: A compact parameterization of gaussian mean field posteriors in bayesian",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                423,
+                                360,
+                                434
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        423,
+                                        360,
+                                        434
+                                    ],
+                                    "score": 1.0,
+                                    "content": "neural networks. arXiv preprint arXiv:2002.02655, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 24.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        109,
+                        440,
+                        504,
+                        474
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                439,
+                                506,
+                                453
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        439,
+                                        506,
+                                        453
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[73] Johannes von Oswald, Christian Henning, João Sacramento, and Benjamin F. Grewe. Continual",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                451,
+                                506,
+                                464
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        451,
+                                        506,
+                                        464
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning with hypernetworks. In International Conference on Learning Representations, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                461,
+                                321,
+                                474
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        461,
+                                        321,
+                                        474
+                                    ],
+                                    "score": 1.0,
+                                    "content": "URL https://arxiv.org/abs/1906.00695.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 28
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        480,
+                        504,
+                        513
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                479,
+                                506,
+                                493
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        479,
+                                        506,
+                                        493
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[74] Maxime Wabartha, Audrey Durand, Vincent François-Lavet, and Joelle Pineau. Handling black",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                491,
+                                506,
+                                504
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        491,
+                                        506,
+                                        504
+                                    ],
+                                    "score": 1.0,
+                                    "content": "swan events in deep learning with diversely extrapolated neural networks. In IJCAI, pages",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                502,
+                                202,
+                                513
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        502,
+                                        202,
+                                        513
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2140–2147, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 31
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        520,
+                        504,
+                        543
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                519,
+                                506,
+                                533
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        519,
+                                        506,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[75] Yifei Wang, Peng Chen, and Wuchen Li. Projected wasserstein gradient descent for high-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                530,
+                                423,
+                                543
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        530,
+                                        423,
+                                        543
+                                    ],
+                                    "score": 1.0,
+                                    "content": "dimensional bayesian inference. arXiv preprint arXiv:2102.06350, 2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        }
+                    ],
+                    "index": 33.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        549,
+                        505,
+                        572
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                549,
+                                505,
+                                562
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        549,
+                                        505,
+                                        562
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[76] Ziyu Wang, Tongzheng Ren, Jun Zhu, and Bo Zhang. Function space particle optimization for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                560,
+                                397,
+                                572
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        560,
+                                        397,
+                                        572
+                                    ],
+                                    "score": 1.0,
+                                    "content": "bayesian neural networks. arXiv preprint arXiv:1902.09754, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 35.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        578,
+                        505,
+                        612
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                578,
+                                506,
+                                591
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        578,
+                                        506,
+                                        591
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[77] Max Welling and Yee W Teh. Bayesian learning via stochastic gradient langevin dynamics.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                588,
+                                505,
+                                603
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        588,
+                                        505,
+                                        603
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In Proceedings of the 28th international conference on machine learning (ICML-11), pages",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                600,
+                                193,
+                                612
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        600,
+                                        193,
+                                        612
+                                    ],
+                                    "score": 1.0,
+                                    "content": "681–688, 2011.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 38
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        618,
+                        505,
+                        641
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                618,
+                                505,
+                                631
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        618,
+                                        505,
+                                        631
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[78] Yeming Wen, Dustin Tran, and Jimmy Ba. Batchensemble: an alternative approach to efficient",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                629,
+                                419,
+                                642
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        629,
+                                        419,
+                                        642
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ensemble and lifelong learning. arXiv preprint arXiv:2002.06715, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        }
+                    ],
+                    "index": 40.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        648,
+                        505,
+                        682
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                648,
+                                506,
+                                661
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        648,
+                                        506,
+                                        661
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[79] Florian Wenzel, Kevin Roth, Bastiaan S Veeling, Jakub Swiatkowski, Linh Tran, Stephan Mandt, ´",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                660,
+                                505,
+                                672
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        660,
+                                        505,
+                                        672
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Jasper Snoek, Tim Salimans, Rodolphe Jenatton, and Sebastian Nowozin. How good is the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                670,
+                                482,
+                                683
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        670,
+                                        482,
+                                        683
+                                    ],
+                                    "score": 1.0,
+                                    "content": "bayes posterior in deep neural networks really? arXiv preprint arXiv:2002.02405, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        }
+                    ],
+                    "index": 43
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        689,
+                        505,
+                        722
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                687,
+                                506,
+                                702
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        687,
+                                        506,
+                                        702
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[80] Florian Wenzel, Jasper Snoek, Dustin Tran, and Rodolphe Jenatton. Hyperparameter ensembles",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                698,
+                                505,
+                                713
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        698,
+                                        505,
+                                        713
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for robustness and uncertainty quantification. In Advances in Neural Information Processing",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                711,
+                                189,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        711,
+                                        189,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Systems, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        }
+                    ],
+                    "index": 46
+                }
+            ],
+            "page_idx": 13,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        741,
+                        311,
+                        750
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                740,
+                                313,
+                                754
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        740,
+                                        313,
+                                        754
+                                    ],
+                                    "score": 1.0,
+                                    "content": "14",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        72,
+                        506,
+                        118
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                72,
+                                506,
+                                86
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        72,
+                                        506,
+                                        86
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[63] Johannes Von Oswald, Seijin Kobayashi, Joao Sacramento, Alexander Meulemans, Christian",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                83,
+                                506,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        83,
+                                        506,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Henning, and Benjamin F Grewe. Neural networks with late-phase weights. In International",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                94,
+                                506,
+                                107
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        94,
+                                        506,
+                                        107
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Conference on Learning Representations, 2021. URL https://openreview.net/forum?",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                106,
+                                205,
+                                118
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        106,
+                                        205,
+                                        118
+                                    ],
+                                    "score": 1.0,
+                                    "content": "id=C0qJUx5dxFb.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 1.5,
+                    "bbox_fs": [
+                        105,
+                        72,
+                        506,
+                        118
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        123,
+                        505,
+                        146
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                122,
+                                506,
+                                136
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        122,
+                                        506,
+                                        136
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[64] Felix Otto. The geometry of dissipative evolution equations: the porous medium equation.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                131,
+                                155,
+                                147
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        131,
+                                        155,
+                                        147
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2001.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        }
+                    ],
+                    "index": 4.5,
+                    "bbox_fs": [
+                        105,
+                        122,
+                        506,
+                        147
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        153,
+                        505,
+                        197
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                152,
+                                506,
+                                165
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        152,
+                                        506,
+                                        165
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[65] Yaniv Ovadia, Emily Fertig, Jie Ren, Zachary Nado, David Sculley, Sebastian Nowozin, Joshua",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                163,
+                                506,
+                                176
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        163,
+                                        506,
+                                        176
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Dillon, Balaji Lakshminarayanan, and Jasper Snoek. Can you trust your model’s uncertainty?",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                175,
+                                505,
+                                188
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        175,
+                                        505,
+                                        188
+                                    ],
+                                    "score": 1.0,
+                                    "content": "evaluating predictive uncertainty under dataset shift. In Advances in Neural Information",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                186,
+                                321,
+                                197
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        186,
+                                        321,
+                                        197
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Processing Systems, pages 13991–14002, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 7.5,
+                    "bbox_fs": [
+                        106,
+                        152,
+                        506,
+                        197
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        203,
+                        504,
+                        226
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                202,
+                                506,
+                                217
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        202,
+                                        506,
+                                        217
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[66] Emanuel Parzen. On estimation of a probability density function and mode. The annals of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                214,
+                                325,
+                                227
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        214,
+                                        325,
+                                        227
+                                    ],
+                                    "score": 1.0,
+                                    "content": "mathematical statistics, 33(3):1065–1076, 1962.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 10.5,
+                    "bbox_fs": [
+                        105,
+                        202,
+                        506,
+                        227
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        232,
+                        504,
+                        255
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                232,
+                                505,
+                                245
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        232,
+                                        505,
+                                        245
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[67] Alexandre Rame and Matthieu Cord. Dice: Diversity in deep ensembles via conditional",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                243,
+                                433,
+                                256
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        243,
+                                        433,
+                                        256
+                                    ],
+                                    "score": 1.0,
+                                    "content": "redundancy adversarial estimation. arXiv preprint arXiv:2101.05544, 2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 12.5,
+                    "bbox_fs": [
+                        107,
+                        232,
+                        505,
+                        256
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        261,
+                        504,
+                        285
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                261,
+                                505,
+                                274
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        261,
+                                        505,
+                                        274
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[68] Geoffrey Roeder, Luke Metz, and Diederik P Kingma. On linear identifiability of learned",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                273,
+                                357,
+                                285
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        273,
+                                        357,
+                                        285
+                                    ],
+                                    "score": 1.0,
+                                    "content": "representations. arXiv preprint arXiv:2007.00810, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 14.5,
+                    "bbox_fs": [
+                        106,
+                        261,
+                        505,
+                        285
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        290,
+                        505,
+                        324
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                290,
+                                505,
+                                304
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        290,
+                                        505,
+                                        304
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[69] Jiaxin Shi, Shengyang Sun, and Jun Zhu. A spectral approach to gradient estimation for implicit",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                302,
+                                506,
+                                314
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        302,
+                                        506,
+                                        314
+                                    ],
+                                    "score": 1.0,
+                                    "content": "distributions. In International Conference on Machine Learning, pages 4644–4653. PMLR,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                312,
+                                154,
+                                325
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        312,
+                                        154,
+                                        325
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 17,
+                    "bbox_fs": [
+                        106,
+                        290,
+                        506,
+                        325
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        330,
+                        504,
+                        354
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                331,
+                                505,
+                                344
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        331,
+                                        505,
+                                        344
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[70] Radhey S Singh. Improvement on some known nonparametric uniformly consistent estimators",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                341,
+                                425,
+                                354
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        341,
+                                        425,
+                                        354
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of derivatives of a density. The Annals of Statistics, pages 394–399, 1977.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 19.5,
+                    "bbox_fs": [
+                        106,
+                        331,
+                        505,
+                        354
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        360,
+                        504,
+                        383
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                359,
+                                505,
+                                374
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        359,
+                                        505,
+                                        374
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[71] Shengyang Sun, Guodong Zhang, Jiaxin Shi, and Roger Grosse. Functional variational bayesian",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                371,
+                                361,
+                                383
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        371,
+                                        361,
+                                        383
+                                    ],
+                                    "score": 1.0,
+                                    "content": "neural networks. arXiv preprint arXiv:1903.05779, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 21.5,
+                    "bbox_fs": [
+                        106,
+                        359,
+                        505,
+                        383
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        389,
+                        506,
+                        433
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                389,
+                                506,
+                                401
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        389,
+                                        506,
+                                        401
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[72] Jakub Swiatkowski, Kevin Roth, Bastiaan S Veeling, Linh Tran, Joshua V Dillon, Stephan",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                400,
+                                505,
+                                412
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        400,
+                                        505,
+                                        412
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Mandt, Jasper Snoek, Tim Salimans, Rodolphe Jenatton, and Sebastian Nowozin. The k-tied",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                411,
+                                506,
+                                424
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        411,
+                                        506,
+                                        424
+                                    ],
+                                    "score": 1.0,
+                                    "content": "normal distribution: A compact parameterization of gaussian mean field posteriors in bayesian",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                423,
+                                360,
+                                434
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        423,
+                                        360,
+                                        434
+                                    ],
+                                    "score": 1.0,
+                                    "content": "neural networks. arXiv preprint arXiv:2002.02655, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 24.5,
+                    "bbox_fs": [
+                        105,
+                        389,
+                        506,
+                        434
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        109,
+                        440,
+                        504,
+                        474
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                439,
+                                506,
+                                453
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        439,
+                                        506,
+                                        453
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[73] Johannes von Oswald, Christian Henning, João Sacramento, and Benjamin F. Grewe. Continual",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                451,
+                                506,
+                                464
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        451,
+                                        506,
+                                        464
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning with hypernetworks. In International Conference on Learning Representations, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                461,
+                                321,
+                                474
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        461,
+                                        321,
+                                        474
+                                    ],
+                                    "score": 1.0,
+                                    "content": "URL https://arxiv.org/abs/1906.00695.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 28,
+                    "bbox_fs": [
+                        105,
+                        439,
+                        506,
+                        474
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        480,
+                        504,
+                        513
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                479,
+                                506,
+                                493
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        479,
+                                        506,
+                                        493
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[74] Maxime Wabartha, Audrey Durand, Vincent François-Lavet, and Joelle Pineau. Handling black",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                491,
+                                506,
+                                504
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        491,
+                                        506,
+                                        504
+                                    ],
+                                    "score": 1.0,
+                                    "content": "swan events in deep learning with diversely extrapolated neural networks. In IJCAI, pages",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                502,
+                                202,
+                                513
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        502,
+                                        202,
+                                        513
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2140–2147, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 31,
+                    "bbox_fs": [
+                        105,
+                        479,
+                        506,
+                        513
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        520,
+                        504,
+                        543
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                519,
+                                506,
+                                533
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        519,
+                                        506,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[75] Yifei Wang, Peng Chen, and Wuchen Li. Projected wasserstein gradient descent for high-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                530,
+                                423,
+                                543
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        530,
+                                        423,
+                                        543
+                                    ],
+                                    "score": 1.0,
+                                    "content": "dimensional bayesian inference. arXiv preprint arXiv:2102.06350, 2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        }
+                    ],
+                    "index": 33.5,
+                    "bbox_fs": [
+                        105,
+                        519,
+                        506,
+                        543
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        549,
+                        505,
+                        572
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                549,
+                                505,
+                                562
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        549,
+                                        505,
+                                        562
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[76] Ziyu Wang, Tongzheng Ren, Jun Zhu, and Bo Zhang. Function space particle optimization for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                560,
+                                397,
+                                572
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        560,
+                                        397,
+                                        572
+                                    ],
+                                    "score": 1.0,
+                                    "content": "bayesian neural networks. arXiv preprint arXiv:1902.09754, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 35.5,
+                    "bbox_fs": [
+                        106,
+                        549,
+                        505,
+                        572
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        578,
+                        505,
+                        612
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                578,
+                                506,
+                                591
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        578,
+                                        506,
+                                        591
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[77] Max Welling and Yee W Teh. Bayesian learning via stochastic gradient langevin dynamics.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                588,
+                                505,
+                                603
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        588,
+                                        505,
+                                        603
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In Proceedings of the 28th international conference on machine learning (ICML-11), pages",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                600,
+                                193,
+                                612
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        600,
+                                        193,
+                                        612
+                                    ],
+                                    "score": 1.0,
+                                    "content": "681–688, 2011.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 38,
+                    "bbox_fs": [
+                        105,
+                        578,
+                        506,
+                        612
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        618,
+                        505,
+                        641
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                618,
+                                505,
+                                631
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        618,
+                                        505,
+                                        631
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[78] Yeming Wen, Dustin Tran, and Jimmy Ba. Batchensemble: an alternative approach to efficient",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                629,
+                                419,
+                                642
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        629,
+                                        419,
+                                        642
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ensemble and lifelong learning. arXiv preprint arXiv:2002.06715, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        }
+                    ],
+                    "index": 40.5,
+                    "bbox_fs": [
+                        106,
+                        618,
+                        505,
+                        642
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        648,
+                        505,
+                        682
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                648,
+                                506,
+                                661
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        648,
+                                        506,
+                                        661
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[79] Florian Wenzel, Kevin Roth, Bastiaan S Veeling, Jakub Swiatkowski, Linh Tran, Stephan Mandt, ´",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                660,
+                                505,
+                                672
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        660,
+                                        505,
+                                        672
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Jasper Snoek, Tim Salimans, Rodolphe Jenatton, and Sebastian Nowozin. How good is the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                670,
+                                482,
+                                683
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        670,
+                                        482,
+                                        683
+                                    ],
+                                    "score": 1.0,
+                                    "content": "bayes posterior in deep neural networks really? arXiv preprint arXiv:2002.02405, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        }
+                    ],
+                    "index": 43,
+                    "bbox_fs": [
+                        105,
+                        648,
+                        506,
+                        683
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        689,
+                        505,
+                        722
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                687,
+                                506,
+                                702
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        687,
+                                        506,
+                                        702
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[80] Florian Wenzel, Jasper Snoek, Dustin Tran, and Rodolphe Jenatton. Hyperparameter ensembles",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                698,
+                                505,
+                                713
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        698,
+                                        505,
+                                        713
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for robustness and uncertainty quantification. In Advances in Neural Information Processing",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                711,
+                                189,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        711,
+                                        189,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Systems, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        }
+                    ],
+                    "index": 46,
+                    "bbox_fs": [
+                        105,
+                        687,
+                        506,
+                        723
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        72,
+                        507,
+                        215
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                72,
+                                506,
+                                87
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        72,
+                                        506,
+                                        87
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[81] Christopher KI Williams. Computation with infinite neural networks. Neural Computation, 10",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                84,
+                                217,
+                                97
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        84,
+                                        217,
+                                        97
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(5):1203–1216, 1998.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                102,
+                                504,
+                                115
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        102,
+                                        504,
+                                        115
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[82] Andrew Gordon Wilson and Pavel Izmailov. Bayesian deep learning and a probabilistic",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                114,
+                                411,
+                                127
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        114,
+                                        411,
+                                        127
+                                    ],
+                                    "score": 1.0,
+                                    "content": "perspective of generalization. arXiv preprint arXiv:2002.08791, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                132,
+                                505,
+                                145
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        132,
+                                        505,
+                                        145
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[83] Han Xiao, Kashif Rasul, and Roland Vollgraf. Fashion-mnist: a novel image dataset for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                142,
+                                470,
+                                156
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        142,
+                                        470,
+                                        156
+                                    ],
+                                    "score": 1.0,
+                                    "content": "benchmarking machine learning algorithms. arXiv preprint arXiv:1708.07747, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                161,
+                                506,
+                                177
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        161,
+                                        506,
+                                        177
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[84] Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals. Understanding",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                173,
+                                487,
+                                187
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        173,
+                                        487,
+                                        187
+                                    ],
+                                    "score": 1.0,
+                                    "content": "deep learning requires rethinking generalization. arXiv preprint arXiv:1611.03530, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                192,
+                                506,
+                                206
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        192,
+                                        506,
+                                        206
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[85] Ruqi Zhang, Chunyuan Li, Jianyi Zhang, Changyou Chen, and Andrew Gordon Wilson. Cyclical",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                203,
+                                506,
+                                217
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        203,
+                                        506,
+                                        217
+                                    ],
+                                    "score": 1.0,
+                                    "content": "stochastic gradient mcmc for bayesian deep learning. arXiv preprint arXiv:1902.03932, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 4.5
+                }
+            ],
+            "page_idx": 14,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        741,
+                        311,
+                        750
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                740,
+                                313,
+                                754
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        740,
+                                        313,
+                                        754
+                                    ],
+                                    "score": 1.0,
+                                    "content": "15",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "list",
+                    "bbox": [
+                        106,
+                        72,
+                        507,
+                        215
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                72,
+                                506,
+                                87
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        72,
+                                        506,
+                                        87
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[81] Christopher KI Williams. Computation with infinite neural networks. Neural Computation, 10",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                84,
+                                217,
+                                97
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        84,
+                                        217,
+                                        97
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(5):1203–1216, 1998.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                102,
+                                504,
+                                115
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        102,
+                                        504,
+                                        115
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[82] Andrew Gordon Wilson and Pavel Izmailov. Bayesian deep learning and a probabilistic",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                114,
+                                411,
+                                127
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        114,
+                                        411,
+                                        127
+                                    ],
+                                    "score": 1.0,
+                                    "content": "perspective of generalization. arXiv preprint arXiv:2002.08791, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                132,
+                                505,
+                                145
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        132,
+                                        505,
+                                        145
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[83] Han Xiao, Kashif Rasul, and Roland Vollgraf. Fashion-mnist: a novel image dataset for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                142,
+                                470,
+                                156
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        142,
+                                        470,
+                                        156
+                                    ],
+                                    "score": 1.0,
+                                    "content": "benchmarking machine learning algorithms. arXiv preprint arXiv:1708.07747, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                161,
+                                506,
+                                177
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        161,
+                                        506,
+                                        177
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[84] Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals. Understanding",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                173,
+                                487,
+                                187
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        173,
+                                        487,
+                                        187
+                                    ],
+                                    "score": 1.0,
+                                    "content": "deep learning requires rethinking generalization. arXiv preprint arXiv:1611.03530, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                192,
+                                506,
+                                206
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        192,
+                                        506,
+                                        206
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[85] Ruqi Zhang, Chunyuan Li, Jianyi Zhang, Changyou Chen, and Andrew Gordon Wilson. Cyclical",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                203,
+                                506,
+                                217
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        203,
+                                        506,
+                                        217
+                                    ],
+                                    "score": 1.0,
+                                    "content": "stochastic gradient mcmc for bayesian deep learning. arXiv preprint arXiv:1902.03932, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 4.5,
+                    "bbox_fs": [
+                        105,
+                        72,
+                        506,
+                        217
+                    ]
+                }
+            ]
+        }
+    ],
+    "_backend": "pipeline",
+    "_version_name": "2.2.2"
+}
\ No newline at end of file
diff --git a/parse/train/LAKplpLMbP8/LAKplpLMbP8_model.json b/parse/train/LAKplpLMbP8/LAKplpLMbP8_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..526d16a7ebb52c456111e259c530bb0eab925850
--- /dev/null
+++ b/parse/train/LAKplpLMbP8/LAKplpLMbP8_model.json
@@ -0,0 +1,19037 @@
+[
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    398,
+                    717,
+                    1303,
+                    717,
+                    1303,
+                    1262,
+                    398,
+                    1262
+                ],
+                "score": 0.984
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1391,
+                    1404,
+                    1391,
+                    1404,
+                    1725,
+                    298,
+                    1725
+                ],
+                "score": 0.982
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1739,
+                    1404,
+                    1739,
+                    1404,
+                    1983,
+                    299,
+                    1983
+                ],
+                "score": 0.977
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    931,
+                    445,
+                    1212,
+                    445,
+                    1212,
+                    566,
+                    931,
+                    566
+                ],
+                "score": 0.933
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    488,
+                    444,
+                    731,
+                    444,
+                    731,
+                    567,
+                    488,
+                    567
+                ],
+                "score": 0.93
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    436,
+                    271,
+                    1265,
+                    271,
+                    1265,
+                    327,
+                    436,
+                    327
+                ],
+                "score": 0.922
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    299,
+                    1320,
+                    530,
+                    1320,
+                    530,
+                    1357,
+                    299,
+                    1357
+                ],
+                "score": 0.907
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    788,
+                    645,
+                    912,
+                    645,
+                    912,
+                    680,
+                    788,
+                    680
+                ],
+                "score": 0.891
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    2033,
+                    1070,
+                    2033,
+                    1070,
+                    2061,
+                    298,
+                    2061
+                ],
+                "score": 0.844
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    548,
+                    1799,
+                    597,
+                    1799,
+                    597,
+                    1831,
+                    548,
+                    1831
+                ],
+                "score": 0.62,
+                "latex": "\\begin{array} { r l } {  { \\| 6 5 \\| } } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1197,
+                    1767,
+                    1287,
+                    1767,
+                    1287,
+                    1801,
+                    1197,
+                    1801
+                ],
+                "score": 0.54,
+                "latex": "\\pm 2 \\sqrt { 8 0 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    619,
+                    1571,
+                    668,
+                    1571,
+                    668,
+                    1604,
+                    619,
+                    1604
+                ],
+                "score": 0.4,
+                "latex": "\\pmb { \\mathbb { B } } \\mathbf { \\mathbb { 1 } }"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    434.0,
+                    268.0,
+                    1266.0,
+                    268.0,
+                    1266.0,
+                    332.0,
+                    434.0,
+                    332.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1316.0,
+                    536.0,
+                    1316.0,
+                    536.0,
+                    1363.0,
+                    292.0,
+                    1363.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    784.0,
+                    645.0,
+                    918.0,
+                    645.0,
+                    918.0,
+                    683.0,
+                    784.0,
+                    683.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    2028.0,
+                    1075.0,
+                    2028.0,
+                    1075.0,
+                    2067.0,
+                    293.0,
+                    2067.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    715.0,
+                    1305.0,
+                    715.0,
+                    1305.0,
+                    754.0,
+                    393.0,
+                    754.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    744.0,
+                    1305.0,
+                    744.0,
+                    1305.0,
+                    782.0,
+                    392.0,
+                    782.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    774.0,
+                    1307.0,
+                    774.0,
+                    1307.0,
+                    812.0,
+                    393.0,
+                    812.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    395.0,
+                    808.0,
+                    1305.0,
+                    808.0,
+                    1305.0,
+                    841.0,
+                    395.0,
+                    841.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    839.0,
+                    1304.0,
+                    839.0,
+                    1304.0,
+                    871.0,
+                    394.0,
+                    871.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    868.0,
+                    1305.0,
+                    868.0,
+                    1305.0,
+                    904.0,
+                    394.0,
+                    904.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    395.0,
+                    898.0,
+                    1304.0,
+                    898.0,
+                    1304.0,
+                    931.0,
+                    395.0,
+                    931.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    395.0,
+                    929.0,
+                    1305.0,
+                    929.0,
+                    1305.0,
+                    962.0,
+                    395.0,
+                    962.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    957.0,
+                    1305.0,
+                    957.0,
+                    1305.0,
+                    995.0,
+                    392.0,
+                    995.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    396.0,
+                    991.0,
+                    1304.0,
+                    991.0,
+                    1304.0,
+                    1020.0,
+                    396.0,
+                    1020.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1019.0,
+                    1307.0,
+                    1019.0,
+                    1307.0,
+                    1055.0,
+                    394.0,
+                    1055.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1049.0,
+                    1307.0,
+                    1049.0,
+                    1307.0,
+                    1085.0,
+                    394.0,
+                    1085.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    1078.0,
+                    1308.0,
+                    1078.0,
+                    1308.0,
+                    1116.0,
+                    393.0,
+                    1116.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    1108.0,
+                    1306.0,
+                    1108.0,
+                    1306.0,
+                    1147.0,
+                    392.0,
+                    1147.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    1139.0,
+                    1307.0,
+                    1139.0,
+                    1307.0,
+                    1176.0,
+                    393.0,
+                    1176.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    1170.0,
+                    1306.0,
+                    1170.0,
+                    1306.0,
+                    1207.0,
+                    393.0,
+                    1207.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1201.0,
+                    1306.0,
+                    1201.0,
+                    1306.0,
+                    1237.0,
+                    394.0,
+                    1237.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1232.0,
+                    706.0,
+                    1232.0,
+                    706.0,
+                    1265.0,
+                    394.0,
+                    1265.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1390.0,
+                    1405.0,
+                    1390.0,
+                    1405.0,
+                    1425.0,
+                    294.0,
+                    1425.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1421.0,
+                    1407.0,
+                    1421.0,
+                    1407.0,
+                    1458.0,
+                    292.0,
+                    1458.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1449.0,
+                    1404.0,
+                    1449.0,
+                    1404.0,
+                    1487.0,
+                    293.0,
+                    1487.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1478.0,
+                    1404.0,
+                    1478.0,
+                    1404.0,
+                    1520.0,
+                    293.0,
+                    1520.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1510.0,
+                    1406.0,
+                    1510.0,
+                    1406.0,
+                    1548.0,
+                    293.0,
+                    1548.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1541.0,
+                    1404.0,
+                    1541.0,
+                    1404.0,
+                    1579.0,
+                    293.0,
+                    1579.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1573.0,
+                    618.0,
+                    1573.0,
+                    618.0,
+                    1607.0,
+                    296.0,
+                    1607.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    669.0,
+                    1573.0,
+                    1405.0,
+                    1573.0,
+                    1405.0,
+                    1607.0,
+                    669.0,
+                    1607.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1602.0,
+                    1405.0,
+                    1602.0,
+                    1405.0,
+                    1636.0,
+                    293.0,
+                    1636.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1633.0,
+                    1404.0,
+                    1633.0,
+                    1404.0,
+                    1668.0,
+                    294.0,
+                    1668.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1663.0,
+                    1404.0,
+                    1663.0,
+                    1404.0,
+                    1701.0,
+                    293.0,
+                    1701.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1695.0,
+                    1088.0,
+                    1695.0,
+                    1088.0,
+                    1729.0,
+                    294.0,
+                    1729.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1738.0,
+                    1409.0,
+                    1738.0,
+                    1409.0,
+                    1775.0,
+                    294.0,
+                    1775.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1768.0,
+                    1196.0,
+                    1768.0,
+                    1196.0,
+                    1804.0,
+                    295.0,
+                    1804.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1288.0,
+                    1768.0,
+                    1406.0,
+                    1768.0,
+                    1406.0,
+                    1804.0,
+                    1288.0,
+                    1804.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1800.0,
+                    547.0,
+                    1800.0,
+                    547.0,
+                    1834.0,
+                    295.0,
+                    1834.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    598.0,
+                    1800.0,
+                    1406.0,
+                    1800.0,
+                    1406.0,
+                    1834.0,
+                    598.0,
+                    1834.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1829.0,
+                    1405.0,
+                    1829.0,
+                    1405.0,
+                    1865.0,
+                    293.0,
+                    1865.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1860.0,
+                    1406.0,
+                    1860.0,
+                    1406.0,
+                    1894.0,
+                    293.0,
+                    1894.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1890.0,
+                    1409.0,
+                    1890.0,
+                    1409.0,
+                    1927.0,
+                    294.0,
+                    1927.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1920.0,
+                    1408.0,
+                    1920.0,
+                    1408.0,
+                    1955.0,
+                    293.0,
+                    1955.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1953.0,
+                    1405.0,
+                    1953.0,
+                    1405.0,
+                    1986.0,
+                    295.0,
+                    1986.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    977.0,
+                    445.0,
+                    1169.0,
+                    445.0,
+                    1169.0,
+                    474.0,
+                    977.0,
+                    474.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    999.0,
+                    472.0,
+                    1144.0,
+                    472.0,
+                    1144.0,
+                    506.0,
+                    999.0,
+                    506.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    959.0,
+                    506.0,
+                    1186.0,
+                    506.0,
+                    1186.0,
+                    535.0,
+                    959.0,
+                    535.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    931.0,
+                    538.0,
+                    1213.0,
+                    538.0,
+                    1213.0,
+                    566.0,
+                    931.0,
+                    566.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    485.0,
+                    442.0,
+                    731.0,
+                    442.0,
+                    731.0,
+                    479.0,
+                    485.0,
+                    479.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    536.0,
+                    471.0,
+                    681.0,
+                    471.0,
+                    681.0,
+                    506.0,
+                    536.0,
+                    506.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    494.0,
+                    501.0,
+                    724.0,
+                    501.0,
+                    724.0,
+                    538.0,
+                    494.0,
+                    538.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    489.0,
+                    535.0,
+                    729.0,
+                    535.0,
+                    729.0,
+                    570.0,
+                    489.0,
+                    570.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 0,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1683,
+                    1406,
+                    1683,
+                    1406,
+                    1929,
+                    297,
+                    1929
+                ],
+                "score": 0.979
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    827,
+                    1405,
+                    827,
+                    1405,
+                    1163,
+                    297,
+                    1163
+                ],
+                "score": 0.979
+            },
+            {
+                "category_id": 3,
+                "poly": [
+                    336,
+                    189,
+                    1371,
+                    189,
+                    1371,
+                    554,
+                    336,
+                    554
+                ],
+                "score": 0.971
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    371,
+                    1235,
+                    1405,
+                    1235,
+                    1405,
+                    1554,
+                    371,
+                    1554
+                ],
+                "score": 0.966
+            },
+            {
+                "category_id": 4,
+                "poly": [
+                    297,
+                    566,
+                    1403,
+                    566,
+                    1403,
+                    658,
+                    297,
+                    658
+                ],
+                "score": 0.963
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    300,
+                    721,
+                    1398,
+                    721,
+                    1398,
+                    815,
+                    300,
+                    815
+                ],
+                "score": 0.959
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    582,
+                    1948,
+                    1114,
+                    1948,
+                    1114,
+                    2015,
+                    582,
+                    2015
+                ],
+                "score": 0.95
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    299,
+                    1612,
+                    728,
+                    1612,
+                    728,
+                    1651,
+                    299,
+                    1651
+                ],
+                "score": 0.923
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    300,
+                    1177,
+                    717,
+                    1177,
+                    717,
+                    1209,
+                    300,
+                    1209
+                ],
+                "score": 0.922
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1366,
+                    1967,
+                    1400,
+                    1967,
+                    1400,
+                    1997,
+                    1366,
+                    1997
+                ],
+                "score": 0.877
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2061,
+                    859,
+                    2061,
+                    859,
+                    2085,
+                    841,
+                    2085
+                ],
+                "score": 0.744
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2061,
+                    859,
+                    2061,
+                    859,
+                    2085,
+                    841,
+                    2085
+                ],
+                "score": 0.174
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    585,
+                    1945,
+                    1113,
+                    1945,
+                    1113,
+                    2017,
+                    585,
+                    2017
+                ],
+                "score": 0.94,
+                "latex": "p ( \\pmb { y } ^ { * } | \\pmb { x } ^ { * } , \\mathcal { D } ) = \\int p ( \\pmb { y } ^ { * } | f ( \\pmb { x } ^ { * } ; \\mathbf { w } ) ) p ( \\mathbf { w } | \\mathcal { D } ) \\mathrm { d } \\mathbf { w }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    657,
+                    1866,
+                    830,
+                    1866,
+                    830,
+                    1899,
+                    657,
+                    1899
+                ],
+                "score": 0.93,
+                "latex": "{ \\pmb y } ^ { * } = f ( { \\pmb x } ^ { * } ; \\widehat { \\mathbf { w } } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1309,
+                    1715,
+                    1403,
+                    1715,
+                    1403,
+                    1748,
+                    1309,
+                    1748
+                ],
+                "score": 0.93,
+                "latex": "f ( \\pmb { x } ; \\mathbf { w } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    513,
+                    1744,
+                    750,
+                    1744,
+                    750,
+                    1778,
+                    513,
+                    1778
+                ],
+                "score": 0.92,
+                "latex": "\\textit { D } = \\{ ( \\boldsymbol { \\mathbf { { x } } } _ { i } , \\boldsymbol { \\mathbf { { y } } } _ { i } ) \\} _ { i = 1 } ^ { n }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1112,
+                    1684,
+                    1266,
+                    1684,
+                    1266,
+                    1718,
+                    1112,
+                    1718
+                ],
+                "score": 0.92,
+                "latex": "p ( \\pmb { y } | f ( \\pmb { x } ; \\mathbf { w } ) )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    1804,
+                    739,
+                    1804,
+                    739,
+                    1840,
+                    298,
+                    1840
+                ],
+                "score": 0.91,
+                "latex": "\\begin{array} { r } { p ( \\mathbf { w } | \\mathcal { D } ) \\propto \\prod _ { i = 1 } ^ { n } p ( \\pmb { y } _ { i } | f ( \\pmb { x } _ { i } ; \\mathbf { w } ) ) p ( \\mathbf { w } ) } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    990,
+                    1745,
+                    1090,
+                    1745,
+                    1090,
+                    1776,
+                    990,
+                    1776
+                ],
+                "score": 0.91,
+                "latex": "\\textbf { \\textit { y } } \\in \\textbf { \\textit { y } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    832,
+                    1805,
+                    894,
+                    1805,
+                    894,
+                    1838,
+                    832,
+                    1838
+                ],
+                "score": 0.91,
+                "latex": "p ( \\mathbf { w } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    824,
+                    1746,
+                    927,
+                    1746,
+                    927,
+                    1774,
+                    824,
+                    1774
+                ],
+                "score": 0.91,
+                "latex": "\\textbf { \\textit { x } } \\in \\textbf { \\textit { X } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    844,
+                    1839,
+                    877,
+                    1839,
+                    877,
+                    1864,
+                    844,
+                    1864
+                ],
+                "score": 0.86,
+                "latex": "\\mathbf { \\boldsymbol { x } } ^ { * }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1032,
+                    1039,
+                    1081,
+                    1039,
+                    1081,
+                    1072,
+                    1032,
+                    1072
+                ],
+                "score": 0.79,
+                "latex": "\\mathbb { \\left[ \\left] \\right. \\right]} 2 "
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    511,
+                    1867,
+                    538,
+                    1867,
+                    538,
+                    1894,
+                    511,
+                    1894
+                ],
+                "score": 0.76,
+                "latex": "\\widehat { \\bf w }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1060,
+                    918,
+                    1095,
+                    918,
+                    1095,
+                    954,
+                    1060,
+                    954
+                ],
+                "score": 0.42,
+                "latex": "\\boxed { \\mathrm { A } }"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    369.0,
+                    196.0,
+                    513.0,
+                    196.0,
+                    513.0,
+                    220.0,
+                    369.0,
+                    220.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    605.0,
+                    200.0,
+                    684.0,
+                    200.0,
+                    684.0,
+                    223.0,
+                    605.0,
+                    223.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    805.0,
+                    200.0,
+                    895.0,
+                    200.0,
+                    895.0,
+                    223.0,
+                    805.0,
+                    223.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1213.0,
+                    196.0,
+                    1305.0,
+                    196.0,
+                    1305.0,
+                    220.0,
+                    1213.0,
+                    220.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    794.0,
+                    258.0,
+                    819.0,
+                    258.0,
+                    819.0,
+                    270.0,
+                    794.0,
+                    270.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1000.0,
+                    259.0,
+                    1024.0,
+                    259.0,
+                    1024.0,
+                    267.0,
+                    1000.0,
+                    267.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    314.0,
+                    349.0,
+                    1383.0,
+                    349.0,
+                    1383.0,
+                    574.0,
+                    314.0,
+                    574.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    481.0,
+                    398.0,
+                    534.0,
+                    398.0,
+                    534.0,
+                    428.0,
+                    481.0,
+                    428.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1005.75,
+                    196.0,
+                    1104.75,
+                    196.0,
+                    1104.75,
+                    220.0,
+                    1005.75,
+                    220.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    565.0,
+                    1405.0,
+                    565.0,
+                    1405.0,
+                    601.0,
+                    293.0,
+                    601.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    596.0,
+                    1404.0,
+                    596.0,
+                    1404.0,
+                    634.0,
+                    293.0,
+                    634.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    625.0,
+                    1032.0,
+                    625.0,
+                    1032.0,
+                    664.0,
+                    292.0,
+                    664.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    289.0,
+                    1606.0,
+                    733.0,
+                    1606.0,
+                    733.0,
+                    1661.0,
+                    289.0,
+                    1661.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    838.0,
+                    2058.0,
+                    862.0,
+                    2058.0,
+                    862.0,
+                    2093.0,
+                    838.0,
+                    2093.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    838.0,
+                    2058.0,
+                    862.0,
+                    2058.0,
+                    862.0,
+                    2093.0,
+                    838.0,
+                    2093.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1682.0,
+                    1111.0,
+                    1682.0,
+                    1111.0,
+                    1719.0,
+                    294.0,
+                    1719.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1267.0,
+                    1682.0,
+                    1409.0,
+                    1682.0,
+                    1409.0,
+                    1719.0,
+                    1267.0,
+                    1719.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1715.0,
+                    1308.0,
+                    1715.0,
+                    1308.0,
+                    1748.0,
+                    295.0,
+                    1748.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1740.0,
+                    512.0,
+                    1740.0,
+                    512.0,
+                    1784.0,
+                    291.0,
+                    1784.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    751.0,
+                    1740.0,
+                    823.0,
+                    1740.0,
+                    823.0,
+                    1784.0,
+                    751.0,
+                    1784.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    928.0,
+                    1740.0,
+                    989.0,
+                    1740.0,
+                    989.0,
+                    1784.0,
+                    928.0,
+                    1784.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1091.0,
+                    1740.0,
+                    1412.0,
+                    1740.0,
+                    1412.0,
+                    1784.0,
+                    1091.0,
+                    1784.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1771.0,
+                    1407.0,
+                    1771.0,
+                    1407.0,
+                    1811.0,
+                    291.0,
+                    1811.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1805.0,
+                    297.0,
+                    1805.0,
+                    297.0,
+                    1842.0,
+                    292.0,
+                    1842.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    740.0,
+                    1805.0,
+                    831.0,
+                    1805.0,
+                    831.0,
+                    1842.0,
+                    740.0,
+                    1842.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    895.0,
+                    1805.0,
+                    1409.0,
+                    1805.0,
+                    1409.0,
+                    1842.0,
+                    895.0,
+                    1842.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1835.0,
+                    843.0,
+                    1835.0,
+                    843.0,
+                    1872.0,
+                    294.0,
+                    1872.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    878.0,
+                    1835.0,
+                    1407.0,
+                    1835.0,
+                    1407.0,
+                    1872.0,
+                    878.0,
+                    1872.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1866.0,
+                    510.0,
+                    1866.0,
+                    510.0,
+                    1900.0,
+                    294.0,
+                    1900.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    539.0,
+                    1866.0,
+                    656.0,
+                    1866.0,
+                    656.0,
+                    1900.0,
+                    539.0,
+                    1900.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    831.0,
+                    1866.0,
+                    1404.0,
+                    1866.0,
+                    1404.0,
+                    1900.0,
+                    831.0,
+                    1900.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1897.0,
+                    926.0,
+                    1897.0,
+                    926.0,
+                    1931.0,
+                    296.0,
+                    1931.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    829.0,
+                    1406.0,
+                    829.0,
+                    1406.0,
+                    864.0,
+                    294.0,
+                    864.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    859.0,
+                    1403.0,
+                    859.0,
+                    1403.0,
+                    893.0,
+                    294.0,
+                    893.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    890.0,
+                    1406.0,
+                    890.0,
+                    1406.0,
+                    924.0,
+                    294.0,
+                    924.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    919.0,
+                    1059.0,
+                    919.0,
+                    1059.0,
+                    954.0,
+                    294.0,
+                    954.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1096.0,
+                    919.0,
+                    1406.0,
+                    919.0,
+                    1406.0,
+                    954.0,
+                    1096.0,
+                    954.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    949.0,
+                    1405.0,
+                    949.0,
+                    1405.0,
+                    984.0,
+                    295.0,
+                    984.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    981.0,
+                    1406.0,
+                    981.0,
+                    1406.0,
+                    1016.0,
+                    295.0,
+                    1016.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1011.0,
+                    1406.0,
+                    1011.0,
+                    1406.0,
+                    1045.0,
+                    294.0,
+                    1045.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1041.0,
+                    1031.0,
+                    1041.0,
+                    1031.0,
+                    1074.0,
+                    292.0,
+                    1074.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1082.0,
+                    1041.0,
+                    1406.0,
+                    1041.0,
+                    1406.0,
+                    1074.0,
+                    1082.0,
+                    1074.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1071.0,
+                    1403.0,
+                    1071.0,
+                    1403.0,
+                    1105.0,
+                    294.0,
+                    1105.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1100.0,
+                    1405.0,
+                    1100.0,
+                    1405.0,
+                    1137.0,
+                    292.0,
+                    1137.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1133.0,
+                    685.0,
+                    1133.0,
+                    685.0,
+                    1166.0,
+                    293.0,
+                    1166.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    368.0,
+                    1231.0,
+                    1405.0,
+                    1231.0,
+                    1405.0,
+                    1272.0,
+                    368.0,
+                    1272.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    395.0,
+                    1267.0,
+                    1303.0,
+                    1267.0,
+                    1303.0,
+                    1300.0,
+                    395.0,
+                    1300.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    368.0,
+                    1306.0,
+                    1404.0,
+                    1306.0,
+                    1404.0,
+                    1347.0,
+                    368.0,
+                    1347.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1343.0,
+                    990.0,
+                    1343.0,
+                    990.0,
+                    1377.0,
+                    394.0,
+                    1377.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    368.0,
+                    1383.0,
+                    1404.0,
+                    1383.0,
+                    1404.0,
+                    1421.0,
+                    368.0,
+                    1421.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1416.0,
+                    842.0,
+                    1416.0,
+                    842.0,
+                    1452.0,
+                    394.0,
+                    1452.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    369.0,
+                    1460.0,
+                    1404.0,
+                    1460.0,
+                    1404.0,
+                    1496.0,
+                    369.0,
+                    1496.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    395.0,
+                    1493.0,
+                    1404.0,
+                    1493.0,
+                    1404.0,
+                    1527.0,
+                    395.0,
+                    1527.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    395.0,
+                    1523.0,
+                    655.0,
+                    1523.0,
+                    655.0,
+                    1556.0,
+                    395.0,
+                    1556.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    722.0,
+                    1404.0,
+                    722.0,
+                    1404.0,
+                    756.0,
+                    295.0,
+                    756.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    750.0,
+                    1404.0,
+                    750.0,
+                    1404.0,
+                    789.0,
+                    294.0,
+                    789.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    783.0,
+                    960.0,
+                    783.0,
+                    960.0,
+                    819.0,
+                    294.0,
+                    819.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1174.0,
+                    720.0,
+                    1174.0,
+                    720.0,
+                    1213.0,
+                    296.0,
+                    1213.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 1,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    497,
+                    1405,
+                    497,
+                    1405,
+                    805,
+                    297,
+                    805
+                ],
+                "score": 0.983
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    817,
+                    1406,
+                    817,
+                    1406,
+                    1124,
+                    298,
+                    1124
+                ],
+                "score": 0.983
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1588,
+                    1406,
+                    1588,
+                    1406,
+                    1774,
+                    297,
+                    1774
+                ],
+                "score": 0.981
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1282,
+                    1408,
+                    1282,
+                    1408,
+                    1499,
+                    298,
+                    1499
+                ],
+                "score": 0.979
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    202,
+                    1406,
+                    202,
+                    1406,
+                    387,
+                    296,
+                    387
+                ],
+                "score": 0.979
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    361,
+                    1145,
+                    1220,
+                    1145,
+                    1220,
+                    1263,
+                    361,
+                    1263
+                ],
+                "score": 0.955
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    612,
+                    1953,
+                    1088,
+                    1953,
+                    1088,
+                    2017,
+                    612,
+                    2017
+                ],
+                "score": 0.948
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1872,
+                    1405,
+                    1872,
+                    1405,
+                    1940,
+                    296,
+                    1940
+                ],
+                "score": 0.945
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    511,
+                    1788,
+                    1181,
+                    1788,
+                    1181,
+                    1859,
+                    511,
+                    1859
+                ],
+                "score": 0.943
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    635,
+                    399,
+                    1063,
+                    399,
+                    1063,
+                    486,
+                    635,
+                    486
+                ],
+                "score": 0.942
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    300,
+                    1533,
+                    732,
+                    1533,
+                    732,
+                    1567,
+                    300,
+                    1567
+                ],
+                "score": 0.924
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1366,
+                    450,
+                    1400,
+                    450,
+                    1400,
+                    479,
+                    1366,
+                    479
+                ],
+                "score": 0.897
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1366,
+                    1808,
+                    1400,
+                    1808,
+                    1400,
+                    1838,
+                    1366,
+                    1838
+                ],
+                "score": 0.878
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2061,
+                    859,
+                    2061,
+                    859,
+                    2085,
+                    841,
+                    2085
+                ],
+                "score": 0.669
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2061,
+                    859,
+                    2061,
+                    859,
+                    2085,
+                    841,
+                    2085
+                ],
+                "score": 0.485
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    611,
+                    1951,
+                    1087,
+                    1951,
+                    1087,
+                    2017,
+                    611,
+                    2017
+                ],
+                "score": 0.94,
+                "latex": "\\nabla _ { \\mathbf { w } _ { i } ^ { t } } k ( \\mathbf { w } _ { i } ^ { t } , \\mathbf { w } _ { j } ^ { t } ) = \\frac { 2 } { h } ( \\mathbf { w } _ { j } ^ { t } - \\mathbf { w } _ { i } ^ { t } ) k ( \\mathbf { w } _ { i } ^ { t } , \\mathbf { w } _ { j } ^ { t } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    944,
+                    324,
+                    1043,
+                    324,
+                    1043,
+                    358,
+                    944,
+                    358
+                ],
+                "score": 0.93,
+                "latex": "\\{ { \\bf w } _ { i } \\} _ { i = 1 } ^ { n }"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    511,
+                    1785,
+                    1189,
+                    1785,
+                    1189,
+                    1862,
+                    511,
+                    1862
+                ],
+                "score": 0.92,
+                "latex": "\\phi ( \\mathbf { w } _ { i } ^ { t } ) = \\nabla _ { \\mathbf { w } _ { i } ^ { t } } \\log p ( \\mathbf { w } _ { i } ^ { t } | \\mathcal { D } ) - \\mathcal { R } \\left( \\left\\{ \\nabla _ { \\mathbf { w } _ { i } ^ { t } } k ( \\mathbf { w } _ { i } ^ { t } , \\mathbf { w } _ { j } ^ { t } ) \\right\\} _ { j = 1 } ^ { n } \\right) ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    374,
+                    1902,
+                    797,
+                    1902,
+                    797,
+                    1940,
+                    374,
+                    1940
+                ],
+                "score": 0.92,
+                "latex": "\\begin{array} { r } { k ( \\mathbf { w } _ { i } , \\mathbf { w } _ { j } ) = \\exp \\big ( - \\frac { 1 } { h } | | \\mathbf { w } _ { i } - \\mathbf { w } _ { j } | | ^ { 2 } \\big ) } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1104,
+                    323,
+                    1206,
+                    323,
+                    1206,
+                    355,
+                    1104,
+                    355
+                ],
+                "score": 0.92,
+                "latex": "{ \\bf w } _ { i } \\in \\mathbb { R } ^ { d }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    659,
+                    1710,
+                    914,
+                    1710,
+                    914,
+                    1745,
+                    659,
+                    1745
+                ],
+                "score": 0.91,
+                "latex": "\\bar { k } ( \\cdot , \\cdot ) : \\mathbb { R } ^ { d } \\times \\mathbb { R } ^ { d } \\to \\mathbb { R }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    991,
+                    1909,
+                    1008,
+                    1909,
+                    1008,
+                    1931,
+                    991,
+                    1931
+                ],
+                "score": 0.87,
+                "latex": "h"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    817,
+                    296,
+                    846,
+                    296,
+                    846,
+                    322,
+                    817,
+                    322
+                ],
+                "score": 0.83,
+                "latex": "K"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    635,
+                    397,
+                    1064,
+                    397,
+                    1064,
+                    492,
+                    635,
+                    492
+                ],
+                "score": 0.83,
+                "latex": "\\begin{array} { r l } & { \\mathbf { w } _ { i } ^ { t + 1 }  \\mathbf { w } _ { i } ^ { t } + \\epsilon _ { t } \\phi ( \\mathbf { w } _ { i } ^ { t } ) } \\\\ { \\mathrm { w i t h } \\quad } & { \\phi ( \\mathbf { w } _ { i } ^ { t } ) = \\nabla _ { \\mathbf { w } _ { i } ^ { t } } \\log p ( \\mathbf { w } _ { i } ^ { t } | \\mathcal { D } ) , } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    586,
+                    1743,
+                    613,
+                    1743,
+                    613,
+                    1769,
+                    586,
+                    1769
+                ],
+                "score": 0.82,
+                "latex": "\\mathcal { R }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1352,
+                    621,
+                    1400,
+                    621,
+                    1400,
+                    653,
+                    1352,
+                    653
+                ],
+                "score": 0.82,
+                "latex": "\\pmb { \\Vert 8 2 \\Vert }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    453,
+                    505,
+                    477,
+                    505,
+                    477,
+                    531,
+                    453,
+                    531
+                ],
+                "score": 0.82,
+                "latex": "\\epsilon _ { t }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    524,
+                    529,
+                    573,
+                    529,
+                    573,
+                    562,
+                    524,
+                    562
+                ],
+                "score": 0.78,
+                "latex": "\\pm 2 \\|"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1272,
+                    743,
+                    1320,
+                    743,
+                    1320,
+                    774,
+                    1272,
+                    774
+                ],
+                "score": 0.78,
+                "latex": "\\mathbb { [ \\breve { ] { ] \\mathrm { ~ Z ~ Z ~ } ] } } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1133,
+                    711,
+                    1182,
+                    711,
+                    1182,
+                    743,
+                    1133,
+                    743
+                ],
+                "score": 0.77,
+                "latex": "[ \\overline { { 1 8 } } ]"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1327,
+                    358,
+                    1339,
+                    358,
+                    1339,
+                    382,
+                    1327,
+                    382
+                ],
+                "score": 0.77,
+                "latex": "t"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    752,
+                    590,
+                    800,
+                    590,
+                    800,
+                    622,
+                    752,
+                    622
+                ],
+                "score": 0.75,
+                "latex": "\\mathbb { \\lVert \\rVert }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1074,
+                    938,
+                    1123,
+                    938,
+                    1123,
+                    970,
+                    1074,
+                    970
+                ],
+                "score": 0.69,
+                "latex": " { \\mathbb { I } }  { \\mathbb { I } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    548,
+                    590,
+                    582,
+                    590,
+                    582,
+                    626,
+                    548,
+                    626
+                ],
+                "score": 0.69,
+                "latex": "\\mathbb { D }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    442,
+                    330,
+                    462,
+                    330,
+                    462,
+                    352,
+                    442,
+                    352
+                ],
+                "score": 0.61,
+                "latex": "n"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    770,
+                    1283,
+                    820,
+                    1283,
+                    820,
+                    1316,
+                    770,
+                    1316
+                ],
+                "score": 0.57,
+                "latex": "\\pmb { \\left. \\pmb { \\left. \\bar { 2 5 } \\right. } \\right. }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1162,
+                    968,
+                    1211,
+                    968,
+                    1211,
+                    1001,
+                    1162,
+                    1001
+                ],
+                "score": 0.56,
+                "latex": "\\overline { { \\| 6 3 \\| } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    419,
+                    1619,
+                    468,
+                    1619,
+                    468,
+                    1652,
+                    419,
+                    1652
+                ],
+                "score": 0.48,
+                "latex": "\\mathbb { \\left[ \\left[ 5 1 \\right] \\right] }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    681,
+                    938,
+                    730,
+                    938,
+                    730,
+                    971,
+                    681,
+                    971
+                ],
+                "score": 0.31,
+                "latex": "\\pmb { \\mathbb { B 3 } }"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1527.0,
+                    735.0,
+                    1527.0,
+                    735.0,
+                    1576.0,
+                    292.0,
+                    1576.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    838.0,
+                    2058.0,
+                    862.0,
+                    2058.0,
+                    862.0,
+                    2091.0,
+                    838.0,
+                    2091.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    838.0,
+                    2058.0,
+                    862.0,
+                    2058.0,
+                    862.0,
+                    2091.0,
+                    838.0,
+                    2091.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    498.0,
+                    452.0,
+                    498.0,
+                    452.0,
+                    538.0,
+                    294.0,
+                    538.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    478.0,
+                    498.0,
+                    1407.0,
+                    498.0,
+                    1407.0,
+                    538.0,
+                    478.0,
+                    538.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    526.0,
+                    523.0,
+                    526.0,
+                    523.0,
+                    568.0,
+                    294.0,
+                    568.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    574.0,
+                    526.0,
+                    1406.0,
+                    526.0,
+                    1406.0,
+                    568.0,
+                    574.0,
+                    568.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    562.0,
+                    1403.0,
+                    562.0,
+                    1403.0,
+                    594.0,
+                    296.0,
+                    594.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    587.0,
+                    547.0,
+                    587.0,
+                    547.0,
+                    629.0,
+                    292.0,
+                    629.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    583.0,
+                    587.0,
+                    751.0,
+                    587.0,
+                    751.0,
+                    629.0,
+                    583.0,
+                    629.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    801.0,
+                    587.0,
+                    1407.0,
+                    587.0,
+                    1407.0,
+                    629.0,
+                    801.0,
+                    629.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    620.0,
+                    1351.0,
+                    620.0,
+                    1351.0,
+                    656.0,
+                    295.0,
+                    656.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    648.0,
+                    1410.0,
+                    648.0,
+                    1410.0,
+                    691.0,
+                    292.0,
+                    691.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    679.0,
+                    1406.0,
+                    679.0,
+                    1406.0,
+                    717.0,
+                    294.0,
+                    717.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    711.0,
+                    1132.0,
+                    711.0,
+                    1132.0,
+                    747.0,
+                    295.0,
+                    747.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1183.0,
+                    711.0,
+                    1405.0,
+                    711.0,
+                    1405.0,
+                    747.0,
+                    1183.0,
+                    747.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    742.0,
+                    1271.0,
+                    742.0,
+                    1271.0,
+                    776.0,
+                    294.0,
+                    776.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1321.0,
+                    742.0,
+                    1405.0,
+                    742.0,
+                    1405.0,
+                    776.0,
+                    1321.0,
+                    776.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    771.0,
+                    1391.0,
+                    771.0,
+                    1391.0,
+                    808.0,
+                    292.0,
+                    808.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    817.0,
+                    1408.0,
+                    817.0,
+                    1408.0,
+                    854.0,
+                    293.0,
+                    854.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    850.0,
+                    1404.0,
+                    850.0,
+                    1404.0,
+                    881.0,
+                    296.0,
+                    881.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    878.0,
+                    1406.0,
+                    878.0,
+                    1406.0,
+                    913.0,
+                    295.0,
+                    913.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    908.0,
+                    1406.0,
+                    908.0,
+                    1406.0,
+                    944.0,
+                    295.0,
+                    944.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    939.0,
+                    680.0,
+                    939.0,
+                    680.0,
+                    974.0,
+                    293.0,
+                    974.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    731.0,
+                    939.0,
+                    1073.0,
+                    939.0,
+                    1073.0,
+                    974.0,
+                    731.0,
+                    974.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1124.0,
+                    939.0,
+                    1408.0,
+                    939.0,
+                    1408.0,
+                    974.0,
+                    1124.0,
+                    974.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    967.0,
+                    1161.0,
+                    967.0,
+                    1161.0,
+                    1004.0,
+                    293.0,
+                    1004.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1212.0,
+                    967.0,
+                    1406.0,
+                    967.0,
+                    1406.0,
+                    1004.0,
+                    1212.0,
+                    1004.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1002.0,
+                    1404.0,
+                    1002.0,
+                    1404.0,
+                    1034.0,
+                    296.0,
+                    1034.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1030.0,
+                    1404.0,
+                    1030.0,
+                    1404.0,
+                    1066.0,
+                    295.0,
+                    1066.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1061.0,
+                    1406.0,
+                    1061.0,
+                    1406.0,
+                    1096.0,
+                    295.0,
+                    1096.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1089.0,
+                    521.0,
+                    1089.0,
+                    521.0,
+                    1128.0,
+                    295.0,
+                    1128.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1587.0,
+                    1406.0,
+                    1587.0,
+                    1406.0,
+                    1624.0,
+                    292.0,
+                    1624.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1617.0,
+                    418.0,
+                    1617.0,
+                    418.0,
+                    1655.0,
+                    294.0,
+                    1655.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    469.0,
+                    1617.0,
+                    1406.0,
+                    1617.0,
+                    1406.0,
+                    1655.0,
+                    469.0,
+                    1655.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1652.0,
+                    1406.0,
+                    1652.0,
+                    1406.0,
+                    1684.0,
+                    295.0,
+                    1684.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1678.0,
+                    1407.0,
+                    1678.0,
+                    1407.0,
+                    1715.0,
+                    294.0,
+                    1715.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1705.0,
+                    658.0,
+                    1705.0,
+                    658.0,
+                    1749.0,
+                    292.0,
+                    1749.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    915.0,
+                    1705.0,
+                    1408.0,
+                    1705.0,
+                    1408.0,
+                    1749.0,
+                    915.0,
+                    1749.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1741.0,
+                    585.0,
+                    1741.0,
+                    585.0,
+                    1777.0,
+                    294.0,
+                    1777.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    614.0,
+                    1741.0,
+                    1090.0,
+                    1741.0,
+                    1090.0,
+                    1777.0,
+                    614.0,
+                    1777.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1282.0,
+                    769.0,
+                    1282.0,
+                    769.0,
+                    1320.0,
+                    295.0,
+                    1320.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    821.0,
+                    1282.0,
+                    1405.0,
+                    1282.0,
+                    1405.0,
+                    1320.0,
+                    821.0,
+                    1320.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1315.0,
+                    1405.0,
+                    1315.0,
+                    1405.0,
+                    1351.0,
+                    293.0,
+                    1351.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1347.0,
+                    1404.0,
+                    1347.0,
+                    1404.0,
+                    1378.0,
+                    296.0,
+                    1378.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1374.0,
+                    1405.0,
+                    1374.0,
+                    1405.0,
+                    1410.0,
+                    293.0,
+                    1410.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1404.0,
+                    1406.0,
+                    1404.0,
+                    1406.0,
+                    1441.0,
+                    293.0,
+                    1441.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1436.0,
+                    1410.0,
+                    1436.0,
+                    1410.0,
+                    1471.0,
+                    293.0,
+                    1471.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1465.0,
+                    1041.0,
+                    1465.0,
+                    1041.0,
+                    1502.0,
+                    292.0,
+                    1502.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    199.0,
+                    1407.0,
+                    199.0,
+                    1407.0,
+                    242.0,
+                    291.0,
+                    242.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    233.0,
+                    1406.0,
+                    233.0,
+                    1406.0,
+                    269.0,
+                    295.0,
+                    269.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    264.0,
+                    1406.0,
+                    264.0,
+                    1406.0,
+                    297.0,
+                    294.0,
+                    297.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    293.0,
+                    816.0,
+                    293.0,
+                    816.0,
+                    329.0,
+                    293.0,
+                    329.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    847.0,
+                    293.0,
+                    1409.0,
+                    293.0,
+                    1409.0,
+                    329.0,
+                    847.0,
+                    329.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    290.0,
+                    317.0,
+                    441.0,
+                    317.0,
+                    441.0,
+                    366.0,
+                    290.0,
+                    366.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    463.0,
+                    317.0,
+                    943.0,
+                    317.0,
+                    943.0,
+                    366.0,
+                    463.0,
+                    366.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1044.0,
+                    317.0,
+                    1103.0,
+                    317.0,
+                    1103.0,
+                    366.0,
+                    1044.0,
+                    366.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1207.0,
+                    317.0,
+                    1411.0,
+                    317.0,
+                    1411.0,
+                    366.0,
+                    1207.0,
+                    366.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    354.0,
+                    1326.0,
+                    354.0,
+                    1326.0,
+                    390.0,
+                    295.0,
+                    390.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1340.0,
+                    354.0,
+                    1353.0,
+                    354.0,
+                    1353.0,
+                    390.0,
+                    1340.0,
+                    390.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    363.0,
+                    1146.0,
+                    793.0,
+                    1146.0,
+                    793.0,
+                    1178.0,
+                    363.0,
+                    1178.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    358.0,
+                    1184.0,
+                    1103.0,
+                    1184.0,
+                    1103.0,
+                    1224.0,
+                    358.0,
+                    1224.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    358.0,
+                    1226.0,
+                    1221.0,
+                    1226.0,
+                    1221.0,
+                    1265.0,
+                    358.0,
+                    1265.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1873.0,
+                    1405.0,
+                    1873.0,
+                    1405.0,
+                    1906.0,
+                    296.0,
+                    1906.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1901.0,
+                    373.0,
+                    1901.0,
+                    373.0,
+                    1941.0,
+                    294.0,
+                    1941.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    798.0,
+                    1901.0,
+                    990.0,
+                    1901.0,
+                    990.0,
+                    1941.0,
+                    798.0,
+                    1941.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1009.0,
+                    1901.0,
+                    1320.0,
+                    1901.0,
+                    1320.0,
+                    1941.0,
+                    1009.0,
+                    1941.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 2,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    481,
+                    1407,
+                    481,
+                    1407,
+                    791,
+                    296,
+                    791
+                ],
+                "score": 0.984
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    201,
+                    1406,
+                    201,
+                    1406,
+                    394,
+                    296,
+                    394
+                ],
+                "score": 0.981
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1627,
+                    1406,
+                    1627,
+                    1406,
+                    1751,
+                    297,
+                    1751
+                ],
+                "score": 0.98
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1117,
+                    1404,
+                    1117,
+                    1404,
+                    1274,
+                    298,
+                    1274
+                ],
+                "score": 0.978
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1883,
+                    1403,
+                    1883,
+                    1403,
+                    2010,
+                    298,
+                    2010
+                ],
+                "score": 0.977
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    305,
+                    931,
+                    1400,
+                    931,
+                    1400,
+                    1025,
+                    305,
+                    1025
+                ],
+                "score": 0.97
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    481,
+                    1524,
+                    1214,
+                    1524,
+                    1214,
+                    1614,
+                    481,
+                    1614
+                ],
+                "score": 0.957
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1031,
+                    1399,
+                    1031,
+                    1399,
+                    1100,
+                    298,
+                    1100
+                ],
+                "score": 0.951
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    425,
+                    1763,
+                    1268,
+                    1763,
+                    1268,
+                    1855,
+                    425,
+                    1855
+                ],
+                "score": 0.951
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    390,
+                    1309,
+                    1307,
+                    1309,
+                    1307,
+                    1391,
+                    390,
+                    1391
+                ],
+                "score": 0.943
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    297,
+                    1421,
+                    946,
+                    1421,
+                    946,
+                    1456,
+                    297,
+                    1456
+                ],
+                "score": 0.929
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    300,
+                    427,
+                    751,
+                    427,
+                    751,
+                    461,
+                    300,
+                    461
+                ],
+                "score": 0.928
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    1474,
+                    1354,
+                    1474,
+                    1354,
+                    1511,
+                    295,
+                    1511
+                ],
+                "score": 0.925
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    470,
+                    803,
+                    1220,
+                    803,
+                    1220,
+                    919,
+                    470,
+                    919
+                ],
+                "score": 0.901
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1366,
+                    1551,
+                    1400,
+                    1551,
+                    1400,
+                    1581,
+                    1366,
+                    1581
+                ],
+                "score": 0.89
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1366,
+                    869,
+                    1400,
+                    869,
+                    1400,
+                    898,
+                    1366,
+                    898
+                ],
+                "score": 0.881
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1366,
+                    1795,
+                    1400,
+                    1795,
+                    1400,
+                    1825,
+                    1366,
+                    1825
+                ],
+                "score": 0.87
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1365,
+                    1338,
+                    1401,
+                    1338,
+                    1401,
+                    1368,
+                    1365,
+                    1368
+                ],
+                "score": 0.842
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    840,
+                    2061,
+                    858,
+                    2061,
+                    858,
+                    2084,
+                    840,
+                    2084
+                ],
+                "score": 0.778
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    588,
+                    802,
+                    844,
+                    802,
+                    844,
+                    844,
+                    588,
+                    844
+                ],
+                "score": 0.264
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    482,
+                    1521,
+                    1217,
+                    1521,
+                    1217,
+                    1617,
+                    482,
+                    1617
+                ],
+                "score": 0.94,
+                "latex": "\\phi ( \\mathbf { w } _ { i } ^ { t } ) = \\sum _ { j = 1 } ^ { n } k ( \\mathbf { w } _ { i } ^ { t } , \\mathbf { w } _ { j } ^ { t } ) \\nabla _ { \\mathbf { w } _ { i } ^ { t } } \\log p ( \\mathbf { w } _ { i } ^ { t } | \\mathcal { D } ) + \\sum _ { j = 1 } ^ { n } \\nabla _ { \\mathbf { w } _ { j } ^ { t } } k ( \\mathbf { w } _ { j } ^ { t } , \\mathbf { w } _ { i } ^ { t } ) ."
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    429,
+                    1761,
+                    1270,
+                    1761,
+                    1270,
+                    1858,
+                    429,
+                    1858
+                ],
+                "score": 0.94,
+                "latex": "\\phi ( \\mathbf { w } _ { i } ^ { t } ) = \\left( \\frac { \\partial f _ { i } ^ { t } } { \\partial \\mathbf { w } _ { i } ^ { t } } \\right) ^ { \\top } \\left( \\frac { 1 } { n } \\sum _ { j = 1 } ^ { n } k ( f _ { i } ^ { t } , f _ { j } ^ { t } ) \\nabla _ { f _ { j } ^ { t } } \\log p ( f _ { j } ^ { t } | \\mathcal { D } ) + \\nabla _ { f _ { j } ^ { t } } k ( f _ { i } ^ { t } , f _ { j } ^ { t } ) \\right) ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    771,
+                    515,
+                    967,
+                    515,
+                    967,
+                    548,
+                    771,
+                    548
+                ],
+                "score": 0.93,
+                "latex": "f : \\mathbf { w } \\mapsto f ( \\cdot ; \\mathbf { w } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    590,
+                    1064,
+                    826,
+                    1064,
+                    826,
+                    1099,
+                    590,
+                    1099
+                ],
+                "score": 0.93,
+                "latex": "\\pi _ { A } ( f ) = \\{ f ( a ) \\} _ { a \\in A }"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    392,
+                    1306,
+                    1307,
+                    1306,
+                    1307,
+                    1391,
+                    392,
+                    1391
+                ],
+                "score": 0.93,
+                "latex": "\\phi ( { \\mathbf w } _ { i } ^ { t } ) = \\left( \\frac { \\partial f _ { i } ^ { t } } { \\partial { \\mathbf w } _ { i } ^ { t } } \\right) ^ { \\top } \\left[ \\nabla _ { f _ { i } ^ { t } } \\log p ( f _ { i } ^ { t } | { \\mathcal D } ) - { \\mathcal R } \\left( \\left\\{ \\nabla _ { f _ { i } ^ { t } } k ( \\pi _ { B } ( f _ { i } ^ { t } ) , \\pi _ { B } ( f _ { j } ^ { t } ) ) \\right\\} _ { j = 1 } ^ { n } \\right) \\right] ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1078,
+                    262,
+                    1345,
+                    262,
+                    1345,
+                    302,
+                    1078,
+                    302
+                ],
+                "score": 0.92,
+                "latex": "\\begin{array} { r } { \\beta \\sum _ { j = 1 } ^ { n } \\nabla _ { \\mathbf { w } _ { i } ^ { t } } k ( \\mathbf { w } _ { i } ^ { t } , \\mathbf { w } _ { j } ^ { t } ) } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    367,
+                    608,
+                    458,
+                    608,
+                    458,
+                    642,
+                    367,
+                    642
+                ],
+                "score": 0.92,
+                "latex": "\\{ f _ { i } \\} _ { i = 1 } ^ { n }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    755,
+                    729,
+                    841,
+                    729,
+                    841,
+                    763,
+                    755,
+                    763
+                ],
+                "score": 0.92,
+                "latex": "p ( \\pmb { f } | \\mathcal { D } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1237,
+                    547,
+                    1403,
+                    547,
+                    1403,
+                    581,
+                    1237,
+                    581
+                ],
+                "score": 0.92,
+                "latex": "f _ { i } : = f ( \\cdot ; { \\mathbf w } _ { i } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    860,
+                    639,
+                    971,
+                    639,
+                    971,
+                    671,
+                    860,
+                    671
+                ],
+                "score": 0.92,
+                "latex": "p ( \\pmb { y } | \\pmb { x } , \\pmb { f } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    520,
+                    609,
+                    598,
+                    609,
+                    598,
+                    640,
+                    520,
+                    640
+                ],
+                "score": 0.92,
+                "latex": "\\pmb { f } \\in \\mathcal { F }"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    506,
+                    798,
+                    1227,
+                    798,
+                    1227,
+                    923,
+                    506,
+                    923
+                ],
+                "score": 0.92,
+                "latex": "\\begin{array} { r l } & { f _ { i } ^ { t + 1 } \\gets f _ { i } ^ { t } + \\epsilon _ { t } \\phi ( f _ { i } ^ { t } ) } \\\\ { \\mathrm { t h } \\quad } & { \\phi ( f _ { i } ^ { t } ) = \\nabla _ { f _ { i } ^ { t } } \\log p ( f _ { i } ^ { t } | \\mathcal { D } ) - \\mathcal { R } \\left( \\left\\{ \\nabla _ { f _ { i } ^ { t } } k ( f _ { i } ^ { t } , f _ { j } ^ { t } ) \\right\\} _ { j = 1 } ^ { n } \\right) . } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1331,
+                    609,
+                    1398,
+                    609,
+                    1398,
+                    641,
+                    1331,
+                    641
+                ],
+                "score": 0.91,
+                "latex": "k ( \\cdot , \\cdot )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1024,
+                    1030,
+                    1207,
+                    1030,
+                    1207,
+                    1064,
+                    1024,
+                    1064
+                ],
+                "score": 0.91,
+                "latex": "\\pi _ { A } : \\mathbb { R } ^ { \\mathcal { X } } \\to \\mathbb { R } ^ { A }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1165,
+                    699,
+                    1226,
+                    699,
+                    1226,
+                    733,
+                    1165,
+                    733
+                ],
+                "score": 0.91,
+                "latex": "p ( \\mathbf { w } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    298,
+                    389,
+                    298,
+                    389,
+                    333,
+                    298,
+                    333
+                ],
+                "score": 0.91,
+                "latex": "\\beta \\in \\mathbb { R } _ { * } ^ { + }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    853,
+                    671,
+                    909,
+                    671,
+                    909,
+                    702,
+                    853,
+                    702
+                ],
+                "score": 0.91,
+                "latex": "p ( f )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    1149,
+                    507,
+                    1149,
+                    507,
+                    1186,
+                    298,
+                    1186
+                ],
+                "score": 0.91,
+                "latex": "k \\big ( \\pi _ { B } ( f ) , \\pi _ { B } ( f ^ { \\prime } ) \\big )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1287,
+                    640,
+                    1403,
+                    640,
+                    1403,
+                    672,
+                    1287,
+                    672
+                ],
+                "score": 0.91,
+                "latex": "p ( \\pmb { y } | \\pmb { x } , \\mathbf { w } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    386,
+                    545,
+                    479,
+                    545,
+                    479,
+                    576,
+                    386,
+                    576
+                ],
+                "score": 0.9,
+                "latex": "\\mathbf { w } \\in \\mathbb { R } ^ { d }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    829,
+                    208,
+                    867,
+                    208,
+                    867,
+                    237,
+                    829,
+                    237
+                ],
+                "score": 0.88,
+                "latex": "{ \\bf w } _ { j }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    814,
+                    1033,
+                    898,
+                    1033,
+                    898,
+                    1062,
+                    814,
+                    1062
+                ],
+                "score": 0.88,
+                "latex": "A \\subset { \\mathcal { X } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    866,
+                    582,
+                    901,
+                    582,
+                    901,
+                    609,
+                    866,
+                    609
+                ],
+                "score": 0.87,
+                "latex": "\\mathbf { w } _ { i }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    372,
+                    208,
+                    408,
+                    208,
+                    408,
+                    234,
+                    372,
+                    234
+                ],
+                "score": 0.86,
+                "latex": "\\mathbf { w } _ { i }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    872,
+                    301,
+                    893,
+                    301,
+                    893,
+                    332,
+                    872,
+                    332
+                ],
+                "score": 0.84,
+                "latex": "\\beta"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1169,
+                    332,
+                    1196,
+                    332,
+                    1196,
+                    358,
+                    1169,
+                    358
+                ],
+                "score": 0.84,
+                "latex": "\\mathcal { R }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1141,
+                    483,
+                    1176,
+                    483,
+                    1176,
+                    519,
+                    1141,
+                    519
+                ],
+                "score": 0.83,
+                "latex": "\\textcircled { 3 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    497,
+                    235,
+                    524,
+                    235,
+                    524,
+                    261,
+                    497,
+                    261
+                ],
+                "score": 0.83,
+                "latex": "\\mathcal { R }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    573,
+                    1151,
+                    599,
+                    1151,
+                    599,
+                    1178,
+                    573,
+                    1178
+                ],
+                "score": 0.81,
+                "latex": "B"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    806,
+                    1977,
+                    841,
+                    1977,
+                    841,
+                    2011,
+                    806,
+                    2011
+                ],
+                "score": 0.8,
+                "latex": "\\textcircled{7}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1207,
+                    1914,
+                    1242,
+                    1914,
+                    1242,
+                    1950,
+                    1207,
+                    1950
+                ],
+                "score": 0.79,
+                "latex": "\\textcircled{6}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    648,
+                    296,
+                    674,
+                    296,
+                    674,
+                    337,
+                    648,
+                    337
+                ],
+                "score": 0.79,
+                "latex": "\\begin{array} { l } { 3 } \\\\ { . } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1027,
+                    1243,
+                    1039,
+                    1243,
+                    1039,
+                    1268,
+                    1027,
+                    1268
+                ],
+                "score": 0.76,
+                "latex": "i"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1155,
+                    584,
+                    1175,
+                    584,
+                    1175,
+                    606,
+                    1155,
+                    606
+                ],
+                "score": 0.75,
+                "latex": "n"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    473,
+                    1066,
+                    496,
+                    1066,
+                    496,
+                    1092,
+                    473,
+                    1092
+                ],
+                "score": 0.69,
+                "latex": "A"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    823,
+                    1719,
+                    872,
+                    1719,
+                    872,
+                    1749,
+                    823,
+                    1749
+                ],
+                "score": 0.43,
+                "latex": "\\pmb { \\mathbb { Z } } 6 \\|"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    806,
+                    1481,
+                    852,
+                    1481,
+                    852,
+                    1508,
+                    806,
+                    1508
+                ],
+                "score": 0.34,
+                "latex": "\\mathbb { \\left[ 5 1 \\right] }"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1418.0,
+                    948.0,
+                    1418.0,
+                    948.0,
+                    1461.0,
+                    292.0,
+                    1461.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    424.0,
+                    754.0,
+                    424.0,
+                    754.0,
+                    467.0,
+                    294.0,
+                    467.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    838.0,
+                    2058.0,
+                    863.0,
+                    2058.0,
+                    863.0,
+                    2091.0,
+                    838.0,
+                    2091.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    484.0,
+                    1140.0,
+                    484.0,
+                    1140.0,
+                    519.0,
+                    295.0,
+                    519.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1177.0,
+                    484.0,
+                    1405.0,
+                    484.0,
+                    1405.0,
+                    519.0,
+                    1177.0,
+                    519.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    516.0,
+                    770.0,
+                    516.0,
+                    770.0,
+                    548.0,
+                    296.0,
+                    548.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    968.0,
+                    516.0,
+                    1405.0,
+                    516.0,
+                    1405.0,
+                    548.0,
+                    968.0,
+                    548.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    545.0,
+                    385.0,
+                    545.0,
+                    385.0,
+                    583.0,
+                    293.0,
+                    583.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    480.0,
+                    545.0,
+                    1236.0,
+                    545.0,
+                    1236.0,
+                    583.0,
+                    480.0,
+                    583.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1404.0,
+                    545.0,
+                    1407.0,
+                    545.0,
+                    1407.0,
+                    583.0,
+                    1404.0,
+                    583.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    576.0,
+                    865.0,
+                    576.0,
+                    865.0,
+                    613.0,
+                    294.0,
+                    613.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    902.0,
+                    576.0,
+                    1154.0,
+                    576.0,
+                    1154.0,
+                    613.0,
+                    902.0,
+                    613.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1176.0,
+                    576.0,
+                    1407.0,
+                    576.0,
+                    1407.0,
+                    613.0,
+                    1176.0,
+                    613.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    290.0,
+                    601.0,
+                    366.0,
+                    601.0,
+                    366.0,
+                    649.0,
+                    290.0,
+                    649.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    459.0,
+                    601.0,
+                    519.0,
+                    601.0,
+                    519.0,
+                    649.0,
+                    459.0,
+                    649.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    599.0,
+                    601.0,
+                    1330.0,
+                    601.0,
+                    1330.0,
+                    649.0,
+                    599.0,
+                    649.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1399.0,
+                    601.0,
+                    1412.0,
+                    601.0,
+                    1412.0,
+                    649.0,
+                    1399.0,
+                    649.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    636.0,
+                    859.0,
+                    636.0,
+                    859.0,
+                    674.0,
+                    293.0,
+                    674.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    972.0,
+                    636.0,
+                    1286.0,
+                    636.0,
+                    1286.0,
+                    674.0,
+                    972.0,
+                    674.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1404.0,
+                    636.0,
+                    1407.0,
+                    636.0,
+                    1407.0,
+                    674.0,
+                    1404.0,
+                    674.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    663.0,
+                    852.0,
+                    663.0,
+                    852.0,
+                    708.0,
+                    292.0,
+                    708.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    910.0,
+                    663.0,
+                    1409.0,
+                    663.0,
+                    1409.0,
+                    708.0,
+                    910.0,
+                    708.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    695.0,
+                    1164.0,
+                    695.0,
+                    1164.0,
+                    739.0,
+                    293.0,
+                    739.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1227.0,
+                    695.0,
+                    1407.0,
+                    695.0,
+                    1407.0,
+                    739.0,
+                    1227.0,
+                    739.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    727.0,
+                    754.0,
+                    727.0,
+                    754.0,
+                    765.0,
+                    293.0,
+                    765.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    842.0,
+                    727.0,
+                    1407.0,
+                    727.0,
+                    1407.0,
+                    765.0,
+                    842.0,
+                    765.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    757.0,
+                    420.0,
+                    757.0,
+                    420.0,
+                    794.0,
+                    293.0,
+                    794.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    202.0,
+                    371.0,
+                    202.0,
+                    371.0,
+                    239.0,
+                    295.0,
+                    239.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    409.0,
+                    202.0,
+                    828.0,
+                    202.0,
+                    828.0,
+                    239.0,
+                    409.0,
+                    239.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    868.0,
+                    202.0,
+                    1406.0,
+                    202.0,
+                    1406.0,
+                    239.0,
+                    868.0,
+                    239.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    233.0,
+                    496.0,
+                    233.0,
+                    496.0,
+                    266.0,
+                    296.0,
+                    266.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    525.0,
+                    233.0,
+                    1404.0,
+                    233.0,
+                    1404.0,
+                    266.0,
+                    525.0,
+                    266.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    282.0,
+                    252.0,
+                    1077.0,
+                    252.0,
+                    1077.0,
+                    314.0,
+                    282.0,
+                    314.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1346.0,
+                    252.0,
+                    1415.0,
+                    252.0,
+                    1415.0,
+                    314.0,
+                    1346.0,
+                    314.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    297.0,
+                    297.0,
+                    297.0,
+                    297.0,
+                    337.0,
+                    294.0,
+                    337.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    390.0,
+                    297.0,
+                    647.0,
+                    297.0,
+                    647.0,
+                    337.0,
+                    390.0,
+                    337.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    675.0,
+                    297.0,
+                    871.0,
+                    297.0,
+                    871.0,
+                    337.0,
+                    675.0,
+                    337.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    894.0,
+                    297.0,
+                    1404.0,
+                    297.0,
+                    1404.0,
+                    337.0,
+                    894.0,
+                    337.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    329.0,
+                    1168.0,
+                    329.0,
+                    1168.0,
+                    366.0,
+                    293.0,
+                    366.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1197.0,
+                    329.0,
+                    1406.0,
+                    329.0,
+                    1406.0,
+                    366.0,
+                    1197.0,
+                    366.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    364.0,
+                    450.0,
+                    364.0,
+                    450.0,
+                    398.0,
+                    295.0,
+                    398.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1627.0,
+                    1404.0,
+                    1627.0,
+                    1404.0,
+                    1660.0,
+                    292.0,
+                    1660.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1656.0,
+                    1407.0,
+                    1656.0,
+                    1407.0,
+                    1693.0,
+                    294.0,
+                    1693.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1684.0,
+                    1406.0,
+                    1684.0,
+                    1406.0,
+                    1724.0,
+                    296.0,
+                    1724.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1719.0,
+                    822.0,
+                    1719.0,
+                    822.0,
+                    1752.0,
+                    295.0,
+                    1752.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    873.0,
+                    1719.0,
+                    1139.0,
+                    1719.0,
+                    1139.0,
+                    1752.0,
+                    873.0,
+                    1752.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1117.0,
+                    1404.0,
+                    1117.0,
+                    1404.0,
+                    1153.0,
+                    295.0,
+                    1153.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1149.0,
+                    297.0,
+                    1149.0,
+                    297.0,
+                    1186.0,
+                    294.0,
+                    1186.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    508.0,
+                    1149.0,
+                    572.0,
+                    1149.0,
+                    572.0,
+                    1186.0,
+                    508.0,
+                    1186.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    600.0,
+                    1149.0,
+                    1408.0,
+                    1149.0,
+                    1408.0,
+                    1186.0,
+                    600.0,
+                    1186.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1179.0,
+                    1408.0,
+                    1179.0,
+                    1408.0,
+                    1217.0,
+                    294.0,
+                    1217.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1210.0,
+                    1406.0,
+                    1210.0,
+                    1406.0,
+                    1245.0,
+                    293.0,
+                    1245.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1238.0,
+                    1026.0,
+                    1238.0,
+                    1026.0,
+                    1277.0,
+                    293.0,
+                    1277.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1040.0,
+                    1238.0,
+                    1327.0,
+                    1238.0,
+                    1327.0,
+                    1277.0,
+                    1040.0,
+                    1277.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1881.0,
+                    1404.0,
+                    1881.0,
+                    1404.0,
+                    1919.0,
+                    292.0,
+                    1919.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1911.0,
+                    1206.0,
+                    1911.0,
+                    1206.0,
+                    1950.0,
+                    293.0,
+                    1950.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1243.0,
+                    1911.0,
+                    1405.0,
+                    1911.0,
+                    1405.0,
+                    1950.0,
+                    1243.0,
+                    1950.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1944.0,
+                    1405.0,
+                    1944.0,
+                    1405.0,
+                    1983.0,
+                    292.0,
+                    1983.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1975.0,
+                    805.0,
+                    1975.0,
+                    805.0,
+                    2012.0,
+                    294.0,
+                    2012.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    842.0,
+                    1975.0,
+                    1404.0,
+                    1975.0,
+                    1404.0,
+                    2012.0,
+                    842.0,
+                    2012.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    299.0,
+                    931.0,
+                    1405.0,
+                    931.0,
+                    1405.0,
+                    968.0,
+                    299.0,
+                    968.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    301.0,
+                    965.0,
+                    1403.0,
+                    965.0,
+                    1403.0,
+                    995.0,
+                    301.0,
+                    995.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    299.0,
+                    994.0,
+                    1120.0,
+                    994.0,
+                    1120.0,
+                    1030.0,
+                    299.0,
+                    1030.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1026.0,
+                    813.0,
+                    1026.0,
+                    813.0,
+                    1071.0,
+                    293.0,
+                    1071.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    899.0,
+                    1026.0,
+                    1023.0,
+                    1026.0,
+                    1023.0,
+                    1071.0,
+                    899.0,
+                    1071.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1208.0,
+                    1026.0,
+                    1408.0,
+                    1026.0,
+                    1408.0,
+                    1071.0,
+                    1208.0,
+                    1071.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1060.0,
+                    472.0,
+                    1060.0,
+                    472.0,
+                    1104.0,
+                    292.0,
+                    1104.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    497.0,
+                    1060.0,
+                    589.0,
+                    1060.0,
+                    589.0,
+                    1104.0,
+                    497.0,
+                    1104.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    827.0,
+                    1060.0,
+                    839.0,
+                    1060.0,
+                    839.0,
+                    1104.0,
+                    827.0,
+                    1104.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1473.0,
+                    805.0,
+                    1473.0,
+                    805.0,
+                    1515.0,
+                    292.0,
+                    1515.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    853.0,
+                    1473.0,
+                    1357.0,
+                    1473.0,
+                    1357.0,
+                    1515.0,
+                    853.0,
+                    1515.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 3,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    433,
+                    1406,
+                    433,
+                    1406,
+                    558,
+                    297,
+                    558
+                ],
+                "score": 0.978
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1027,
+                    1405,
+                    1027,
+                    1405,
+                    1152,
+                    297,
+                    1152
+                ],
+                "score": 0.978
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    815,
+                    1405,
+                    815,
+                    1405,
+                    941,
+                    297,
+                    941
+                ],
+                "score": 0.977
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    202,
+                    1405,
+                    202,
+                    1405,
+                    327,
+                    298,
+                    327
+                ],
+                "score": 0.977
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1230,
+                    1405,
+                    1230,
+                    1405,
+                    1322,
+                    297,
+                    1322
+                ],
+                "score": 0.976
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    580,
+                    1777,
+                    1119,
+                    1777,
+                    1119,
+                    1929,
+                    580,
+                    1929
+                ],
+                "score": 0.966
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    701,
+                    722,
+                    996,
+                    722,
+                    996,
+                    807,
+                    701,
+                    807
+                ],
+                "score": 0.959
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    647,
+                    1402,
+                    647,
+                    1402,
+                    709,
+                    295,
+                    709
+                ],
+                "score": 0.959
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1557,
+                    1401,
+                    1557,
+                    1401,
+                    1622,
+                    296,
+                    1622
+                ],
+                "score": 0.954
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    605,
+                    1480,
+                    1093,
+                    1480,
+                    1093,
+                    1548,
+                    605,
+                    1548
+                ],
+                "score": 0.952
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    305,
+                    1407,
+                    1397,
+                    1407,
+                    1397,
+                    1470,
+                    305,
+                    1470
+                ],
+                "score": 0.948
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    444,
+                    1326,
+                    1253,
+                    1326,
+                    1253,
+                    1401,
+                    444,
+                    1401
+                ],
+                "score": 0.946
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    754,
+                    1162,
+                    942,
+                    1162,
+                    942,
+                    1225,
+                    754,
+                    1225
+                ],
+                "score": 0.945
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1707,
+                    1405,
+                    1707,
+                    1405,
+                    1770,
+                    299,
+                    1770
+                ],
+                "score": 0.944
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    299,
+                    366,
+                    906,
+                    366,
+                    906,
+                    405,
+                    299,
+                    405
+                ],
+                "score": 0.944
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    520,
+                    1632,
+                    1177,
+                    1632,
+                    1177,
+                    1701,
+                    520,
+                    1701
+                ],
+                "score": 0.943
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    299,
+                    590,
+                    638,
+                    590,
+                    638,
+                    624,
+                    299,
+                    624
+                ],
+                "score": 0.93
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    301,
+                    974,
+                    759,
+                    974,
+                    759,
+                    1007,
+                    301,
+                    1007
+                ],
+                "score": 0.926
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1352,
+                    1497,
+                    1400,
+                    1497,
+                    1400,
+                    1527,
+                    1352,
+                    1527
+                ],
+                "score": 0.904
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1366,
+                    1180,
+                    1400,
+                    1180,
+                    1400,
+                    1209,
+                    1366,
+                    1209
+                ],
+                "score": 0.895
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1351,
+                    1837,
+                    1401,
+                    1837,
+                    1401,
+                    1868,
+                    1351,
+                    1868
+                ],
+                "score": 0.895
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1366,
+                    745,
+                    1400,
+                    745,
+                    1400,
+                    775,
+                    1366,
+                    775
+                ],
+                "score": 0.884
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    330,
+                    1946,
+                    1060,
+                    1946,
+                    1060,
+                    2008,
+                    330,
+                    2008
+                ],
+                "score": 0.818
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2061,
+                    859,
+                    2061,
+                    859,
+                    2085,
+                    841,
+                    2085
+                ],
+                "score": 0.763
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    329,
+                    1946,
+                    1059,
+                    1946,
+                    1059,
+                    2008,
+                    329,
+                    2008
+                ],
+                "score": 0.232
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    443,
+                    1323,
+                    1254,
+                    1323,
+                    1254,
+                    1401,
+                    443,
+                    1401
+                ],
+                "score": 0.96,
+                "latex": "\\mathcal { P } _ { 2 } ( \\mathcal { M } ) = \\left\\{ \\varphi : \\mathcal { M } \\to [ 0 , \\infty ) \\bigg | \\int _ { \\mathcal { M } } \\mathrm { d } \\varphi = 1 , ~ \\int _ { \\mathcal { M } } | x | ^ { 2 } \\varphi ( x ) \\mathrm { d } x < + \\infty \\right\\} ."
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    703,
+                    718,
+                    995,
+                    718,
+                    995,
+                    808,
+                    703,
+                    808
+                ],
+                "score": 0.95,
+                "latex": "\\rho ( x ) = \\sum _ { i = 1 } ^ { n } w _ { i } \\delta ( x - x _ { i } ) ,"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    605,
+                    1476,
+                    1094,
+                    1476,
+                    1094,
+                    1549,
+                    605,
+                    1549
+                ],
+                "score": 0.94,
+                "latex": "W _ { 2 } ^ { 2 } ( \\mu , \\nu ) = \\operatorname* { i n f } _ { \\pi \\in \\Pi ( \\mu , \\nu ) } \\int | x - y | ^ { 2 } { \\mathrm { d } } \\pi ( x , y ) ."
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    579,
+                    1775,
+                    1119,
+                    1775,
+                    1119,
+                    1932,
+                    579,
+                    1932
+                ],
+                "score": 0.94,
+                "latex": "\\begin{array} { l } { \\displaystyle \\frac { \\partial \\rho ( \\boldsymbol { x } ) } { \\partial t } = \\nabla \\cdot \\left( \\rho ( \\boldsymbol { x } ) \\nabla \\frac { \\delta } { \\delta \\rho } D _ { K L } ( \\rho , \\pi ) \\right) } \\\\ { \\displaystyle = \\nabla \\cdot \\left( \\rho ( \\boldsymbol { x } ) \\nabla \\big ( \\log \\rho ( \\boldsymbol { x } ) - \\log \\pi ( \\boldsymbol { x } ) \\big ) \\right) , } \\end{array}"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    753,
+                    1160,
+                    946,
+                    1160,
+                    946,
+                    1226,
+                    753,
+                    1226
+                ],
+                "score": 0.93,
+                "latex": "\\frac { d \\boldsymbol { x } } { d t } = - \\boldsymbol { \\nabla } J ( \\boldsymbol { x } ) ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    656,
+                    1438,
+                    745,
+                    1438,
+                    745,
+                    1471,
+                    656,
+                    1471
+                ],
+                "score": 0.93,
+                "latex": "\\mathcal { P } _ { 2 } ( \\mathcal { M } )"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    520,
+                    1628,
+                    1176,
+                    1628,
+                    1176,
+                    1701,
+                    520,
+                    1701
+                ],
+                "score": 0.93,
+                "latex": "\\operatorname* { i n f } _ { \\rho \\in \\mathcal { P } _ { 2 } ( \\mathcal { M } ) } D _ { K L } ( \\rho , \\pi ) = \\int _ { \\mathcal { M } } ( \\log \\rho ( x ) - \\log \\pi ( x ) ) \\rho ( x ) \\mathrm { d } x ,"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    865,
+                    1261,
+                    953,
+                    1261,
+                    953,
+                    1295,
+                    865,
+                    1295
+                ],
+                "score": 0.92,
+                "latex": "\\mathcal { P } _ { 2 } ( \\mathcal { M } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    384,
+                    1407,
+                    474,
+                    1407,
+                    474,
+                    1440,
+                    384,
+                    1440
+                ],
+                "score": 0.92,
+                "latex": "\\Pi ( \\mu , \\nu )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    831,
+                    907,
+                    950,
+                    907,
+                    950,
+                    941,
+                    831,
+                    941
+                ],
+                "score": 0.92,
+                "latex": "w _ { i } = 1 / N"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1025,
+                    816,
+                    1148,
+                    816,
+                    1148,
+                    849,
+                    1025,
+                    849
+                ],
+                "score": 0.92,
+                "latex": "w _ { i } \\in [ 0 , 1 ]"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1071,
+                    1589,
+                    1126,
+                    1589,
+                    1126,
+                    1622,
+                    1071,
+                    1622
+                ],
+                "score": 0.92,
+                "latex": "\\pi ( x )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    345,
+                    908,
+                    399,
+                    908,
+                    399,
+                    941,
+                    345,
+                    941
+                ],
+                "score": 0.92,
+                "latex": "\\rho ( x )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    299,
+                    677,
+                    452,
+                    677,
+                    452,
+                    712,
+                    299,
+                    712
+                ],
+                "score": 0.92,
+                "latex": "\\{ ( \\bar { x _ { i } } , w _ { i } ) \\} _ { i = 1 } ^ { n }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    671,
+                    849,
+                    727,
+                    849,
+                    727,
+                    880,
+                    671,
+                    880
+                ],
+                "score": 0.92,
+                "latex": "\\pi ( x )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    900,
+                    1557,
+                    1093,
+                    1557,
+                    1093,
+                    1592,
+                    900,
+                    1592
+                ],
+                "score": 0.92,
+                "latex": "J : \\mathcal { P } _ { 2 } ( \\mathcal { M } )  \\mathbb { R }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1202,
+                    1060,
+                    1252,
+                    1060,
+                    1252,
+                    1093,
+                    1202,
+                    1093
+                ],
+                "score": 0.91,
+                "latex": "x ( t )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1200,
+                    815,
+                    1355,
+                    815,
+                    1355,
+                    851,
+                    1200,
+                    851
+                ],
+                "score": 0.91,
+                "latex": "\\textstyle \\sum _ { i = 1 } ^ { n } w _ { i } = 1"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    373,
+                    816,
+                    418,
+                    816,
+                    418,
+                    850,
+                    373,
+                    850
+                ],
+                "score": 0.91,
+                "latex": "\\delta ( \\cdot )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1347,
+                    878,
+                    1403,
+                    878,
+                    1403,
+                    911,
+                    1347,
+                    911
+                ],
+                "score": 0.91,
+                "latex": "\\pi ( x )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    576,
+                    1027,
+                    715,
+                    1027,
+                    715,
+                    1057,
+                    576,
+                    1057
+                ],
+                "score": 0.9,
+                "latex": "J : \\mathbb { R } ^ { d }  \\mathbb { R }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1128,
+                    1413,
+                    1176,
+                    1413,
+                    1176,
+                    1440,
+                    1128,
+                    1440
+                ],
+                "score": 0.87,
+                "latex": "\\mu , \\nu"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1038,
+                    1064,
+                    1069,
+                    1064,
+                    1069,
+                    1092,
+                    1038,
+                    1092
+                ],
+                "score": 0.86,
+                "latex": "x _ { 0 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    908,
+                    821,
+                    940,
+                    821,
+                    940,
+                    847,
+                    908,
+                    847
+                ],
+                "score": 0.86,
+                "latex": "w _ { i }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    553,
+                    911,
+                    580,
+                    911,
+                    580,
+                    935,
+                    553,
+                    935
+                ],
+                "score": 0.85,
+                "latex": "N"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    363,
+                    1094,
+                    396,
+                    1094,
+                    396,
+                    1121,
+                    363,
+                    1121
+                ],
+                "score": 0.85,
+                "latex": "x _ { 0 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    769,
+                    1587,
+                    804,
+                    1587,
+                    804,
+                    1625,
+                    769,
+                    1625
+                ],
+                "score": 0.83,
+                "latex": "\\textcircled { 8 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    880,
+                    1295,
+                    915,
+                    1295,
+                    915,
+                    1319,
+                    880,
+                    1319
+                ],
+                "score": 0.83,
+                "latex": "\\mathcal { M }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    701,
+                    1713,
+                    720,
+                    1713,
+                    720,
+                    1740,
+                    701,
+                    1740
+                ],
+                "score": 0.8,
+                "latex": "\\rho"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    817,
+                    206,
+                    830,
+                    206,
+                    830,
+                    231,
+                    817,
+                    231
+                ],
+                "score": 0.72,
+                "latex": "i"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1232,
+                    1559,
+                    1273,
+                    1559,
+                    1273,
+                    1587,
+                    1232,
+                    1587
+                ],
+                "score": 0.39,
+                "latex": "\\mathrm { K L }"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    289.0,
+                    363.0,
+                    909.0,
+                    363.0,
+                    909.0,
+                    414.0,
+                    289.0,
+                    414.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    585.0,
+                    640.0,
+                    585.0,
+                    640.0,
+                    631.0,
+                    292.0,
+                    631.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    969.0,
+                    765.0,
+                    969.0,
+                    765.0,
+                    1013.0,
+                    292.0,
+                    1013.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    331.0,
+                    1941.0,
+                    1061.0,
+                    1941.0,
+                    1061.0,
+                    1981.0,
+                    331.0,
+                    1981.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    330.0,
+                    1974.0,
+                    739.0,
+                    1974.0,
+                    739.0,
+                    2011.0,
+                    330.0,
+                    2011.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    838.0,
+                    2058.0,
+                    862.0,
+                    2058.0,
+                    862.0,
+                    2092.0,
+                    838.0,
+                    2092.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    331.0,
+                    1941.0,
+                    1061.0,
+                    1941.0,
+                    1061.0,
+                    1981.0,
+                    331.0,
+                    1981.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    330.0,
+                    1972.0,
+                    739.0,
+                    1972.0,
+                    739.0,
+                    2013.0,
+                    330.0,
+                    2013.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    433.0,
+                    1406.0,
+                    433.0,
+                    1406.0,
+                    470.0,
+                    294.0,
+                    470.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    463.0,
+                    1404.0,
+                    463.0,
+                    1404.0,
+                    499.0,
+                    294.0,
+                    499.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    497.0,
+                    1404.0,
+                    497.0,
+                    1404.0,
+                    529.0,
+                    296.0,
+                    529.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    524.0,
+                    1409.0,
+                    524.0,
+                    1409.0,
+                    561.0,
+                    292.0,
+                    561.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1025.0,
+                    575.0,
+                    1025.0,
+                    575.0,
+                    1064.0,
+                    294.0,
+                    1064.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    716.0,
+                    1025.0,
+                    1406.0,
+                    1025.0,
+                    1406.0,
+                    1064.0,
+                    716.0,
+                    1064.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1057.0,
+                    1037.0,
+                    1057.0,
+                    1037.0,
+                    1095.0,
+                    292.0,
+                    1095.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1070.0,
+                    1057.0,
+                    1201.0,
+                    1057.0,
+                    1201.0,
+                    1095.0,
+                    1070.0,
+                    1095.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1253.0,
+                    1057.0,
+                    1406.0,
+                    1057.0,
+                    1406.0,
+                    1095.0,
+                    1253.0,
+                    1095.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1091.0,
+                    362.0,
+                    1091.0,
+                    362.0,
+                    1123.0,
+                    294.0,
+                    1123.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    397.0,
+                    1091.0,
+                    1408.0,
+                    1091.0,
+                    1408.0,
+                    1123.0,
+                    397.0,
+                    1123.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1120.0,
+                    1338.0,
+                    1120.0,
+                    1338.0,
+                    1153.0,
+                    292.0,
+                    1153.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    285.0,
+                    799.0,
+                    372.0,
+                    799.0,
+                    372.0,
+                    865.0,
+                    285.0,
+                    865.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    419.0,
+                    799.0,
+                    907.0,
+                    799.0,
+                    907.0,
+                    865.0,
+                    419.0,
+                    865.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    941.0,
+                    799.0,
+                    1024.0,
+                    799.0,
+                    1024.0,
+                    865.0,
+                    941.0,
+                    865.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1149.0,
+                    799.0,
+                    1199.0,
+                    799.0,
+                    1199.0,
+                    865.0,
+                    1149.0,
+                    865.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1356.0,
+                    799.0,
+                    1416.0,
+                    799.0,
+                    1416.0,
+                    865.0,
+                    1356.0,
+                    865.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    846.0,
+                    670.0,
+                    846.0,
+                    670.0,
+                    880.0,
+                    292.0,
+                    880.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    728.0,
+                    846.0,
+                    1406.0,
+                    846.0,
+                    1406.0,
+                    880.0,
+                    728.0,
+                    880.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    877.0,
+                    1346.0,
+                    877.0,
+                    1346.0,
+                    913.0,
+                    294.0,
+                    913.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    906.0,
+                    344.0,
+                    906.0,
+                    344.0,
+                    942.0,
+                    294.0,
+                    942.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    400.0,
+                    906.0,
+                    552.0,
+                    906.0,
+                    552.0,
+                    942.0,
+                    400.0,
+                    942.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    581.0,
+                    906.0,
+                    830.0,
+                    906.0,
+                    830.0,
+                    942.0,
+                    581.0,
+                    942.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    951.0,
+                    906.0,
+                    1356.0,
+                    906.0,
+                    1356.0,
+                    942.0,
+                    951.0,
+                    942.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    202.0,
+                    816.0,
+                    202.0,
+                    816.0,
+                    238.0,
+                    292.0,
+                    238.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    831.0,
+                    202.0,
+                    1406.0,
+                    202.0,
+                    1406.0,
+                    238.0,
+                    831.0,
+                    238.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    233.0,
+                    1406.0,
+                    233.0,
+                    1406.0,
+                    268.0,
+                    292.0,
+                    268.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    263.0,
+                    1406.0,
+                    263.0,
+                    1406.0,
+                    300.0,
+                    293.0,
+                    300.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    295.0,
+                    1304.0,
+                    295.0,
+                    1304.0,
+                    330.0,
+                    292.0,
+                    330.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1229.0,
+                    1402.0,
+                    1229.0,
+                    1402.0,
+                    1266.0,
+                    294.0,
+                    1266.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1260.0,
+                    864.0,
+                    1260.0,
+                    864.0,
+                    1296.0,
+                    294.0,
+                    1296.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    954.0,
+                    1260.0,
+                    1403.0,
+                    1260.0,
+                    1403.0,
+                    1296.0,
+                    954.0,
+                    1296.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1290.0,
+                    879.0,
+                    1290.0,
+                    879.0,
+                    1324.0,
+                    295.0,
+                    1324.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    916.0,
+                    1290.0,
+                    926.0,
+                    1290.0,
+                    926.0,
+                    1324.0,
+                    916.0,
+                    1324.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    645.0,
+                    1404.0,
+                    645.0,
+                    1404.0,
+                    684.0,
+                    293.0,
+                    684.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    673.0,
+                    298.0,
+                    673.0,
+                    298.0,
+                    716.0,
+                    294.0,
+                    716.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    453.0,
+                    673.0,
+                    1022.0,
+                    673.0,
+                    1022.0,
+                    716.0,
+                    453.0,
+                    716.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1553.0,
+                    899.0,
+                    1553.0,
+                    899.0,
+                    1595.0,
+                    295.0,
+                    1595.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1094.0,
+                    1553.0,
+                    1231.0,
+                    1553.0,
+                    1231.0,
+                    1595.0,
+                    1094.0,
+                    1595.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1274.0,
+                    1553.0,
+                    1405.0,
+                    1553.0,
+                    1405.0,
+                    1595.0,
+                    1274.0,
+                    1595.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1588.0,
+                    768.0,
+                    1588.0,
+                    768.0,
+                    1624.0,
+                    295.0,
+                    1624.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    805.0,
+                    1588.0,
+                    1070.0,
+                    1588.0,
+                    1070.0,
+                    1624.0,
+                    805.0,
+                    1624.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1127.0,
+                    1588.0,
+                    1138.0,
+                    1588.0,
+                    1138.0,
+                    1624.0,
+                    1127.0,
+                    1624.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    298.0,
+                    1403.0,
+                    383.0,
+                    1403.0,
+                    383.0,
+                    1444.0,
+                    298.0,
+                    1444.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    475.0,
+                    1403.0,
+                    1127.0,
+                    1403.0,
+                    1127.0,
+                    1444.0,
+                    475.0,
+                    1444.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1177.0,
+                    1403.0,
+                    1402.0,
+                    1403.0,
+                    1402.0,
+                    1444.0,
+                    1177.0,
+                    1444.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    299.0,
+                    1435.0,
+                    655.0,
+                    1435.0,
+                    655.0,
+                    1473.0,
+                    299.0,
+                    1473.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    746.0,
+                    1435.0,
+                    786.0,
+                    1435.0,
+                    786.0,
+                    1473.0,
+                    746.0,
+                    1473.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1704.0,
+                    700.0,
+                    1704.0,
+                    700.0,
+                    1741.0,
+                    294.0,
+                    1741.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    721.0,
+                    1704.0,
+                    1405.0,
+                    1704.0,
+                    1405.0,
+                    1741.0,
+                    721.0,
+                    1741.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1732.0,
+                    920.0,
+                    1732.0,
+                    920.0,
+                    1773.0,
+                    295.0,
+                    1773.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 4,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    661,
+                    1407,
+                    661,
+                    1407,
+                    933,
+                    295,
+                    933
+                ],
+                "score": 0.983
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1319,
+                    1407,
+                    1319,
+                    1407,
+                    1535,
+                    296,
+                    1535
+                ],
+                "score": 0.981
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1130,
+                    1405,
+                    1130,
+                    1405,
+                    1310,
+                    297,
+                    1310
+                ],
+                "score": 0.98
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1882,
+                    1403,
+                    1882,
+                    1403,
+                    2009,
+                    298,
+                    2009
+                ],
+                "score": 0.978
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1629,
+                    1405,
+                    1629,
+                    1405,
+                    1782,
+                    298,
+                    1782
+                ],
+                "score": 0.977
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    199,
+                    1406,
+                    199,
+                    1406,
+                    301,
+                    297,
+                    301
+                ],
+                "score": 0.971
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    594,
+                    306,
+                    1104,
+                    306,
+                    1104,
+                    414,
+                    594,
+                    414
+                ],
+                "score": 0.956
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    458,
+                    1539,
+                    1237,
+                    1539,
+                    1237,
+                    1624,
+                    458,
+                    1624
+                ],
+                "score": 0.951
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    335,
+                    1787,
+                    1310,
+                    1787,
+                    1310,
+                    1878,
+                    335,
+                    1878
+                ],
+                "score": 0.949
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    643,
+                    931,
+                    1055,
+                    931,
+                    1055,
+                    1012,
+                    643,
+                    1012
+                ],
+                "score": 0.945
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    658,
+                    486,
+                    1040,
+                    486,
+                    1040,
+                    547,
+                    658,
+                    547
+                ],
+                "score": 0.944
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    534,
+                    1048,
+                    1160,
+                    1048,
+                    1160,
+                    1127,
+                    534,
+                    1127
+                ],
+                "score": 0.944
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    417,
+                    1400,
+                    417,
+                    1400,
+                    480,
+                    296,
+                    480
+                ],
+                "score": 0.944
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    292,
+                    560,
+                    1402,
+                    560,
+                    1402,
+                    625,
+                    292,
+                    625
+                ],
+                "score": 0.94
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1010,
+                    831,
+                    1010,
+                    831,
+                    1044,
+                    299,
+                    1044
+                ],
+                "score": 0.929
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    593,
+                    623,
+                    1099,
+                    623,
+                    1099,
+                    662,
+                    593,
+                    662
+                ],
+                "score": 0.927
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1351,
+                    957,
+                    1400,
+                    957,
+                    1400,
+                    987,
+                    1351,
+                    987
+                ],
+                "score": 0.9
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1352,
+                    1562,
+                    1400,
+                    1562,
+                    1400,
+                    1592,
+                    1352,
+                    1592
+                ],
+                "score": 0.899
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1352,
+                    1071,
+                    1400,
+                    1071,
+                    1400,
+                    1103,
+                    1352,
+                    1103
+                ],
+                "score": 0.896
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1351,
+                    500,
+                    1400,
+                    500,
+                    1400,
+                    530,
+                    1351,
+                    530
+                ],
+                "score": 0.89
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1352,
+                    1815,
+                    1400,
+                    1815,
+                    1400,
+                    1846,
+                    1352,
+                    1846
+                ],
+                "score": 0.862
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1352,
+                    627,
+                    1400,
+                    627,
+                    1400,
+                    657,
+                    1352,
+                    657
+                ],
+                "score": 0.855
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    840,
+                    2061,
+                    859,
+                    2061,
+                    859,
+                    2085,
+                    840,
+                    2085
+                ],
+                "score": 0.806
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    643,
+                    928,
+                    1057,
+                    928,
+                    1057,
+                    1015,
+                    643,
+                    1015
+                ],
+                "score": 0.95,
+                "latex": "\\nabla \\log \\rho ( x _ { i } ^ { t } ) \\approx \\frac { \\sum _ { j = 1 } ^ { n } \\nabla _ { x _ { i } ^ { t } } k ( x _ { i } ^ { t } , x _ { j } ^ { t } ) } { \\sum _ { j = 1 } ^ { n } k ( x _ { i } ^ { t } , x _ { j } ^ { t } ) } ."
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    657,
+                    481,
+                    1043,
+                    481,
+                    1043,
+                    547,
+                    657,
+                    547
+                ],
+                "score": 0.94,
+                "latex": "\\frac { d x } { d t } = - \\nabla \\big ( \\log \\rho ( x ) - \\log \\pi ( x ) \\big ) ."
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    461,
+                    1534,
+                    1236,
+                    1534,
+                    1236,
+                    1627,
+                    461,
+                    1627
+                ],
+                "score": 0.94,
+                "latex": "x _ { i } ^ { t + 1 } = x _ { i } ^ { t } + \\epsilon _ { t } \\bigg ( \\nabla \\log \\pi ( x _ { i } ^ { t } ) + \\sum _ { j = 1 } ^ { n } ( K + \\eta \\mathbb { I } ) _ { i j } ^ { - 1 } \\sum _ { k = 1 } ^ { n } \\nabla _ { x _ { k } ^ { t } } k ( x _ { k } ^ { t } , x _ { j } ^ { t } ) \\bigg ) ,"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    338,
+                    1783,
+                    1314,
+                    1783,
+                    1314,
+                    1880,
+                    338,
+                    1880
+                ],
+                "score": 0.94,
+                "latex": "x _ { t + 1 } ^ { i } = x _ { t } ^ { i } + \\epsilon _ { t } \\bigg ( \\nabla \\log \\pi ( x _ { t } ^ { i } ) + \\sum _ { j = 1 } ^ { J } \\frac { 1 } { \\lambda _ { j } ^ { 2 } } \\sum _ { m = 1 } ^ { n } \\sum _ { k = 1 } ^ { n } u _ { j k } \\nabla _ { x _ { m } } k ( x _ { m } ^ { t } , x _ { k } ^ { t } ) \\cdot \\sum _ { l = 1 } ^ { n } u _ { j l } k ( x _ { i } ^ { t } , x _ { l } ^ { t } ) \\bigg )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    299,
+                    1190,
+                    800,
+                    1190,
+                    800,
+                    1251,
+                    299,
+                    1251
+                ],
+                "score": 0.93,
+                "latex": "\\begin{array} { r } { \\left( \\bar { \\sum _ { j = 1 } ^ { n } } k ( \\mathbf { w } _ { i } ^ { t } , \\mathbf { w } _ { j } ^ { t } ) \\right) ^ { - 1 } \\sum _ { j = 1 } ^ { n } \\nabla _ { \\mathbf { w } _ { i } ^ { t } } k ( \\mathbf { w } _ { i } ^ { t } , \\mathbf { w } _ { j } ^ { t } ) } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    985,
+                    563,
+                    1068,
+                    563,
+                    1068,
+                    598,
+                    985,
+                    598
+                ],
+                "score": 0.93,
+                "latex": "\\{ x \\} _ { i = 1 } ^ { n }"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    537,
+                    1044,
+                    1160,
+                    1044,
+                    1160,
+                    1129,
+                    537,
+                    1129
+                ],
+                "score": 0.93,
+                "latex": "x _ { i } ^ { t + 1 } = x _ { i } ^ { t } + \\epsilon _ { t } \\Bigg ( \\nabla \\log \\pi ( x _ { i } ^ { t } ) - \\frac { \\sum _ { j = 1 } ^ { n } \\nabla _ { x _ { i } ^ { t } } k ( x _ { i } ^ { t } , x _ { j } ^ { t } ) } { \\sum _ { j = 1 } ^ { n } k ( x _ { i } ^ { t } , x _ { j } ^ { t } ) } \\Bigg ) ,"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    377,
+                    200,
+                    803,
+                    200,
+                    803,
+                    241,
+                    377,
+                    241
+                ],
+                "score": 0.93,
+                "latex": "\\nabla _ { \\delta \\rho } ^ { \\delta } D _ { K L } ( \\rho , \\pi ) \\ = : \\ \\nabla _ { \\mathcal { W } _ { 2 } } D _ { K L } ( \\rho , \\pi )"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    593,
+                    304,
+                    1102,
+                    304,
+                    1102,
+                    417,
+                    593,
+                    417
+                ],
+                "score": 0.92,
+                "latex": "\\begin{array} { r l r } & { } & { \\frac { \\partial \\rho ( x ) } { \\partial t } = \\nabla \\cdot \\left( \\rho ( x ) \\nabla ( \\log \\rho ( x ) - \\log \\pi ( x ) ) \\right) } \\\\ & { } & { = - \\nabla \\cdot \\left( \\rho ( x ) \\nabla \\log \\pi ( x ) \\right) + \\nabla ^ { 2 } \\rho ( x ) , } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    933,
+                    418,
+                    989,
+                    418,
+                    989,
+                    451,
+                    933,
+                    451
+                ],
+                "score": 0.92,
+                "latex": "\\pi ( x )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    1975,
+                    460,
+                    1975,
+                    460,
+                    2009,
+                    298,
+                    2009
+                ],
+                "score": 0.92,
+                "latex": "\\mathcal { O } ( M ( d + J ) )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    672,
+                    870,
+                    925,
+                    870,
+                    925,
+                    905,
+                    672,
+                    905
+                ],
+                "score": 0.91,
+                "latex": "\\boldsymbol { k } ( \\cdot , \\cdot ) : \\mathbb { R } ^ { d } \\times \\mathbb { R } ^ { d }  \\dot { \\mathbb { R } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1051,
+                    1912,
+                    1228,
+                    1912,
+                    1228,
+                    1948,
+                    1051,
+                    1948
+                ],
+                "score": 0.91,
+                "latex": "\\mathcal { O } ( M ^ { 3 } + M ^ { 2 } d )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    240,
+                    465,
+                    240,
+                    465,
+                    273,
+                    298,
+                    273
+                ],
+                "score": 0.91,
+                "latex": "\\mathcal { P } _ { 2 } ( \\mathcal { M } ) \\stackrel { \\cdot } {  } \\mathbb { R }"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    593,
+                    621,
+                    1105,
+                    621,
+                    1105,
+                    663,
+                    593,
+                    663
+                ],
+                "score": 0.91,
+                "latex": "x _ { i } ^ { t + 1 } = x _ { i } ^ { t } + \\epsilon _ { t } \\bigl ( \\nabla \\log \\pi ( x _ { i } ^ { t } ) - \\nabla \\log \\rho ( x _ { i } ^ { t } ) \\bigr ) ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    297,
+                    870,
+                    585,
+                    870,
+                    585,
+                    908,
+                    297,
+                    908
+                ],
+                "score": 0.91,
+                "latex": "\\begin{array} { r } { \\tilde { \\rho } _ { t } ( x ) = \\frac { 1 } { n } \\sum _ { i = 1 } ^ { n } \\dot { k } ( x , x _ { t } ^ { i } ) } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1151,
+                    661,
+                    1236,
+                    661,
+                    1236,
+                    691,
+                    1151,
+                    691
+                ],
+                "score": 0.9,
+                "latex": "\\nabla \\log \\rho"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    375,
+                    1882,
+                    406,
+                    1882,
+                    406,
+                    1916,
+                    375,
+                    1916
+                ],
+                "score": 0.89,
+                "latex": "\\lambda _ { j }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    751,
+                    719,
+                    801,
+                    719,
+                    801,
+                    756,
+                    751,
+                    756
+                ],
+                "score": 0.89,
+                "latex": "\\textcircled { 1 3 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    874,
+                    1159,
+                    910,
+                    1159,
+                    910,
+                    1196,
+                    874,
+                    1196
+                ],
+                "score": 0.88,
+                "latex": "( 3 )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1262,
+                    238,
+                    1294,
+                    238,
+                    1294,
+                    276,
+                    1262,
+                    276
+                ],
+                "score": 0.87,
+                "latex": "\\boxed { \\mathsf { C } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1169,
+                    719,
+                    1206,
+                    719,
+                    1206,
+                    755,
+                    1169,
+                    755
+                ],
+                "score": 0.87,
+                "latex": "( 3 )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1185,
+                    1249,
+                    1275,
+                    1249,
+                    1275,
+                    1274,
+                    1185,
+                    1274
+                ],
+                "score": 0.85,
+                "latex": "n \\to \\infty"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    683,
+                    1412,
+                    732,
+                    1412,
+                    732,
+                    1444,
+                    683,
+                    1444
+                ],
+                "score": 0.85,
+                "latex": "\\mathbb { \\left. \\boldsymbol { \\mathfrak { G } } \\boldsymbol { \\mathfrak { A } } \\right. }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1345,
+                    1161,
+                    1406,
+                    1161,
+                    1406,
+                    1191,
+                    1345,
+                    1191
+                ],
+                "score": 0.85,
+                "latex": "\\mathcal { R } ="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    927,
+                    1351,
+                    975,
+                    1351,
+                    975,
+                    1383,
+                    927,
+                    1383
+                ],
+                "score": 0.84,
+                "latex": "[ \\overline { { | 4 6 | } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    343,
+                    1160,
+                    377,
+                    1160,
+                    377,
+                    1195,
+                    343,
+                    1195
+                ],
+                "score": 0.84,
+                "latex": "\\textcircled{3}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    962,
+                    1887,
+                    1004,
+                    1887,
+                    1004,
+                    1916,
+                    962,
+                    1916
+                ],
+                "score": 0.83,
+                "latex": "u _ { j k }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1283,
+                    570,
+                    1307,
+                    570,
+                    1307,
+                    594,
+                    1283,
+                    594
+                ],
+                "score": 0.83,
+                "latex": "\\epsilon _ { t }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    548,
+                    1977,
+                    569,
+                    1977,
+                    569,
+                    2003,
+                    548,
+                    2003
+                ],
+                "score": 0.83,
+                "latex": "J"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    372,
+                    1630,
+                    400,
+                    1630,
+                    400,
+                    1656,
+                    372,
+                    1656
+                ],
+                "score": 0.83,
+                "latex": "K"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    485,
+                    1884,
+                    501,
+                    1884,
+                    501,
+                    1914,
+                    485,
+                    1914
+                ],
+                "score": 0.82,
+                "latex": "j"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1353,
+                    1885,
+                    1369,
+                    1885,
+                    1369,
+                    1914,
+                    1353,
+                    1914
+                ],
+                "score": 0.82,
+                "latex": "j"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1298,
+                    1918,
+                    1330,
+                    1918,
+                    1330,
+                    1942,
+                    1298,
+                    1942
+                ],
+                "score": 0.82,
+                "latex": "M"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    659,
+                    1011,
+                    708,
+                    1011,
+                    708,
+                    1047,
+                    659,
+                    1047
+                ],
+                "score": 0.82,
+                "latex": "( 1 3 )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1084,
+                    1883,
+                    1102,
+                    1883,
+                    1102,
+                    1909,
+                    1084,
+                    1909
+                ],
+                "score": 0.82,
+                "latex": "k"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    705,
+                    1635,
+                    723,
+                    1635,
+                    723,
+                    1661,
+                    705,
+                    1661
+                ],
+                "score": 0.82,
+                "latex": "\\eta"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    595,
+                    1947,
+                    612,
+                    1947,
+                    612,
+                    1973,
+                    595,
+                    1973
+                ],
+                "score": 0.82,
+                "latex": "d"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    338,
+                    1692,
+                    350,
+                    1692,
+                    350,
+                    1717,
+                    338,
+                    1717
+                ],
+                "score": 0.81,
+                "latex": "i"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    621,
+                    1276,
+                    668,
+                    1276,
+                    668,
+                    1308,
+                    621,
+                    1308
+                ],
+                "score": 0.77,
+                "latex": "\\left[ \\left[ 6 6 \\right] \\right]"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    342,
+                    1472,
+                    389,
+                    1472,
+                    389,
+                    1509,
+                    342,
+                    1509
+                ],
+                "score": 0.77,
+                "latex": "\\textcircled { 1 3 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    775,
+                    1137,
+                    795,
+                    1137,
+                    795,
+                    1157,
+                    775,
+                    1157
+                ],
+                "score": 0.77,
+                "latex": "\\pi"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    333,
+                    904,
+                    381,
+                    904,
+                    381,
+                    934,
+                    333,
+                    934
+                ],
+                "score": 0.75,
+                "latex": "\\mathbb { \\ m }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1348,
+                    200,
+                    1380,
+                    200,
+                    1380,
+                    243,
+                    1348,
+                    243
+                ],
+                "score": 0.7,
+                "latex": "\\frac { \\delta } { \\delta \\rho }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    427,
+                    593,
+                    476,
+                    593,
+                    476,
+                    629,
+                    427,
+                    629
+                ],
+                "score": 0.7,
+                "latex": "\\mathbb { \\underline { { ( 1 2 ) } } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1369,
+                    841,
+                    1403,
+                    841,
+                    1403,
+                    877,
+                    1369,
+                    877
+                ],
+                "score": 0.68,
+                "latex": "\\dot { \\mathrm { ~ E ~ } } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    362,
+                    446,
+                    397,
+                    446,
+                    397,
+                    479,
+                    362,
+                    479
+                ],
+                "score": 0.61,
+                "latex": "\\left[ \\left[ 2 \\right] \\right]"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    556,
+                    446,
+                    604,
+                    446,
+                    604,
+                    482,
+                    556,
+                    482
+                ],
+                "score": 0.58,
+                "latex": "\\mathbb { ( 1 1 ) }"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    840.0,
+                    2059.0,
+                    862.0,
+                    2059.0,
+                    862.0,
+                    2089.0,
+                    840.0,
+                    2089.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    656.0,
+                    1150.0,
+                    656.0,
+                    1150.0,
+                    695.0,
+                    294.0,
+                    695.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1237.0,
+                    656.0,
+                    1409.0,
+                    656.0,
+                    1409.0,
+                    695.0,
+                    1237.0,
+                    695.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    692.0,
+                    1403.0,
+                    692.0,
+                    1403.0,
+                    721.0,
+                    297.0,
+                    721.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    718.0,
+                    750.0,
+                    718.0,
+                    750.0,
+                    758.0,
+                    293.0,
+                    758.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    802.0,
+                    718.0,
+                    1168.0,
+                    718.0,
+                    1168.0,
+                    758.0,
+                    802.0,
+                    758.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1207.0,
+                    718.0,
+                    1408.0,
+                    718.0,
+                    1408.0,
+                    758.0,
+                    1207.0,
+                    758.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    749.0,
+                    1405.0,
+                    749.0,
+                    1405.0,
+                    785.0,
+                    294.0,
+                    785.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    780.0,
+                    1409.0,
+                    780.0,
+                    1409.0,
+                    816.0,
+                    294.0,
+                    816.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    809.0,
+                    1405.0,
+                    809.0,
+                    1405.0,
+                    846.0,
+                    293.0,
+                    846.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    841.0,
+                    1368.0,
+                    841.0,
+                    1368.0,
+                    877.0,
+                    293.0,
+                    877.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    586.0,
+                    866.0,
+                    671.0,
+                    866.0,
+                    671.0,
+                    912.0,
+                    586.0,
+                    912.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    926.0,
+                    866.0,
+                    1410.0,
+                    866.0,
+                    1410.0,
+                    912.0,
+                    926.0,
+                    912.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    899.0,
+                    332.0,
+                    899.0,
+                    332.0,
+                    939.0,
+                    294.0,
+                    939.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    382.0,
+                    900.0,
+                    394.0,
+                    900.0,
+                    394.0,
+                    937.0,
+                    382.0,
+                    937.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1318.0,
+                    1409.0,
+                    1318.0,
+                    1409.0,
+                    1358.0,
+                    293.0,
+                    1358.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1352.0,
+                    926.0,
+                    1352.0,
+                    926.0,
+                    1386.0,
+                    295.0,
+                    1386.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    976.0,
+                    1352.0,
+                    1407.0,
+                    1352.0,
+                    1407.0,
+                    1386.0,
+                    976.0,
+                    1386.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1383.0,
+                    1405.0,
+                    1383.0,
+                    1405.0,
+                    1417.0,
+                    294.0,
+                    1417.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1412.0,
+                    682.0,
+                    1412.0,
+                    682.0,
+                    1447.0,
+                    294.0,
+                    1447.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    733.0,
+                    1412.0,
+                    1407.0,
+                    1412.0,
+                    1407.0,
+                    1447.0,
+                    733.0,
+                    1447.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1443.0,
+                    1407.0,
+                    1443.0,
+                    1407.0,
+                    1478.0,
+                    294.0,
+                    1478.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1470.0,
+                    341.0,
+                    1470.0,
+                    341.0,
+                    1512.0,
+                    294.0,
+                    1512.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    390.0,
+                    1470.0,
+                    1407.0,
+                    1470.0,
+                    1407.0,
+                    1512.0,
+                    390.0,
+                    1512.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1505.0,
+                    875.0,
+                    1505.0,
+                    875.0,
+                    1536.0,
+                    295.0,
+                    1536.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1126.0,
+                    774.0,
+                    1126.0,
+                    774.0,
+                    1164.0,
+                    294.0,
+                    1164.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    796.0,
+                    1126.0,
+                    1405.0,
+                    1126.0,
+                    1405.0,
+                    1164.0,
+                    796.0,
+                    1164.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1154.0,
+                    342.0,
+                    1154.0,
+                    342.0,
+                    1200.0,
+                    293.0,
+                    1200.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    378.0,
+                    1154.0,
+                    873.0,
+                    1154.0,
+                    873.0,
+                    1200.0,
+                    378.0,
+                    1200.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    911.0,
+                    1154.0,
+                    1344.0,
+                    1154.0,
+                    1344.0,
+                    1200.0,
+                    911.0,
+                    1200.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    801.0,
+                    1181.0,
+                    1419.0,
+                    1181.0,
+                    1419.0,
+                    1264.0,
+                    801.0,
+                    1264.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1244.0,
+                    1184.0,
+                    1244.0,
+                    1184.0,
+                    1279.0,
+                    295.0,
+                    1279.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1276.0,
+                    1244.0,
+                    1402.0,
+                    1244.0,
+                    1402.0,
+                    1279.0,
+                    1276.0,
+                    1279.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1274.0,
+                    620.0,
+                    1274.0,
+                    620.0,
+                    1312.0,
+                    295.0,
+                    1312.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    669.0,
+                    1274.0,
+                    1192.0,
+                    1274.0,
+                    1192.0,
+                    1312.0,
+                    669.0,
+                    1312.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1880.0,
+                    374.0,
+                    1880.0,
+                    374.0,
+                    1917.0,
+                    294.0,
+                    1917.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    407.0,
+                    1880.0,
+                    484.0,
+                    1880.0,
+                    484.0,
+                    1917.0,
+                    407.0,
+                    1917.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    502.0,
+                    1880.0,
+                    961.0,
+                    1880.0,
+                    961.0,
+                    1917.0,
+                    502.0,
+                    1917.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1005.0,
+                    1880.0,
+                    1083.0,
+                    1880.0,
+                    1083.0,
+                    1917.0,
+                    1005.0,
+                    1917.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1103.0,
+                    1880.0,
+                    1352.0,
+                    1880.0,
+                    1352.0,
+                    1917.0,
+                    1103.0,
+                    1917.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1370.0,
+                    1880.0,
+                    1405.0,
+                    1880.0,
+                    1405.0,
+                    1917.0,
+                    1370.0,
+                    1917.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1910.0,
+                    1050.0,
+                    1910.0,
+                    1050.0,
+                    1953.0,
+                    292.0,
+                    1953.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1229.0,
+                    1910.0,
+                    1297.0,
+                    1910.0,
+                    1297.0,
+                    1953.0,
+                    1229.0,
+                    1953.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1331.0,
+                    1910.0,
+                    1407.0,
+                    1910.0,
+                    1407.0,
+                    1953.0,
+                    1331.0,
+                    1953.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1947.0,
+                    594.0,
+                    1947.0,
+                    594.0,
+                    1980.0,
+                    294.0,
+                    1980.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    613.0,
+                    1947.0,
+                    1405.0,
+                    1947.0,
+                    1405.0,
+                    1980.0,
+                    613.0,
+                    1980.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    461.0,
+                    1975.0,
+                    547.0,
+                    1975.0,
+                    547.0,
+                    2011.0,
+                    461.0,
+                    2011.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    570.0,
+                    1975.0,
+                    901.0,
+                    1975.0,
+                    901.0,
+                    2011.0,
+                    570.0,
+                    2011.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1625.0,
+                    371.0,
+                    1625.0,
+                    371.0,
+                    1663.0,
+                    293.0,
+                    1663.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    401.0,
+                    1625.0,
+                    704.0,
+                    1625.0,
+                    704.0,
+                    1663.0,
+                    401.0,
+                    1663.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    724.0,
+                    1625.0,
+                    1406.0,
+                    1625.0,
+                    1406.0,
+                    1663.0,
+                    724.0,
+                    1663.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1657.0,
+                    1406.0,
+                    1657.0,
+                    1406.0,
+                    1692.0,
+                    293.0,
+                    1692.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1690.0,
+                    337.0,
+                    1690.0,
+                    337.0,
+                    1723.0,
+                    296.0,
+                    1723.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    351.0,
+                    1690.0,
+                    1405.0,
+                    1690.0,
+                    1405.0,
+                    1723.0,
+                    351.0,
+                    1723.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1717.0,
+                    1408.0,
+                    1717.0,
+                    1408.0,
+                    1754.0,
+                    293.0,
+                    1754.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1750.0,
+                    681.0,
+                    1750.0,
+                    681.0,
+                    1783.0,
+                    296.0,
+                    1783.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    197.0,
+                    376.0,
+                    197.0,
+                    376.0,
+                    241.0,
+                    291.0,
+                    241.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    804.0,
+                    197.0,
+                    1347.0,
+                    197.0,
+                    1347.0,
+                    241.0,
+                    804.0,
+                    241.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    466.0,
+                    239.0,
+                    1261.0,
+                    239.0,
+                    1261.0,
+                    274.0,
+                    466.0,
+                    274.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1295.0,
+                    239.0,
+                    1406.0,
+                    239.0,
+                    1406.0,
+                    274.0,
+                    1295.0,
+                    274.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    269.0,
+                    1364.0,
+                    269.0,
+                    1364.0,
+                    306.0,
+                    294.0,
+                    306.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1351.0,
+                    214.5,
+                    1379.0,
+                    214.5,
+                    1379.0,
+                    243.0,
+                    1351.0,
+                    243.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    414.0,
+                    932.0,
+                    414.0,
+                    932.0,
+                    451.0,
+                    294.0,
+                    451.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    990.0,
+                    414.0,
+                    1404.0,
+                    414.0,
+                    1404.0,
+                    451.0,
+                    990.0,
+                    451.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    443.0,
+                    361.0,
+                    443.0,
+                    361.0,
+                    483.0,
+                    295.0,
+                    483.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    398.0,
+                    443.0,
+                    555.0,
+                    443.0,
+                    555.0,
+                    483.0,
+                    398.0,
+                    483.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    605.0,
+                    443.0,
+                    1276.0,
+                    443.0,
+                    1276.0,
+                    483.0,
+                    605.0,
+                    483.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    558.0,
+                    984.0,
+                    558.0,
+                    984.0,
+                    602.0,
+                    295.0,
+                    602.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1069.0,
+                    558.0,
+                    1282.0,
+                    558.0,
+                    1282.0,
+                    602.0,
+                    1069.0,
+                    602.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1308.0,
+                    558.0,
+                    1407.0,
+                    558.0,
+                    1407.0,
+                    602.0,
+                    1308.0,
+                    602.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    583.0,
+                    426.0,
+                    583.0,
+                    426.0,
+                    633.0,
+                    291.0,
+                    633.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    477.0,
+                    583.0,
+                    519.0,
+                    583.0,
+                    519.0,
+                    633.0,
+                    477.0,
+                    633.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1008.0,
+                    658.0,
+                    1008.0,
+                    658.0,
+                    1048.0,
+                    296.0,
+                    1048.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    709.0,
+                    1008.0,
+                    834.0,
+                    1008.0,
+                    834.0,
+                    1048.0,
+                    709.0,
+                    1048.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 5,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1264,
+                    1406,
+                    1264,
+                    1406,
+                    1544,
+                    297,
+                    1544
+                ],
+                "score": 0.984
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1641,
+                    1405,
+                    1641,
+                    1405,
+                    2007,
+                    297,
+                    2007
+                ],
+                "score": 0.984
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    576,
+                    774,
+                    1123,
+                    774,
+                    1123,
+                    930,
+                    576,
+                    930
+                ],
+                "score": 0.97
+            },
+            {
+                "category_id": 3,
+                "poly": [
+                    309,
+                    191,
+                    1395,
+                    191,
+                    1395,
+                    469,
+                    309,
+                    469
+                ],
+                "score": 0.966
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    523,
+                    1162,
+                    1175,
+                    1162,
+                    1175,
+                    1249,
+                    523,
+                    1249
+                ],
+                "score": 0.961
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    653,
+                    999,
+                    1045,
+                    999,
+                    1045,
+                    1065,
+                    653,
+                    1065
+                ],
+                "score": 0.959
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    292,
+                    1080,
+                    1403,
+                    1080,
+                    1403,
+                    1147,
+                    292,
+                    1147
+                ],
+                "score": 0.957
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    692,
+                    1401,
+                    692,
+                    1401,
+                    760,
+                    296,
+                    760
+                ],
+                "score": 0.956
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    945,
+                    988,
+                    945,
+                    988,
+                    979,
+                    296,
+                    979
+                ],
+                "score": 0.926
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    299,
+                    1583,
+                    647,
+                    1583,
+                    647,
+                    1616,
+                    299,
+                    1616
+                ],
+                "score": 0.925
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    299,
+                    636,
+                    733,
+                    636,
+                    733,
+                    669,
+                    299,
+                    669
+                ],
+                "score": 0.924
+            },
+            {
+                "category_id": 4,
+                "poly": [
+                    297,
+                    480,
+                    1406,
+                    480,
+                    1406,
+                    574,
+                    297,
+                    574
+                ],
+                "score": 0.923
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1352,
+                    1017,
+                    1400,
+                    1017,
+                    1400,
+                    1048,
+                    1352,
+                    1048
+                ],
+                "score": 0.911
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1351,
+                    837,
+                    1400,
+                    837,
+                    1400,
+                    868,
+                    1351,
+                    868
+                ],
+                "score": 0.901
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1352,
+                    1189,
+                    1400,
+                    1189,
+                    1400,
+                    1220,
+                    1352,
+                    1220
+                ],
+                "score": 0.893
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2061,
+                    858,
+                    2061,
+                    858,
+                    2084,
+                    841,
+                    2084
+                ],
+                "score": 0.717
+            },
+            {
+                "category_id": 4,
+                "poly": [
+                    300,
+                    480,
+                    1401,
+                    480,
+                    1401,
+                    574,
+                    300,
+                    574
+                ],
+                "score": 0.123
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2060,
+                    859,
+                    2060,
+                    859,
+                    2084,
+                    841,
+                    2084
+                ],
+                "score": 0.103
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    652,
+                    996,
+                    1048,
+                    996,
+                    1048,
+                    1065,
+                    652,
+                    1065
+                ],
+                "score": 0.94,
+                "latex": "\\frac { d \\pmb f } { d t } = - \\nabla \\big ( \\log \\rho ( \\pmb f ) - \\log \\pi ( \\pmb f ) \\big ) ."
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    574,
+                    775,
+                    1128,
+                    775,
+                    1128,
+                    933,
+                    574,
+                    933
+                ],
+                "score": 0.93,
+                "latex": "\\begin{array} { l } { \\displaystyle \\frac { \\partial \\rho ( { \\pmb f } ) } { \\partial t } = \\nabla \\cdot \\left( \\rho ( { \\pmb f } ) \\nabla \\frac { \\delta } { \\delta \\rho } D _ { K L } ( \\rho , \\pi ) \\right) } \\\\ { \\displaystyle = \\nabla \\cdot \\left( \\rho ( { \\pmb f } ) \\nabla \\big ( \\log \\rho ( { \\pmb f } ) - \\log \\pi ( { \\pmb f } ) \\big ) \\right) . } \\end{array}"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    523,
+                    1161,
+                    1177,
+                    1161,
+                    1177,
+                    1250,
+                    523,
+                    1250
+                ],
+                "score": 0.93,
+                "latex": "\\pmb { f } _ { t + 1 } ^ { i } = \\pmb { f } _ { t } ^ { i } + \\epsilon _ { t } \\bigg ( \\nabla _ { \\pmb { f } } \\log \\pi ( \\pmb { f } _ { t } ^ { i } ) - \\frac { \\sum _ { j = 1 } ^ { n } \\nabla _ { \\pmb { f } _ { i } ^ { t } } k ( \\pmb { f } _ { i } ^ { t } , \\pmb { f } _ { j } ^ { t } ) } { \\sum _ { j = 1 } ^ { n } k ( \\pmb { f } _ { i } ^ { t } , \\pmb { f } _ { j } ^ { t } ) } \\bigg ) ."
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1159,
+                    1296,
+                    1406,
+                    1296,
+                    1406,
+                    1332,
+                    1159,
+                    1332
+                ],
+                "score": 0.91,
+                "latex": "\\nabla _ { f _ { j } } \\log { p ( f _ { j } | x , y ) } ="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    296,
+                    1328,
+                    700,
+                    1328,
+                    700,
+                    1366,
+                    296,
+                    1366
+                ],
+                "score": 0.9,
+                "latex": "\\nabla _ { f _ { j } } \\log p ( \\pmb { y } | \\pmb { x } , \\pmb { f _ { j } } ) + \\nabla _ { f _ { j } } \\log p ( \\pmb { f _ { j } } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    845,
+                    1419,
+                    894,
+                    1419,
+                    894,
+                    1456,
+                    845,
+                    1456
+                ],
+                "score": 0.88,
+                "latex": "\\textcircled { 1 2 0 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    930,
+                    1111,
+                    966,
+                    1111,
+                    966,
+                    1148,
+                    930,
+                    1148
+                ],
+                "score": 0.86,
+                "latex": "\\textcircled{4}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    568,
+                    1389,
+                    617,
+                    1389,
+                    617,
+                    1422,
+                    568,
+                    1422
+                ],
+                "score": 0.85,
+                "latex": "\\mathbb { \\lVert \\boldsymbol { 6 9 } \\rVert }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    814,
+                    724,
+                    863,
+                    724,
+                    863,
+                    760,
+                    814,
+                    760
+                ],
+                "score": 0.79,
+                "latex": "\\textcircled { 1 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1292,
+                    1389,
+                    1340,
+                    1389,
+                    1340,
+                    1422,
+                    1292,
+                    1422
+                ],
+                "score": 0.77,
+                "latex": "\\pmb { \\mathbb { Z } 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1179,
+                    1732,
+                    1201,
+                    1732,
+                    1201,
+                    1768,
+                    1179,
+                    1768
+                ],
+                "score": 0.68,
+                "latex": "\\checkmark"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    941,
+                    1793,
+                    990,
+                    1793,
+                    990,
+                    1825,
+                    941,
+                    1825
+                ],
+                "score": 0.64,
+                "latex": "\\dot { \\overline { { \\vert 6 9 \\vert } } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1141,
+                    693,
+                    1175,
+                    693,
+                    1175,
+                    730,
+                    1141,
+                    730
+                ],
+                "score": 0.54,
+                "latex": "\\textcircled{5}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    890,
+                    1732,
+                    940,
+                    1732,
+                    940,
+                    1768,
+                    890,
+                    1768
+                ],
+                "score": 0.52,
+                "latex": "( 1 3 )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    929,
+                    1511,
+                    978,
+                    1511,
+                    978,
+                    1543,
+                    929,
+                    1543
+                ],
+                "score": 0.49,
+                "latex": "\\checkmark"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    469.0,
+                    245.0,
+                    485.0,
+                    245.0,
+                    485.0,
+                    258.0,
+                    469.0,
+                    258.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    489.0,
+                    243.0,
+                    530.0,
+                    243.0,
+                    530.0,
+                    259.0,
+                    489.0,
+                    259.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    730.0,
+                    245.0,
+                    747.0,
+                    245.0,
+                    747.0,
+                    258.0,
+                    730.0,
+                    258.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    748.0,
+                    241.0,
+                    811.0,
+                    241.0,
+                    811.0,
+                    260.0,
+                    748.0,
+                    260.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    997.0,
+                    245.0,
+                    1013.0,
+                    245.0,
+                    1013.0,
+                    258.0,
+                    997.0,
+                    258.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1015.0,
+                    241.0,
+                    1081.0,
+                    241.0,
+                    1081.0,
+                    260.0,
+                    1015.0,
+                    260.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1278.0,
+                    244.0,
+                    1346.0,
+                    244.0,
+                    1346.0,
+                    259.0,
+                    1278.0,
+                    259.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    857.0,
+                    295.0,
+                    868.0,
+                    295.0,
+                    868.0,
+                    304.0,
+                    857.0,
+                    304.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    857.0,
+                    323.0,
+                    867.0,
+                    323.0,
+                    867.0,
+                    332.0,
+                    857.0,
+                    332.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1126.0,
+                    406.0,
+                    1136.0,
+                    406.0,
+                    1136.0,
+                    414.0,
+                    1126.0,
+                    414.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    583.0,
+                    432.0,
+                    595.0,
+                    432.0,
+                    595.0,
+                    441.0,
+                    583.0,
+                    441.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    385.0,
+                    456.0,
+                    395.0,
+                    456.0,
+                    395.0,
+                    465.0,
+                    385.0,
+                    465.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    652.0,
+                    456.0,
+                    667.0,
+                    456.0,
+                    667.0,
+                    465.0,
+                    652.0,
+                    465.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    677.0,
+                    456.0,
+                    691.0,
+                    456.0,
+                    691.0,
+                    465.0,
+                    677.0,
+                    465.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    698.0,
+                    456.0,
+                    711.0,
+                    456.0,
+                    711.0,
+                    465.0,
+                    698.0,
+                    465.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    724.0,
+                    456.0,
+                    735.0,
+                    456.0,
+                    735.0,
+                    465.0,
+                    724.0,
+                    465.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    948.0,
+                    456.0,
+                    958.0,
+                    456.0,
+                    958.0,
+                    465.0,
+                    948.0,
+                    465.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    968.0,
+                    456.0,
+                    983.0,
+                    456.0,
+                    983.0,
+                    465.0,
+                    968.0,
+                    465.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1041.0,
+                    456.0,
+                    1052.0,
+                    456.0,
+                    1052.0,
+                    465.0,
+                    1041.0,
+                    465.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1195.0,
+                    456.0,
+                    1210.0,
+                    456.0,
+                    1210.0,
+                    465.0,
+                    1195.0,
+                    465.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1215.0,
+                    456.0,
+                    1231.0,
+                    456.0,
+                    1231.0,
+                    465.0,
+                    1215.0,
+                    465.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1240.0,
+                    456.0,
+                    1255.0,
+                    456.0,
+                    1255.0,
+                    465.0,
+                    1240.0,
+                    465.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1265.0,
+                    456.0,
+                    1276.0,
+                    456.0,
+                    1276.0,
+                    465.0,
+                    1265.0,
+                    465.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    716.0,
+                    307.5,
+                    730.0,
+                    307.5,
+                    730.0,
+                    354.5,
+                    716.0,
+                    354.5
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1581.0,
+                    649.0,
+                    1581.0,
+                    649.0,
+                    1620.0,
+                    294.0,
+                    1620.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    632.0,
+                    737.0,
+                    632.0,
+                    737.0,
+                    675.0,
+                    292.0,
+                    675.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    478.0,
+                    1409.0,
+                    478.0,
+                    1409.0,
+                    516.0,
+                    295.0,
+                    516.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    508.0,
+                    1404.0,
+                    508.0,
+                    1404.0,
+                    546.0,
+                    292.0,
+                    546.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    539.0,
+                    1209.0,
+                    539.0,
+                    1209.0,
+                    576.0,
+                    294.0,
+                    576.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    839.0,
+                    2059.0,
+                    860.0,
+                    2059.0,
+                    860.0,
+                    2091.0,
+                    839.0,
+                    2091.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    478.0,
+                    1406.0,
+                    478.0,
+                    1406.0,
+                    516.0,
+                    295.0,
+                    516.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    508.0,
+                    1406.0,
+                    508.0,
+                    1406.0,
+                    546.0,
+                    294.0,
+                    546.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    539.0,
+                    1210.0,
+                    539.0,
+                    1210.0,
+                    576.0,
+                    295.0,
+                    576.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    839.0,
+                    2059.0,
+                    860.0,
+                    2059.0,
+                    860.0,
+                    2091.0,
+                    839.0,
+                    2091.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1267.0,
+                    1408.0,
+                    1267.0,
+                    1408.0,
+                    1300.0,
+                    296.0,
+                    1300.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1296.0,
+                    1158.0,
+                    1296.0,
+                    1158.0,
+                    1333.0,
+                    294.0,
+                    1333.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1323.0,
+                    295.0,
+                    1323.0,
+                    295.0,
+                    1371.0,
+                    291.0,
+                    1371.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    701.0,
+                    1323.0,
+                    1411.0,
+                    1323.0,
+                    1411.0,
+                    1371.0,
+                    701.0,
+                    1371.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1360.0,
+                    1407.0,
+                    1360.0,
+                    1407.0,
+                    1393.0,
+                    295.0,
+                    1393.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1387.0,
+                    567.0,
+                    1387.0,
+                    567.0,
+                    1426.0,
+                    292.0,
+                    1426.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    618.0,
+                    1387.0,
+                    1291.0,
+                    1387.0,
+                    1291.0,
+                    1426.0,
+                    618.0,
+                    1426.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1341.0,
+                    1387.0,
+                    1408.0,
+                    1387.0,
+                    1408.0,
+                    1426.0,
+                    1341.0,
+                    1426.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1418.0,
+                    844.0,
+                    1418.0,
+                    844.0,
+                    1457.0,
+                    292.0,
+                    1457.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    895.0,
+                    1418.0,
+                    1404.0,
+                    1418.0,
+                    1404.0,
+                    1457.0,
+                    895.0,
+                    1457.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1450.0,
+                    1406.0,
+                    1450.0,
+                    1406.0,
+                    1487.0,
+                    294.0,
+                    1487.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1481.0,
+                    1406.0,
+                    1481.0,
+                    1406.0,
+                    1517.0,
+                    295.0,
+                    1517.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1510.0,
+                    928.0,
+                    1510.0,
+                    928.0,
+                    1544.0,
+                    294.0,
+                    1544.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    979.0,
+                    1510.0,
+                    982.0,
+                    1510.0,
+                    982.0,
+                    1544.0,
+                    979.0,
+                    1544.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1641.0,
+                    1406.0,
+                    1641.0,
+                    1406.0,
+                    1678.0,
+                    294.0,
+                    1678.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1669.0,
+                    1406.0,
+                    1669.0,
+                    1406.0,
+                    1710.0,
+                    292.0,
+                    1710.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1701.0,
+                    1406.0,
+                    1701.0,
+                    1406.0,
+                    1737.0,
+                    292.0,
+                    1737.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1733.0,
+                    889.0,
+                    1733.0,
+                    889.0,
+                    1771.0,
+                    294.0,
+                    1771.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    941.0,
+                    1733.0,
+                    1178.0,
+                    1733.0,
+                    1178.0,
+                    1771.0,
+                    941.0,
+                    1771.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1202.0,
+                    1733.0,
+                    1408.0,
+                    1733.0,
+                    1408.0,
+                    1771.0,
+                    1202.0,
+                    1771.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1763.0,
+                    1407.0,
+                    1763.0,
+                    1407.0,
+                    1796.0,
+                    294.0,
+                    1796.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1792.0,
+                    940.0,
+                    1792.0,
+                    940.0,
+                    1826.0,
+                    294.0,
+                    1826.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    991.0,
+                    1792.0,
+                    1407.0,
+                    1792.0,
+                    1407.0,
+                    1826.0,
+                    991.0,
+                    1826.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1820.0,
+                    1408.0,
+                    1820.0,
+                    1408.0,
+                    1859.0,
+                    292.0,
+                    1859.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1854.0,
+                    1405.0,
+                    1854.0,
+                    1405.0,
+                    1888.0,
+                    295.0,
+                    1888.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1882.0,
+                    1405.0,
+                    1882.0,
+                    1405.0,
+                    1920.0,
+                    294.0,
+                    1920.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1911.0,
+                    1406.0,
+                    1911.0,
+                    1406.0,
+                    1951.0,
+                    292.0,
+                    1951.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1947.0,
+                    1403.0,
+                    1947.0,
+                    1403.0,
+                    1981.0,
+                    295.0,
+                    1981.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1977.0,
+                    724.0,
+                    1977.0,
+                    724.0,
+                    2007.0,
+                    295.0,
+                    2007.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1077.0,
+                    1405.0,
+                    1077.0,
+                    1405.0,
+                    1117.0,
+                    295.0,
+                    1117.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1107.0,
+                    929.0,
+                    1107.0,
+                    929.0,
+                    1151.0,
+                    292.0,
+                    1151.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    967.0,
+                    1107.0,
+                    1005.0,
+                    1107.0,
+                    1005.0,
+                    1151.0,
+                    967.0,
+                    1151.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    689.0,
+                    1140.0,
+                    689.0,
+                    1140.0,
+                    730.0,
+                    294.0,
+                    730.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1176.0,
+                    689.0,
+                    1405.0,
+                    689.0,
+                    1405.0,
+                    730.0,
+                    1176.0,
+                    730.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    725.0,
+                    813.0,
+                    725.0,
+                    813.0,
+                    761.0,
+                    294.0,
+                    761.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    864.0,
+                    725.0,
+                    1095.0,
+                    725.0,
+                    1095.0,
+                    761.0,
+                    864.0,
+                    761.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    945.0,
+                    988.0,
+                    945.0,
+                    988.0,
+                    982.0,
+                    296.0,
+                    982.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 6,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    894,
+                    1404,
+                    894,
+                    1404,
+                    1321,
+                    298,
+                    1321
+                ],
+                "score": 0.984
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1356,
+                    1405,
+                    1356,
+                    1405,
+                    1539,
+                    297,
+                    1539
+                ],
+                "score": 0.979
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1574,
+                    1404,
+                    1574,
+                    1404,
+                    1819,
+                    297,
+                    1819
+                ],
+                "score": 0.979
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1854,
+                    1403,
+                    1854,
+                    1403,
+                    2007,
+                    299,
+                    2007
+                ],
+                "score": 0.976
+            },
+            {
+                "category_id": 3,
+                "poly": [
+                    336,
+                    207,
+                    1416,
+                    207,
+                    1416,
+                    646,
+                    336,
+                    646
+                ],
+                "score": 0.974
+            },
+            {
+                "category_id": 4,
+                "poly": [
+                    301,
+                    674,
+                    1409,
+                    674,
+                    1409,
+                    766,
+                    301,
+                    766
+                ],
+                "score": 0.957
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    298,
+                    824,
+                    532,
+                    824,
+                    532,
+                    862,
+                    298,
+                    862
+                ],
+                "score": 0.911
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2062,
+                    858,
+                    2062,
+                    858,
+                    2085,
+                    841,
+                    2085
+                ],
+                "score": 0.8
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1136,
+                    1137,
+                    1238,
+                    1137,
+                    1238,
+                    1170,
+                    1136,
+                    1170
+                ],
+                "score": 0.91,
+                "latex": "( H _ { o } / H _ { t } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1017,
+                    1260,
+                    1175,
+                    1260,
+                    1175,
+                    1292,
+                    1017,
+                    1292
+                ],
+                "score": 0.91,
+                "latex": "( M D _ { o } / M D _ { t } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    699,
+                    1477,
+                    748,
+                    1477,
+                    748,
+                    1509,
+                    699,
+                    1509
+                ],
+                "score": 0.82,
+                "latex": "\\mathbb { \\left[ \\left[ 5 9 \\right] \\right] }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    717,
+                    1636,
+                    809,
+                    1636,
+                    809,
+                    1667,
+                    717,
+                    1667
+                ],
+                "score": 0.66,
+                "latex": "\\pm 1 , 2 , 3"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    894,
+                    1416,
+                    924,
+                    1416,
+                    924,
+                    1452,
+                    894,
+                    1452
+                ],
+                "score": 0.66,
+                "latex": "^ { 2 ) }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1323,
+                    955,
+                    1372,
+                    955,
+                    1372,
+                    988,
+                    1323,
+                    988
+                ],
+                "score": 0.64,
+                "latex": "\\mathbb { \\left[ \\left[ 5 1 \\right] \\right] }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    869,
+                    1167,
+                    919,
+                    1167,
+                    919,
+                    1200,
+                    869,
+                    1200
+                ],
+                "score": 0.47,
+                "latex": "\\mathbb { H }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    916,
+                    1228,
+                    949,
+                    1228,
+                    949,
+                    1264,
+                    916,
+                    1264
+                ],
+                "score": 0.43,
+                "latex": "\\bar { \\bigtriangledown } \\bar { \\bigtriangledown }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1099,
+                    1476,
+                    1143,
+                    1476,
+                    1143,
+                    1513,
+                    1099,
+                    1513
+                ],
+                "score": 0.36,
+                "latex": "\\mathrm { F . l }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    508,
+                    1913,
+                    537,
+                    1913,
+                    537,
+                    1950,
+                    508,
+                    1950
+                ],
+                "score": 0.31,
+                "latex": "\\textcircled { 3 }"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    363.0,
+                    210.0,
+                    511.0,
+                    210.0,
+                    511.0,
+                    239.0,
+                    363.0,
+                    239.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    598.0,
+                    212.0,
+                    679.0,
+                    212.0,
+                    679.0,
+                    236.0,
+                    598.0,
+                    236.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    795.0,
+                    212.0,
+                    885.0,
+                    212.0,
+                    885.0,
+                    236.0,
+                    795.0,
+                    236.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    990.0,
+                    212.0,
+                    1090.0,
+                    212.0,
+                    1090.0,
+                    236.0,
+                    990.0,
+                    236.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1195.0,
+                    214.0,
+                    1286.0,
+                    214.0,
+                    1286.0,
+                    235.0,
+                    1195.0,
+                    235.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1374.0,
+                    223.0,
+                    1414.0,
+                    223.0,
+                    1414.0,
+                    244.0,
+                    1374.0,
+                    244.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    397.0,
+                    313.0,
+                    425.0,
+                    313.0,
+                    425.0,
+                    331.0,
+                    397.0,
+                    331.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    443.0,
+                    313.0,
+                    473.0,
+                    313.0,
+                    473.0,
+                    336.0,
+                    443.0,
+                    336.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    597.0,
+                    312.0,
+                    626.0,
+                    312.0,
+                    626.0,
+                    334.0,
+                    597.0,
+                    334.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    646.0,
+                    313.0,
+                    674.0,
+                    313.0,
+                    674.0,
+                    336.0,
+                    646.0,
+                    336.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    800.0,
+                    315.0,
+                    827.0,
+                    315.0,
+                    827.0,
+                    333.0,
+                    800.0,
+                    333.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    848.0,
+                    313.0,
+                    876.0,
+                    313.0,
+                    876.0,
+                    336.0,
+                    848.0,
+                    336.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1001.0,
+                    315.0,
+                    1028.0,
+                    315.0,
+                    1028.0,
+                    331.0,
+                    1001.0,
+                    331.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1048.0,
+                    313.0,
+                    1075.0,
+                    313.0,
+                    1075.0,
+                    337.0,
+                    1048.0,
+                    337.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1202.0,
+                    313.0,
+                    1230.0,
+                    313.0,
+                    1230.0,
+                    331.0,
+                    1202.0,
+                    331.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1247.0,
+                    312.0,
+                    1277.0,
+                    312.0,
+                    1277.0,
+                    336.0,
+                    1247.0,
+                    336.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1373.0,
+                    301.0,
+                    1418.0,
+                    301.0,
+                    1418.0,
+                    331.0,
+                    1373.0,
+                    331.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    410.0,
+                    339.0,
+                    435.0,
+                    339.0,
+                    435.0,
+                    364.0,
+                    410.0,
+                    364.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    437.0,
+                    339.0,
+                    464.0,
+                    339.0,
+                    464.0,
+                    362.0,
+                    437.0,
+                    362.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    611.0,
+                    337.0,
+                    665.0,
+                    337.0,
+                    665.0,
+                    364.0,
+                    611.0,
+                    364.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    812.0,
+                    337.0,
+                    838.0,
+                    337.0,
+                    838.0,
+                    365.0,
+                    812.0,
+                    365.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    844.0,
+                    341.0,
+                    865.0,
+                    341.0,
+                    865.0,
+                    359.0,
+                    844.0,
+                    359.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1012.0,
+                    337.0,
+                    1064.0,
+                    337.0,
+                    1064.0,
+                    363.0,
+                    1012.0,
+                    363.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1212.0,
+                    336.0,
+                    1242.0,
+                    336.0,
+                    1242.0,
+                    365.0,
+                    1212.0,
+                    365.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1252.0,
+                    346.0,
+                    1263.0,
+                    346.0,
+                    1263.0,
+                    354.0,
+                    1252.0,
+                    354.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1370.0,
+                    383.0,
+                    1418.0,
+                    383.0,
+                    1418.0,
+                    413.0,
+                    1370.0,
+                    413.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    406.0,
+                    428.0,
+                    462.0,
+                    428.0,
+                    462.0,
+                    452.0,
+                    406.0,
+                    452.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    601.0,
+                    428.0,
+                    676.0,
+                    428.0,
+                    676.0,
+                    452.0,
+                    601.0,
+                    452.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    789.0,
+                    429.0,
+                    888.0,
+                    429.0,
+                    888.0,
+                    453.0,
+                    789.0,
+                    453.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    983.0,
+                    428.0,
+                    1096.0,
+                    428.0,
+                    1096.0,
+                    453.0,
+                    983.0,
+                    453.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1189.0,
+                    428.0,
+                    1292.0,
+                    428.0,
+                    1292.0,
+                    453.0,
+                    1189.0,
+                    453.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1373.0,
+                    467.0,
+                    1417.0,
+                    467.0,
+                    1417.0,
+                    494.0,
+                    1373.0,
+                    494.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    397.0,
+                    531.0,
+                    418.0,
+                    531.0,
+                    418.0,
+                    546.0,
+                    397.0,
+                    546.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    447.0,
+                    532.0,
+                    472.0,
+                    532.0,
+                    472.0,
+                    550.0,
+                    447.0,
+                    550.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    601.0,
+                    534.0,
+                    619.0,
+                    534.0,
+                    619.0,
+                    547.0,
+                    601.0,
+                    547.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    644.0,
+                    531.0,
+                    674.0,
+                    531.0,
+                    674.0,
+                    553.0,
+                    644.0,
+                    553.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    851.0,
+                    532.0,
+                    875.0,
+                    532.0,
+                    875.0,
+                    555.0,
+                    851.0,
+                    555.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1049.0,
+                    531.0,
+                    1075.0,
+                    531.0,
+                    1075.0,
+                    555.0,
+                    1049.0,
+                    555.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1251.0,
+                    532.0,
+                    1274.0,
+                    532.0,
+                    1274.0,
+                    553.0,
+                    1251.0,
+                    553.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    406.0,
+                    550.0,
+                    465.0,
+                    550.0,
+                    465.0,
+                    580.0,
+                    406.0,
+                    580.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    633.0,
+                    552.0,
+                    665.0,
+                    552.0,
+                    665.0,
+                    580.0,
+                    633.0,
+                    580.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    818.0,
+                    567.0,
+                    833.0,
+                    567.0,
+                    833.0,
+                    577.0,
+                    818.0,
+                    577.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    838.0,
+                    556.0,
+                    865.0,
+                    556.0,
+                    865.0,
+                    574.0,
+                    838.0,
+                    574.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1037.0,
+                    554.0,
+                    1067.0,
+                    554.0,
+                    1067.0,
+                    576.0,
+                    1037.0,
+                    576.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1210.0,
+                    552.0,
+                    1241.0,
+                    552.0,
+                    1241.0,
+                    583.0,
+                    1210.0,
+                    583.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1371.0,
+                    548.0,
+                    1417.0,
+                    548.0,
+                    1417.0,
+                    578.0,
+                    1371.0,
+                    578.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1379.0,
+                    633.0,
+                    1413.0,
+                    633.0,
+                    1413.0,
+                    650.0,
+                    1379.0,
+                    650.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1249.0,
+                    553.0,
+                    1261.0,
+                    553.0,
+                    1261.0,
+                    575.5,
+                    1249.0,
+                    575.5
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    602.0,
+                    551.5,
+                    648.0,
+                    551.5,
+                    648.0,
+                    580.5,
+                    602.0,
+                    580.5
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1007.0,
+                    560.5,
+                    1047.0,
+                    560.5,
+                    1047.0,
+                    575.5,
+                    1007.0,
+                    575.5
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    671.0,
+                    1405.0,
+                    671.0,
+                    1405.0,
+                    710.0,
+                    294.0,
+                    710.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    701.0,
+                    1405.0,
+                    701.0,
+                    1405.0,
+                    743.0,
+                    294.0,
+                    743.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    298.0,
+                    736.0,
+                    678.0,
+                    736.0,
+                    678.0,
+                    769.0,
+                    298.0,
+                    769.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    289.0,
+                    819.0,
+                    537.0,
+                    819.0,
+                    537.0,
+                    870.0,
+                    289.0,
+                    870.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    839.0,
+                    2059.0,
+                    860.0,
+                    2059.0,
+                    860.0,
+                    2089.0,
+                    839.0,
+                    2089.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    896.0,
+                    1401.0,
+                    896.0,
+                    1401.0,
+                    928.0,
+                    296.0,
+                    928.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    925.0,
+                    1409.0,
+                    925.0,
+                    1409.0,
+                    959.0,
+                    293.0,
+                    959.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    955.0,
+                    1322.0,
+                    955.0,
+                    1322.0,
+                    991.0,
+                    294.0,
+                    991.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1373.0,
+                    955.0,
+                    1402.0,
+                    955.0,
+                    1402.0,
+                    991.0,
+                    1373.0,
+                    991.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    986.0,
+                    1406.0,
+                    986.0,
+                    1406.0,
+                    1021.0,
+                    294.0,
+                    1021.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1016.0,
+                    1406.0,
+                    1016.0,
+                    1406.0,
+                    1052.0,
+                    294.0,
+                    1052.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1048.0,
+                    1404.0,
+                    1048.0,
+                    1404.0,
+                    1080.0,
+                    293.0,
+                    1080.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1077.0,
+                    1406.0,
+                    1077.0,
+                    1406.0,
+                    1113.0,
+                    294.0,
+                    1113.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1108.0,
+                    1408.0,
+                    1108.0,
+                    1408.0,
+                    1143.0,
+                    294.0,
+                    1143.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1137.0,
+                    1135.0,
+                    1137.0,
+                    1135.0,
+                    1172.0,
+                    293.0,
+                    1172.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1239.0,
+                    1137.0,
+                    1406.0,
+                    1137.0,
+                    1406.0,
+                    1172.0,
+                    1239.0,
+                    1172.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1167.0,
+                    868.0,
+                    1167.0,
+                    868.0,
+                    1203.0,
+                    294.0,
+                    1203.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    920.0,
+                    1167.0,
+                    1405.0,
+                    1167.0,
+                    1405.0,
+                    1203.0,
+                    920.0,
+                    1203.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1195.0,
+                    1404.0,
+                    1195.0,
+                    1404.0,
+                    1234.0,
+                    293.0,
+                    1234.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1229.0,
+                    915.0,
+                    1229.0,
+                    915.0,
+                    1265.0,
+                    296.0,
+                    1265.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    950.0,
+                    1229.0,
+                    1405.0,
+                    1229.0,
+                    1405.0,
+                    1265.0,
+                    950.0,
+                    1265.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1260.0,
+                    1016.0,
+                    1260.0,
+                    1016.0,
+                    1295.0,
+                    294.0,
+                    1295.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1176.0,
+                    1260.0,
+                    1404.0,
+                    1260.0,
+                    1404.0,
+                    1295.0,
+                    1176.0,
+                    1295.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1287.0,
+                    1218.0,
+                    1287.0,
+                    1218.0,
+                    1327.0,
+                    293.0,
+                    1327.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1355.0,
+                    1406.0,
+                    1355.0,
+                    1406.0,
+                    1391.0,
+                    295.0,
+                    1391.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1386.0,
+                    1405.0,
+                    1386.0,
+                    1405.0,
+                    1421.0,
+                    295.0,
+                    1421.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1416.0,
+                    893.0,
+                    1416.0,
+                    893.0,
+                    1451.0,
+                    294.0,
+                    1451.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    925.0,
+                    1416.0,
+                    1405.0,
+                    1416.0,
+                    1405.0,
+                    1451.0,
+                    925.0,
+                    1451.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1446.0,
+                    1405.0,
+                    1446.0,
+                    1405.0,
+                    1482.0,
+                    295.0,
+                    1482.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1474.0,
+                    698.0,
+                    1474.0,
+                    698.0,
+                    1513.0,
+                    294.0,
+                    1513.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    749.0,
+                    1474.0,
+                    1098.0,
+                    1474.0,
+                    1098.0,
+                    1513.0,
+                    749.0,
+                    1513.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1144.0,
+                    1474.0,
+                    1409.0,
+                    1474.0,
+                    1409.0,
+                    1513.0,
+                    1144.0,
+                    1513.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1504.0,
+                    767.0,
+                    1504.0,
+                    767.0,
+                    1542.0,
+                    294.0,
+                    1542.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1573.0,
+                    1407.0,
+                    1573.0,
+                    1407.0,
+                    1611.0,
+                    292.0,
+                    1611.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1605.0,
+                    1395.0,
+                    1605.0,
+                    1395.0,
+                    1643.0,
+                    294.0,
+                    1643.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1637.0,
+                    716.0,
+                    1637.0,
+                    716.0,
+                    1670.0,
+                    295.0,
+                    1670.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    810.0,
+                    1637.0,
+                    1405.0,
+                    1637.0,
+                    1405.0,
+                    1670.0,
+                    810.0,
+                    1670.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1667.0,
+                    1405.0,
+                    1667.0,
+                    1405.0,
+                    1700.0,
+                    295.0,
+                    1700.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1698.0,
+                    1404.0,
+                    1698.0,
+                    1404.0,
+                    1731.0,
+                    295.0,
+                    1731.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1725.0,
+                    1404.0,
+                    1725.0,
+                    1404.0,
+                    1761.0,
+                    292.0,
+                    1761.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1754.0,
+                    1405.0,
+                    1754.0,
+                    1405.0,
+                    1794.0,
+                    292.0,
+                    1794.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1785.0,
+                    1131.0,
+                    1785.0,
+                    1131.0,
+                    1825.0,
+                    292.0,
+                    1825.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1850.0,
+                    1405.0,
+                    1850.0,
+                    1405.0,
+                    1891.0,
+                    293.0,
+                    1891.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1883.0,
+                    1404.0,
+                    1883.0,
+                    1404.0,
+                    1919.0,
+                    295.0,
+                    1919.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1912.0,
+                    507.0,
+                    1912.0,
+                    507.0,
+                    1953.0,
+                    293.0,
+                    1953.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    538.0,
+                    1912.0,
+                    1407.0,
+                    1912.0,
+                    1407.0,
+                    1953.0,
+                    538.0,
+                    1953.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1946.0,
+                    1407.0,
+                    1946.0,
+                    1407.0,
+                    1979.0,
+                    295.0,
+                    1979.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1977.0,
+                    1403.0,
+                    1977.0,
+                    1403.0,
+                    2010.0,
+                    295.0,
+                    2010.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 7,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 5,
+                "poly": [
+                    298,
+                    399,
+                    1403,
+                    399,
+                    1403,
+                    869,
+                    298,
+                    869
+                ],
+                "score": 0.985,
+                "html": "<table><tr><td rowspan=\"11\">Prroiiiie</td><td></td><td>AUROC(H)</td><td>AUROC(MD)</td><td>Accuracy</td><td>H/Ht</td><td>MD/MDt</td><td>ECE</td><td>NLL</td></tr><tr><td>Deep ensemble 4</td><td>0.958±0.001</td><td>0.975±0.001</td><td>91.122±0.013</td><td>6.257±0.005</td><td>6.394±0.001</td><td>0.012±0.001</td><td>0.129±0.001</td></tr><tr><td>SVGD [51</td><td>0.960±0.001</td><td>0.973±0.001</td><td>91.134±0.024</td><td>6.315±0.019</td><td>6.395±0.018</td><td>0.014±0.001</td><td>0.127±0.001</td></tr><tr><td>f-SVGD [76</td><td>0.956±0.001</td><td>0.975±0.001</td><td>89.884±0.015</td><td>5.652±0.009</td><td>6.531±0.005</td><td>0.013±0.001</td><td>0.150±0.001</td></tr><tr><td>hyper-DE [80]</td><td>0.968±0.001</td><td>0.981±0.001</td><td>91.160±0.007</td><td>6.682±0.065</td><td>7.059±0.152</td><td>0.014±0.001</td><td>0.128±0.001</td></tr><tr><td>kde-WGD (ours)</td><td>0.960±0.001</td><td>0.970±0.001</td><td>91.238±0.019</td><td>6.587±0.019</td><td>6.379±0.018</td><td>0.014±0.001</td><td>0.128±0.001</td></tr><tr><td>sge-WGD (ours)</td><td>0.960±0.001</td><td>0.970±0.001</td><td>91.312±0.016</td><td>6.562±0.007</td><td>6.363±0.009</td><td>0.012±0.001</td><td>0.128±0.001</td></tr><tr><td>ssge-WGD (ours)</td><td>0.968±0.001</td><td>0.979±0.001</td><td>91.198±0.024</td><td>6.522±0.009</td><td>6.610±0.012</td><td>0.012±0.001</td><td>0.130±0.001</td></tr><tr><td>kde-fWGD (ours)</td><td>0.971±0.001</td><td>0.980±0.001</td><td>91.260±0.011</td><td>7.079±0.016</td><td>6.887±0.015</td><td>0.015±0.001</td><td>0.125±0.001</td></tr><tr><td>sge-fWGD (ours)</td><td>0.969±0.001</td><td>0.978±0.001</td><td>91.192±0.013</td><td>7.076±0.004</td><td>6.900±0.005</td><td>0.015±0.001</td><td>0.125±0.001</td></tr><tr><td>ssge-fWGD (ours)</td><td>0.971±0.001</td><td>0.980±0.001</td><td>91.240±0.022</td><td>7.129±0.006</td><td>6.951±0.005</td><td>0.016±0.001</td><td>0.124±0.001</td></tr><tr><td rowspan=\"11\">CITIIIO</td><td>Deep ensemble 42</td><td>0.843±0.004</td><td>0.736±0.005</td><td>85,552±0.076</td><td>2.244±0.006</td><td>1.667±0.008</td><td>0.049±0.001</td><td>0.277±0.001</td></tr><tr><td>SVGD [51</td><td>0.825±0.001</td><td>0.710±0.002</td><td>85.142±0.017</td><td>2.106±0.003</td><td>1.567±0.004</td><td>0.052±0.001</td><td>0.287±0.001</td></tr><tr><td>fSVGD 回</td><td>0.783±0.001</td><td>0.712±0.001</td><td>84.510±0.031</td><td>1.968±0.004</td><td>1.624±0.003</td><td>0.049±0.001</td><td>0.292±0.001</td></tr><tr><td>hyper-DE [80]</td><td>0.789±0.001</td><td>0.743±0.001</td><td>84.743±0.011</td><td>1.951±0.010</td><td>1.690±0.015</td><td>0.046±0.001</td><td>0.288±0.001</td></tr><tr><td>kde-WGD (ours)</td><td>0.838±0.001</td><td>0.735±0.004</td><td>85.904±0.030</td><td>2.205±0.003</td><td>1.661±0.008</td><td>0.053±0.001</td><td>0.276±0.001</td></tr><tr><td>sge-WGD (ours)</td><td>0.837±0.003</td><td>0.725±0.004</td><td>85.792±0.035</td><td>2.214±0.010</td><td>1.634±0.004</td><td>0.051±0.001</td><td>0.275±0.001</td></tr><tr><td>ssge-WGD (ours)</td><td>0.832±0.003</td><td>0.731±0.005</td><td>85.638±0.038</td><td>2.182±0.015</td><td>1.655±0.001</td><td>0.049±0.001</td><td>0.276±0.001</td></tr><tr><td>kde-fWGD (ours)</td><td>0.791±0.002</td><td>0.758±0.002</td><td>84.888±0.030</td><td>1.970±0.004</td><td>1.749±0.005</td><td>0.044±0.001</td><td>0.282±0.001</td></tr><tr><td>sge-fWGD (ours)</td><td>0.795±0.001</td><td>0.754±0.002</td><td>84.766±0.060</td><td>1.984±0.003</td><td>1.729±0.002</td><td>0.047±0.001</td><td>0.288±0.001</td></tr><tr><td>ssge-fWGD (ours)</td><td>0.792±0.002</td><td>0.752±0.002</td><td>84.762±0.034</td><td>1.970±0.006</td><td>1.723±0.005</td><td>0.046±0.001</td><td>0.286±0.001</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></table>"
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1181,
+                    1405,
+                    1181,
+                    1405,
+                    1606,
+                    297,
+                    1606
+                ],
+                "score": 0.984
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1643,
+                    1404,
+                    1643,
+                    1404,
+                    1827,
+                    298,
+                    1827
+                ],
+                "score": 0.98
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    930,
+                    1405,
+                    930,
+                    1405,
+                    1144,
+                    297,
+                    1144
+                ],
+                "score": 0.976
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1943,
+                    1398,
+                    1943,
+                    1398,
+                    2007,
+                    299,
+                    2007
+                ],
+                "score": 0.934
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    298,
+                    1872,
+                    548,
+                    1872,
+                    548,
+                    1910,
+                    298,
+                    1910
+                ],
+                "score": 0.912
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    840,
+                    2061,
+                    858,
+                    2061,
+                    858,
+                    2084,
+                    840,
+                    2084
+                ],
+                "score": 0.798
+            },
+            {
+                "category_id": 6,
+                "poly": [
+                    296,
+                    194,
+                    1403,
+                    194,
+                    1403,
+                    380,
+                    296,
+                    380
+                ],
+                "score": 0.773
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    194,
+                    1403,
+                    194,
+                    1403,
+                    380,
+                    296,
+                    380
+                ],
+                "score": 0.409
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    964,
+                    227,
+                    1057,
+                    227,
+                    1057,
+                    261,
+                    964,
+                    261
+                ],
+                "score": 0.93,
+                "latex": "\\mathbf { H _ { o } / H _ { t } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    715,
+                    258,
+                    867,
+                    258,
+                    867,
+                    290,
+                    715,
+                    290
+                ],
+                "score": 0.9,
+                "latex": "\\mathbf { M D _ { o } / M D _ { t } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1208,
+                    1211,
+                    1257,
+                    1211,
+                    1257,
+                    1243,
+                    1208,
+                    1243
+                ],
+                "score": 0.78,
+                "latex": "\\bar { \\mathbb { E } 3 } \\mathbb { I }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    754,
+                    1211,
+                    803,
+                    1211,
+                    803,
+                    1244,
+                    754,
+                    1244
+                ],
+                "score": 0.78,
+                "latex": "\\dot { \\left[ \\left| 8 3 \\right| \\right] }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1131,
+                    1052,
+                    1222,
+                    1052,
+                    1222,
+                    1085,
+                    1131,
+                    1085
+                ],
+                "score": 0.56,
+                "latex": "\\mathbb { H 9 } \\mathbb { L O }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    947,
+                    1242,
+                    973,
+                    1242,
+                    973,
+                    1279,
+                    947,
+                    1279
+                ],
+                "score": 0.55,
+                "latex": "^ 1 { } _ { . }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    461,
+                    1673,
+                    509,
+                    1673,
+                    509,
+                    1706,
+                    461,
+                    1706
+                ],
+                "score": 0.46,
+                "latex": "\\mathbb { \\left[ 6 1 \\right] }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    715,
+                    1544,
+                    764,
+                    1544,
+                    764,
+                    1577,
+                    715,
+                    1577
+                ],
+                "score": 0.44,
+                "latex": "[ \\textcircled { 8 0 } ]"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1032,
+                    1642,
+                    1082,
+                    1642,
+                    1082,
+                    1675,
+                    1032,
+                    1675
+                ],
+                "score": 0.4,
+                "latex": "\\mathbb { \\left| \\left[ 2 9 \\right] \\right| }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    802,
+                    197,
+                    840,
+                    197,
+                    840,
+                    227,
+                    802,
+                    227
+                ],
+                "score": 0.29,
+                "latex": "\\mathbf { ( H ) }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1123,
+                    1514,
+                    1171,
+                    1514,
+                    1171,
+                    1547,
+                    1123,
+                    1547
+                ],
+                "score": 0.27,
+                "latex": "\\pmb { \\mathbb { B } } \\mathbf { \\mathbb { 1 } }"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1871.0,
+                    551.0,
+                    1871.0,
+                    551.0,
+                    1915.0,
+                    292.0,
+                    1915.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    839.0,
+                    2060.0,
+                    860.0,
+                    2060.0,
+                    860.0,
+                    2090.0,
+                    839.0,
+                    2090.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    194.0,
+                    801.0,
+                    194.0,
+                    801.0,
+                    232.0,
+                    293.0,
+                    232.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    841.0,
+                    194.0,
+                    1405.0,
+                    194.0,
+                    1405.0,
+                    232.0,
+                    841.0,
+                    232.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    226.0,
+                    963.0,
+                    226.0,
+                    963.0,
+                    264.0,
+                    293.0,
+                    264.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1058.0,
+                    226.0,
+                    1405.0,
+                    226.0,
+                    1405.0,
+                    264.0,
+                    1058.0,
+                    264.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    259.0,
+                    714.0,
+                    259.0,
+                    714.0,
+                    291.0,
+                    296.0,
+                    291.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    868.0,
+                    259.0,
+                    1404.0,
+                    259.0,
+                    1404.0,
+                    291.0,
+                    868.0,
+                    291.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    287.0,
+                    1404.0,
+                    287.0,
+                    1404.0,
+                    323.0,
+                    295.0,
+                    323.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    314.0,
+                    1408.0,
+                    314.0,
+                    1408.0,
+                    356.0,
+                    293.0,
+                    356.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    347.0,
+                    1098.0,
+                    347.0,
+                    1098.0,
+                    387.0,
+                    293.0,
+                    387.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1180.0,
+                    1405.0,
+                    1180.0,
+                    1405.0,
+                    1216.0,
+                    295.0,
+                    1216.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1211.0,
+                    753.0,
+                    1211.0,
+                    753.0,
+                    1246.0,
+                    294.0,
+                    1246.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    804.0,
+                    1211.0,
+                    1207.0,
+                    1211.0,
+                    1207.0,
+                    1246.0,
+                    804.0,
+                    1246.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1258.0,
+                    1211.0,
+                    1408.0,
+                    1211.0,
+                    1408.0,
+                    1246.0,
+                    1258.0,
+                    1246.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1242.0,
+                    946.0,
+                    1242.0,
+                    946.0,
+                    1277.0,
+                    295.0,
+                    1277.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    974.0,
+                    1242.0,
+                    1405.0,
+                    1242.0,
+                    1405.0,
+                    1277.0,
+                    974.0,
+                    1277.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1272.0,
+                    1406.0,
+                    1272.0,
+                    1406.0,
+                    1308.0,
+                    295.0,
+                    1308.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1304.0,
+                    1406.0,
+                    1304.0,
+                    1406.0,
+                    1337.0,
+                    294.0,
+                    1337.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1333.0,
+                    1405.0,
+                    1333.0,
+                    1405.0,
+                    1368.0,
+                    294.0,
+                    1368.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1363.0,
+                    1405.0,
+                    1363.0,
+                    1405.0,
+                    1399.0,
+                    295.0,
+                    1399.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1395.0,
+                    1403.0,
+                    1395.0,
+                    1403.0,
+                    1430.0,
+                    295.0,
+                    1430.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1422.0,
+                    1405.0,
+                    1422.0,
+                    1405.0,
+                    1460.0,
+                    294.0,
+                    1460.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1454.0,
+                    1407.0,
+                    1454.0,
+                    1407.0,
+                    1489.0,
+                    294.0,
+                    1489.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1482.0,
+                    1405.0,
+                    1482.0,
+                    1405.0,
+                    1520.0,
+                    292.0,
+                    1520.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1510.0,
+                    1122.0,
+                    1510.0,
+                    1122.0,
+                    1554.0,
+                    291.0,
+                    1554.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1172.0,
+                    1510.0,
+                    1405.0,
+                    1510.0,
+                    1405.0,
+                    1554.0,
+                    1172.0,
+                    1554.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1544.0,
+                    714.0,
+                    1544.0,
+                    714.0,
+                    1582.0,
+                    294.0,
+                    1582.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    765.0,
+                    1544.0,
+                    1405.0,
+                    1544.0,
+                    1405.0,
+                    1582.0,
+                    765.0,
+                    1582.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1578.0,
+                    718.0,
+                    1578.0,
+                    718.0,
+                    1609.0,
+                    296.0,
+                    1609.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1642.0,
+                    1031.0,
+                    1642.0,
+                    1031.0,
+                    1678.0,
+                    296.0,
+                    1678.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1083.0,
+                    1642.0,
+                    1405.0,
+                    1642.0,
+                    1405.0,
+                    1678.0,
+                    1083.0,
+                    1678.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1674.0,
+                    460.0,
+                    1674.0,
+                    460.0,
+                    1710.0,
+                    296.0,
+                    1710.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    510.0,
+                    1674.0,
+                    1406.0,
+                    1674.0,
+                    1406.0,
+                    1710.0,
+                    510.0,
+                    1710.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1706.0,
+                    1404.0,
+                    1706.0,
+                    1404.0,
+                    1738.0,
+                    296.0,
+                    1738.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1735.0,
+                    1405.0,
+                    1735.0,
+                    1405.0,
+                    1771.0,
+                    294.0,
+                    1771.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1763.0,
+                    1408.0,
+                    1763.0,
+                    1408.0,
+                    1802.0,
+                    294.0,
+                    1802.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1793.0,
+                    1039.0,
+                    1793.0,
+                    1039.0,
+                    1833.0,
+                    295.0,
+                    1833.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    930.0,
+                    1408.0,
+                    930.0,
+                    1408.0,
+                    966.0,
+                    292.0,
+                    966.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    962.0,
+                    1407.0,
+                    962.0,
+                    1407.0,
+                    998.0,
+                    292.0,
+                    998.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    993.0,
+                    1405.0,
+                    993.0,
+                    1405.0,
+                    1027.0,
+                    295.0,
+                    1027.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1022.0,
+                    1406.0,
+                    1022.0,
+                    1406.0,
+                    1057.0,
+                    292.0,
+                    1057.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1052.0,
+                    1130.0,
+                    1052.0,
+                    1130.0,
+                    1090.0,
+                    295.0,
+                    1090.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1223.0,
+                    1052.0,
+                    1405.0,
+                    1052.0,
+                    1405.0,
+                    1090.0,
+                    1223.0,
+                    1090.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1082.0,
+                    1406.0,
+                    1082.0,
+                    1406.0,
+                    1119.0,
+                    291.0,
+                    1119.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1112.0,
+                    479.0,
+                    1112.0,
+                    479.0,
+                    1146.0,
+                    295.0,
+                    1146.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1939.0,
+                    1404.0,
+                    1939.0,
+                    1404.0,
+                    1981.0,
+                    293.0,
+                    1981.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1972.0,
+                    1403.0,
+                    1972.0,
+                    1403.0,
+                    2010.0,
+                    293.0,
+                    2010.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    194.0,
+                    801.0,
+                    194.0,
+                    801.0,
+                    232.0,
+                    293.0,
+                    232.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    841.0,
+                    194.0,
+                    1405.0,
+                    194.0,
+                    1405.0,
+                    232.0,
+                    841.0,
+                    232.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    226.0,
+                    963.0,
+                    226.0,
+                    963.0,
+                    264.0,
+                    293.0,
+                    264.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1058.0,
+                    226.0,
+                    1405.0,
+                    226.0,
+                    1405.0,
+                    264.0,
+                    1058.0,
+                    264.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    259.0,
+                    714.0,
+                    259.0,
+                    714.0,
+                    291.0,
+                    296.0,
+                    291.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    868.0,
+                    259.0,
+                    1404.0,
+                    259.0,
+                    1404.0,
+                    291.0,
+                    868.0,
+                    291.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    287.0,
+                    1404.0,
+                    287.0,
+                    1404.0,
+                    323.0,
+                    295.0,
+                    323.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    314.0,
+                    1408.0,
+                    314.0,
+                    1408.0,
+                    356.0,
+                    293.0,
+                    356.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    347.0,
+                    1098.0,
+                    347.0,
+                    1098.0,
+                    387.0,
+                    293.0,
+                    387.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 8,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    202,
+                    1404,
+                    202,
+                    1404,
+                    689,
+                    298,
+                    689
+                ],
+                "score": 0.984
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    796,
+                    1404,
+                    796,
+                    1404,
+                    1040,
+                    298,
+                    1040
+                ],
+                "score": 0.977
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1054,
+                    1404,
+                    1054,
+                    1404,
+                    1207,
+                    299,
+                    1207
+                ],
+                "score": 0.974
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1296,
+                    1405,
+                    1296,
+                    1405,
+                    1480,
+                    298,
+                    1480
+                ],
+                "score": 0.972
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    308,
+                    1572,
+                    1407,
+                    1572,
+                    1407,
+                    2008,
+                    308,
+                    2008
+                ],
+                "score": 0.955
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    300,
+                    1241,
+                    517,
+                    1241,
+                    517,
+                    1273,
+                    300,
+                    1273
+                ],
+                "score": 0.911
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    299,
+                    1522,
+                    455,
+                    1522,
+                    455,
+                    1557,
+                    299,
+                    1557
+                ],
+                "score": 0.908
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    298,
+                    729,
+                    509,
+                    729,
+                    509,
+                    767,
+                    298,
+                    767
+                ],
+                "score": 0.903
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    836,
+                    2061,
+                    865,
+                    2061,
+                    865,
+                    2085,
+                    836,
+                    2085
+                ],
+                "score": 0.838
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1264,
+                    626,
+                    1314,
+                    626,
+                    1314,
+                    659,
+                    1264,
+                    659
+                ],
+                "score": 0.83,
+                "latex": "\\mathbb { \\ m }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1169,
+                    566,
+                    1218,
+                    566,
+                    1218,
+                    598,
+                    1169,
+                    598
+                ],
+                "score": 0.8,
+                "latex": "\\bar { \\| 5 3 \\| }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1035,
+                    323,
+                    1084,
+                    323,
+                    1084,
+                    356,
+                    1035,
+                    356
+                ],
+                "score": 0.71,
+                "latex": "\\mathbb { \\left. \\overline { { \\boldsymbol { \\mathscr { Q } } \\boldsymbol { \\cdot } \\boldsymbol { \\cdot } } } \\right. }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1000,
+                    535,
+                    1133,
+                    535,
+                    1133,
+                    568,
+                    1000,
+                    568
+                ],
+                "score": 0.64,
+                "latex": "\\boxed { 6 2 } , \\boxed { 1 2 } , \\boxed { 2 7 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    753,
+                    1113,
+                    803,
+                    1113,
+                    803,
+                    1146,
+                    753,
+                    1146
+                ],
+                "score": 0.59,
+                "latex": "\\pmb { \\Vert 3 7 } \\Vert"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    565,
+                    347,
+                    565,
+                    347,
+                    598,
+                    298,
+                    598
+                ],
+                "score": 0.48,
+                "latex": "\\lVert 8 2 \\rVert"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1321,
+                    504,
+                    1397,
+                    504,
+                    1397,
+                    538,
+                    1321,
+                    538
+                ],
+                "score": 0.47,
+                "latex": "[ \\sqrt { 5 6 } , \\sqrt ] { 8 } ]"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    614,
+                    535,
+                    663,
+                    535,
+                    663,
+                    567,
+                    614,
+                    567
+                ],
+                "score": 0.39,
+                "latex": "\\dot { \\bigtriangledown } 5 7 \\big |"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    819,
+                    233,
+                    868,
+                    233,
+                    868,
+                    265,
+                    819,
+                    265
+                ],
+                "score": 0.35,
+                "latex": "\\dot { \\left. \\overline { { 4 8 } } \\right. }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1172,
+                    353,
+                    1263,
+                    353,
+                    1263,
+                    385,
+                    1172,
+                    385
+                ],
+                "score": 0.35,
+                "latex": "\\pm \\pm \\infty"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    297,
+                    626,
+                    346,
+                    626,
+                    346,
+                    659,
+                    297,
+                    659
+                ],
+                "score": 0.31,
+                "latex": "\\left[ \\left[ 3 6 \\right] \\right]"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1349,
+                    1113,
+                    1398,
+                    1113,
+                    1398,
+                    1146,
+                    1349,
+                    1146
+                ],
+                "score": 0.26,
+                "latex": "\\boldsymbol { \\left[ \\left[ 3 5 \\right] \\right] }"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1236.0,
+                    522.0,
+                    1236.0,
+                    522.0,
+                    1280.0,
+                    295.0,
+                    1280.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1518.0,
+                    460.0,
+                    1518.0,
+                    460.0,
+                    1563.0,
+                    295.0,
+                    1563.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    725.0,
+                    514.0,
+                    725.0,
+                    514.0,
+                    774.0,
+                    292.0,
+                    774.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    832.0,
+                    2057.0,
+                    871.0,
+                    2057.0,
+                    871.0,
+                    2096.0,
+                    832.0,
+                    2096.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    201.0,
+                    1408.0,
+                    201.0,
+                    1408.0,
+                    239.0,
+                    293.0,
+                    239.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    233.0,
+                    818.0,
+                    233.0,
+                    818.0,
+                    267.0,
+                    294.0,
+                    267.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    869.0,
+                    233.0,
+                    1404.0,
+                    233.0,
+                    1404.0,
+                    267.0,
+                    869.0,
+                    267.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    262.0,
+                    1404.0,
+                    262.0,
+                    1404.0,
+                    298.0,
+                    294.0,
+                    298.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    294.0,
+                    1405.0,
+                    294.0,
+                    1405.0,
+                    328.0,
+                    294.0,
+                    328.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    323.0,
+                    1034.0,
+                    323.0,
+                    1034.0,
+                    357.0,
+                    297.0,
+                    357.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1085.0,
+                    323.0,
+                    1404.0,
+                    323.0,
+                    1404.0,
+                    357.0,
+                    1085.0,
+                    357.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    353.0,
+                    1171.0,
+                    353.0,
+                    1171.0,
+                    389.0,
+                    292.0,
+                    389.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1264.0,
+                    353.0,
+                    1406.0,
+                    353.0,
+                    1406.0,
+                    389.0,
+                    1264.0,
+                    389.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    382.0,
+                    1407.0,
+                    382.0,
+                    1407.0,
+                    419.0,
+                    292.0,
+                    419.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    415.0,
+                    1404.0,
+                    415.0,
+                    1404.0,
+                    449.0,
+                    294.0,
+                    449.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    444.0,
+                    1402.0,
+                    444.0,
+                    1402.0,
+                    479.0,
+                    294.0,
+                    479.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    474.0,
+                    1403.0,
+                    474.0,
+                    1403.0,
+                    509.0,
+                    293.0,
+                    509.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    505.0,
+                    1320.0,
+                    505.0,
+                    1320.0,
+                    540.0,
+                    293.0,
+                    540.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1398.0,
+                    505.0,
+                    1405.0,
+                    505.0,
+                    1405.0,
+                    540.0,
+                    1398.0,
+                    540.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    532.0,
+                    613.0,
+                    532.0,
+                    613.0,
+                    573.0,
+                    292.0,
+                    573.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    664.0,
+                    532.0,
+                    999.0,
+                    532.0,
+                    999.0,
+                    573.0,
+                    664.0,
+                    573.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1134.0,
+                    532.0,
+                    1406.0,
+                    532.0,
+                    1406.0,
+                    573.0,
+                    1134.0,
+                    573.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    348.0,
+                    565.0,
+                    1168.0,
+                    565.0,
+                    1168.0,
+                    600.0,
+                    348.0,
+                    600.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1219.0,
+                    565.0,
+                    1405.0,
+                    565.0,
+                    1405.0,
+                    600.0,
+                    1219.0,
+                    600.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    595.0,
+                    1404.0,
+                    595.0,
+                    1404.0,
+                    633.0,
+                    295.0,
+                    633.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    347.0,
+                    626.0,
+                    1263.0,
+                    626.0,
+                    1263.0,
+                    661.0,
+                    347.0,
+                    661.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1315.0,
+                    626.0,
+                    1406.0,
+                    626.0,
+                    1406.0,
+                    661.0,
+                    1315.0,
+                    661.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    658.0,
+                    1051.0,
+                    658.0,
+                    1051.0,
+                    689.0,
+                    297.0,
+                    689.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    794.0,
+                    1406.0,
+                    794.0,
+                    1406.0,
+                    832.0,
+                    293.0,
+                    832.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    828.0,
+                    1402.0,
+                    828.0,
+                    1402.0,
+                    858.0,
+                    296.0,
+                    858.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    857.0,
+                    1406.0,
+                    857.0,
+                    1406.0,
+                    894.0,
+                    293.0,
+                    894.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    886.0,
+                    1405.0,
+                    886.0,
+                    1405.0,
+                    924.0,
+                    292.0,
+                    924.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    918.0,
+                    1404.0,
+                    918.0,
+                    1404.0,
+                    951.0,
+                    294.0,
+                    951.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    948.0,
+                    1405.0,
+                    948.0,
+                    1405.0,
+                    984.0,
+                    292.0,
+                    984.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    979.0,
+                    1404.0,
+                    979.0,
+                    1404.0,
+                    1012.0,
+                    294.0,
+                    1012.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1010.0,
+                    556.0,
+                    1010.0,
+                    556.0,
+                    1045.0,
+                    294.0,
+                    1045.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1054.0,
+                    1403.0,
+                    1054.0,
+                    1403.0,
+                    1087.0,
+                    295.0,
+                    1087.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    1084.0,
+                    1404.0,
+                    1084.0,
+                    1404.0,
+                    1117.0,
+                    297.0,
+                    1117.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1113.0,
+                    752.0,
+                    1113.0,
+                    752.0,
+                    1150.0,
+                    294.0,
+                    1150.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    804.0,
+                    1113.0,
+                    1348.0,
+                    1113.0,
+                    1348.0,
+                    1150.0,
+                    804.0,
+                    1150.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1399.0,
+                    1113.0,
+                    1405.0,
+                    1113.0,
+                    1405.0,
+                    1150.0,
+                    1399.0,
+                    1150.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1144.0,
+                    1406.0,
+                    1144.0,
+                    1406.0,
+                    1181.0,
+                    295.0,
+                    1181.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1175.0,
+                    884.0,
+                    1175.0,
+                    884.0,
+                    1208.0,
+                    294.0,
+                    1208.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1295.0,
+                    1405.0,
+                    1295.0,
+                    1405.0,
+                    1331.0,
+                    296.0,
+                    1331.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1327.0,
+                    1402.0,
+                    1327.0,
+                    1402.0,
+                    1359.0,
+                    296.0,
+                    1359.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1355.0,
+                    1403.0,
+                    1355.0,
+                    1403.0,
+                    1392.0,
+                    293.0,
+                    1392.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1387.0,
+                    1408.0,
+                    1387.0,
+                    1408.0,
+                    1422.0,
+                    295.0,
+                    1422.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1416.0,
+                    1406.0,
+                    1416.0,
+                    1406.0,
+                    1454.0,
+                    293.0,
+                    1454.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1449.0,
+                    474.0,
+                    1449.0,
+                    474.0,
+                    1482.0,
+                    295.0,
+                    1482.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    307.0,
+                    1571.0,
+                    1408.0,
+                    1571.0,
+                    1408.0,
+                    1608.0,
+                    307.0,
+                    1608.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    1602.0,
+                    1406.0,
+                    1602.0,
+                    1406.0,
+                    1638.0,
+                    355.0,
+                    1638.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    354.0,
+                    1634.0,
+                    714.0,
+                    1634.0,
+                    714.0,
+                    1667.0,
+                    354.0,
+                    1667.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    307.0,
+                    1679.0,
+                    1407.0,
+                    1679.0,
+                    1407.0,
+                    1717.0,
+                    307.0,
+                    1717.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    1710.0,
+                    1408.0,
+                    1710.0,
+                    1408.0,
+                    1745.0,
+                    353.0,
+                    1745.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    1742.0,
+                    561.0,
+                    1742.0,
+                    561.0,
+                    1775.0,
+                    355.0,
+                    1775.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    309.0,
+                    1789.0,
+                    1405.0,
+                    1789.0,
+                    1405.0,
+                    1825.0,
+                    309.0,
+                    1825.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    354.0,
+                    1821.0,
+                    1227.0,
+                    1821.0,
+                    1227.0,
+                    1854.0,
+                    354.0,
+                    1854.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    309.0,
+                    1867.0,
+                    1405.0,
+                    1867.0,
+                    1405.0,
+                    1903.0,
+                    309.0,
+                    1903.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    1897.0,
+                    1012.0,
+                    1897.0,
+                    1012.0,
+                    1932.0,
+                    353.0,
+                    1932.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    307.0,
+                    1942.0,
+                    1405.0,
+                    1942.0,
+                    1405.0,
+                    1985.0,
+                    307.0,
+                    1985.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    352.0,
+                    1976.0,
+                    1031.0,
+                    1976.0,
+                    1031.0,
+                    2009.0,
+                    352.0,
+                    2009.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 9,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 2,
+                "poly": [
+                    835,
+                    2061,
+                    863,
+                    2061,
+                    863,
+                    2086,
+                    835,
+                    2086
+                ],
+                "score": 0.801
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1376,
+                    1402,
+                    1376,
+                    1402,
+                    1439,
+                    297,
+                    1439
+                ],
+                "score": 0.577
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1094,
+                    1400,
+                    1094,
+                    1400,
+                    1161,
+                    297,
+                    1161
+                ],
+                "score": 0.577
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1011,
+                    1400,
+                    1011,
+                    1400,
+                    1077,
+                    298,
+                    1077
+                ],
+                "score": 0.535
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1178,
+                    1400,
+                    1178,
+                    1400,
+                    1273,
+                    299,
+                    1273
+                ],
+                "score": 0.526
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1292,
+                    1400,
+                    1292,
+                    1400,
+                    1358,
+                    298,
+                    1358
+                ],
+                "score": 0.523
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    928,
+                    1399,
+                    928,
+                    1399,
+                    994,
+                    296,
+                    994
+                ],
+                "score": 0.516
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1602,
+                    1402,
+                    1602,
+                    1402,
+                    1698,
+                    297,
+                    1698
+                ],
+                "score": 0.503
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    844,
+                    1399,
+                    844,
+                    1399,
+                    911,
+                    296,
+                    911
+                ],
+                "score": 0.503
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    732,
+                    1401,
+                    732,
+                    1401,
+                    826,
+                    299,
+                    826
+                ],
+                "score": 0.479
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    535,
+                    1403,
+                    535,
+                    1403,
+                    628,
+                    297,
+                    628
+                ],
+                "score": 0.476
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    648,
+                    1403,
+                    648,
+                    1403,
+                    713,
+                    295,
+                    713
+                ],
+                "score": 0.471
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    303,
+                    255,
+                    1401,
+                    255,
+                    1401,
+                    321,
+                    303,
+                    321
+                ],
+                "score": 0.46
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1944,
+                    1397,
+                    1944,
+                    1397,
+                    2008,
+                    297,
+                    2008
+                ],
+                "score": 0.448
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1716,
+                    1402,
+                    1716,
+                    1402,
+                    1811,
+                    298,
+                    1811
+                ],
+                "score": 0.447
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    304,
+                    338,
+                    1402,
+                    338,
+                    1402,
+                    433,
+                    304,
+                    433
+                ],
+                "score": 0.439
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    303,
+                    452,
+                    1403,
+                    452,
+                    1403,
+                    517,
+                    303,
+                    517
+                ],
+                "score": 0.437
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1830,
+                    1399,
+                    1830,
+                    1399,
+                    1925,
+                    299,
+                    1925
+                ],
+                "score": 0.416
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    308,
+                    202,
+                    1204,
+                    202,
+                    1204,
+                    238,
+                    308,
+                    238
+                ],
+                "score": 0.392
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1458,
+                    1407,
+                    1458,
+                    1407,
+                    1582,
+                    298,
+                    1582
+                ],
+                "score": 0.391
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    835,
+                    2061,
+                    863,
+                    2061,
+                    863,
+                    2086,
+                    835,
+                    2086
+                ],
+                "score": 0.13
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    832.0,
+                    2058.0,
+                    868.0,
+                    2058.0,
+                    868.0,
+                    2098.0,
+                    832.0,
+                    2098.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    832.0,
+                    2058.0,
+                    868.0,
+                    2058.0,
+                    868.0,
+                    2098.0,
+                    832.0,
+                    2098.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1373.0,
+                    1407.0,
+                    1373.0,
+                    1407.0,
+                    1413.0,
+                    295.0,
+                    1413.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    351.0,
+                    1404.0,
+                    432.0,
+                    1404.0,
+                    432.0,
+                    1442.0,
+                    351.0,
+                    1442.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1095.0,
+                    1404.0,
+                    1095.0,
+                    1404.0,
+                    1131.0,
+                    296.0,
+                    1131.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    1126.0,
+                    907.0,
+                    1126.0,
+                    907.0,
+                    1161.0,
+                    355.0,
+                    1161.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1010.0,
+                    1406.0,
+                    1010.0,
+                    1406.0,
+                    1048.0,
+                    293.0,
+                    1048.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    354.0,
+                    1045.0,
+                    940.0,
+                    1045.0,
+                    940.0,
+                    1075.0,
+                    354.0,
+                    1075.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1177.0,
+                    1405.0,
+                    1177.0,
+                    1405.0,
+                    1217.0,
+                    293.0,
+                    1217.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    1211.0,
+                    1404.0,
+                    1211.0,
+                    1404.0,
+                    1245.0,
+                    355.0,
+                    1245.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    1240.0,
+                    1033.0,
+                    1240.0,
+                    1033.0,
+                    1274.0,
+                    355.0,
+                    1274.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1290.0,
+                    1404.0,
+                    1290.0,
+                    1404.0,
+                    1332.0,
+                    293.0,
+                    1332.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    1325.0,
+                    949.0,
+                    1325.0,
+                    949.0,
+                    1357.0,
+                    353.0,
+                    1357.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    930.0,
+                    1404.0,
+                    930.0,
+                    1404.0,
+                    966.0,
+                    297.0,
+                    966.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    354.0,
+                    960.0,
+                    1246.0,
+                    960.0,
+                    1246.0,
+                    995.0,
+                    354.0,
+                    995.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1602.0,
+                    1408.0,
+                    1602.0,
+                    1408.0,
+                    1640.0,
+                    295.0,
+                    1640.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    352.0,
+                    1633.0,
+                    1404.0,
+                    1633.0,
+                    1404.0,
+                    1670.0,
+                    352.0,
+                    1670.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    356.0,
+                    1665.0,
+                    684.0,
+                    1665.0,
+                    684.0,
+                    1700.0,
+                    356.0,
+                    1700.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    845.0,
+                    1403.0,
+                    845.0,
+                    1403.0,
+                    881.0,
+                    296.0,
+                    881.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    351.0,
+                    878.0,
+                    739.0,
+                    878.0,
+                    739.0,
+                    909.0,
+                    351.0,
+                    909.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    732.0,
+                    1407.0,
+                    732.0,
+                    1407.0,
+                    769.0,
+                    294.0,
+                    769.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    352.0,
+                    760.0,
+                    1405.0,
+                    760.0,
+                    1405.0,
+                    802.0,
+                    352.0,
+                    802.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    794.0,
+                    617.0,
+                    794.0,
+                    617.0,
+                    828.0,
+                    355.0,
+                    828.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    533.0,
+                    1408.0,
+                    533.0,
+                    1408.0,
+                    572.0,
+                    292.0,
+                    572.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    354.0,
+                    565.0,
+                    1408.0,
+                    565.0,
+                    1408.0,
+                    602.0,
+                    354.0,
+                    602.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    592.0,
+                    430.0,
+                    592.0,
+                    430.0,
+                    633.0,
+                    353.0,
+                    633.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    648.0,
+                    1405.0,
+                    648.0,
+                    1405.0,
+                    684.0,
+                    294.0,
+                    684.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    679.0,
+                    1000.0,
+                    679.0,
+                    1000.0,
+                    714.0,
+                    353.0,
+                    714.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    307.0,
+                    253.0,
+                    1406.0,
+                    253.0,
+                    1406.0,
+                    295.0,
+                    307.0,
+                    295.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    354.0,
+                    285.0,
+                    1249.0,
+                    285.0,
+                    1249.0,
+                    320.0,
+                    354.0,
+                    320.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1943.0,
+                    1402.0,
+                    1943.0,
+                    1402.0,
+                    1981.0,
+                    294.0,
+                    1981.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    1975.0,
+                    809.0,
+                    1975.0,
+                    809.0,
+                    2009.0,
+                    353.0,
+                    2009.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1716.0,
+                    1407.0,
+                    1716.0,
+                    1407.0,
+                    1751.0,
+                    294.0,
+                    1751.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    352.0,
+                    1746.0,
+                    1407.0,
+                    1746.0,
+                    1407.0,
+                    1785.0,
+                    352.0,
+                    1785.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    354.0,
+                    1779.0,
+                    643.0,
+                    1779.0,
+                    643.0,
+                    1809.0,
+                    354.0,
+                    1809.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    308.0,
+                    337.0,
+                    1407.0,
+                    337.0,
+                    1407.0,
+                    377.0,
+                    308.0,
+                    377.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    354.0,
+                    368.0,
+                    1403.0,
+                    368.0,
+                    1403.0,
+                    406.0,
+                    354.0,
+                    406.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    400.0,
+                    827.0,
+                    400.0,
+                    827.0,
+                    434.0,
+                    355.0,
+                    434.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    309.0,
+                    452.0,
+                    1404.0,
+                    452.0,
+                    1404.0,
+                    488.0,
+                    309.0,
+                    488.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    482.0,
+                    1168.0,
+                    482.0,
+                    1168.0,
+                    517.0,
+                    353.0,
+                    517.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1829.0,
+                    1405.0,
+                    1829.0,
+                    1405.0,
+                    1865.0,
+                    294.0,
+                    1865.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    1858.0,
+                    1405.0,
+                    1858.0,
+                    1405.0,
+                    1898.0,
+                    353.0,
+                    1898.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    1892.0,
+                    643.0,
+                    1892.0,
+                    643.0,
+                    1926.0,
+                    355.0,
+                    1926.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    309.0,
+                    200.0,
+                    1205.0,
+                    200.0,
+                    1205.0,
+                    239.0,
+                    309.0,
+                    239.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1458.0,
+                    1410.0,
+                    1458.0,
+                    1410.0,
+                    1497.0,
+                    293.0,
+                    1497.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    350.0,
+                    1485.0,
+                    1408.0,
+                    1485.0,
+                    1408.0,
+                    1529.0,
+                    350.0,
+                    1529.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    351.0,
+                    1519.0,
+                    1408.0,
+                    1519.0,
+                    1408.0,
+                    1557.0,
+                    351.0,
+                    1557.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    351.0,
+                    1549.0,
+                    431.0,
+                    1549.0,
+                    431.0,
+                    1585.0,
+                    351.0,
+                    1585.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 10,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 2,
+                "poly": [
+                    836,
+                    2061,
+                    865,
+                    2061,
+                    865,
+                    2086,
+                    836,
+                    2086
+                ],
+                "score": 0.778
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    288,
+                    97,
+                    1409,
+                    97,
+                    1409,
+                    2016,
+                    288,
+                    2016
+                ],
+                "score": 0.578
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    836,
+                    2061,
+                    865,
+                    2061,
+                    865,
+                    2086,
+                    836,
+                    2086
+                ],
+                "score": 0.182
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    832.0,
+                    2058.0,
+                    870.0,
+                    2058.0,
+                    870.0,
+                    2097.0,
+                    832.0,
+                    2097.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    832.0,
+                    2058.0,
+                    870.0,
+                    2058.0,
+                    870.0,
+                    2097.0,
+                    832.0,
+                    2097.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    201.0,
+                    1408.0,
+                    201.0,
+                    1408.0,
+                    240.0,
+                    293.0,
+                    240.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    232.0,
+                    1408.0,
+                    232.0,
+                    1408.0,
+                    272.0,
+                    355.0,
+                    272.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    352.0,
+                    264.0,
+                    1408.0,
+                    264.0,
+                    1408.0,
+                    304.0,
+                    352.0,
+                    304.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    350.0,
+                    293.0,
+                    761.0,
+                    293.0,
+                    761.0,
+                    331.0,
+                    350.0,
+                    331.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    348.0,
+                    1406.0,
+                    348.0,
+                    1406.0,
+                    381.0,
+                    295.0,
+                    381.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    377.0,
+                    1408.0,
+                    377.0,
+                    1408.0,
+                    411.0,
+                    355.0,
+                    411.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    352.0,
+                    407.0,
+                    834.0,
+                    407.0,
+                    834.0,
+                    447.0,
+                    352.0,
+                    447.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    459.0,
+                    1408.0,
+                    459.0,
+                    1408.0,
+                    499.0,
+                    293.0,
+                    499.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    350.0,
+                    489.0,
+                    1060.0,
+                    489.0,
+                    1060.0,
+                    526.0,
+                    350.0,
+                    526.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    541.0,
+                    1410.0,
+                    541.0,
+                    1410.0,
+                    581.0,
+                    295.0,
+                    581.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    575.0,
+                    1404.0,
+                    575.0,
+                    1404.0,
+                    609.0,
+                    355.0,
+                    609.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    350.0,
+                    602.0,
+                    1141.0,
+                    602.0,
+                    1141.0,
+                    640.0,
+                    350.0,
+                    640.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    653.0,
+                    1406.0,
+                    653.0,
+                    1406.0,
+                    695.0,
+                    291.0,
+                    695.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    352.0,
+                    688.0,
+                    1406.0,
+                    688.0,
+                    1406.0,
+                    722.0,
+                    352.0,
+                    722.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    350.0,
+                    716.0,
+                    608.0,
+                    716.0,
+                    608.0,
+                    751.0,
+                    350.0,
+                    751.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    766.0,
+                    1408.0,
+                    766.0,
+                    1408.0,
+                    806.0,
+                    293.0,
+                    806.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    350.0,
+                    800.0,
+                    1046.0,
+                    800.0,
+                    1046.0,
+                    840.0,
+                    350.0,
+                    840.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    852.0,
+                    1406.0,
+                    852.0,
+                    1406.0,
+                    886.0,
+                    297.0,
+                    886.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    357.0,
+                    884.0,
+                    1406.0,
+                    884.0,
+                    1406.0,
+                    918.0,
+                    357.0,
+                    918.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    352.0,
+                    911.0,
+                    1205.0,
+                    911.0,
+                    1205.0,
+                    951.0,
+                    352.0,
+                    951.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    964.0,
+                    1410.0,
+                    964.0,
+                    1410.0,
+                    1004.0,
+                    293.0,
+                    1004.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    352.0,
+                    996.0,
+                    1313.0,
+                    996.0,
+                    1313.0,
+                    1035.0,
+                    352.0,
+                    1035.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1046.0,
+                    1410.0,
+                    1046.0,
+                    1410.0,
+                    1086.0,
+                    295.0,
+                    1086.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    1078.0,
+                    1410.0,
+                    1078.0,
+                    1410.0,
+                    1120.0,
+                    355.0,
+                    1120.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    350.0,
+                    1107.0,
+                    747.0,
+                    1107.0,
+                    747.0,
+                    1145.0,
+                    350.0,
+                    1145.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1160.0,
+                    1408.0,
+                    1160.0,
+                    1408.0,
+                    1200.0,
+                    293.0,
+                    1200.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    1191.0,
+                    1402.0,
+                    1191.0,
+                    1402.0,
+                    1225.0,
+                    355.0,
+                    1225.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    350.0,
+                    1221.0,
+                    742.0,
+                    1221.0,
+                    742.0,
+                    1258.0,
+                    350.0,
+                    1258.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1273.0,
+                    1406.0,
+                    1273.0,
+                    1406.0,
+                    1313.0,
+                    295.0,
+                    1313.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    352.0,
+                    1303.0,
+                    1408.0,
+                    1303.0,
+                    1408.0,
+                    1343.0,
+                    352.0,
+                    1343.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    352.0,
+                    1334.0,
+                    812.0,
+                    1334.0,
+                    812.0,
+                    1374.0,
+                    352.0,
+                    1374.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1389.0,
+                    1406.0,
+                    1389.0,
+                    1406.0,
+                    1422.0,
+                    295.0,
+                    1422.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    350.0,
+                    1416.0,
+                    1334.0,
+                    1416.0,
+                    1334.0,
+                    1454.0,
+                    350.0,
+                    1454.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1469.0,
+                    1406.0,
+                    1469.0,
+                    1406.0,
+                    1509.0,
+                    293.0,
+                    1509.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    350.0,
+                    1500.0,
+                    1408.0,
+                    1500.0,
+                    1408.0,
+                    1538.0,
+                    350.0,
+                    1538.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    352.0,
+                    1530.0,
+                    1086.0,
+                    1530.0,
+                    1086.0,
+                    1570.0,
+                    352.0,
+                    1570.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1580.0,
+                    1410.0,
+                    1580.0,
+                    1410.0,
+                    1620.0,
+                    295.0,
+                    1620.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    350.0,
+                    1612.0,
+                    1211.0,
+                    1612.0,
+                    1211.0,
+                    1650.0,
+                    350.0,
+                    1650.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1664.0,
+                    1406.0,
+                    1664.0,
+                    1406.0,
+                    1704.0,
+                    295.0,
+                    1704.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    1698.0,
+                    628.0,
+                    1698.0,
+                    628.0,
+                    1732.0,
+                    355.0,
+                    1732.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1748.0,
+                    1408.0,
+                    1748.0,
+                    1408.0,
+                    1788.0,
+                    293.0,
+                    1788.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    350.0,
+                    1776.0,
+                    1406.0,
+                    1776.0,
+                    1406.0,
+                    1820.0,
+                    350.0,
+                    1820.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    350.0,
+                    1810.0,
+                    572.0,
+                    1810.0,
+                    572.0,
+                    1845.0,
+                    350.0,
+                    1845.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1860.0,
+                    1294.0,
+                    1860.0,
+                    1294.0,
+                    1898.0,
+                    291.0,
+                    1898.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1912.0,
+                    1408.0,
+                    1912.0,
+                    1408.0,
+                    1952.0,
+                    295.0,
+                    1952.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    352.0,
+                    1944.0,
+                    1408.0,
+                    1944.0,
+                    1408.0,
+                    1984.0,
+                    352.0,
+                    1984.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    348.0,
+                    1976.0,
+                    861.0,
+                    1976.0,
+                    861.0,
+                    2013.0,
+                    348.0,
+                    2013.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 11,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 2,
+                "poly": [
+                    836,
+                    2061,
+                    865,
+                    2061,
+                    865,
+                    2086,
+                    836,
+                    2086
+                ],
+                "score": 0.829
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    293,
+                    126,
+                    1410,
+                    126,
+                    1410,
+                    2023,
+                    293,
+                    2023
+                ],
+                "score": 0.678
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    832.0,
+                    2058.0,
+                    870.0,
+                    2058.0,
+                    870.0,
+                    2096.0,
+                    832.0,
+                    2096.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    205.0,
+                    1407.0,
+                    205.0,
+                    1407.0,
+                    238.0,
+                    296.0,
+                    238.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    351.0,
+                    225.0,
+                    430.0,
+                    225.0,
+                    430.0,
+                    275.0,
+                    351.0,
+                    275.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    284.0,
+                    1409.0,
+                    284.0,
+                    1409.0,
+                    324.0,
+                    294.0,
+                    324.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    351.0,
+                    315.0,
+                    1407.0,
+                    315.0,
+                    1407.0,
+                    355.0,
+                    351.0,
+                    355.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    351.0,
+                    344.0,
+                    646.0,
+                    344.0,
+                    646.0,
+                    382.0,
+                    351.0,
+                    382.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    394.0,
+                    1405.0,
+                    394.0,
+                    1405.0,
+                    434.0,
+                    296.0,
+                    434.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    351.0,
+                    428.0,
+                    1318.0,
+                    428.0,
+                    1318.0,
+                    465.0,
+                    351.0,
+                    465.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    480.0,
+                    1407.0,
+                    480.0,
+                    1407.0,
+                    519.0,
+                    294.0,
+                    519.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    509.0,
+                    644.0,
+                    509.0,
+                    644.0,
+                    548.0,
+                    353.0,
+                    548.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    561.0,
+                    1409.0,
+                    561.0,
+                    1409.0,
+                    600.0,
+                    294.0,
+                    600.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    594.0,
+                    1344.0,
+                    594.0,
+                    1344.0,
+                    627.0,
+                    355.0,
+                    627.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    644.0,
+                    1407.0,
+                    644.0,
+                    1407.0,
+                    683.0,
+                    294.0,
+                    683.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    349.0,
+                    671.0,
+                    1409.0,
+                    671.0,
+                    1409.0,
+                    715.0,
+                    349.0,
+                    715.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    351.0,
+                    704.0,
+                    841.0,
+                    704.0,
+                    841.0,
+                    744.0,
+                    351.0,
+                    744.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    756.0,
+                    1405.0,
+                    756.0,
+                    1405.0,
+                    790.0,
+                    296.0,
+                    790.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    785.0,
+                    1407.0,
+                    785.0,
+                    1407.0,
+                    825.0,
+                    353.0,
+                    825.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    814.0,
+                    1035.0,
+                    814.0,
+                    1035.0,
+                    854.0,
+                    353.0,
+                    854.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    298.0,
+                    871.0,
+                    1405.0,
+                    871.0,
+                    1405.0,
+                    904.0,
+                    298.0,
+                    904.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    349.0,
+                    900.0,
+                    862.0,
+                    900.0,
+                    862.0,
+                    937.0,
+                    349.0,
+                    937.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    289.0,
+                    948.0,
+                    1409.0,
+                    948.0,
+                    1409.0,
+                    991.0,
+                    289.0,
+                    991.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    981.0,
+                    1407.0,
+                    981.0,
+                    1407.0,
+                    1020.0,
+                    353.0,
+                    1020.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    1008.0,
+                    433.0,
+                    1008.0,
+                    433.0,
+                    1050.0,
+                    353.0,
+                    1050.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1062.0,
+                    1407.0,
+                    1062.0,
+                    1407.0,
+                    1102.0,
+                    296.0,
+                    1102.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    1093.0,
+                    1314.0,
+                    1093.0,
+                    1314.0,
+                    1133.0,
+                    353.0,
+                    1133.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1145.0,
+                    1407.0,
+                    1145.0,
+                    1407.0,
+                    1185.0,
+                    294.0,
+                    1185.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    1174.0,
+                    1409.0,
+                    1174.0,
+                    1409.0,
+                    1214.0,
+                    353.0,
+                    1214.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    351.0,
+                    1203.0,
+                    431.0,
+                    1203.0,
+                    431.0,
+                    1245.0,
+                    351.0,
+                    1245.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1260.0,
+                    1405.0,
+                    1260.0,
+                    1405.0,
+                    1293.0,
+                    296.0,
+                    1293.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    351.0,
+                    1289.0,
+                    746.0,
+                    1289.0,
+                    746.0,
+                    1326.0,
+                    351.0,
+                    1326.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1339.0,
+                    1405.0,
+                    1339.0,
+                    1405.0,
+                    1378.0,
+                    296.0,
+                    1378.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    348.0,
+                    1370.0,
+                    741.0,
+                    1370.0,
+                    741.0,
+                    1407.0,
+                    348.0,
+                    1407.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1418.0,
+                    1409.0,
+                    1418.0,
+                    1409.0,
+                    1463.0,
+                    292.0,
+                    1463.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    1453.0,
+                    1179.0,
+                    1453.0,
+                    1179.0,
+                    1493.0,
+                    353.0,
+                    1493.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1503.0,
+                    1409.0,
+                    1503.0,
+                    1409.0,
+                    1543.0,
+                    296.0,
+                    1543.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    1534.0,
+                    1407.0,
+                    1534.0,
+                    1407.0,
+                    1574.0,
+                    353.0,
+                    1574.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    357.0,
+                    1568.0,
+                    828.0,
+                    1568.0,
+                    828.0,
+                    1601.0,
+                    357.0,
+                    1601.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1615.0,
+                    1407.0,
+                    1615.0,
+                    1407.0,
+                    1655.0,
+                    294.0,
+                    1655.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    1644.0,
+                    1405.0,
+                    1644.0,
+                    1405.0,
+                    1684.0,
+                    353.0,
+                    1684.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    1676.0,
+                    704.0,
+                    1676.0,
+                    704.0,
+                    1715.0,
+                    353.0,
+                    1715.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1728.0,
+                    1065.0,
+                    1728.0,
+                    1065.0,
+                    1765.0,
+                    294.0,
+                    1765.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1780.0,
+                    1409.0,
+                    1780.0,
+                    1409.0,
+                    1819.0,
+                    296.0,
+                    1819.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    1813.0,
+                    615.0,
+                    1813.0,
+                    615.0,
+                    1846.0,
+                    355.0,
+                    1846.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1863.0,
+                    1409.0,
+                    1863.0,
+                    1409.0,
+                    1902.0,
+                    294.0,
+                    1902.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    1896.0,
+                    1192.0,
+                    1896.0,
+                    1192.0,
+                    1929.0,
+                    355.0,
+                    1929.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1944.0,
+                    1407.0,
+                    1944.0,
+                    1407.0,
+                    1984.0,
+                    296.0,
+                    1984.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    1977.0,
+                    1156.0,
+                    1977.0,
+                    1156.0,
+                    2011.0,
+                    353.0,
+                    2011.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 12,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 2,
+                "poly": [
+                    836,
+                    2061,
+                    865,
+                    2061,
+                    865,
+                    2085,
+                    836,
+                    2085
+                ],
+                "score": 0.828
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    202,
+                    1406,
+                    202,
+                    1406,
+                    328,
+                    298,
+                    328
+                ],
+                "score": 0.643
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    291,
+                    343,
+                    1403,
+                    343,
+                    1403,
+                    406,
+                    291,
+                    406
+                ],
+                "score": 0.616
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    808,
+                    1403,
+                    808,
+                    1403,
+                    902,
+                    297,
+                    902
+                ],
+                "score": 0.578
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    646,
+                    1402,
+                    646,
+                    1402,
+                    711,
+                    296,
+                    711
+                ],
+                "score": 0.566
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    300,
+                    1607,
+                    1403,
+                    1607,
+                    1403,
+                    1701,
+                    300,
+                    1701
+                ],
+                "score": 0.557
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    919,
+                    1400,
+                    919,
+                    1400,
+                    985,
+                    297,
+                    985
+                ],
+                "score": 0.555
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    727,
+                    1402,
+                    727,
+                    1402,
+                    792,
+                    296,
+                    792
+                ],
+                "score": 0.551
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1526,
+                    1403,
+                    1526,
+                    1403,
+                    1590,
+                    297,
+                    1590
+                ],
+                "score": 0.539
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1000,
+                    1401,
+                    1000,
+                    1401,
+                    1065,
+                    296,
+                    1065
+                ],
+                "score": 0.538
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    303,
+                    1223,
+                    1402,
+                    1223,
+                    1402,
+                    1319,
+                    303,
+                    1319
+                ],
+                "score": 0.537
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    292,
+                    1718,
+                    1403,
+                    1718,
+                    1403,
+                    1783,
+                    292,
+                    1783
+                ],
+                "score": 0.533
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    566,
+                    1400,
+                    566,
+                    1400,
+                    630,
+                    295,
+                    630
+                ],
+                "score": 0.527
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1801,
+                    1403,
+                    1801,
+                    1403,
+                    1897,
+                    296,
+                    1897
+                ],
+                "score": 0.521
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    301,
+                    1334,
+                    1401,
+                    1334,
+                    1401,
+                    1427,
+                    301,
+                    1427
+                ],
+                "score": 0.496
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1445,
+                    1402,
+                    1445,
+                    1402,
+                    1509,
+                    298,
+                    1509
+                ],
+                "score": 0.489
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    425,
+                    1405,
+                    425,
+                    1405,
+                    548,
+                    299,
+                    548
+                ],
+                "score": 0.375
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1914,
+                    1405,
+                    1914,
+                    1405,
+                    2007,
+                    299,
+                    2007
+                ],
+                "score": 0.336
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1081,
+                    1406,
+                    1081,
+                    1406,
+                    1205,
+                    298,
+                    1205
+                ],
+                "score": 0.305
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    832.0,
+                    2057.0,
+                    871.0,
+                    2057.0,
+                    871.0,
+                    2095.0,
+                    832.0,
+                    2095.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    200.0,
+                    1407.0,
+                    200.0,
+                    1407.0,
+                    239.0,
+                    292.0,
+                    239.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    352.0,
+                    232.0,
+                    1408.0,
+                    232.0,
+                    1408.0,
+                    267.0,
+                    352.0,
+                    267.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    354.0,
+                    263.0,
+                    1407.0,
+                    263.0,
+                    1407.0,
+                    299.0,
+                    354.0,
+                    299.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    354.0,
+                    296.0,
+                    571.0,
+                    296.0,
+                    571.0,
+                    330.0,
+                    354.0,
+                    330.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    340.0,
+                    1406.0,
+                    340.0,
+                    1406.0,
+                    380.0,
+                    294.0,
+                    380.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    351.0,
+                    366.0,
+                    432.0,
+                    366.0,
+                    432.0,
+                    409.0,
+                    351.0,
+                    409.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    808.0,
+                    1405.0,
+                    808.0,
+                    1405.0,
+                    845.0,
+                    295.0,
+                    845.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    840.0,
+                    1408.0,
+                    840.0,
+                    1408.0,
+                    874.0,
+                    355.0,
+                    874.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    351.0,
+                    867.0,
+                    430.0,
+                    867.0,
+                    430.0,
+                    904.0,
+                    351.0,
+                    904.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    298.0,
+                    646.0,
+                    1404.0,
+                    646.0,
+                    1404.0,
+                    682.0,
+                    298.0,
+                    682.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    354.0,
+                    677.0,
+                    1204.0,
+                    677.0,
+                    1204.0,
+                    712.0,
+                    354.0,
+                    712.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1607.0,
+                    1407.0,
+                    1607.0,
+                    1407.0,
+                    1644.0,
+                    294.0,
+                    1644.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    352.0,
+                    1635.0,
+                    1405.0,
+                    1635.0,
+                    1405.0,
+                    1676.0,
+                    352.0,
+                    1676.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    357.0,
+                    1669.0,
+                    538.0,
+                    1669.0,
+                    538.0,
+                    1700.0,
+                    357.0,
+                    1700.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    920.0,
+                    1404.0,
+                    920.0,
+                    1404.0,
+                    956.0,
+                    296.0,
+                    956.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    949.0,
+                    1183.0,
+                    949.0,
+                    1183.0,
+                    984.0,
+                    353.0,
+                    984.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    726.0,
+                    1403.0,
+                    726.0,
+                    1403.0,
+                    762.0,
+                    296.0,
+                    762.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    760.0,
+                    992.0,
+                    760.0,
+                    992.0,
+                    793.0,
+                    353.0,
+                    793.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1527.0,
+                    1405.0,
+                    1527.0,
+                    1405.0,
+                    1563.0,
+                    296.0,
+                    1563.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    1557.0,
+                    1105.0,
+                    1557.0,
+                    1105.0,
+                    1591.0,
+                    353.0,
+                    1591.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    999.0,
+                    1405.0,
+                    999.0,
+                    1405.0,
+                    1039.0,
+                    296.0,
+                    1039.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    1031.0,
+                    1003.0,
+                    1031.0,
+                    1003.0,
+                    1066.0,
+                    353.0,
+                    1066.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1222.0,
+                    1406.0,
+                    1222.0,
+                    1406.0,
+                    1259.0,
+                    294.0,
+                    1259.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    1253.0,
+                    1407.0,
+                    1253.0,
+                    1407.0,
+                    1291.0,
+                    353.0,
+                    1291.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    1283.0,
+                    894.0,
+                    1283.0,
+                    894.0,
+                    1319.0,
+                    355.0,
+                    1319.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1718.0,
+                    1405.0,
+                    1718.0,
+                    1405.0,
+                    1754.0,
+                    296.0,
+                    1754.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    1748.0,
+                    1165.0,
+                    1748.0,
+                    1165.0,
+                    1784.0,
+                    353.0,
+                    1784.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    563.0,
+                    1407.0,
+                    563.0,
+                    1407.0,
+                    604.0,
+                    294.0,
+                    604.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    595.0,
+                    903.0,
+                    595.0,
+                    903.0,
+                    631.0,
+                    353.0,
+                    631.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1800.0,
+                    1408.0,
+                    1800.0,
+                    1408.0,
+                    1838.0,
+                    294.0,
+                    1838.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    354.0,
+                    1834.0,
+                    1405.0,
+                    1834.0,
+                    1405.0,
+                    1869.0,
+                    354.0,
+                    1869.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    1862.0,
+                    1340.0,
+                    1862.0,
+                    1340.0,
+                    1899.0,
+                    355.0,
+                    1899.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1333.0,
+                    1406.0,
+                    1333.0,
+                    1406.0,
+                    1371.0,
+                    293.0,
+                    1371.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    351.0,
+                    1364.0,
+                    1406.0,
+                    1364.0,
+                    1406.0,
+                    1402.0,
+                    351.0,
+                    1402.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    1395.0,
+                    563.0,
+                    1395.0,
+                    563.0,
+                    1426.0,
+                    355.0,
+                    1426.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1444.0,
+                    1407.0,
+                    1444.0,
+                    1407.0,
+                    1482.0,
+                    293.0,
+                    1482.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    1474.0,
+                    1175.0,
+                    1474.0,
+                    1175.0,
+                    1510.0,
+                    353.0,
+                    1510.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    424.0,
+                    1406.0,
+                    424.0,
+                    1406.0,
+                    460.0,
+                    295.0,
+                    460.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    455.0,
+                    1406.0,
+                    455.0,
+                    1406.0,
+                    491.0,
+                    355.0,
+                    491.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    487.0,
+                    1405.0,
+                    487.0,
+                    1405.0,
+                    523.0,
+                    355.0,
+                    523.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    517.0,
+                    892.0,
+                    517.0,
+                    892.0,
+                    549.0,
+                    353.0,
+                    549.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1910.0,
+                    1406.0,
+                    1910.0,
+                    1406.0,
+                    1952.0,
+                    293.0,
+                    1952.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    352.0,
+                    1941.0,
+                    1405.0,
+                    1941.0,
+                    1405.0,
+                    1983.0,
+                    352.0,
+                    1983.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    1975.0,
+                    525.0,
+                    1975.0,
+                    525.0,
+                    2010.0,
+                    355.0,
+                    2010.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1081.0,
+                    1406.0,
+                    1081.0,
+                    1406.0,
+                    1116.0,
+                    293.0,
+                    1116.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    354.0,
+                    1113.0,
+                    1404.0,
+                    1113.0,
+                    1404.0,
+                    1145.0,
+                    354.0,
+                    1145.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    354.0,
+                    1144.0,
+                    1406.0,
+                    1144.0,
+                    1406.0,
+                    1180.0,
+                    354.0,
+                    1180.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    354.0,
+                    1175.0,
+                    1000.0,
+                    1175.0,
+                    1000.0,
+                    1206.0,
+                    354.0,
+                    1206.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 13,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    202,
+                    1410,
+                    202,
+                    1410,
+                    598,
+                    295,
+                    598
+                ],
+                "score": 0.793
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    836,
+                    2061,
+                    865,
+                    2061,
+                    865,
+                    2086,
+                    836,
+                    2086
+                ],
+                "score": 0.773
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    836,
+                    2061,
+                    865,
+                    2061,
+                    865,
+                    2086,
+                    836,
+                    2086
+                ],
+                "score": 0.197
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    832.0,
+                    2058.0,
+                    870.0,
+                    2058.0,
+                    870.0,
+                    2096.0,
+                    832.0,
+                    2096.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    832.0,
+                    2058.0,
+                    870.0,
+                    2058.0,
+                    870.0,
+                    2096.0,
+                    832.0,
+                    2096.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    202.0,
+                    1406.0,
+                    202.0,
+                    1406.0,
+                    242.0,
+                    294.0,
+                    242.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    235.0,
+                    603.0,
+                    235.0,
+                    603.0,
+                    271.0,
+                    355.0,
+                    271.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    286.0,
+                    1402.0,
+                    286.0,
+                    1402.0,
+                    322.0,
+                    296.0,
+                    322.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    351.0,
+                    317.0,
+                    1143.0,
+                    317.0,
+                    1143.0,
+                    353.0,
+                    351.0,
+                    353.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    368.0,
+                    1404.0,
+                    368.0,
+                    1404.0,
+                    404.0,
+                    296.0,
+                    404.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    397.0,
+                    1308.0,
+                    397.0,
+                    1308.0,
+                    436.0,
+                    353.0,
+                    436.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    449.0,
+                    1406.0,
+                    449.0,
+                    1406.0,
+                    492.0,
+                    293.0,
+                    492.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    483.0,
+                    1354.0,
+                    483.0,
+                    1354.0,
+                    520.0,
+                    353.0,
+                    520.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    534.0,
+                    1407.0,
+                    534.0,
+                    1407.0,
+                    574.0,
+                    296.0,
+                    574.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    354.0,
+                    564.0,
+                    1408.0,
+                    564.0,
+                    1408.0,
+                    603.0,
+                    354.0,
+                    603.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 14,
+            "width": 1700,
+            "height": 2200
+        }
+    }
+]
\ No newline at end of file
diff --git a/parse/train/Xh5eMZVONGF/Xh5eMZVONGF.md b/parse/train/Xh5eMZVONGF/Xh5eMZVONGF.md
new file mode 100644
index 0000000000000000000000000000000000000000..17a65f63b68aa6afe84121f828168987809b3182
--- /dev/null
+++ b/parse/train/Xh5eMZVONGF/Xh5eMZVONGF.md
@@ -0,0 +1,501 @@
+# LANGUAGE-AGNOSTIC REPRESENTATION LEARNING OF SOURCE CODE FROM STRUCTURE AND CONTEXT
+
+Daniel Zugner, Tobias Kirschstein ¨ Technical University of Munich {zuegnerd,kirschto}@in.tum.de
+
+Michele Catasta   
+Stanford University   
+pirroh@cs.stanford.edu
+
+Jure Leskovec Stanford University jure@cs.stanford.edu
+
+Stephan Gunnemann ¨ Technical University of Munich guennemann@in.tum.de
+
+# ABSTRACT
+
+Source code (Context) and its parsed abstract syntax tree (AST; Structure) are two complementary representations of the same computer program. Traditionally, designers of machine learning models have relied predominantly either on Structure or Context. We propose a new model, which jointly learns on Context and Structure of source code. In contrast to previous approaches, our model uses only language-agnostic features, i.e., source code and features that can be computed directly from the AST. Besides obtaining state-of-the-art on monolingual code summarization on all five programming languages considered in this work, we propose the first multilingual code summarization model. We show that jointly training on non-parallel data from multiple programming languages improves results on all individual languages, where the strongest gains are on low-resource languages. Remarkably, multilingual training only from Context does not lead to the same improvements, highlighting the benefits of combining Structure and Context for representation learning on code.
+
+# 1 INTRODUCTION
+
+Machine learning for code is an active and growing area of research which aims at building models that can learn semantically meaningful representations of programs. These embeddings can be used on downstream tasks, such as code generation, bug detection, or code summarization. We focus our work on two complementary data representations of programs: the source code (referred to as Context in this work), and the abstract syntax tree (AST; referred to as Structure). Traditionally, researchers and practitioners have decided to predominantly leverage either Structure or Context in their machine learning models. In this work, we show that jointly learning on Context and Structure improves representation learning on source code (see Fig. 1).
+
+The source code representation naturally lends itself to models from natural language processing (NLP), e.g., long short-term memory networks (Hochreiter & Schmidhuber, 1997) (LSTM) or Transformers (Vaswani et al., 2017; Radford et al., 2019; Dai et al., 2019; Yang et al., 2019; Shaw et al., 2018). On the other hand, models leveraging the structure representations are typically based on graph neural networks (GNNs) (Kipf & Welling, 2017; Xu et al., 2019; Velickovi ˇ c et al., 2018; ´ You et al., 2019; Hamilton et al., 2017; Li et al., 2015; Klicpera et al., 2020). While the AST representation makes the highly structured nature of source code explicit to the models, since most GNNs use the message-passing framework, their learned representations are inherently local and struggle to leverage long-range interactions.
+
+Recently, Hellendoorn et al. (2020) have explored models that can leverage several representations, including both Structure and Context. Their Graph Relational Embedding Attention Transformer (GREAT) extends Shaw et al. (2018), which biases the self-attention computation in a localized way given the underlying graph. The language-specific representations used by GREAT include a combination of the data flow graph, control flow graph, syntactic edges (inspired by Allamanis et al. (2018)), etc. which require specialized pipelines and static analysis tools to be obtained.
+
+![](images/7701ebd563c4ccbab0fb3932736f0a3f5ce8408d760ee36d22e78173cbc12d18.jpg)  
+Figure 1: Context and Structure both encapsulate valuable information about source code. In this realistic example, token 1 and 4 are distant in the sequence of tokens (Context), but only 5 hops away when traversing the Abstract Syntax Tree (Structure). As such, a method that relies only on the sequence of tokens could neglect the relationship between a method name and its return variable. Conversely, token 1 and 2 showcase the opposite setting. Hence, unifying Structure and Context leads to a more powerful representation of source code.
+
+We propose the CODE TRANSFORMER1, which combines distances computed on Structure and Context in the self-attention operation. In contrast to the localized treatment via edges described above, we make the full Structure accessible to the model at each layer by computing pairwise distances on the AST, such as shortest path lengths. To this end, we draw inspiration from the XLNet architecture (Yang et al., 2019), which uses relative distances instead of absolute positions in the attention computation. Importantly, all our features are language-agnostic2, i.e., can easily be computed for any programming language based on the source code and AST.
+
+We use two datasets comprising 5 different programming languages in total, and evaluate the representations learned by our model on the task of code summarization, where the model predicts a method’s name based on its body. Besides setting the state-of-the-art on all five languages for singlelanguage training, we also train the first multilingual model for code summarization. This is enabled by the fact that our model uses only language-agnostic features that can easily be obtained for any programming language. Remarkably, training our model on multiple programming languages substantially improves the performance on all languages. Moreover, multilingual training only from Context does not lead to the same improvements, highlighting the benefits of combining Structure and Context for representation learning on code.
+
+# 2 RELATED WORK
+
+Machine Learning for Code. Early research learned language models on raw text data, e.g., (Wang et al., 2016; Raychev et al., 2014; Dam et al., 2016), providing evidence for the naturalness assumption (Hindle et al., 2012). For example, Allamanis et al. (2015) learned distributed representations of variables and methods, finding that they were indeed able to encode common semantic properties from the regularities present in source code. Alon et al. (2019b) also found evidence of semantic arithmetic in their embedding space, dubbed code2vec. These representations—and their variants like (Mou et al., 2016)—can then be used to predict sequences of identifier sub-tokens (Allamanis et al., 2015) or API calls (Acharya et al., 2007; Nguyen et al., 2017). They can be used as advanced auto-completion tools (Hindle et al., 2012; Bhoopchand et al., 2016), including for user-provided tokens like Variable Names (Raychev et al., 2014; Allamanis et al., 2014). These are useful for deobfuscating Android applications (Bichsel et al., 2016) for example.
+
+Several works leverage structured graphical models for probabilistic models of source code, usually through parse trees (Maddison & Tarlow, 2014; Bielik et al., 2016). Unlike previous works where hand-crafted features were used as node features (Raychev et al., 2014) or as explicit semantic edges (Allamanis et al., 2018), our work does not augment the existing syntactic relationships between the different elements to enhance the predictive capabilities of the model. Other approaches (Alon et al., 2018; Li et al., 2017) also leverage the AST structure, but linearize the graph by first traversing it.
+
+Learning representations of structured languages. While models of language have dramatically improved in their ability to learn structure (syntax) and semantics from scratch, it can be argued that directly providing the model with the underlying structure of the language can help with generalization (Battaglia et al., 2018), managing long-ranging dependencies (Tai et al., 2015), or representing the compositional aspect of natural language (Socher et al., 2013). Notably, tree structures have shown promising results and inspired new architectures (Shen et al., 2019), including in the domain of source code (Fernandes et al., 2019), where the underlying syntax is directly available. Our work pursues this line of research, showing the benefits of explicitly integrating structural information as an inductive bias. Shiv & Quirk (2019) propose positional encodings for nodes on trees; however, their approach assumes regular trees, which is an unrealistic assumption when working with Abstract Syntax Trees, as an AST node can have arbitrarily many children, e.g., the arguments of a function.
+
+Graph Neural Networks. GNNs provide a powerful tool for machine learning on graphs, thanks to their ability to recursively incorporate information from neighboring nodes in the network (Battaglia et al., 2018), naturally capturing the graph structure simultaneously with the nodes’ features. (Gori et al., 2005; Scarselli et al., 2008) are able to learn vector representations of nodes and graphs in an end-to-end fashion, encoding structural and feature information in the embedding space. Under this model, GNNs have achieved state-of-the-art performance across a variety of tasks, such as node classification (Kipf & Welling, 2017; Hamilton et al., 2017; Klicpera et al., 2019a), link prediction (Zhang & Chen, 2018; Schlichtkrull et al., 2018), graph clustering (Defferrard et al., 2016; Ying et al., 2018) or graph classification (Ying et al., 2018; Dai et al., 2016; Duvenaud et al., 2015).
+
+# 3 INTEGRATING STRUCTURE AND CONTEXT IN THE CODE TRANSFORMER
+
+Self-attention is the core operation powering the Transformer. It enables the model to selectively focus on relevant parts of the input. The matrix form equation for attention with a single head is
+
+$$
+{ \mathrm { A t t e n t i o n } } ( Q , K , V ) = { \mathrm { s o f t m a x } } \left( { \frac { Q K ^ { T } } { \sqrt { d _ { k } } } } \right) V ,
+$$
+
+where $Q , K \in \mathbb { R } ^ { N \times d _ { k } }$ and $V \in \mathbb { R } ^ { N \times d _ { v } }$ . $N$ is the number of input tokens, $d _ { k }$ the key dimension, and $d _ { v }$ the value dimension (typically we have $d _ { k } = d _ { v }$ ). The attention score of query $Q _ { i }$ and key $K _ { j }$ before softmax is
+
+$$
+\pmb { A } _ { i j } = \pmb { Q } _ { i } ^ { T } \pmb { K } _ { j } = \pmb { E } _ { i } ^ { T } \pmb { W } _ { q } ^ { T } \pmb { W } _ { k } \pmb { E } _ { j } ,
+$$
+
+where $E _ { i } , E _ { j } \in \mathbb { R } ^ { d }$ are the $d$ -dimensional embeddings of tokens $i$ and $j$ , and $W _ { q }$ , $W _ { k } \in \mathbb { R } ^ { d _ { k } \times d }$ are the query and key projection matrices, respectively.
+
+Observe that Eq. (2) contains no assumption about potential structure in the input domain: in the attention operation we compute all dot products of query and key vectors equally, effectively viewing them as unordered sets of vectors. This means, however, that the model is oblivious to structured inputs (such as text or graphs) and therefore is unable to distinguish, for example, a variable name occurring as an argument and in the return statement of a method.
+
+In NLP, it is common to bias Transformers towards sequential inputs by adding positional encodings to the token embeddings. These positional encodings are obtained by applying an encoding function $\phi : \mathbb { R } \to \mathbb { R } ^ { d }$ to each token’s position $p _ { i }$ . These positional encodings make the information about the sequence of tokens available to the model. Eq. (2) becomes:
+
+$$
+A _ { i j } = ( E _ { i } + \phi ( p _ { i } ) ) ^ { T } W _ { q } ^ { T } W _ { k } ( E _ { j } + \phi ( p _ { j } ) ) , ,
+$$
+
+which factorizes into
+
+$$
+A _ { i j } = \underbrace { { E } _ { i } ^ { T } W _ { q } ^ { T } W _ { k } } _ { ( \mathrm { u } ) { A } _ { i j } ^ { \mathrm { c e } } } { + \underbrace { { E } _ { i } ^ { T } W _ { q } ^ { T } W _ { k } { \phi } ( p _ { j } ) } _ { ( \mathrm { b } ) { A } _ { i j } ^ { \mathrm { c p } } } } + \underbrace { { \phi } ( p _ { i } ) ^ { T } W _ { q } ^ { T } W _ { k } { E } _ { j } } _ { ( \mathrm { c } ) { A } _ { i j } ^ { \mathrm { c e } } } { + \underbrace { { { \phi } ( p _ { i } ) } ^ { T } W _ { q } ^ { T } W _ { k } { \phi } ( p _ { j } ) } _ { ( \mathrm { d } ) { A } _ { i j } ^ { \mathrm { p } } } } .
+$$
+
+We can interpret the terms (a)-(d) as follows. (a) ${ \cal { A } } _ { i j } ^ { \mathrm { c c } }$ is the contribution from the ‘match’ between the content embeddings of tokens $i$ and $j$ ; (b) $A _ { i j } ^ { \mathrm { c p } }$ steers the attention towards certain positions based
+
+on the content of token $i$ ; (c) $A _ { i j } ^ { \mathrm { p c } }$ biases towards content embeddings based on the position of token $i$ ; (d) $A _ { i j } ^ { \mathrm { p p } }$ controls which positions should attend to which other positions.
+
+In our model, we adopt the formulation of Dai et al. (2019); Yang et al. (2019). They modify Eq. (4) by replacing the absolute position encodings $\phi ( p _ { i } )$ with relative position encodings $\phi ( r _ { i \to j } )$ :
+
+$$
+\begin{array} { r } { A _ { i j } ^ { \mathrm { r e l } } = \ E _ { i } ^ { T } W _ { q } ^ { T } W _ { k } E _ { j } + E _ { i } ^ { T } W _ { q } ^ { T } W _ { r } \phi ( r _ { i  j } ) + u ^ { T } W _ { k } E _ { j } + v ^ { T } W _ { r } \phi ( r _ { i  j } ) , } \end{array}
+$$
+
+where $r _ { i \to j }$ is the relative distance from token $i$ to token $j$ in the sequence, $\boldsymbol { u } , \boldsymbol { v } \in \mathbb { R } ^ { d _ { k } }$ are learnable bias vectors, and $W _ { r }$ is a key projection matrix for the relative distances. Besides fixing issues with absolute position encodings such as ambiguity when processing two sentences at a time, Eq. (5) enables native application of the powerful self-attention operation on domains such as graphs, where absolute coordinates are not available. We adopt the (non-trainable) sinusoidal encoding function proposed by (Vaswani et al., 2017) for all relations; see Appendix A.1 for details on the distance encoding function.
+
+# 3.1 INTEGRATING SOURCE CODE AND AST REPRESENTATIONS OF PROGRAMS.
+
+To enable the model to integrate information both the Context and Structure of programs, we modify Eq. (5) to be able to incorporate multiple different relations. To this end, we use one key projection matrix W (s)r per relation $s$ , and sum their contributions in the raw attention score. This enables the CODE TRANSFORMER to combine information from multiple relations between tokens in the attention computation. Besides the token distance in the Context, we include pairwise relations based on the AST as described in the following. See Fig. 2 for a visualization of the Structure distances we use.
+
+Shortest path length. We include the number of hops required to reach node $j$ starting from node $i$ and vice versa. Here, we treat the AST as an undirected graph, since otherwise most distances would be undefined: e.g., all other nodes in the AST would be unreachable from the leaves.
+
+Similar to the distance of two tokens on the source code sequence, the shortestpath length is a global distance. This makes the whole graph structure acces
+
+![](images/971f2174ff96f3b5b7aea4b5cb4f59f9af4bf791dc6a632edbb218691a5d22cf.jpg)  
+Figure 2: Structure distances used by our model.
+
+sible to the model at each layer. In contrast, Hellendoorn et al. (2020) add bias terms to the attention computation only for edges (i.e. shortest-path distance of 1), which is a local operation that only exchanges information between immediate neighbors (similar to message passing in GNNs). The equivalent localized operation on the source code sequence would be to treat the sequence as a chain graph and only compute attention terms for neighboring tokens, which in turn highlights the benefit of non-local attention operations.
+
+Ancestor distance. Since we treat the ASTs as undirected for the computation of the shortest-path length, we lose the direction information of the edges. To avoid this, we also include the distance on the ordered set of ancestors and descendants of a node in the AST (red arrow in Fig. 2). Again, we include number of (vertical) hops to avoid locality in the attention computation. For example, a node $r _ { i \to j } = 2$ for “grand-children” $j$ of $i$ , and $r _ { j  i } = - 2$ in the other direction.
+
+Sibling distance. The neighbor sets in graphs are typically considered to be unordered, but in an AST, the order of children encodes their order of occurrence in the source code. To avoid information loss when encoding the AST, we further include the distance on the ordered set of siblings $\{ v _ { i } \}$ of a node, where we again avoid locality by encoding the number of hops, i.e. $r _ { v _ { 1 }  v _ { 3 } } ~ = ~ 2$ and rv3→v1 = −2.
+
+Personalized PageRank (Page et al., 1999) (PPR). PPR is a well-studied proximity measure which has been shown to be very effective in learning with graphs (Klicpera et al., 2019a;b; Bojchevski et al., 2020). PPR captures the local graph structure around a pair of nodes $( i , j )$ . E.g., if $i$ has many neighbors, its PPR score for $j$ will be low even when they are only few hops apart, which complements the purely hop-based distances described above.
+
+![](images/2ae4d77322414ffc49b55c0b5e39c6d3b3d0f5b89a9cfca8c5f81d4390780d66.jpg)  
+Figure 3: Left: Sequence (Context) and AST (Structure) representation of an input code snippet. Center: The CODE TRANSFORMER jointly leverages the sequence of tokens and the Abstract Syntax Tree to learn expressive representations of source code. In addition to the input token and node embeddings the model uses different distances between the tokens, e.g., shortest paths on the AST or personalized PageRank, to reason about their relative positions. The output embeddings can be used for downstream tasks such as code summarization (right).
+
+Input embeddings to the model. To combine the Context and Structure information, we assign each token in the sequence to an AST node by selecting the AST node whose range in the source code is the shortest one containing the token. We concatenate the (sub-) token embeddings with the embedding of the token’s assigned AST node type as well as the token type returned by the tokenizer. That is, among all the internal nodes, we use as input only those corresponding to a token in the sequence; however, the remaining internal nodes can used by the model since their presence affects the distances between the remaining AST nodes. See Appendices A.3 and A.4 for details.
+
+# 3.2 EFFICIENT RELATIVE ATTENTION COMPUTATION.
+
+Na¨ıvely, we need to compute and materialize a tensor of dimension $N \times N \times d$ to hold all pairwise relative position encodings $\phi ( r _ { i \to j } )$ in Eq. (5) , where $N$ is the input length. This is prohibitive for fast GPU training. While for discrete distance values (e.g., sequence distance or shortest-path length on a graph) we only need to compute unique distance values occurring in the input, this does not generalize to continuous distances such as PPR. Therefore, we propose a constant-time approximation of the relational attention computation by grouping the values into $k \ll N ^ { 2 }$ bins. Since closer samples are typically more relevant for a query sample, we increase the bin widths exponentially with growing distance values. Throughout our experiments we have found the CODE TRANSFORMER to be relatively insensitive to the number of bins; we thus set $k = 3 2$ in our experiments.
+
+# 4 EXPERIMENTAL SETUP
+
+Code summarization is one of the most popular tasks in machine learning for code. Given the body of a function, the task is to predict the function’s name. As observed by Alon et al. (2019b) and Allamanis et al. (2016), this is a useful benchmark as method names in open-source projects tend to be precise and descriptive, and functions typically form complete logical units. See Fig. 3 (right) for a visual overview of the task. We use two complementary representations of programs: the source code as a sequence of tokens (Context) and the AST (Structure). As shown in Fig. 3 (left), tokens that are far away on the sequence may be very close on the AST and vice versa. In this task we make use of the CODE TRANSFORMER’s ability jointly leverage both Structure and Context and show that it improves learning. Further, we show the benefit of using only language-agnostic features in our model by training the first multilingual model for code summarization.
+
+Datasets. To highlight the benefit of only relying on language-agnostic representations such as source code and abstract syntax trees, we evaluate on challenging datasets in four programming languages introduced in the CodeSearchNet (CSN) Challenge (Husain et al., 2019): Python, Javascript, Go, and Ruby. Similar to Java-small, the datasets from CodeSearchNet have been carefully deduplicated by the creators to avoid data leakage from the training set, e.g., via copy-and-paste code.
+
+We further evaluate on Java-small (Allamanis et al., 2016), a popular and challenging code summarization dataset. It contains 11 open-source Java projects. We use the split as in Alon et al. (2019a), where 9 of these projects are used for training, one for validation, and one for test. The dataset contains roughly 700K samples (function definitions). Moreover, we also experiment with pre-training our model on Java-medium and Java-large (Alon et al., 2019a) before fine-tuning on Java-small, making sure to avoid leakage by removing the test and validation projects of Java-small from the pre-training dataset. See Table 1 for a summary of the datasets we use in this work.
+
+<table><tr><td></td><td colspan="3">Samples per partition</td></tr><tr><td>Dataset</td><td>Train</td><td>Val.</td><td>Test</td></tr><tr><td>CSN-Python</td><td>412,178</td><td>23,107</td><td>22,176</td></tr><tr><td>CSN-Javascript</td><td>123,889</td><td>8,253</td><td>6,483</td></tr><tr><td>CSN-Ruby</td><td>48,791</td><td>2,209</td><td>2,279</td></tr><tr><td>CSN-Go</td><td>317,832</td><td>14,242</td><td>14,291</td></tr><tr><td>Java-small</td><td>691,974</td><td>23,844</td><td>57,088</td></tr></table>
+
+Table 1: Dataset statistics.
+
+Preprocessing. Each token of the source code is split into subtokens respective to code naming conventions, i.e., get TrainingData is converted to [get, training, data]. Following Alon et al. (2019a) we use at most six subtokens for the method names, truncating longer function names if necessary. In addition to the tokenized source code we produce an AST for each method using the open-source AST parser Semantic3. We limit the vocabulary to subtokens with at least 100 occurrences in the training set, and only consider snippets with 512 or fewer tokens (after removing punctuation). We refer the reader to the appendix for further details on the data preprocessing.
+
+Pointer network. We add a pointer network (Vinyals et al., 2015) (as described in Fernandes et al. (2019)) to the decoders of all Transformer-based models. This enables them to enhance their predictions by pointing at positions in the input sequence. For instance, when predicting the method name get url, the model can point directly to occurrences of the variable url. This often improves results for less frequent tokens, and even enables the model to predict tokens which are not in the vocabulary by pointing at their positions in the input.
+
+Baselines. We compare with code2seq (Alon et al., 2019a), the Graph Relational Embedding Attention Transformer (GREAT) (Hellendoorn et al., 2020), and the BiLSTM+GNN LSTM+Pointer model presented in Fernandes et al. (2019). Code2seq is a non-Transformer model and state of the art for code summarization using only AST information. GREAT is a recent Transformer model using the framework presented in (Shaw et al., 2018) to bias the attention via edges. In the original formulation, GREAT additionally uses hand-crafted, language-specific edges such as dataflow, ‘computed from’, or ‘next lexical use’ edges, which require specialized preprocessing and static analysis tools. While this approach of leveraging language-specific features can certainly improve results on specific tasks and programming languages, our goal is to have a flexible model that can be used on any programming language. Since the specialized preprocessing used by GREAT is proprietary and not public, we produce the results for GREAT using edges from the AST instead, i.e. it has access to the same information as our proposed model. Note that the preprocessing of Fernandes et al. (2019) is language specific, which is why we only compare with their results on Java-small.
+
+# 5 RESULTS
+
+# 5.1 MONOLINGUAL CODE SUMMARIZATION
+
+CSN dataset. First, we study the performance (measured by F1 score) of our model and the baselines on the traditional setting, where training and evaluation are performed on a single programming language. The results are shown in the upper part of Table 2. The CODE TRANSFORMER (without multi-language training) substantially outperforms all other models on all but one language, highlighting the effectiveness of jointly learning from Structure and Context. The only exception is Ruby, where it performs on par with its Context-only variant. We attribute this to the fact that there are relatively few samples in the Ruby dataset, and that Ruby is an dynamically typed language, which could make the Structure less powerful for learning. Interestingly, the Context-only CODE TRANSFORMER outperforms GREAT on all languages. We attribute this to the fact that GREAT uses the Structure of the programs only in a localized way (see Sec. 3.1). Another noteworthy finding is that code2seq performs comparably to the Transformer-based baselines on Go. We hypothesize that ASTs are more informative on Go since it is a compiled and strongly typed language.
+
+Table 2: Code summarization results on the CSN dataset (micro F1).   
+
+<table><tr><td rowspan="2">Model</td><td colspan="3">Python</td><td colspan="3">Javascript</td><td colspan="3">Ruby</td><td colspan="3">Go</td></tr><tr><td>Prec.</td><td>Rec.</td><td>F1</td><td>Prec.</td><td>Rec.</td><td>F1</td><td>Prec.</td><td>Rec.</td><td>F1</td><td>Prec.</td><td>Rec.</td><td>F1</td></tr><tr><td>code2seq</td><td>35.79</td><td>24.85</td><td>29.34</td><td>30.18</td><td>19.88</td><td>23.97</td><td>23.23</td><td>10.31</td><td>14.28</td><td>52.30</td><td>43.43</td><td>47.45</td></tr><tr><td>GREAT</td><td>35.07</td><td>31.59</td><td>33.24</td><td>31.20</td><td>26.84</td><td>28.86</td><td>24.64</td><td>22.23</td><td>23.38</td><td>50.01</td><td>46.51</td><td>48.20</td></tr><tr><td>Ours w/o structure</td><td>37.38</td><td>31.98</td><td>34.47</td><td>33.17</td><td>26.70</td><td>29.59</td><td>29.85</td><td>25.87</td><td>27.72</td><td>51.78</td><td>47.57</td><td>49.59</td></tr><tr><td>Ours w/o pointer net</td><td>37.74</td><td>31.85</td><td>34.55</td><td>33.12</td><td>28.70</td><td>30.75</td><td>23.32</td><td>25.21</td><td>24.23</td><td>54.31</td><td>50.12</td><td>52.13</td></tr><tr><td>Ours</td><td>36.40</td><td>33.66</td><td>34.97</td><td>35.06</td><td>29.61</td><td>32.11</td><td>31.42</td><td>24.46</td><td>27.50</td><td>55.10</td><td>48.05</td><td>51.34</td></tr><tr><td>code2seq (Multilanguage)</td><td>34.49</td><td>25.49</td><td>29.32</td><td>31.62</td><td>22.16</td><td>26.06</td><td>23.97</td><td>17.06</td><td>19.93</td><td>52.70</td><td>44.36</td><td>48.17</td></tr><tr><td>GREAT (Multilanguage)</td><td>36.75</td><td>31.54</td><td>33.94</td><td>33.58</td><td>27.78</td><td>30.41</td><td>30.05</td><td>24.33</td><td>26.89</td><td>52.65</td><td>48.30</td><td>50.38</td></tr><tr><td>Ours w/o structure (Mult.)</td><td>38.48</td><td>30.14</td><td>33.80</td><td>35.38</td><td>27.41</td><td>30.89</td><td>32.61</td><td>26.76</td><td>29.40</td><td>55.03</td><td>47.34</td><td>50.90</td></tr><tr><td>Ours w/o pointer (Mult.)</td><td>38.91</td><td>33.12</td><td>35.78</td><td>37.21</td><td>29.75</td><td>33.07</td><td>34.52</td><td>27.31</td><td>30.50</td><td>56.07</td><td>50.76</td><td>53.28</td></tr><tr><td>Ours (Multilanguage)</td><td>38.89</td><td>33.82</td><td>36.18</td><td>36.95</td><td>29.98</td><td>33.10</td><td>33.93</td><td>28.94</td><td>31.24</td><td>56.00</td><td>50.44</td><td>53.07</td></tr><tr><td>Ours (Mult.+ Finetune)</td><td>39.85</td><td>32.79</td><td>35.98</td><td>37.00</td><td>29.79</td><td>33.00</td><td>35.85</td><td>27.75</td><td>31.28</td><td>55.63</td><td>51.12</td><td>53.28</td></tr><tr><td>Ours (Mult. + LM Pretrain)</td><td>39.67</td><td>35.29</td><td>37.35</td><td>37.06</td><td>31.94</td><td>34.31</td><td>35.19</td><td>29.36</td><td>32.01</td><td>57.73</td><td>51.89</td><td>54.65</td></tr></table>
+
+Java-small results. In Table 3 we present code summarization results on the Java-small dataset. Among all models equipped with a pointer network, the CODE TRANSFORMER (without pretraining) obtains state-of-the-art on code summarization, outperforming all baselines, including the previous state-of-the-art on Java-small proposed by Fernandes et al. (2019). Further, pre-training on Java-medium and Java-large on the permutation language modeling objective (Yang et al., 2019) substantially improves precision, recall, and F1 score after fine-tuning on Java-small. To avoid leakage, we exclude the projects used in the validation and test splits of Java-small from pre-training.
+
+Ablation study. We further perform ablations where we remove our model’s access to the Context or Structure, also presented in Table 3.
+
+With pointer network. We find that both ablations lead to a substantial drop in performance, highlighting the benefit of learning jointly from Structure and Context. Interestingly, the model without access to the Structure performs slightly better than the variant without Context. Note that our model without Structure is related to the XLNet (Yang et al., 2019) model, where we add a pointer network to the decoder and concatenate the token types to their respective input tokens (see Appendix A.4). Without pointer network. We repeat the ablation on the variants without pointer network. Here, the variant without Context performs better than the variant without Structure,
+
+<table><tr><td>Model</td><td>Prec.</td><td>Rec.</td><td>F1</td></tr><tr><td>Without pointer net code2seq Ours w/o structure Ours w/o context</td><td>51.23 50.70 51.81</td><td>37.31 45.49 46.04</td><td>43.18 47.96</td></tr><tr><td>Ours With pointer net</td><td>50.33</td><td>46.80</td><td>48.75 48.50</td></tr><tr><td>Fernandes et al. (2019)</td><td>=</td><td>1</td><td>51.4</td></tr><tr><td>GREAT Ours w/o structure</td><td>53.60</td><td>46.41</td><td>49.75</td></tr><tr><td>Ours w/o context</td><td>55.48</td><td>46.07</td><td>50.34</td></tr><tr><td></td><td>54.45</td><td>45.29</td><td>49.45</td></tr><tr><td>Ours</td><td>54.85</td><td>49.84</td><td>52.22</td></tr><tr><td>Ours + Pretrain</td><td>57.02</td><td>50.87</td><td>53.77</td></tr></table>
+
+Table 3: Results on Java-small and ablation study.
+
+indicating that the pointer network helps to compensate for the lack of access to Structure. The Structure-only variant (w/o pointer net) of our model even outperforms the full variant in this scenario. Inspection of the results revealed that the Structure-only variant has better performance on longer method names, which have an outsize influence on the micro-F1 score used in this work.
+
+Ablation of the AST-based distances. In Table 4 we compare the performance of our model when trained with each of the four different AST distances (sibling shortest paths, ancestor shortest paths, shortest paths, personalized PageRank; see Section 3.1). Here, the model is trained on Java-small in the Structure-only setting and without pointer network. For reference, we also show the results of training our model using all four AST distance functions (c.f. Table 3). We find that, while the personalized PageRank distance performs best on its own, each of the individual distances on their own performs substantially worse than their combination, highlighting the usefulness of combining the distances in our model as well as their complementary nature.
+
+# 5.2 MULTILINGUAL CODE SUMMARIZATION
+
+Setup. A key contribution of our proposed architecture is that it only uses language-agnostic features, i.e. the source code and features that can be directly computed from the AST. We use this fact to study the first multilanguage code summarization model. We train our model jointly on Python, Javascript, Ruby, and Go. The shared sub-token vocabulary is the union of the individual vocabularies, enabling us to evaluate the multi-language model on the individual languages and compare with the single-language models. As proposed by Conneau & Lample (2019), we add a learned language embedding to each input embedding.
+
+Table 4: AST distance ablation study.   
+
+<table><tr><td>AST distance</td><td>F1 score</td></tr><tr><td>Sibling shortest paths</td><td>46.17</td></tr><tr><td>Ancestor shortest paths</td><td>47.89</td></tr><tr><td>Shortest paths</td><td>47.76</td></tr><tr><td>Personalized PageRank</td><td>48.47</td></tr><tr><td>All the above (c.f. Table 3)</td><td>48.75</td></tr></table>
+
+Results. In the lower part of Table 2 we can see the results of training our CODE TRANSFORMER jointly on all four programming languages. Our multi-lingual variants substantially outperform the mono-lingual models on all languages. The strongest improvement is on Ruby, which is also the programming language with the smallest number of samples in the dataset. Fine-tuning on the individual languages after joint training on code summarization only has a marginal effect on performance, indicating that the multilingual objective is well-aligned with the individual languages. In the last row, we have a variant of our model where we pre-train on the multi-lingual masked language modeling task, followed by finetuning on code summarization on the individual languages.
+
+Further, we observe that similar to the results on Java-small, removing the pointer network generally leads to weaker performance. One notable exception is Go, where the variant without the pointer network performs better in terms of F1 score. Our investigation revealed that there seems to be some violation of the i.i.d. assumption in the split provided by the creators of the dataset. In Figure 7 we show that in the test partition of the Go dataset, the share of tokens from the labels also occurring in the methods’ bodies – exactly the scenario where the pointer network can improve predictions – is substantially lower compared to the train/validation partitions.
+
+Remarkably, the multi-language Context-only variant (i.e. without access to the Structure) performs substantially worse than the full multi-language variant. This highlights that Structure is crucial to exploit the commonalities of different programming languages. Also notably, the GREAT baseline’s results also improve substantially when trained in the multi-language setting, though it is still outperformed by our model. However, our results indicate that any representation learning model for code can benefit from multi-language training, especially when evaluating on low-resource languages.
+
+In Table 16 we present results using the sample-F1 score. At the time of submission, our monolingual model on Python outperforms the state of the art on the ogbg-code $2 ^ { 4 }$ (Hu et al., 2020) leaderboard by $112 \%$ , and our multilanguage variant with LM pretraining outperforms it by $122 \%$ .
+
+Qualitative analysis of multilingual representations. Learning the CODE TRANSFORMER on multiple programming languages jointly provides us with embeddings in a shared representation space. In Fig. 4 we show a t-SNE (Maaten & Hinton, 2008) visualization of the ca. 40,000 snippets from the validation sets of four programming languages from the CSN dataset. For the embedding of a snippet, we use the representation of the method name in the final layer of the encoder. Note that the true method names are masked, i.e., inaccessible to the model. Further, note that in contrast to the monolingual embeddings learned by Kanade et al. (2020), the embeddings we evaluate are learned on the task of code summarization (though a similar study could be performed by using our model that was trained on the traditional language modeling pretraining task on multiple languages).
+
+While snippets from the same language tend to be grouped together, there are interesting intersections of the different programming languages. For example, we highlight all methods whose names start with the subtoken parse or main. We see that snippets starting with parse are predominantly in an intersection region of Python and Javascript. From these snippets, we display the cross-language pair with smallest Euclidean embedding distance in Fig. 5. Remarkably, both snippets are effectively the same method in Javascript and Python – it is worth reminding that the model has never seen any parallel data during training. On the other hand, snippets starting with main tend to lie at an intersectional region of Python, Javascript, and Go. In Table 6 in the appendix we show additional cross-lingual pairs with similar embeddings, including a failure case of a main function, where embedding distance is not representative of semantic similarity. We attribute this to the fact that we used the encoder output embedding of the masked method name – the representation used by the decoder to predict the method name – as a snippet’s representation. Thus, snippets with completely different semantics (as is to be expected for very generic method names starting with main) have similar representations because they are predictive of the method name.
+
+![](images/e875f6f92fb5baf876c7eada99cff2f2f6a1ae4c2907de273c6e3de07dd8a6a8.jpg)  
+Figure 4: t-SNE visualization of the CODE TRANSFORMER’s learned multilingual representations.
+
+![](images/b4f73ecaf41d7a935e9b22345a3d4464c58d6b6b17f19a5180425db1c0483a08.jpg)  
+Figure 5: Example snippet starting with parse (left) and its best embedding match from other languages (right). Both methods parse an input string to convert it into a boolean value. Note that even though they are semantically very similar, their method names are not; nonetheless, their representations in the CODE TRANSFORMER encoder reflect their semantic similarity.
+
+As another qualitative insight into the representations learned by the CODE TRANSFORMER we have found that the language embeddings of languages with similar roots in language design are close; see Table 5 in the appendix for the pairwise similarity matrix of the learned language embeddings.
+
+# 6 CONCLUSION
+
+We present the CODE TRANSFORMER, which learns jointly from Structure and Context of programs while only relying on language-agnostic features. Our model obtains state-of-the-art performance on code summarization on five different programming languages. Besides these results for training on individual languages, the language-agnostic nature of our model allows us to train it jointly on multiple programming languages. The resulting multilingual model substantially outperforms its mono-lingual variant on all programming languages, setting the state of the art on each language. We observe the largest improvement from multilingual training on the language with fewest resources, indicating that multilingual training can improve learning for less widely used programming languages. Remarkably, multilingual training only from Context does not lead to the same improvements, highlighting the benefits of combining Structure and Context.
+
+# REFERENCES
+
+Mithun Acharya, Tao Xie, Jian Pei, and Jun Xu. Mining api patterns as partial orders from source code: From usage scenarios to specifications. In Proceedings of the the 6th Joint Meeting of the European Software Engineering Conference and the ACM SIGSOFT Symposium on The Foundations of Software Engineering, ESEC-FSE ’07, pp. 25–34, New York, NY, USA, 2007. Association for Computing Machinery. ISBN 9781595938114. doi: 10.1145/1287624.1287630. URL https://doi.org/10.1145/1287624.1287630.
+
+Miltiadis Allamanis, Earl T. Barr, Christian Bird, and Charles Sutton. Learning natural coding conventions. In Proceedings of the 22nd ACM SIGSOFT International Symposium on Foundations of Software Engineering, FSE 2014, pp. 281–293, New York, NY, USA, 2014. Association for Computing Machinery. ISBN 9781450330565. doi: 10.1145/2635868.2635883. URL https://doi.org/10.1145/2635868.2635883.
+
+Miltiadis Allamanis, Earl T. Barr, Christian Bird, and Charles Sutton. Suggesting accurate method and class names. In Proceedings of the 2015 10th Joint Meeting on Foundations of Software Engineering, ESEC/FSE 2015, pp. 38–49, New York, NY, USA, 2015. Association for Computing Machinery. ISBN 9781450336758. doi: 10.1145/2786805.2786849. URL https://doi. org/10.1145/2786805.2786849.
+
+Miltiadis Allamanis, Hao Peng, and Charles Sutton. A convolutional attention network for extreme summarization of source code. In International conference on machine learning, pp. 2091–2100, 2016.
+
+Miltiadis Allamanis, Marc Brockschmidt, and Mahmoud Khademi. Learning to represent programs with graphs. In International Conference on Learning Representations, 2018. URL https: //openreview.net/forum?id $=$ BJOFETxR-.
+
+Uri Alon, Meital Zilberstein, Omer Levy, and Eran Yahav. A general path-based representation for predicting program properties. In Proceedings of the 39th ACM SIGPLAN Conference on Programming Language Design and Implementation, PLDI 2018, pp. 404–419, New York, NY, USA, 2018. Association for Computing Machinery. ISBN 9781450356985. doi: 10.1145/3192366.3192412. URL https://doi.org/10.1145/3192366.3192412.
+
+Uri Alon, Shaked Brody, Omer Levy, and Eran Yahav. code2seq: Generating sequences from structured representations of code. In International Conference on Learning Representations, 2019a. URL https://openreview.net/forum?id $=$ H1gKYo09tX.
+
+Uri Alon, Meital Zilberstein, Omer Levy, and Eran Yahav. code2vec: Learning distributed representations of code. Proceedings of the ACM on Programming Languages, 3(POPL):1–29, 2019b.
+
+Peter W Battaglia, Jessica B Hamrick, Victor Bapst, Alvaro Sanchez-Gonzalez, Vinicius Zambaldi, Mateusz Malinowski, Andrea Tacchetti, David Raposo, Adam Santoro, Ryan Faulkner, et al. Relational inductive biases, deep learning, and graph networks. arXiv preprint arXiv:1806.01261, 2018.
+
+Avishkar Bhoopchand, Tim Rocktaschel, Earl Barr, and Sebastian Riedel. Learning python code ¨ suggestion with a sparse pointer network. arXiv preprint arXiv:1611.08307, 2016.
+
+Benjamin Bichsel, Veselin Raychev, Petar Tsankov, and Martin Vechev. Statistical deobfuscation of android applications. In Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security, CCS ’16, pp. 343–355, New York, NY, USA, 2016. Association for Computing Machinery. ISBN 9781450341394. doi: 10.1145/2976749.2978422. URL https: //doi.org/10.1145/2976749.2978422.
+
+Pavol Bielik, Veselin Raychev, and Martin Vechev. Phog: probabilistic model for code. In International Conference on Machine Learning, pp. 2933–2942, 2016.
+
+Aleksandar Bojchevski, Johannes Klicpera, Bryan Perozzi, Amol Kapoor, Martin Blais, Benedek Rozemberczki, Michal Lukasik, and Stephan G ´ unnemann. Scaling graph neural networks with ¨ approximate pagerank. In Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery amp; Data Mining, KDD ’20, pp. 2464–2473, New York, NY, USA, 2020.
+
+Association for Computing Machinery. ISBN 9781450379984. doi: 10.1145/3394486.3403296.   
+URL https://doi.org/10.1145/3394486.3403296.
+
+Dylan Bourgeois. Learning representations of source code from structure and context. 2019. URL http://infoscience.epfl.ch/record/277163.
+
+Alexis Conneau and Guillaume Lample. Cross-lingual language model pretraining. In H. Wallach, H. Larochelle, A. Beygelzimer, F. d'Alche-Buc, E. Fox, and ´ R. Garnett (eds.), Advances in Neural Information Processing Systems 32, pp. 7059– 7069. Curran Associates, Inc., 2019. URL http://papers.nips.cc/paper/ 8928-cross-lingual-language-model-pretraining.pdf.
+
+Hanjun Dai, Bo Dai, and Le Song. Discriminative embeddings of latent variable models for structured data. In International conference on machine learning, pp. 2702–2711, 2016.
+
+Zihang Dai, Zhilin Yang, Yiming Yang, Jaime Carbonell, Quoc V Le, and Ruslan Salakhutdinov. Transformer-xl: Attentive language models beyond a fixed-length context. arXiv preprint arXiv:1901.02860, 2019.
+
+Hoa Khanh Dam, Truyen Tran, and Trang Pham. A deep language model for software code. In FSE 2016: Proceedings of the Foundations Software Engineering International Symposium [The Conference], 2016.
+
+Michael Defferrard, Xavier Bresson, and Pierre Vandergheynst. Convolutional neural networks on ¨ graphs with fast localized spectral filtering. In Advances in neural information processing systems, pp. 3844–3852, 2016.
+
+David K Duvenaud, Dougal Maclaurin, Jorge Iparraguirre, Rafael Bombarell, Timothy Hirzel, Alan´ Aspuru-Guzik, and Ryan P Adams. Convolutional networks on graphs for learning molecular fingerprints. In Advances in neural information processing systems, pp. 2224–2232, 2015.
+
+Patrick Fernandes, Miltiadis Allamanis, and Marc Brockschmidt. Structured neural summarization. In International Conference on Learning Representations, 2019. URL https: //openreview.net/forum?id $=$ H1ersoRqtm.
+
+Marco Gori, Gabriele Monfardini, and Franco Scarselli. A new model for learning in graph domains. In Proceedings. 2005 IEEE International Joint Conference on Neural Networks, 2005., volume 2, pp. 729–734. IEEE, 2005.
+
+William L. Hamilton, Rex Ying, and Jure Leskovec. Inductive representation learning on large graphs. In NIPS, 2017.
+
+Vincent J. Hellendoorn, Charles Sutton, Rishabh Singh, Petros Maniatis, and David Bieber. Global relational models of source code. In International Conference on Learning Representations, 2020. URL https://openreview.net/forum?id $=$ B1lnbRNtwr.
+
+Abram Hindle, Earl T. Barr, Zhendong Su, Mark Gabel, and Premkumar Devanbu. On the naturalness of software. In Proceedings of the 34th International Conference on Software Engineering, ICSE ’12, pp. 837–847. IEEE Press, 2012. ISBN 9781467310673.
+
+Sepp Hochreiter and Jurgen Schmidhuber. Long short-term memory. ¨ Neural computation, 9(8): 1735–1780, 1997.
+
+Weihua Hu, Matthias Fey, Marinka Zitnik, Yuxiao Dong, Hongyu Ren, Bowen Liu, Michele Catasta, and Jure Leskovec. Open graph benchmark: Datasets for machine learning on graphs. In H. Larochelle, M. Ranzato, R. Hadsell, M. F. Balcan, and H. Lin (eds.), Advances in Neural Information Processing Systems, volume 33, pp. 22118–22133. Curran Associates, Inc., 2020. URL https://proceedings.neurips.cc/paper/2020/file/ fb60d411a5c5b72b2e7d3527cfc84fd0-Paper.pdf.
+
+Hamel Husain, Ho-Hsiang Wu, Tiferet Gazit, Miltiadis Allamanis, and Marc Brockschmidt. Codesearchnet challenge: Evaluating the state of semantic code search. arXiv preprint arXiv:1909.09436, 2019.
+
+Aditya Kanade, Petros Maniatis, Gogul Balakrishnan, and Kensen Shi. Learning and evaluating contextual embedding of source code. In Proceedings of the 37th International Conference on Machine Learning, 2020.
+
+Thomas N. Kipf and Max Welling. Semi-supervised classification with graph convolutional networks. In International Conference on Learning Representations (ICLR), 2017.
+
+Johannes Klicpera, Aleksandar Bojchevski, and Stephan Gunnemann. Predict then propagate: ¨ Graph neural networks meet personalized pagerank. In International Conference on Learning Representations (ICLR), 2019a.
+
+Johannes Klicpera, Stefan Weißenberger, and Stephan Gunnemann. Diffusion improves graph learn-¨ ing. In Conference on Neural Information Processing Systems (NeurIPS), 2019b.
+
+Johannes Klicpera, Janek Groß, and Stephan Gunnemann. Directional message passing for molec- ¨ ular graphs. In International Conference on Learning Representations (ICLR), 2020.
+
+Jian Li, Yue Wang, Michael R Lyu, and Irwin King. Code completion with neural attention and pointer networks. arXiv preprint arXiv:1711.09573, 2017.
+
+Yujia Li, Daniel Tarlow, Marc Brockschmidt, and Richard Zemel. Gated graph sequence neural networks. arXiv preprint arXiv:1511.05493, 2015.
+
+Laurens van der Maaten and Geoffrey Hinton. Visualizing data using t-sne. Journal of machine learning research, 9(Nov):2579–2605, 2008.
+
+Chris Maddison and Daniel Tarlow. Structured generative models of natural source code. In International Conference on Machine Learning, pp. 649–657, 2014.
+
+Lili Mou, Ge Li, Lu Zhang, Tao Wang, and Zhi Jin. Convolutional neural networks over tree structures for programming language processing. In Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence, AAAI’16, pp. 1287–1293. AAAI Press, 2016.
+
+Trong Duc Nguyen, Anh Tuan Nguyen, Hung Dang Phan, and Tien N. Nguyen. Exploring api embedding for api usages and applications. In Proceedings of the 39th International Conference on Software Engineering, ICSE ’17, pp. 438–449. IEEE Press, 2017. ISBN 9781538638682. doi: 10.1109/ICSE.2017.47. URL https://doi.org/10.1109/ICSE.2017.47.
+
+Lawrence Page, Sergey Brin, Rajeev Motwani, and Terry Winograd. The pagerank citation ranking: Bringing order to the web. Technical report, Stanford InfoLab, 1999.
+
+Alec Radford, Jeffrey Wu, Rewon Child, David Luan, Dario Amodei, and Ilya Sutskever. Language models are unsupervised multitask learners. OpenAI Blog, 1(8):9, 2019.
+
+Veselin Raychev, Martin Vechev, and Eran Yahav. Code completion with statistical language models. In Proceedings of the 35th ACM SIGPLAN Conference on Programming Language Design and Implementation, PLDI ’14, pp. 419–428, New York, NY, USA, 2014. Association for Computing Machinery. ISBN 9781450327848. doi: 10.1145/2594291.2594321. URL https://doi. org/10.1145/2594291.2594321.
+
+Franco Scarselli, Marco Gori, Ah Chung Tsoi, Markus Hagenbuchner, and Gabriele Monfardini. The graph neural network model. IEEE Transactions on Neural Networks, 20(1):61–80, 2008.
+
+Michael Schlichtkrull, Thomas N. Kipf, Peter Bloem, Rianne van den Berg, Ivan Titov, and Max Welling. Modeling relational data with graph convolutional networks. In Aldo Gangemi, Roberto Navigli, Maria-Esther Vidal, Pascal Hitzler, Raphael Troncy, Laura Hollink, Anna Tordai, and ¨ Mehwish Alam (eds.), The Semantic Web, pp. 593–607, Cham, 2018. Springer International Publishing. ISBN 978-3-319-93417-4.
+
+Peter Shaw, Jakob Uszkoreit, and Ashish Vaswani. Self-attention with relative position representations. In Proceedings of the 2018 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 2 (Short Papers), pp. 464–468, New Orleans, Louisiana, June 2018. Association for Computational Linguistics. doi: 10.18653/v1/N18-2074. URL https://www.aclweb.org/anthology/N18-2074.
+
+Yikang Shen, Shawn Tan, Alessandro Sordoni, and Aaron Courville. Ordered neurons: Integrating tree structures into recurrent neural networks. In International Conference on Learning Representations, 2019. URL https://openreview.net/forum?id ${ . } =$ B1l6qiR5F7.
+
+Vighnesh Shiv and Chris Quirk. Novel positional encodings to enable tree-based transformers. In Advances in Neural Information Processing Systems, pp. 12081–12091, 2019.
+
+Richard Socher, Alex Perelygin, Jean Wu, Jason Chuang, Christopher D Manning, Andrew Y Ng, and Christopher Potts. Recursive deep models for semantic compositionality over a sentiment treebank. In Proceedings of the 2013 conference on empirical methods in natural language processing, pp. 1631–1642, 2013.
+
+Kai Sheng Tai, Richard Socher, and Christopher D Manning. Improved semantic representations from tree-structured long short-term memory networks. arXiv preprint arXiv:1503.00075, 2015.
+
+Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention is all you need. In Advances in neural information processing systems, pp. 5998–6008, 2017.
+
+Petar Velickovi ˇ c, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Li ´ o, and Yoshua \` Bengio. Graph Attention Networks. International Conference on Learning Representations, 2018. URL https://openreview.net/forum?id $=$ rJXMpikCZ.
+
+Oriol Vinyals, Meire Fortunato, and Navdeep Jaitly. Pointer networks. In Advances in neural information processing systems, pp. 2692–2700, 2015.
+
+Song Wang, Devin Chollak, Dana Movshovitz-Attias, and Lin Tan. Bugram: Bug detection with n-gram language models. In Proceedings of the 31st IEEE/ACM International Conference on Automated Software Engineering, ASE 2016, pp. 708–719, New York, NY, USA, 2016. Association for Computing Machinery. ISBN 9781450338455. doi: 10.1145/2970276.2970341. URL https://doi.org/10.1145/2970276.2970341.
+
+Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka. How powerful are graph neural networks? In International Conference on Learning Representations, 2019. URL https: //openreview.net/forum?id $=$ ryGs6iA5Km.
+
+Zhilin Yang, Zihang Dai, Yiming Yang, Jaime Carbonell, Russ R Salakhutdinov, and Quoc V Le. Xlnet: Generalized autoregressive pretraining for language understanding. In Advances in neural information processing systems, pp. 5754–5764, 2019.
+
+Zhitao Ying, Jiaxuan You, Christopher Morris, Xiang Ren, Will Hamilton, and Jure Leskovec. Hierarchical graph representation learning with differentiable pooling. In Advances in neural information processing systems, pp. 4800–4810, 2018.
+
+Jiaxuan You, Rex Ying, and Jure Leskovec. Position-aware graph neural networks. In Kamalika Chaudhuri and Ruslan Salakhutdinov (eds.), Proceedings of the 36th International Conference on Machine Learning, volume 97 of Proceedings of Machine Learning Research, pp. 7134– 7143. PMLR, 09–15 Jun 2019. URL http://proceedings.mlr.press/v97/you19b. html.
+
+Muhan Zhang and Yixin Chen. Link prediction based on graph neural networks. In Advances in Neural Information Processing Systems, pp. 5165–5175, 2018.
+
+Table 5: Pairwise cosine similarities of the learned language embeddings of the CODE TRANSFORMER.   
+
+<table><tr><td></td><td>Python</td><td>Javascript</td><td>Go</td><td>Ruby</td></tr><tr><td>Python</td><td>1.00</td><td>0.43</td><td>0.42</td><td>0.79</td></tr><tr><td>Javascript</td><td>0.43</td><td>1.00</td><td>0.84</td><td>0.39</td></tr><tr><td>Go</td><td>0.43</td><td>0.84</td><td>1.00</td><td>0.38</td></tr><tr><td>Ruby</td><td>0.79</td><td>0.39</td><td>0.38</td><td>1.00</td></tr></table>
+
+# ACKNOWLEDGEMENTS
+
+We are grateful to Dylan Bourgeois for having paved the way to this research contribution with his thesis work (Bourgeois, 2019). We further thank Simon Geisler for his helpful suggestions and proofreading the paper, as well as the anonymous reviewers for their constructive feedback and fruitful discussions.
+
+This research was supported by the TUM International Graduate School of Science and Engineering (IGSSE). Stanford University is supported by DARPA under Nos. N660011924033 (MCS); ARO under Nos. W911NF-16-1- 0342 (MURI), W911NF-16-1-0171 (DURIP); NSF under Nos. OAC1835598 (CINES), OAC-1934578 (HDR), CCF-1918940 (Expeditions), IIS-2030477 (RAPID); Stanford Data Science Initiative, Wu Tsai Neurosciences Institute, Chan Zuckerberg Biohub, Amazon, JPMorgan Chase, Docomo, Hitachi, JD.com, KDDI, NVIDIA, Dell, Toshiba, Intel, and UnitedHealth Group. Jure Leskovec is a Chan Zuckerberg Biohub investigator.
+
+# A APPENDIX
+
+# A.1 DISTANCE ENCODING FUNCTION
+
+For encoding scalar relation values via vectors we employ encoding functions $\phi : \mathbb { R } \to \mathbb { R } ^ { d }$ , where $d$ is the model’s embedding dimension. We choose the popular sinusoidal encoding function presented in Vaswani et al. (2017):
+
+$$
+\phi ( r _ { i  j } ) _ { 2 k } = \sin ( \frac { r _ { i  j } } { M ^ { 2 k / d } } ) \qquad \phi ( r _ { i  j } ) _ { 2 k + 1 } = \cos ( \frac { r _ { i  j } } { M ^ { 2 k / d } } ) ,
+$$
+
+where $1 \leq k < d / 2$ is the position in the encoding vector and $M$ is some constant; we adopt $M = 1 0 , 0 0 0$ as chosen by (Vaswani et al., 2017). Note that the distance encoding functions have no trainable parameters.
+
+# A.2 MULTILINGUAL REPRESENTATION ANALYSIS
+
+In Table 5, we show the pairwise cosine similarities of the learned language embeddings of the CODE TRANSFORMER. We can see that the pairs Python-Ruby and Javascript-Go have similar language embeddings. This aligns well with roots of language design and common use cases of the languages.
+
+Moreover, in Table 6, we show selected snippets starting with is, main, or load (left) and their best embedding matches from other languages (right).
+
+# A.3 DATA PREPROCESSING
+
+# A.3.1 TEXTUAL CODE SNIPPET PREPROCESSING
+
+1. Tokenize code snippets with Pygments language-specific tokenizer.
+
+2. Remove comments (both multi-line, single-line and doc comments). The comment token types. pygments.token.Comment and pygments.token.Literal.String.Doc that are generated by Pygments are used to identify comments.
+
+<table><tr><td colspan="2">Published as a conference paper at ICLR 2021</td></tr><tr><td></td><td></td></tr><tr><td>function isEqualArray(a，b){ if (a return true;</td><td></td></tr><tr><td>if ((a === undefined) undefined)）{ return false;</td><td>func areSameFloat32Array(a，b []float32） bool if len(a) != len(b){ return false</td></tr><tr><td>var =a.length; if (i !== b.length){ return false;</td><td>for i := O;i &lt; len(a);i++{ if a[i]!=b[i]{ return false J</td></tr><tr><td>while (i--）{ if(a[i] !== b[i]）{ return false; }</td><td>return true</td></tr><tr><td>return true;</td><td></td></tr><tr><td>function main() var rawData $(&#x27; .HeaderTexture[data-login- user-email]&#x27;) .data() ;</td><td>func TaskSayHello(t *tasking.T){</td></tr><tr><td>if (rawData) 1 me={</td><td>username := t.Flags.String(&quot;name&quot;) if username user, := user.Current ()</td></tr><tr><td>name:rawData.loginUserName, mail: rawData.loginUserEmail }；</td><td>username = user.Name</td></tr><tr><td>getCartId(function (cart）{ me.cart = cart;</td><td>} ift.Flags.Bool(&quot;verbose&quot;)</td></tr><tr><td>injectMenu(); refreshUsers(actions.updateUsers); listenOnChanges(onChange);</td><td>t.Logf(&quot;Hello %s, the time now is %s\n&quot;, username，time.Now())</td></tr><tr><td>listenonorderConfirm(onConfirm); ）；</td><td>}else{ t.Logf(&quot;Hello %s\n&quot;,username)</td></tr><tr><td>} else{ caliback(&#x27;no user&#x27;);</td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>func Backup(filename string)error{</td></tr><tr><td></td><td></td></tr><tr><td></td><td>info，err := os.Stat(filename) if err != nil</td></tr><tr><td></td><td>if os.IsNotExist(err）{</td></tr><tr><td></td><td>return nil</td></tr><tr><td></td><td>return err</td></tr><tr><td></td><td></td></tr><tr><td>def _load_rule_file(self, filename):</td><td>if info.Size() == 0{ return nil</td></tr><tr><td>if not (os.path.exists(filename)):</td><td>}</td></tr><tr><td>sys.stderr.write(</td><td>files，err ：= filepath.Glob(</td></tr><tr><td>&quot;rflint: %s: No such file or &quot;directory\n&quot; % filename</td><td>filename + _BACKUP_SUFFIX</td></tr><tr><td>return</td><td>） if err nil 1</td></tr><tr><td>try:</td><td>return err</td></tr><tr><td>basename = os.path.basename(filename)</td><td>}</td></tr><tr><td>(name，ext）= os.path.splitext(basename) imp.load_source(name,filename)</td><td> numBackup := byte(1)</td></tr><tr><td>except Exception as e: sys.stderr.write(</td><td>if len(files) !=0{</td></tr><tr><td>&quot;rflint: %s: exception while</td><td>lastFile := files[len(files)-1]</td></tr><tr><td>&quot;loading:%s\n&quot; % (filename, str(e))</td><td>numBackup = lastFile[len(lastFile)-2] + 1</td></tr><tr><td></td><td>if numBackup &gt;</td></tr><tr><td></td><td>numBackup = &#x27;1&#x27;</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>else{</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>&#x27;1&#x27;</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>numBackup =</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>return Copy (filename,</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>fmt.Sprintf(&quot;%s+%s~&quot;,</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>string(numBackup)))</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr></table>
+
+Table 6: Selected snippets starting with is, main, or load (left) and their best embedding matches from other languages (right).
+
+![](images/e37f9cb44d930542340c5ad3d88619f8535c0f5512daf8c0c8d8a050432bff4b.jpg)  
+Figure 6: Example snippet and its corresponding AST obtained from GitHub Semantic.
+
+3. Empty lines are removed.
+
+4. Hard coded strings and numbers are replaced with a special [MASK STRING] and [MASK NUMBER] token.
+
+5. Indentation style of the code snippet is detected and whitespace characters at the beginning of a line are replaced with a single [INDENT] or [DEDENT] token when indentation changes.
+
+6. Tokens are further split into sub tokens, e.g., setBottomHeight [‘set’, ‘bottom’, ‘height’]. Throughout our experiments, we use 5 input sub tokens. If a token consists of less than 5 sub tokens, the remaining spaces are filled with a special [PAD] token.
+
+7. Any remaining tokens that only consist of white spaces are removed. The only white space characters that are kept are line breaks $^ { \bullet } \backslash \boldsymbol { \mathrm { n } } ^ { \prime }$ .
+
+8. Any code snippets where the Pygments tokenizer cannot parse a token are discarded.
+
+# A.3.2 STAGE 1 PREPROCESSING (GENERATION OF ASTS)
+
+1. Stripped code snippets are used to generate language-specific ASTs. For Java, we use the AST parser from the java-parser project. The ASTs contain node types and source ranges. For Python, JavaScript, Ruby and Go, we use semantic.
+
+2. Snippets that lead to an AST parse error are discarded.
+
+3. We calculate a mapping between tokens and nodes in the AST. Every token is assigned to the node in the AST with shortest source range that still encompasses the source range of the token.
+
+To find such a node, we originally intended to make use of the assumption that source ranges of child nodes do not overlap. Then, one could easily find the node with smallest encompassing source range by greedily selecting at every layer in the AST the child that encompasses the token’s source range (there can only be at most one child that fulfills this). However, this assumption does not hold for all ASTs (see Figure 6 for an example). As a heuristic, we greedily select the child node with the shorter source range in case there were multiple child nodes with encompassing source ranges. This approximation seems to be sufficient in our case, and limits runtime as we do not have to consider multiple paths in the AST. It is also sufficient to stop when no child node encompasses the source range of the token, as in ASTs the source ranges of child nodes are always contained in the source ranges of their parent.
+
+1. Tokens are vocabularized. Any token occurring less than 100 times in the training set is replaced by an <unk $>$ token.
+
+2. We calculate multiple pair-wise relations between nodes in the AST:
+
+• Personalized Page Rank (PPR) We interpret the negative logarithm of PPR as a distance. We use a teleport probability of $\alpha = 0 . 1 5$ and a threshold of $e ^ { - 5 }$ , i.e., anything with $- \log P P R > 5$ is considered unreachable   
+• Shortest path length between two nodes   
+• Ancestor shortest paths (bidirectional). That is, the parent has an ancestor shortest path distance of 1 to all its children and the child has a distance of -1 to its parents. We consider nodes that are not ancestors or descendants of a node (i.e. not reachable by following only parent or only child relations) as not connected in the ancestor shortest paths relation. We encode this with a very large value in their distance; we have found a value of $1 , 0 0 0$ to work well in practice.   
+• Next sibling shortest paths (bidirectional, analogous to the ancestor shortest paths)
+
+Note that the ancestor shortest paths and next sibling shortest paths are required because treating the AST as a normal graph leads to ambiguity. In a graph, the neighbors of a node have no ordering; however in the AST, the order of the children of a node reflects their order in the code. Therefore, we explicitly include the next sibling shortest paths. The ancestor shortest paths would not be required if we treated the AST as a directed graph; in this case, however, a leaf node could not reach any other node in the AST, and therefore both PPR and shortest path length are not useful in this case. Therefore, we model the AST as undirected and inject the ancestor / child edges to avoid ambiguity.
+
+3. Distance values are binned into 32 bins using area-based exponential binning with a growth factor of 1.3, i.e., the area of a bin’s rectangle ( $x$ : bin range, $y$ : number of values in bin) will be approximately 1.3 times bigger for the next bin (going away from the bin that contains the zero value). Additionally, for discrete distance measures (such as sequence distance or shortest path length), we hard-code 9 values around 0 to have their own bins. For instance, on the sequence distance the values $- 4 , - 3 , \dots , 4$ have their individual bins, and around those values we employ the exponential binning.
+
+4. Punctuation tokens (such as points or brackets) are removed from the input sequence, as experiments showed that their presence does not improve performance but slows down training due to bigger input sizes.
+
+5. Snippets that are longer than MAX NUM TOKENS after punctuation tokens are removed are discarded from the training set. Throughout our experiments, we use MAX NUM TOKENS $= ~ 5 1 2$ . During evaluation on the test set, we use MAX NUM TOKENS $= ~ 1 0 0 0$ .
+
+# A.4 INPUT EMBEDDINGS TO THE MODEL
+
+Besides its five subtokens (e.g., [‘get’, ‘data’, ‘[PAD]’, ‘[PAD]’, ‘[PAD]’]), each input token has a token type (coming from the Pygments tokenizer) and an AST node type. The AST node type is the type of the node assigned to each respective token, as described in Section A.3.2. We concatenate the embeddings of the five subtokens, the token type, and the AST node type. Then, we apply a linear layer (without activation function) to project down to the model’s embedding dimension.
+
+# A.5 INPUT TO THE GREAT BASELINE
+
+As mentioned in the main text, we also compare with GREAT Hellendoorn et al. (2020). Since their preprocessing pipeline is proprietary and could not be shared with us even after contacting the authors, we provide to GREAT the same AST distances as our model. Since GREAT uses edges instead of distances to encode relations in the Structure, we essentially threshold the ancestor, sibling, and shortest-paths distances and provide the edges where the distances are equal to 1 (including their edge types) to the model.
+
+(a) CODE TRANSFORMER   
+Table 7: Code Summarization hyperparameters   
+
+<table><tr><td>Hyperparameter</td><td>Value</td></tr><tr><td>Activation</td><td>GELU</td></tr><tr><td>Input Nonlinearity</td><td>tanh</td></tr><tr><td>Num. layers</td><td>3</td></tr><tr><td>d</td><td>1024</td></tr><tr><td>dFF</td><td>2048</td></tr><tr><td>Pdropout</td><td>0.2</td></tr><tr><td>Num.heads</td><td>8</td></tr></table>
+
+(b) GREAT (Hellendoorn et al., 2020)   
+
+<table><tr><td>Hyperparameter</td><td>Value</td></tr><tr><td>Activation</td><td>GELU</td></tr><tr><td>Num. layers</td><td>3</td></tr><tr><td>d</td><td>1024</td></tr><tr><td>dFF</td><td>2048</td></tr><tr><td>Pdropout</td><td>0.2</td></tr><tr><td>Num.heads</td><td>8</td></tr></table>
+
+# A.6 EXPERIMENTAL SETUP
+
+Table 7 shows hyperparameters of our models for code summarization. For all our experiments, we use a Transformer Decoder with one layer and teacher forcing to generate 6 output sub tokens. We also employ label smoothing of 0.1. As optimizer, we use Adam with a learning rate of $8 e ^ { - 5 }$ and weight decay of $3 e ^ { - 5 }$ . Batch size during training is 8 with a simulated batch size of 128 achieved by gradient accumulation.
+
+Apart from comparing the CODE TRANSFORMER to baselines, we performed the following hyperparameter comparisons and ablation studies:
+
+• CODE TRANSFORMER (structure-only) Using only AST information as input, i.e., masking all tokens that do not correspond to a leaf of the AST, and removing the token distance as a relation to be used by the model. Further, token types are not fed into the model.   
+• CODE TRANSFORMER (context-only) Here, we do not include any information on the AST (i.e. node types and distances on the AST). This is effectively the XLNet backbone plus encoding of the token type returned by the tokenizer.   
+• CODE TRANSFORMER (Max-Dist.) Applying a Max Distance Mask of 5 to the shortest paths distance (i.e., model cannot see a node that is more than 5 hops away no matter how small the other distances are). Early results showed that, as expected, results deteriorate substantially when limiting our model’s receptive field. Hence, we do not include these results in this work.   
+• Using 16 and 64 bins instead of 32 bins. This had no noticeable effect on performance.
+
+# A.7 CODE SUMMARIZATION EXAMPLES
+
+In the Tables 8, 9, 10, 11, 12, 13, 14 and 15 we present example functions from the Java-small dataset along with the different models’ predictions for the function name.
+
+public Summation next() { return parts $[ \dot { 1 } + + ]$ ; }
+
+Table 8: The CODE TRANSFORMER is the only model to correctly identify the notion of getting the next entry.   
+
+<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td> get x map</td></tr><tr><td>code2seq</td><td> get parts</td></tr><tr><td>Ours w/o structure</td><td>get</td></tr><tr><td>CODE TRANSFORMER</td><td>get next</td></tr><tr><td>Ground Truth</td><td>next</td></tr></table>
+
+private Path findCacheFile(Path[] cacheFiles, String fileName) { if (cacheFiles $! =$ null && cacheFiles.length $> 0$ ) { for (Path file : cacheFiles) { if (file.getName().equals(fileName)) { return file; } return null;   
+}
+
+<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td>get path</td></tr><tr><td>code2seq</td><td>find file</td></tr><tr><td>Ours w/o structure</td><td>get file</td></tr><tr><td>CODE TRANSFORMER</td><td>find cache</td></tr><tr><td>Ground Truth</td><td>find cache file</td></tr></table>
+
+Table 9: The CODE TRANSFORMER is the only model to both recognize that the task is to find a file as well as the fact that it is about the cache. However, it did not correctly predict the file part of the method name.
+
+public int compare(Pair<LoggedJob, JobTraceReader> p1, Pair<LoggedJob, JobTraceReader> p2) { LoggedJob $\ j 1 \ = \ \mathtt { p 1 }$ .first(); LoggedJob $\begin{array} { r } { \dot { \bf { \ j } } 2 { \bf { \nu } } = { \bf { \ p } } 2 } \end{array}$ .first(); return (j1.getSubmitTime() $<$ j2.getSubmitTime()) ? -1 : (j1.getSubmitTime() $= =$ j2.getSubmitTime()) ? 0 : 1; }
+
+<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td>run</td></tr><tr><td>code2seq</td><td> get submit time</td></tr><tr><td>Ours w/o structure</td><td>compare</td></tr><tr><td>CODE TRANSFORMER</td><td>compare</td></tr><tr><td>Ground Truth</td><td>compare</td></tr></table>
+
+Table 10: The CODE TRANSFORMER and the its context-only variant are the only models correctly recognizing the ‘compare’ template in the method body.
+
+public static MNTPROC fromValue(int value) { if (value $< ~ 0$ || value $> =$ values().length) { return null; } return values()[value];   
+}
+
+<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td> get value</td></tr><tr><td>code2seq</td><td> get value</td></tr><tr><td>Ours w/o structure</td><td>to</td></tr><tr><td>CODE TRANSFORMER</td><td>from value</td></tr><tr><td>Ground Truth</td><td>from value</td></tr></table>
+
+Table 11: The CODE TRANSFORMER is the only model to recognize that the snippet is similar to a static factory method which is often preceded with from.
+
+private Iterable<ListBlobItem> listRootBlobs(String aPrefix,
+
+boolean useFlatBlobListing,   
+EnumSet<BlobListingDetails> listingDetails,   
+BlobRequestOptions options,   
+OperationContext opContext)
+
+throws StorageException, URISyntaxException {
+
+CloudBlobDirectoryWrapper directory $=$ this.container.getDirectoryReference(aPrefix); return directory.listBlobs(null, useFlatBlobListing, listingDetails, options, opContext);
+
+}
+
+<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td>list blobs</td></tr><tr><td>code2seq</td><td>list blobs</td></tr><tr><td>Ours w/o structure</td><td>list blobs</td></tr><tr><td>CODE TRANSFORMER</td><td>list blobs by prefix</td></tr><tr><td>Ground Truth</td><td>list root blobs</td></tr></table>
+
+Table 12: All models could correctly identify the listBlobs() call in the return statement. However, the CODE TRANSFORMER additionally comprehended that the specified prefix is quite important.
+
+private static void dumpOpCounts(EnumMap $<$ FSEditLogOpCodes, Holder $<$ <Integer>> opCounts) { StringBuilder sb $=$ new StringBuilder(); sb.append("Summary of operations loaded from edit log:\n "); Joiner.on("\n ").withKeyValueSeparator(" $^ { 1 1 } =$ ").appendTo(sb, opCounts); FSImage.LOG.debug(sb.toString());   
+}
+
+Table 13: Only the CODE TRANSFORMER could correctly identify that it is the op counts that should be logged.   
+
+<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td>append</td></tr><tr><td>code2seq</td><td>add</td></tr><tr><td>Ours w/o structure</td><td>log</td></tr><tr><td>CODE TRANSFORMER</td><td>log op counts</td></tr><tr><td>Ground Truth</td><td>dump op counts</td></tr></table>
+
+static String execCommand(File f, String... cmd) throws IOException { String[] args $=$ new String[cmd.length $^ +$ 1]; System.arraycopy(cmd, 0, args, 0, cmd.length); args[cmd.length] $=$ f.getCanonicalPath(); String output $=$ Shell.execCommand(args); return output;
+
+Table 14: Only the CODE TRANSFORMER and code2seq could identify that the relevant part of the method is concerned with executing a command instead of returning something.   
+
+<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td>get canonical path</td></tr><tr><td>code2seq</td><td>exec</td></tr><tr><td>Ours w/o structure</td><td> get output</td></tr><tr><td>CODE TRANSFORMER</td><td>exec command</td></tr><tr><td>Ground Truth</td><td>exec command</td></tr></table>
+
+# protected void subView(Class<? extends SubView> cls) {
+
+indent(of(ENDTAG));   
+sb.setLength(0);   
+out.print(sb.append('[').append(cls.getName()).append(']').toString());   
+out.println();
+
+Table 15: Only the CODE TRANSFORMER was able to link the print functionality to the object that should be printed, which can only be inferred from the object’s class in the method parameters.   
+
+<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td>print</td></tr><tr><td>code2seq</td><td>print</td></tr><tr><td>Ours w/o structure</td><td>print</td></tr><tr><td>CODE TRANSFORMER</td><td>print sub view</td></tr><tr><td>Ground Truth</td><td>sub view</td></tr></table>
+
+![](images/1225dc2212652b0900da96594dc1baedeb731793c2a7f99b2f39f0a306a759b8.jpg)  
+Figure 7: Share of tokens in the labels also occurring in the bodies of methods.
+
+Table 16: Code summarization results on the CSN dataset (sample-F1).   
+
+<table><tr><td rowspan="2">Model</td><td colspan="2">Python</td><td colspan="3">Javascript</td><td colspan="2"></td><td colspan="2">Ruby</td><td colspan="3">Go</td></tr><tr><td>Prec.</td><td>Rec.</td><td>F1</td><td>Prec.</td><td>Rec.</td><td>F1</td><td>Prec.</td><td>Rec.</td><td>F1</td><td>Prec.</td><td>Rec.</td><td>F1</td></tr><tr><td>code2seq</td><td>1</td><td>1</td><td>1</td><td>-</td><td>1</td><td>1</td><td>=</td><td>1</td><td>1</td><td>1</td><td>1</td><td>-</td></tr><tr><td>GREAT</td><td>34.93</td><td>31.12</td><td>31.61</td><td>29.69</td><td>24.24</td><td>25.55</td><td>25.69</td><td>21.49</td><td>22.18</td><td>48.38</td><td>45.97</td><td>45.71</td></tr><tr><td>Ours w/o structure</td><td>36.87</td><td>32.17</td><td>32.97</td><td>31.30</td><td>25.03</td><td>26.64</td><td>31.43</td><td>25.34</td><td>26.63</td><td>49.78</td><td>46.73</td><td>46.69</td></tr><tr><td>Ours w/o pointer net</td><td>38.77</td><td>31.72</td><td>33.27</td><td>32.70</td><td>25.50</td><td>27.33</td><td>32.12</td><td>30.17</td><td>29.36</td><td>53.09</td><td>48.70</td><td>49.26</td></tr><tr><td>Ours</td><td>36.68</td><td>33.86</td><td>33.84</td><td>33.36</td><td>27.55</td><td>29.02</td><td>31.53</td><td>24.72</td><td>26.43</td><td>52.00</td><td>47.35</td><td>47.93</td></tr><tr><td>code2seq (Multilanguage)</td><td>-</td><td>=</td><td>=</td><td></td><td>=</td><td>=</td><td></td><td></td><td></td><td></td><td></td><td>-</td></tr><tr><td>GREAT (Multilanguage)</td><td>35.73</td><td>30.81</td><td>31.74</td><td>31.49</td><td>26.17</td><td>27.41</td><td>29.72</td><td>24.20</td><td>25.43</td><td>50.32</td><td>47.94</td><td>47.66</td></tr><tr><td>Ours w/o structure (Mult.)</td><td>36.78</td><td>29.92</td><td>31.58</td><td>32.60</td><td>26.02</td><td>27.74</td><td>31.71</td><td>26.07</td><td>27.24</td><td>51.91</td><td>47.58</td><td>48.15</td></tr><tr><td>Ours w/o pointer (Mult.)</td><td>37.18</td><td>30.52</td><td>32.04</td><td>33.95</td><td>25.92</td><td>28.11</td><td>32.76</td><td>25.04</td><td>27.01</td><td>53.50</td><td>48.54</td><td>49.35</td></tr><tr><td>Ours (Multilanguage)</td><td>38.10</td><td>33.32</td><td>34.18</td><td>34.29</td><td>28.69</td><td>30.08</td><td>33.30</td><td>28.33</td><td>29.29</td><td>53.86</td><td>50.46</td><td>50.61</td></tr><tr><td>Ours (Mult. + Finetune)</td><td>38.29</td><td>32.41</td><td>33.65</td><td>34.43</td><td>28.28</td><td>29.91</td><td>32.89</td><td>27.15</td><td>28.49</td><td>53.85</td><td>50.85</td><td></td></tr><tr><td>Ours (Mult.+ LMPretrain)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>50.81</td></tr><tr><td></td><td>38.97</td><td>34.77</td><td>35.34</td><td>35.23</td><td>30.26</td><td>31.38</td><td>33.73</td><td>29.15</td><td>29.94</td><td>55.31</td><td>52.03</td><td>52.13</td></tr></table>
+
+# A.8 ESTIMATION OF POINTER NETWORK POTENTIAL
+
+In Table 2 we observe that the pointer network improves the F1 score for all languages except Go, where counterintuitively it leads to reduced performance as measured by F1 score on the test set (while it improves by about 3 points on validation). To investigate this, in Figure 7 we plot the share of tokens in the labels also occurring in the bodies of methods in the different languages. Intuitively, this gives an indication on how much gain we can expect from using a pointer network. If the share were zero, then no token in the labels ever occur in the bodies of the methods, so the pointer network cannot improve the prediction by pointing at the input. We see that for Go, there is a strong mismatch between the test partition and the train/validation partitions, which much fewer tokens from the labels occurring in the bodies of methods on test compared to train/validation. Thus, we attribute the drop in performance observed by adding a pointer network on Go to this apparent violation of the i.i.d. assumption.
+
+# A.9 CODE SUMMARIZATION RESULTS ON THE CSN DATASET (SAMPLE-F1)
+
+In Table 16, we present our results on the CSN dataset as measured by the sample-F1 score.
\ No newline at end of file
diff --git a/parse/train/Xh5eMZVONGF/Xh5eMZVONGF_content_list.json b/parse/train/Xh5eMZVONGF/Xh5eMZVONGF_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..3f4b80266dca43fd05f47158e384ef2e7dc5a076
--- /dev/null
+++ b/parse/train/Xh5eMZVONGF/Xh5eMZVONGF_content_list.json
@@ -0,0 +1,2644 @@
+[
+    {
+        "type": "text",
+        "text": "LANGUAGE-AGNOSTIC REPRESENTATION LEARNING OF SOURCE CODE FROM STRUCTURE AND CONTEXT ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            99,
+            823,
+            146
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Daniel Zugner, Tobias Kirschstein ¨ Technical University of Munich {zuegnerd,kirschto}@in.tum.de ",
+        "bbox": [
+            184,
+            170,
+            465,
+            213
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Michele Catasta   \nStanford University   \npirroh@cs.stanford.edu ",
+        "bbox": [
+            596,
+            170,
+            813,
+            212
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Jure Leskovec Stanford University jure@cs.stanford.edu ",
+        "bbox": [
+            184,
+            234,
+            382,
+            275
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Stephan Gunnemann ¨ Technical University of Munich guennemann@in.tum.de ",
+        "bbox": [
+            596,
+            234,
+            807,
+            275
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            313,
+            544,
+            327
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Source code (Context) and its parsed abstract syntax tree (AST; Structure) are two complementary representations of the same computer program. Traditionally, designers of machine learning models have relied predominantly either on Structure or Context. We propose a new model, which jointly learns on Context and Structure of source code. In contrast to previous approaches, our model uses only language-agnostic features, i.e., source code and features that can be computed directly from the AST. Besides obtaining state-of-the-art on monolingual code summarization on all five programming languages considered in this work, we propose the first multilingual code summarization model. We show that jointly training on non-parallel data from multiple programming languages improves results on all individual languages, where the strongest gains are on low-resource languages. Remarkably, multilingual training only from Context does not lead to the same improvements, highlighting the benefits of combining Structure and Context for representation learning on code. ",
+        "bbox": [
+            233,
+            342,
+            764,
+            535
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            559,
+            336,
+            575
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Machine learning for code is an active and growing area of research which aims at building models that can learn semantically meaningful representations of programs. These embeddings can be used on downstream tasks, such as code generation, bug detection, or code summarization. We focus our work on two complementary data representations of programs: the source code (referred to as Context in this work), and the abstract syntax tree (AST; referred to as Structure). Traditionally, researchers and practitioners have decided to predominantly leverage either Structure or Context in their machine learning models. In this work, we show that jointly learning on Context and Structure improves representation learning on source code (see Fig. 1). ",
+        "bbox": [
+            174,
+            589,
+            825,
+            702
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "The source code representation naturally lends itself to models from natural language processing (NLP), e.g., long short-term memory networks (Hochreiter & Schmidhuber, 1997) (LSTM) or Transformers (Vaswani et al., 2017; Radford et al., 2019; Dai et al., 2019; Yang et al., 2019; Shaw et al., 2018). On the other hand, models leveraging the structure representations are typically based on graph neural networks (GNNs) (Kipf & Welling, 2017; Xu et al., 2019; Velickovi ˇ c et al., 2018; ´ You et al., 2019; Hamilton et al., 2017; Li et al., 2015; Klicpera et al., 2020). While the AST representation makes the highly structured nature of source code explicit to the models, since most GNNs use the message-passing framework, their learned representations are inherently local and struggle to leverage long-range interactions. ",
+        "bbox": [
+            174,
+            708,
+            825,
+            833
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Recently, Hellendoorn et al. (2020) have explored models that can leverage several representations, including both Structure and Context. Their Graph Relational Embedding Attention Transformer (GREAT) extends Shaw et al. (2018), which biases the self-attention computation in a localized way given the underlying graph. The language-specific representations used by GREAT include a combination of the data flow graph, control flow graph, syntactic edges (inspired by Allamanis et al. (2018)), etc. which require specialized pipelines and static analysis tools to be obtained. ",
+        "bbox": [
+            174,
+            840,
+            825,
+            924
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/7701ebd563c4ccbab0fb3932736f0a3f5ce8408d760ee36d22e78173cbc12d18.jpg",
+        "image_caption": [
+            "Figure 1: Context and Structure both encapsulate valuable information about source code. In this realistic example, token 1 and 4 are distant in the sequence of tokens (Context), but only 5 hops away when traversing the Abstract Syntax Tree (Structure). As such, a method that relies only on the sequence of tokens could neglect the relationship between a method name and its return variable. Conversely, token 1 and 2 showcase the opposite setting. Hence, unifying Structure and Context leads to a more powerful representation of source code. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            271,
+            101,
+            728,
+            234
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We propose the CODE TRANSFORMER1, which combines distances computed on Structure and Context in the self-attention operation. In contrast to the localized treatment via edges described above, we make the full Structure accessible to the model at each layer by computing pairwise distances on the AST, such as shortest path lengths. To this end, we draw inspiration from the XLNet architecture (Yang et al., 2019), which uses relative distances instead of absolute positions in the attention computation. Importantly, all our features are language-agnostic2, i.e., can easily be computed for any programming language based on the source code and AST. ",
+        "bbox": [
+            174,
+            358,
+            825,
+            455
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We use two datasets comprising 5 different programming languages in total, and evaluate the representations learned by our model on the task of code summarization, where the model predicts a method’s name based on its body. Besides setting the state-of-the-art on all five languages for singlelanguage training, we also train the first multilingual model for code summarization. This is enabled by the fact that our model uses only language-agnostic features that can easily be obtained for any programming language. Remarkably, training our model on multiple programming languages substantially improves the performance on all languages. Moreover, multilingual training only from Context does not lead to the same improvements, highlighting the benefits of combining Structure and Context for representation learning on code. ",
+        "bbox": [
+            174,
+            463,
+            825,
+            588
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            608,
+            339,
+            625
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Machine Learning for Code. Early research learned language models on raw text data, e.g., (Wang et al., 2016; Raychev et al., 2014; Dam et al., 2016), providing evidence for the naturalness assumption (Hindle et al., 2012). For example, Allamanis et al. (2015) learned distributed representations of variables and methods, finding that they were indeed able to encode common semantic properties from the regularities present in source code. Alon et al. (2019b) also found evidence of semantic arithmetic in their embedding space, dubbed code2vec. These representations—and their variants like (Mou et al., 2016)—can then be used to predict sequences of identifier sub-tokens (Allamanis et al., 2015) or API calls (Acharya et al., 2007; Nguyen et al., 2017). They can be used as advanced auto-completion tools (Hindle et al., 2012; Bhoopchand et al., 2016), including for user-provided tokens like Variable Names (Raychev et al., 2014; Allamanis et al., 2014). These are useful for deobfuscating Android applications (Bichsel et al., 2016) for example. ",
+        "bbox": [
+            173,
+            643,
+            825,
+            797
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Several works leverage structured graphical models for probabilistic models of source code, usually through parse trees (Maddison & Tarlow, 2014; Bielik et al., 2016). Unlike previous works where hand-crafted features were used as node features (Raychev et al., 2014) or as explicit semantic edges (Allamanis et al., 2018), our work does not augment the existing syntactic relationships between the different elements to enhance the predictive capabilities of the model. Other approaches (Alon et al., 2018; Li et al., 2017) also leverage the AST structure, but linearize the graph by first traversing it. ",
+        "bbox": [
+            174,
+            804,
+            825,
+            859
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            171,
+            103,
+            821,
+            132
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Learning representations of structured languages. While models of language have dramatically improved in their ability to learn structure (syntax) and semantics from scratch, it can be argued that directly providing the model with the underlying structure of the language can help with generalization (Battaglia et al., 2018), managing long-ranging dependencies (Tai et al., 2015), or representing the compositional aspect of natural language (Socher et al., 2013). Notably, tree structures have shown promising results and inspired new architectures (Shen et al., 2019), including in the domain of source code (Fernandes et al., 2019), where the underlying syntax is directly available. Our work pursues this line of research, showing the benefits of explicitly integrating structural information as an inductive bias. Shiv & Quirk (2019) propose positional encodings for nodes on trees; however, their approach assumes regular trees, which is an unrealistic assumption when working with Abstract Syntax Trees, as an AST node can have arbitrarily many children, e.g., the arguments of a function. ",
+        "bbox": [
+            173,
+            142,
+            825,
+            309
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Graph Neural Networks. GNNs provide a powerful tool for machine learning on graphs, thanks to their ability to recursively incorporate information from neighboring nodes in the network (Battaglia et al., 2018), naturally capturing the graph structure simultaneously with the nodes’ features. (Gori et al., 2005; Scarselli et al., 2008) are able to learn vector representations of nodes and graphs in an end-to-end fashion, encoding structural and feature information in the embedding space. Under this model, GNNs have achieved state-of-the-art performance across a variety of tasks, such as node classification (Kipf & Welling, 2017; Hamilton et al., 2017; Klicpera et al., 2019a), link prediction (Zhang & Chen, 2018; Schlichtkrull et al., 2018), graph clustering (Defferrard et al., 2016; Ying et al., 2018) or graph classification (Ying et al., 2018; Dai et al., 2016; Duvenaud et al., 2015). ",
+        "bbox": [
+            173,
+            319,
+            825,
+            445
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 INTEGRATING STRUCTURE AND CONTEXT IN THE CODE TRANSFORMER ",
+        "text_level": 1,
+        "bbox": [
+            169,
+            464,
+            805,
+            482
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Self-attention is the core operation powering the Transformer. It enables the model to selectively focus on relevant parts of the input. The matrix form equation for attention with a single head is ",
+        "bbox": [
+            174,
+            494,
+            823,
+            525
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/bf5062f76acf55f459a4ae89adb1abed3d6a40f640c4bd316cd5ed6cd5cde38d.jpg",
+        "text": "$$\n{ \\mathrm { A t t e n t i o n } } ( Q , K , V ) = { \\mathrm { s o f t m a x } } \\left( { \\frac { Q K ^ { T } } { \\sqrt { d _ { k } } } } \\right) V ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            341,
+            529,
+            653,
+            564
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where $Q , K \\in \\mathbb { R } ^ { N \\times d _ { k } }$ and $V \\in \\mathbb { R } ^ { N \\times d _ { v } }$ . $N$ is the number of input tokens, $d _ { k }$ the key dimension, and $d _ { v }$ the value dimension (typically we have $d _ { k } = d _ { v }$ ). The attention score of query $Q _ { i }$ and key $K _ { j }$ before softmax is ",
+        "bbox": [
+            174,
+            568,
+            825,
+            611
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/a084e175bb3c6930841d0180a4202d6eff0f84ecb6a8a9cc250c5cd2833a474e.jpg",
+        "text": "$$\n\\pmb { A } _ { i j } = \\pmb { Q } _ { i } ^ { T } \\pmb { K } _ { j } = \\pmb { E } _ { i } ^ { T } \\pmb { W } _ { q } ^ { T } \\pmb { W } _ { k } \\pmb { E } _ { j } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            385,
+            609,
+            611,
+            631
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where $E _ { i } , E _ { j } \\in \\mathbb { R } ^ { d }$ are the $d$ -dimensional embeddings of tokens $i$ and $j$ , and $W _ { q }$ , $W _ { k } \\in \\mathbb { R } ^ { d _ { k } \\times d }$ are the query and key projection matrices, respectively. ",
+        "bbox": [
+            174,
+            633,
+            823,
+            661
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Observe that Eq. (2) contains no assumption about potential structure in the input domain: in the attention operation we compute all dot products of query and key vectors equally, effectively viewing them as unordered sets of vectors. This means, however, that the model is oblivious to structured inputs (such as text or graphs) and therefore is unable to distinguish, for example, a variable name occurring as an argument and in the return statement of a method. ",
+        "bbox": [
+            174,
+            667,
+            825,
+            738
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In NLP, it is common to bias Transformers towards sequential inputs by adding positional encodings to the token embeddings. These positional encodings are obtained by applying an encoding function $\\phi : \\mathbb { R } \\to \\mathbb { R } ^ { d }$ to each token’s position $p _ { i }$ . These positional encodings make the information about the sequence of tokens available to the model. Eq. (2) becomes: ",
+        "bbox": [
+            173,
+            744,
+            825,
+            801
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/b96beefee59c632a287223572ec7702368e163a81b493e1a921e5c4d74a409f9.jpg",
+        "text": "$$\nA _ { i j } = ( E _ { i } + \\phi ( p _ { i } ) ) ^ { T } W _ { q } ^ { T } W _ { k } ( E _ { j } + \\phi ( p _ { j } ) ) , ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            344,
+            804,
+            650,
+            825
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "which factorizes into ",
+        "bbox": [
+            173,
+            828,
+            313,
+            842
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/df07c855af71840c08fb5fcac8d0a6450e30cf45761ee10da8da265d06d28ade.jpg",
+        "text": "$$\nA _ { i j } = \\underbrace { { E } _ { i } ^ { T } W _ { q } ^ { T } W _ { k } } _ { ( \\mathrm { u } ) { A } _ { i j } ^ { \\mathrm { c e } } } { + \\underbrace { { E } _ { i } ^ { T } W _ { q } ^ { T } W _ { k } { \\phi } ( p _ { j } ) } _ { ( \\mathrm { b } ) { A } _ { i j } ^ { \\mathrm { c p } } } } + \\underbrace { { \\phi } ( p _ { i } ) ^ { T } W _ { q } ^ { T } W _ { k } { E } _ { j } } _ { ( \\mathrm { c } ) { A } _ { i j } ^ { \\mathrm { c e } } } { + \\underbrace { { { \\phi } ( p _ { i } ) } ^ { T } W _ { q } ^ { T } W _ { k } { \\phi } ( p _ { j } ) } _ { ( \\mathrm { d } ) { A } _ { i j } ^ { \\mathrm { p } } } } .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            192,
+            844,
+            787,
+            888
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We can interpret the terms (a)-(d) as follows. (a) ${ \\cal { A } } _ { i j } ^ { \\mathrm { c c } }$ is the contribution from the ‘match’ between the content embeddings of tokens $i$ and $j$ ; (b) $A _ { i j } ^ { \\mathrm { c p } }$ steers the attention towards certain positions based ",
+        "bbox": [
+            176,
+            892,
+            825,
+            926
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "on the content of token $i$ ; (c) $A _ { i j } ^ { \\mathrm { p c } }$ biases towards content embeddings based on the position of token $i$ ; (d) $A _ { i j } ^ { \\mathrm { p p } }$ controls which positions should attend to which other positions. ",
+        "bbox": [
+            169,
+            102,
+            823,
+            135
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In our model, we adopt the formulation of Dai et al. (2019); Yang et al. (2019). They modify Eq. (4) by replacing the absolute position encodings $\\phi ( p _ { i } )$ with relative position encodings $\\phi ( r _ { i \\to j } )$ : ",
+        "bbox": [
+            169,
+            141,
+            825,
+            170
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/4abc95bdea1392a92734f005afce75f982c5226661a1db2266b0c52e16c233d4.jpg",
+        "text": "$$\n\\begin{array} { r } { A _ { i j } ^ { \\mathrm { r e l } } = \\ E _ { i } ^ { T } W _ { q } ^ { T } W _ { k } E _ { j } + E _ { i } ^ { T } W _ { q } ^ { T } W _ { r } \\phi ( r _ { i  j } ) + u ^ { T } W _ { k } E _ { j } + v ^ { T } W _ { r } \\phi ( r _ { i  j } ) , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            236,
+            175,
+            759,
+            195
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $r _ { i \\to j }$ is the relative distance from token $i$ to token $j$ in the sequence, $\\boldsymbol { u } , \\boldsymbol { v } \\in \\mathbb { R } ^ { d _ { k } }$ are learnable bias vectors, and $W _ { r }$ is a key projection matrix for the relative distances. Besides fixing issues with absolute position encodings such as ambiguity when processing two sentences at a time, Eq. (5) enables native application of the powerful self-attention operation on domains such as graphs, where absolute coordinates are not available. We adopt the (non-trainable) sinusoidal encoding function proposed by (Vaswani et al., 2017) for all relations; see Appendix A.1 for details on the distance encoding function. ",
+        "bbox": [
+            173,
+            202,
+            825,
+            300
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.1 INTEGRATING SOURCE CODE AND AST REPRESENTATIONS OF PROGRAMS. ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            315,
+            736,
+            330
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To enable the model to integrate information both the Context and Structure of programs, we modify Eq. (5) to be able to incorporate multiple different relations. To this end, we use one key projection matrix W (s)r per relation $s$ , and sum their contributions in the raw attention score. This enables the CODE TRANSFORMER to combine information from multiple relations between tokens in the attention computation. Besides the token distance in the Context, we include pairwise relations based on the AST as described in the following. See Fig. 2 for a visualization of the Structure distances we use. ",
+        "bbox": [
+            173,
+            342,
+            825,
+            443
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Shortest path length. We include the number of hops required to reach node $j$ starting from node $i$ and vice versa. Here, we treat the AST as an undirected graph, since otherwise most distances would be undefined: e.g., all other nodes in the AST would be unreachable from the leaves. ",
+        "bbox": [
+            173,
+            454,
+            436,
+            564
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Similar to the distance of two tokens on the source code sequence, the shortestpath length is a global distance. This makes the whole graph structure acces",
+        "bbox": [
+            174,
+            571,
+            436,
+            627
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/971f2174ff96f3b5b7aea4b5cb4f59f9af4bf791dc6a632edbb218691a5d22cf.jpg",
+        "image_caption": [
+            "Figure 2: Structure distances used by our model. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            454,
+            469,
+            820,
+            592
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "sible to the model at each layer. In contrast, Hellendoorn et al. (2020) add bias terms to the attention computation only for edges (i.e. shortest-path distance of 1), which is a local operation that only exchanges information between immediate neighbors (similar to message passing in GNNs). The equivalent localized operation on the source code sequence would be to treat the sequence as a chain graph and only compute attention terms for neighboring tokens, which in turn highlights the benefit of non-local attention operations. ",
+        "bbox": [
+            174,
+            627,
+            825,
+            710
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Ancestor distance. Since we treat the ASTs as undirected for the computation of the shortest-path length, we lose the direction information of the edges. To avoid this, we also include the distance on the ordered set of ancestors and descendants of a node in the AST (red arrow in Fig. 2). Again, we include number of (vertical) hops to avoid locality in the attention computation. For example, a node $r _ { i \\to j } = 2$ for “grand-children” $j$ of $i$ , and $r _ { j  i } = - 2$ in the other direction. ",
+        "bbox": [
+            173,
+            720,
+            825,
+            791
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Sibling distance. The neighbor sets in graphs are typically considered to be unordered, but in an AST, the order of children encodes their order of occurrence in the source code. To avoid information loss when encoding the AST, we further include the distance on the ordered set of siblings $\\{ v _ { i } \\}$ of a node, where we again avoid locality by encoding the number of hops, i.e. $r _ { v _ { 1 }  v _ { 3 } } ~ = ~ 2$ and rv3→v1 = −2. ",
+        "bbox": [
+            173,
+            801,
+            825,
+            871
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Personalized PageRank (Page et al., 1999) (PPR). PPR is a well-studied proximity measure which has been shown to be very effective in learning with graphs (Klicpera et al., 2019a;b; Bojchevski et al., 2020). PPR captures the local graph structure around a pair of nodes $( i , j )$ . E.g., if $i$ has many neighbors, its PPR score for $j$ will be low even when they are only few hops apart, which complements the purely hop-based distances described above. ",
+        "bbox": [
+            174,
+            881,
+            823,
+            924
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/2ae4d77322414ffc49b55c0b5e39c6d3b3d0f5b89a9cfca8c5f81d4390780d66.jpg",
+        "image_caption": [
+            "Figure 3: Left: Sequence (Context) and AST (Structure) representation of an input code snippet. Center: The CODE TRANSFORMER jointly leverages the sequence of tokens and the Abstract Syntax Tree to learn expressive representations of source code. In addition to the input token and node embeddings the model uses different distances between the tokens, e.g., shortest paths on the AST or personalized PageRank, to reason about their relative positions. The output embeddings can be used for downstream tasks such as code summarization (right). "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            187,
+            101,
+            813,
+            314
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            443,
+            823,
+            472
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Input embeddings to the model. To combine the Context and Structure information, we assign each token in the sequence to an AST node by selecting the AST node whose range in the source code is the shortest one containing the token. We concatenate the (sub-) token embeddings with the embedding of the token’s assigned AST node type as well as the token type returned by the tokenizer. That is, among all the internal nodes, we use as input only those corresponding to a token in the sequence; however, the remaining internal nodes can used by the model since their presence affects the distances between the remaining AST nodes. See Appendices A.3 and A.4 for details. ",
+        "bbox": [
+            174,
+            483,
+            825,
+            580
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.2 EFFICIENT RELATIVE ATTENTION COMPUTATION. ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            602,
+            552,
+            616
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Na¨ıvely, we need to compute and materialize a tensor of dimension $N \\times N \\times d$ to hold all pairwise relative position encodings $\\phi ( r _ { i \\to j } )$ in Eq. (5) , where $N$ is the input length. This is prohibitive for fast GPU training. While for discrete distance values (e.g., sequence distance or shortest-path length on a graph) we only need to compute unique distance values occurring in the input, this does not generalize to continuous distances such as PPR. Therefore, we propose a constant-time approximation of the relational attention computation by grouping the values into $k \\ll N ^ { 2 }$ bins. Since closer samples are typically more relevant for a query sample, we increase the bin widths exponentially with growing distance values. Throughout our experiments we have found the CODE TRANSFORMER to be relatively insensitive to the number of bins; we thus set $k = 3 2$ in our experiments. ",
+        "bbox": [
+            174,
+            628,
+            825,
+            753
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4 EXPERIMENTAL SETUP ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            779,
+            395,
+            794
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Code summarization is one of the most popular tasks in machine learning for code. Given the body of a function, the task is to predict the function’s name. As observed by Alon et al. (2019b) and Allamanis et al. (2016), this is a useful benchmark as method names in open-source projects tend to be precise and descriptive, and functions typically form complete logical units. See Fig. 3 (right) for a visual overview of the task. We use two complementary representations of programs: the source code as a sequence of tokens (Context) and the AST (Structure). As shown in Fig. 3 (left), tokens that are far away on the sequence may be very close on the AST and vice versa. In this task we make use of the CODE TRANSFORMER’s ability jointly leverage both Structure and Context and show that it improves learning. Further, we show the benefit of using only language-agnostic features in our model by training the first multilingual model for code summarization. ",
+        "bbox": [
+            174,
+            811,
+            825,
+            924
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            171,
+            103,
+            823,
+            132
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Datasets. To highlight the benefit of only relying on language-agnostic representations such as source code and abstract syntax trees, we evaluate on challenging datasets in four programming languages introduced in the CodeSearchNet (CSN) Challenge (Husain et al., 2019): Python, Javascript, Go, and Ruby. Similar to Java-small, the datasets from CodeSearchNet have been carefully deduplicated by the creators to avoid data leakage from the training set, e.g., via copy-and-paste code. ",
+        "bbox": [
+            174,
+            142,
+            823,
+            212
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We further evaluate on Java-small (Allamanis et al., 2016), a popular and challenging code summarization dataset. It contains 11 open-source Java projects. We use the split as in Alon et al. (2019a), where 9 of these projects are used for training, one for validation, and one for test. The dataset contains roughly 700K samples (function definitions). Moreover, we also experiment with pre-training our model on Java-medium and Java-large (Alon et al., 2019a) before fine-tuning on Java-small, making sure to avoid leakage by removing the test and validation projects of Java-small from the pre-training dataset. See Table 1 for a summary of the datasets we use in this work. ",
+        "bbox": [
+            174,
+            219,
+            529,
+            377
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/b4225af91868e1a8a78db0e52181e077f82a2809a40ec936d5ee0af636f96fb7.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 1: Dataset statistics. "
+        ],
+        "table_body": "<table><tr><td></td><td colspan=\"3\">Samples per partition</td></tr><tr><td>Dataset</td><td>Train</td><td>Val.</td><td>Test</td></tr><tr><td>CSN-Python</td><td>412,178</td><td>23,107</td><td>22,176</td></tr><tr><td>CSN-Javascript</td><td>123,889</td><td>8,253</td><td>6,483</td></tr><tr><td>CSN-Ruby</td><td>48,791</td><td>2,209</td><td>2,279</td></tr><tr><td>CSN-Go</td><td>317,832</td><td>14,242</td><td>14,291</td></tr><tr><td>Java-small</td><td>691,974</td><td>23,844</td><td>57,088</td></tr></table>",
+        "bbox": [
+            545,
+            236,
+            825,
+            339
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            372,
+            717,
+            386
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Preprocessing. Each token of the source code is split into subtokens respective to code naming conventions, i.e., get TrainingData is converted to [get, training, data]. Following Alon et al. (2019a) we use at most six subtokens for the method names, truncating longer function names if necessary. In addition to the tokenized source code we produce an AST for each method using the open-source AST parser Semantic3. We limit the vocabulary to subtokens with at least 100 occurrences in the training set, and only consider snippets with 512 or fewer tokens (after removing punctuation). We refer the reader to the appendix for further details on the data preprocessing. ",
+        "bbox": [
+            174,
+            396,
+            825,
+            494
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Pointer network. We add a pointer network (Vinyals et al., 2015) (as described in Fernandes et al. (2019)) to the decoders of all Transformer-based models. This enables them to enhance their predictions by pointing at positions in the input sequence. For instance, when predicting the method name get url, the model can point directly to occurrences of the variable url. This often improves results for less frequent tokens, and even enables the model to predict tokens which are not in the vocabulary by pointing at their positions in the input. ",
+        "bbox": [
+            174,
+            503,
+            823,
+            588
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Baselines. We compare with code2seq (Alon et al., 2019a), the Graph Relational Embedding Attention Transformer (GREAT) (Hellendoorn et al., 2020), and the BiLSTM+GNN LSTM+Pointer model presented in Fernandes et al. (2019). Code2seq is a non-Transformer model and state of the art for code summarization using only AST information. GREAT is a recent Transformer model using the framework presented in (Shaw et al., 2018) to bias the attention via edges. In the original formulation, GREAT additionally uses hand-crafted, language-specific edges such as dataflow, ‘computed from’, or ‘next lexical use’ edges, which require specialized preprocessing and static analysis tools. While this approach of leveraging language-specific features can certainly improve results on specific tasks and programming languages, our goal is to have a flexible model that can be used on any programming language. Since the specialized preprocessing used by GREAT is proprietary and not public, we produce the results for GREAT using edges from the AST instead, i.e. it has access to the same information as our proposed model. Note that the preprocessing of Fernandes et al. (2019) is language specific, which is why we only compare with their results on Java-small. ",
+        "bbox": [
+            174,
+            598,
+            825,
+            779
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5 RESULTS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            799,
+            281,
+            815
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.1 MONOLINGUAL CODE SUMMARIZATION ",
+        "text_level": 1,
+        "bbox": [
+            178,
+            832,
+            490,
+            844
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "CSN dataset. First, we study the performance (measured by F1 score) of our model and the baselines on the traditional setting, where training and evaluation are performed on a single programming language. The results are shown in the upper part of Table 2. The CODE TRANSFORMER (without multi-language training) substantially outperforms all other models on all but one language, highlighting the effectiveness of jointly learning from Structure and Context. The only exception is Ruby, where it performs on par with its Context-only variant. We attribute this to the fact that there are relatively few samples in the Ruby dataset, and that Ruby is an dynamically typed language, which could make the Structure less powerful for learning. Interestingly, the Context-only CODE TRANSFORMER outperforms GREAT on all languages. We attribute this to the fact that GREAT uses the Structure of the programs only in a localized way (see Sec. 3.1). Another noteworthy finding is that code2seq performs comparably to the Transformer-based baselines on Go. We hypothesize that ASTs are more informative on Go since it is a compiled and strongly typed language. ",
+        "bbox": [
+            176,
+            857,
+            823,
+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/6ea8249b1a6b65be5a059f68d87e3dba30b23b79c16802b7d266349476c02871.jpg",
+        "table_caption": [
+            "Table 2: Code summarization results on the CSN dataset (micro F1). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Model</td><td colspan=\"3\">Python</td><td colspan=\"3\">Javascript</td><td colspan=\"3\">Ruby</td><td colspan=\"3\">Go</td></tr><tr><td>Prec.</td><td>Rec.</td><td>F1</td><td>Prec.</td><td>Rec.</td><td>F1</td><td>Prec.</td><td>Rec.</td><td>F1</td><td>Prec.</td><td>Rec.</td><td>F1</td></tr><tr><td>code2seq</td><td>35.79</td><td>24.85</td><td>29.34</td><td>30.18</td><td>19.88</td><td>23.97</td><td>23.23</td><td>10.31</td><td>14.28</td><td>52.30</td><td>43.43</td><td>47.45</td></tr><tr><td>GREAT</td><td>35.07</td><td>31.59</td><td>33.24</td><td>31.20</td><td>26.84</td><td>28.86</td><td>24.64</td><td>22.23</td><td>23.38</td><td>50.01</td><td>46.51</td><td>48.20</td></tr><tr><td>Ours w/o structure</td><td>37.38</td><td>31.98</td><td>34.47</td><td>33.17</td><td>26.70</td><td>29.59</td><td>29.85</td><td>25.87</td><td>27.72</td><td>51.78</td><td>47.57</td><td>49.59</td></tr><tr><td>Ours w/o pointer net</td><td>37.74</td><td>31.85</td><td>34.55</td><td>33.12</td><td>28.70</td><td>30.75</td><td>23.32</td><td>25.21</td><td>24.23</td><td>54.31</td><td>50.12</td><td>52.13</td></tr><tr><td>Ours</td><td>36.40</td><td>33.66</td><td>34.97</td><td>35.06</td><td>29.61</td><td>32.11</td><td>31.42</td><td>24.46</td><td>27.50</td><td>55.10</td><td>48.05</td><td>51.34</td></tr><tr><td>code2seq (Multilanguage)</td><td>34.49</td><td>25.49</td><td>29.32</td><td>31.62</td><td>22.16</td><td>26.06</td><td>23.97</td><td>17.06</td><td>19.93</td><td>52.70</td><td>44.36</td><td>48.17</td></tr><tr><td>GREAT (Multilanguage)</td><td>36.75</td><td>31.54</td><td>33.94</td><td>33.58</td><td>27.78</td><td>30.41</td><td>30.05</td><td>24.33</td><td>26.89</td><td>52.65</td><td>48.30</td><td>50.38</td></tr><tr><td>Ours w/o structure (Mult.)</td><td>38.48</td><td>30.14</td><td>33.80</td><td>35.38</td><td>27.41</td><td>30.89</td><td>32.61</td><td>26.76</td><td>29.40</td><td>55.03</td><td>47.34</td><td>50.90</td></tr><tr><td>Ours w/o pointer (Mult.)</td><td>38.91</td><td>33.12</td><td>35.78</td><td>37.21</td><td>29.75</td><td>33.07</td><td>34.52</td><td>27.31</td><td>30.50</td><td>56.07</td><td>50.76</td><td>53.28</td></tr><tr><td>Ours (Multilanguage)</td><td>38.89</td><td>33.82</td><td>36.18</td><td>36.95</td><td>29.98</td><td>33.10</td><td>33.93</td><td>28.94</td><td>31.24</td><td>56.00</td><td>50.44</td><td>53.07</td></tr><tr><td>Ours (Mult.+ Finetune)</td><td>39.85</td><td>32.79</td><td>35.98</td><td>37.00</td><td>29.79</td><td>33.00</td><td>35.85</td><td>27.75</td><td>31.28</td><td>55.63</td><td>51.12</td><td>53.28</td></tr><tr><td>Ours (Mult. + LM Pretrain)</td><td>39.67</td><td>35.29</td><td>37.35</td><td>37.06</td><td>31.94</td><td>34.31</td><td>35.19</td><td>29.36</td><td>32.01</td><td>57.73</td><td>51.89</td><td>54.65</td></tr></table>",
+        "bbox": [
+            176,
+            79,
+            821,
+            242
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            173,
+            294,
+            825,
+            420
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Java-small results. In Table 3 we present code summarization results on the Java-small dataset. Among all models equipped with a pointer network, the CODE TRANSFORMER (without pretraining) obtains state-of-the-art on code summarization, outperforming all baselines, including the previous state-of-the-art on Java-small proposed by Fernandes et al. (2019). Further, pre-training on Java-medium and Java-large on the permutation language modeling objective (Yang et al., 2019) substantially improves precision, recall, and F1 score after fine-tuning on Java-small. To avoid leakage, we exclude the projects used in the validation and test splits of Java-small from pre-training. ",
+        "bbox": [
+            174,
+            435,
+            825,
+            532
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Ablation study. We further perform ablations where we remove our model’s access to the Context or Structure, also presented in Table 3. ",
+        "bbox": [
+            174,
+            547,
+            823,
+            577
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "With pointer network. We find that both ablations lead to a substantial drop in performance, highlighting the benefit of learning jointly from Structure and Context. Interestingly, the model without access to the Structure performs slightly better than the variant without Context. Note that our model without Structure is related to the XLNet (Yang et al., 2019) model, where we add a pointer network to the decoder and concatenate the token types to their respective input tokens (see Appendix A.4). Without pointer network. We repeat the ablation on the variants without pointer network. Here, the variant without Context performs better than the variant without Structure, ",
+        "bbox": [
+            174,
+            584,
+            482,
+            790
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/93c3db634ac78ceb6a3e42a79f6c881109ae26412d90ebf329ef70021d85d788.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 3: Results on Java-small and ablation study. "
+        ],
+        "table_body": "<table><tr><td>Model</td><td>Prec.</td><td>Rec.</td><td>F1</td></tr><tr><td>Without pointer net code2seq Ours w/o structure Ours w/o context</td><td>51.23 50.70 51.81</td><td>37.31 45.49 46.04</td><td>43.18 47.96</td></tr><tr><td>Ours With pointer net</td><td>50.33</td><td>46.80</td><td>48.75 48.50</td></tr><tr><td>Fernandes et al. (2019)</td><td>=</td><td>1</td><td>51.4</td></tr><tr><td>GREAT Ours w/o structure</td><td>53.60</td><td>46.41</td><td>49.75</td></tr><tr><td>Ours w/o context</td><td>55.48</td><td>46.07</td><td>50.34</td></tr><tr><td></td><td>54.45</td><td>45.29</td><td>49.45</td></tr><tr><td>Ours</td><td>54.85</td><td>49.84</td><td>52.22</td></tr><tr><td>Ours + Pretrain</td><td>57.02</td><td>50.87</td><td>53.77</td></tr></table>",
+        "bbox": [
+            514,
+            583,
+            810,
+            761
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "indicating that the pointer network helps to compensate for the lack of access to Structure. The Structure-only variant (w/o pointer net) of our model even outperforms the full variant in this scenario. Inspection of the results revealed that the Structure-only variant has better performance on longer method names, which have an outsize influence on the micro-F1 score used in this work. ",
+        "bbox": [
+            174,
+            791,
+            825,
+            847
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Ablation of the AST-based distances. In Table 4 we compare the performance of our model when trained with each of the four different AST distances (sibling shortest paths, ancestor shortest paths, shortest paths, personalized PageRank; see Section 3.1). Here, the model is trained on Java-small in the Structure-only setting and without pointer network. For reference, we also show the results of training our model using all four AST distance functions (c.f. Table 3). We find that, while the personalized PageRank distance performs best on its own, each of the individual distances on their own performs substantially worse than their combination, highlighting the usefulness of combining the distances in our model as well as their complementary nature. ",
+        "bbox": [
+            174,
+            854,
+            823,
+            924
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            176,
+            103,
+            823,
+            146
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.2 MULTILINGUAL CODE SUMMARIZATION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            162,
+            490,
+            176
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Setup. A key contribution of our proposed architecture is that it only uses language-agnostic features, i.e. the source code and features that can be directly computed from the AST. We use this fact to study the first multilanguage code summarization model. We train our model jointly on Python, Javascript, Ruby, and Go. The shared sub-token vocabulary is the union of the individual vocabularies, enabling us to evaluate the multi-language model on the individual languages and compare with the single-language models. As proposed by Conneau & Lample (2019), we add a learned language embedding to each input embedding. ",
+        "bbox": [
+            174,
+            188,
+            552,
+            299
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/44d93ce3802abbb255784a0d5f66ef881ac7c557a4abf8c4d5752cc699deb37d.jpg",
+        "table_caption": [
+            "Table 4: AST distance ablation study. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>AST distance</td><td>F1 score</td></tr><tr><td>Sibling shortest paths</td><td>46.17</td></tr><tr><td>Ancestor shortest paths</td><td>47.89</td></tr><tr><td>Shortest paths</td><td>47.76</td></tr><tr><td>Personalized PageRank</td><td>48.47</td></tr><tr><td>All the above (c.f. Table 3)</td><td>48.75</td></tr></table>",
+        "bbox": [
+            578,
+            184,
+            810,
+            267
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            300,
+            825,
+            327
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Results. In the lower part of Table 2 we can see the results of training our CODE TRANSFORMER jointly on all four programming languages. Our multi-lingual variants substantially outperform the mono-lingual models on all languages. The strongest improvement is on Ruby, which is also the programming language with the smallest number of samples in the dataset. Fine-tuning on the individual languages after joint training on code summarization only has a marginal effect on performance, indicating that the multilingual objective is well-aligned with the individual languages. In the last row, we have a variant of our model where we pre-train on the multi-lingual masked language modeling task, followed by finetuning on code summarization on the individual languages. ",
+        "bbox": [
+            173,
+            342,
+            825,
+            454
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Further, we observe that similar to the results on Java-small, removing the pointer network generally leads to weaker performance. One notable exception is Go, where the variant without the pointer network performs better in terms of F1 score. Our investigation revealed that there seems to be some violation of the i.i.d. assumption in the split provided by the creators of the dataset. In Figure 7 we show that in the test partition of the Go dataset, the share of tokens from the labels also occurring in the methods’ bodies – exactly the scenario where the pointer network can improve predictions – is substantially lower compared to the train/validation partitions. ",
+        "bbox": [
+            174,
+            460,
+            825,
+            558
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Remarkably, the multi-language Context-only variant (i.e. without access to the Structure) performs substantially worse than the full multi-language variant. This highlights that Structure is crucial to exploit the commonalities of different programming languages. Also notably, the GREAT baseline’s results also improve substantially when trained in the multi-language setting, though it is still outperformed by our model. However, our results indicate that any representation learning model for code can benefit from multi-language training, especially when evaluating on low-resource languages. ",
+        "bbox": [
+            174,
+            565,
+            825,
+            648
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In Table 16 we present results using the sample-F1 score. At the time of submission, our monolingual model on Python outperforms the state of the art on the ogbg-code $2 ^ { 4 }$ (Hu et al., 2020) leaderboard by $112 \\%$ , and our multilanguage variant with LM pretraining outperforms it by $122 \\%$ . ",
+        "bbox": [
+            176,
+            655,
+            823,
+            698
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Qualitative analysis of multilingual representations. Learning the CODE TRANSFORMER on multiple programming languages jointly provides us with embeddings in a shared representation space. In Fig. 4 we show a t-SNE (Maaten & Hinton, 2008) visualization of the ca. 40,000 snippets from the validation sets of four programming languages from the CSN dataset. For the embedding of a snippet, we use the representation of the method name in the final layer of the encoder. Note that the true method names are masked, i.e., inaccessible to the model. Further, note that in contrast to the monolingual embeddings learned by Kanade et al. (2020), the embeddings we evaluate are learned on the task of code summarization (though a similar study could be performed by using our model that was trained on the traditional language modeling pretraining task on multiple languages). ",
+        "bbox": [
+            174,
+            713,
+            825,
+            838
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "While snippets from the same language tend to be grouped together, there are interesting intersections of the different programming languages. For example, we highlight all methods whose names start with the subtoken parse or main. We see that snippets starting with parse are predominantly in an intersection region of Python and Javascript. From these snippets, we display the cross-language pair with smallest Euclidean embedding distance in Fig. 5. Remarkably, both snippets are effectively the same method in Javascript and Python – it is worth reminding that the model has never seen any parallel data during training. On the other hand, snippets starting with main tend to lie at an intersectional region of Python, Javascript, and Go. In Table 6 in the appendix we show additional cross-lingual pairs with similar embeddings, including a failure case of a main function, where embedding distance is not representative of semantic similarity. We attribute this to the fact that we used the encoder output embedding of the masked method name – the representation used by the decoder to predict the method name – as a snippet’s representation. Thus, snippets with completely different semantics (as is to be expected for very generic method names starting with main) have similar representations because they are predictive of the method name. ",
+        "bbox": [
+            176,
+            844,
+            823,
+            901
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/e875f6f92fb5baf876c7eada99cff2f2f6a1ae4c2907de273c6e3de07dd8a6a8.jpg",
+        "image_caption": [
+            "Figure 4: t-SNE visualization of the CODE TRANSFORMER’s learned multilingual representations. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            223,
+            80,
+            774,
+            304
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/b4f73ecaf41d7a935e9b22345a3d4464c58d6b6b17f19a5180425db1c0483a08.jpg",
+        "image_caption": [
+            "Figure 5: Example snippet starting with parse (left) and its best embedding match from other languages (right). Both methods parse an input string to convert it into a boolean value. Note that even though they are semantically very similar, their method names are not; nonetheless, their representations in the CODE TRANSFORMER encoder reflect their semantic similarity. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            204,
+            340,
+            776,
+            440
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            534,
+            825,
+            672
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "As another qualitative insight into the representations learned by the CODE TRANSFORMER we have found that the language embeddings of languages with similar roots in language design are close; see Table 5 in the appendix for the pairwise similarity matrix of the learned language embeddings. ",
+        "bbox": [
+            176,
+            679,
+            823,
+            722
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "6 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            742,
+            318,
+            758
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We present the CODE TRANSFORMER, which learns jointly from Structure and Context of programs while only relying on language-agnostic features. Our model obtains state-of-the-art performance on code summarization on five different programming languages. Besides these results for training on individual languages, the language-agnostic nature of our model allows us to train it jointly on multiple programming languages. The resulting multilingual model substantially outperforms its mono-lingual variant on all programming languages, setting the state of the art on each language. We observe the largest improvement from multilingual training on the language with fewest resources, indicating that multilingual training can improve learning for less widely used programming languages. Remarkably, multilingual training only from Context does not lead to the same improvements, highlighting the benefits of combining Structure and Context. ",
+        "bbox": [
+            174,
+            773,
+            825,
+            912
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "REFERENCES ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            103,
+            285,
+            117
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Mithun Acharya, Tao Xie, Jian Pei, and Jun Xu. Mining api patterns as partial orders from source code: From usage scenarios to specifications. In Proceedings of the the 6th Joint Meeting of the European Software Engineering Conference and the ACM SIGSOFT Symposium on The Foundations of Software Engineering, ESEC-FSE ’07, pp. 25–34, New York, NY, USA, 2007. Association for Computing Machinery. ISBN 9781595938114. doi: 10.1145/1287624.1287630. URL https://doi.org/10.1145/1287624.1287630. ",
+        "bbox": [
+            173,
+            126,
+            825,
+            209
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Miltiadis Allamanis, Earl T. Barr, Christian Bird, and Charles Sutton. Learning natural coding conventions. In Proceedings of the 22nd ACM SIGSOFT International Symposium on Foundations of Software Engineering, FSE 2014, pp. 281–293, New York, NY, USA, 2014. Association for Computing Machinery. ISBN 9781450330565. doi: 10.1145/2635868.2635883. URL https://doi.org/10.1145/2635868.2635883. ",
+        "bbox": [
+            173,
+            218,
+            825,
+            289
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Miltiadis Allamanis, Earl T. Barr, Christian Bird, and Charles Sutton. Suggesting accurate method and class names. In Proceedings of the 2015 10th Joint Meeting on Foundations of Software Engineering, ESEC/FSE 2015, pp. 38–49, New York, NY, USA, 2015. Association for Computing Machinery. ISBN 9781450336758. doi: 10.1145/2786805.2786849. URL https://doi. org/10.1145/2786805.2786849. ",
+        "bbox": [
+            173,
+            297,
+            825,
+            367
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Miltiadis Allamanis, Hao Peng, and Charles Sutton. A convolutional attention network for extreme summarization of source code. In International conference on machine learning, pp. 2091–2100, 2016. ",
+        "bbox": [
+            173,
+            377,
+            821,
+            419
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Miltiadis Allamanis, Marc Brockschmidt, and Mahmoud Khademi. Learning to represent programs with graphs. In International Conference on Learning Representations, 2018. URL https: //openreview.net/forum?id $=$ BJOFETxR-. ",
+        "bbox": [
+            173,
+            428,
+            823,
+            472
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Uri Alon, Meital Zilberstein, Omer Levy, and Eran Yahav. A general path-based representation for predicting program properties. In Proceedings of the 39th ACM SIGPLAN Conference on Programming Language Design and Implementation, PLDI 2018, pp. 404–419, New York, NY, USA, 2018. Association for Computing Machinery. ISBN 9781450356985. doi: 10.1145/3192366.3192412. URL https://doi.org/10.1145/3192366.3192412. ",
+        "bbox": [
+            174,
+            479,
+            825,
+            550
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Uri Alon, Shaked Brody, Omer Levy, and Eran Yahav. code2seq: Generating sequences from structured representations of code. In International Conference on Learning Representations, 2019a. URL https://openreview.net/forum?id $=$ H1gKYo09tX. ",
+        "bbox": [
+            174,
+            559,
+            825,
+            602
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Uri Alon, Meital Zilberstein, Omer Levy, and Eran Yahav. code2vec: Learning distributed representations of code. Proceedings of the ACM on Programming Languages, 3(POPL):1–29, 2019b. ",
+        "bbox": [
+            173,
+            609,
+            823,
+            640
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Peter W Battaglia, Jessica B Hamrick, Victor Bapst, Alvaro Sanchez-Gonzalez, Vinicius Zambaldi, Mateusz Malinowski, Andrea Tacchetti, David Raposo, Adam Santoro, Ryan Faulkner, et al. Relational inductive biases, deep learning, and graph networks. arXiv preprint arXiv:1806.01261, 2018. ",
+        "bbox": [
+            173,
+            647,
+            825,
+            704
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Avishkar Bhoopchand, Tim Rocktaschel, Earl Barr, and Sebastian Riedel. Learning python code ¨ suggestion with a sparse pointer network. arXiv preprint arXiv:1611.08307, 2016. ",
+        "bbox": [
+            173,
+            713,
+            825,
+            742
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Benjamin Bichsel, Veselin Raychev, Petar Tsankov, and Martin Vechev. Statistical deobfuscation of android applications. In Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security, CCS ’16, pp. 343–355, New York, NY, USA, 2016. Association for Computing Machinery. ISBN 9781450341394. doi: 10.1145/2976749.2978422. URL https: //doi.org/10.1145/2976749.2978422. ",
+        "bbox": [
+            173,
+            751,
+            825,
+            820
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Pavol Bielik, Veselin Raychev, and Martin Vechev. Phog: probabilistic model for code. In International Conference on Machine Learning, pp. 2933–2942, 2016. ",
+        "bbox": [
+            169,
+            829,
+            823,
+            859
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Aleksandar Bojchevski, Johannes Klicpera, Bryan Perozzi, Amol Kapoor, Martin Blais, Benedek Rozemberczki, Michal Lukasik, and Stephan G ´ unnemann. Scaling graph neural networks with ¨ approximate pagerank. In Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery amp; Data Mining, KDD ’20, pp. 2464–2473, New York, NY, USA, 2020. ",
+        "bbox": [
+            176,
+            867,
+            825,
+            924
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Association for Computing Machinery. ISBN 9781450379984. doi: 10.1145/3394486.3403296.   \nURL https://doi.org/10.1145/3394486.3403296. ",
+        "bbox": [
+            183,
+            103,
+            821,
+            132
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Dylan Bourgeois. Learning representations of source code from structure and context. 2019. URL http://infoscience.epfl.ch/record/277163. ",
+        "bbox": [
+            173,
+            142,
+            823,
+            170
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Alexis Conneau and Guillaume Lample. Cross-lingual language model pretraining. In H. Wallach, H. Larochelle, A. Beygelzimer, F. d'Alche-Buc, E. Fox, and ´ R. Garnett (eds.), Advances in Neural Information Processing Systems 32, pp. 7059– 7069. Curran Associates, Inc., 2019. URL http://papers.nips.cc/paper/ 8928-cross-lingual-language-model-pretraining.pdf. ",
+        "bbox": [
+            173,
+            179,
+            825,
+            250
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Hanjun Dai, Bo Dai, and Le Song. Discriminative embeddings of latent variable models for structured data. In International conference on machine learning, pp. 2702–2711, 2016. ",
+        "bbox": [
+            173,
+            258,
+            821,
+            289
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Zihang Dai, Zhilin Yang, Yiming Yang, Jaime Carbonell, Quoc V Le, and Ruslan Salakhutdinov. Transformer-xl: Attentive language models beyond a fixed-length context. arXiv preprint arXiv:1901.02860, 2019. ",
+        "bbox": [
+            173,
+            296,
+            823,
+            339
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Hoa Khanh Dam, Truyen Tran, and Trang Pham. A deep language model for software code. In FSE 2016: Proceedings of the Foundations Software Engineering International Symposium [The Conference], 2016. ",
+        "bbox": [
+            173,
+            348,
+            825,
+            391
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Michael Defferrard, Xavier Bresson, and Pierre Vandergheynst. Convolutional neural networks on ¨ graphs with fast localized spectral filtering. In Advances in neural information processing systems, pp. 3844–3852, 2016. ",
+        "bbox": [
+            171,
+            400,
+            823,
+            443
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "David K Duvenaud, Dougal Maclaurin, Jorge Iparraguirre, Rafael Bombarell, Timothy Hirzel, Alan´ Aspuru-Guzik, and Ryan P Adams. Convolutional networks on graphs for learning molecular fingerprints. In Advances in neural information processing systems, pp. 2224–2232, 2015. ",
+        "bbox": [
+            176,
+            452,
+            821,
+            496
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Patrick Fernandes, Miltiadis Allamanis, and Marc Brockschmidt. Structured neural summarization. In International Conference on Learning Representations, 2019. URL https: //openreview.net/forum?id $=$ H1ersoRqtm. ",
+        "bbox": [
+            176,
+            503,
+            820,
+            547
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Marco Gori, Gabriele Monfardini, and Franco Scarselli. A new model for learning in graph domains. In Proceedings. 2005 IEEE International Joint Conference on Neural Networks, 2005., volume 2, pp. 729–734. IEEE, 2005. ",
+        "bbox": [
+            174,
+            556,
+            823,
+            598
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "William L. Hamilton, Rex Ying, and Jure Leskovec. Inductive representation learning on large graphs. In NIPS, 2017. ",
+        "bbox": [
+            173,
+            608,
+            821,
+            637
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Vincent J. Hellendoorn, Charles Sutton, Rishabh Singh, Petros Maniatis, and David Bieber. Global relational models of source code. In International Conference on Learning Representations, 2020. URL https://openreview.net/forum?id $=$ B1lnbRNtwr. ",
+        "bbox": [
+            174,
+            645,
+            825,
+            689
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Abram Hindle, Earl T. Barr, Zhendong Su, Mark Gabel, and Premkumar Devanbu. On the naturalness of software. In Proceedings of the 34th International Conference on Software Engineering, ICSE ’12, pp. 837–847. IEEE Press, 2012. ISBN 9781467310673. ",
+        "bbox": [
+            174,
+            698,
+            825,
+            741
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Sepp Hochreiter and Jurgen Schmidhuber. Long short-term memory. ¨ Neural computation, 9(8): 1735–1780, 1997. ",
+        "bbox": [
+            171,
+            750,
+            821,
+            779
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Weihua Hu, Matthias Fey, Marinka Zitnik, Yuxiao Dong, Hongyu Ren, Bowen Liu, Michele Catasta, and Jure Leskovec. Open graph benchmark: Datasets for machine learning on graphs. In H. Larochelle, M. Ranzato, R. Hadsell, M. F. Balcan, and H. Lin (eds.), Advances in Neural Information Processing Systems, volume 33, pp. 22118–22133. Curran Associates, Inc., 2020. URL https://proceedings.neurips.cc/paper/2020/file/ fb60d411a5c5b72b2e7d3527cfc84fd0-Paper.pdf. ",
+        "bbox": [
+            174,
+            787,
+            825,
+            872
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Hamel Husain, Ho-Hsiang Wu, Tiferet Gazit, Miltiadis Allamanis, and Marc Brockschmidt. Codesearchnet challenge: Evaluating the state of semantic code search. arXiv preprint arXiv:1909.09436, 2019. ",
+        "bbox": [
+            174,
+            882,
+            823,
+            924
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Aditya Kanade, Petros Maniatis, Gogul Balakrishnan, and Kensen Shi. Learning and evaluating contextual embedding of source code. In Proceedings of the 37th International Conference on Machine Learning, 2020. ",
+        "bbox": [
+            174,
+            103,
+            821,
+            146
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Thomas N. Kipf and Max Welling. Semi-supervised classification with graph convolutional networks. In International Conference on Learning Representations (ICLR), 2017. ",
+        "bbox": [
+            169,
+            155,
+            821,
+            184
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Johannes Klicpera, Aleksandar Bojchevski, and Stephan Gunnemann. Predict then propagate: ¨ Graph neural networks meet personalized pagerank. In International Conference on Learning Representations (ICLR), 2019a. ",
+        "bbox": [
+            174,
+            191,
+            823,
+            234
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Johannes Klicpera, Stefan Weißenberger, and Stephan Gunnemann. Diffusion improves graph learn-¨ ing. In Conference on Neural Information Processing Systems (NeurIPS), 2019b. ",
+        "bbox": [
+            169,
+            242,
+            823,
+            272
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Johannes Klicpera, Janek Groß, and Stephan Gunnemann. Directional message passing for molec- ¨ ular graphs. In International Conference on Learning Representations (ICLR), 2020. ",
+        "bbox": [
+            173,
+            280,
+            823,
+            309
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Jian Li, Yue Wang, Michael R Lyu, and Irwin King. Code completion with neural attention and pointer networks. arXiv preprint arXiv:1711.09573, 2017. ",
+        "bbox": [
+            171,
+            318,
+            823,
+            347
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Yujia Li, Daniel Tarlow, Marc Brockschmidt, and Richard Zemel. Gated graph sequence neural networks. arXiv preprint arXiv:1511.05493, 2015. ",
+        "bbox": [
+            171,
+            354,
+            823,
+            385
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Laurens van der Maaten and Geoffrey Hinton. Visualizing data using t-sne. Journal of machine learning research, 9(Nov):2579–2605, 2008. ",
+        "bbox": [
+            171,
+            392,
+            823,
+            421
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Chris Maddison and Daniel Tarlow. Structured generative models of natural source code. In International Conference on Machine Learning, pp. 649–657, 2014. ",
+        "bbox": [
+            171,
+            430,
+            821,
+            459
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Lili Mou, Ge Li, Lu Zhang, Tao Wang, and Zhi Jin. Convolutional neural networks over tree structures for programming language processing. In Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence, AAAI’16, pp. 1287–1293. AAAI Press, 2016. ",
+        "bbox": [
+            174,
+            467,
+            823,
+            511
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Trong Duc Nguyen, Anh Tuan Nguyen, Hung Dang Phan, and Tien N. Nguyen. Exploring api embedding for api usages and applications. In Proceedings of the 39th International Conference on Software Engineering, ICSE ’17, pp. 438–449. IEEE Press, 2017. ISBN 9781538638682. doi: 10.1109/ICSE.2017.47. URL https://doi.org/10.1109/ICSE.2017.47. ",
+        "bbox": [
+            173,
+            518,
+            825,
+            575
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Lawrence Page, Sergey Brin, Rajeev Motwani, and Terry Winograd. The pagerank citation ranking: Bringing order to the web. Technical report, Stanford InfoLab, 1999. ",
+        "bbox": [
+            174,
+            583,
+            823,
+            613
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Alec Radford, Jeffrey Wu, Rewon Child, David Luan, Dario Amodei, and Ilya Sutskever. Language models are unsupervised multitask learners. OpenAI Blog, 1(8):9, 2019. ",
+        "bbox": [
+            173,
+            621,
+            823,
+            650
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Veselin Raychev, Martin Vechev, and Eran Yahav. Code completion with statistical language models. In Proceedings of the 35th ACM SIGPLAN Conference on Programming Language Design and Implementation, PLDI ’14, pp. 419–428, New York, NY, USA, 2014. Association for Computing Machinery. ISBN 9781450327848. doi: 10.1145/2594291.2594321. URL https://doi. org/10.1145/2594291.2594321. ",
+        "bbox": [
+            173,
+            659,
+            825,
+            729
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Franco Scarselli, Marco Gori, Ah Chung Tsoi, Markus Hagenbuchner, and Gabriele Monfardini. The graph neural network model. IEEE Transactions on Neural Networks, 20(1):61–80, 2008. ",
+        "bbox": [
+            173,
+            737,
+            821,
+            766
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Michael Schlichtkrull, Thomas N. Kipf, Peter Bloem, Rianne van den Berg, Ivan Titov, and Max Welling. Modeling relational data with graph convolutional networks. In Aldo Gangemi, Roberto Navigli, Maria-Esther Vidal, Pascal Hitzler, Raphael Troncy, Laura Hollink, Anna Tordai, and ¨ Mehwish Alam (eds.), The Semantic Web, pp. 593–607, Cham, 2018. Springer International Publishing. ISBN 978-3-319-93417-4. ",
+        "bbox": [
+            173,
+            775,
+            825,
+            844
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Peter Shaw, Jakob Uszkoreit, and Ashish Vaswani. Self-attention with relative position representations. In Proceedings of the 2018 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 2 (Short Papers), pp. 464–468, New Orleans, Louisiana, June 2018. Association for Computational Linguistics. doi: 10.18653/v1/N18-2074. URL https://www.aclweb.org/anthology/N18-2074. ",
+        "bbox": [
+            174,
+            853,
+            825,
+            924
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Yikang Shen, Shawn Tan, Alessandro Sordoni, and Aaron Courville. Ordered neurons: Integrating tree structures into recurrent neural networks. In International Conference on Learning Representations, 2019. URL https://openreview.net/forum?id ${ . } =$ B1l6qiR5F7. ",
+        "bbox": [
+            178,
+            103,
+            823,
+            146
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Vighnesh Shiv and Chris Quirk. Novel positional encodings to enable tree-based transformers. In Advances in Neural Information Processing Systems, pp. 12081–12091, 2019. ",
+        "bbox": [
+            171,
+            155,
+            823,
+            184
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Richard Socher, Alex Perelygin, Jean Wu, Jason Chuang, Christopher D Manning, Andrew Y Ng, and Christopher Potts. Recursive deep models for semantic compositionality over a sentiment treebank. In Proceedings of the 2013 conference on empirical methods in natural language processing, pp. 1631–1642, 2013. ",
+        "bbox": [
+            173,
+            193,
+            825,
+            250
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Kai Sheng Tai, Richard Socher, and Christopher D Manning. Improved semantic representations from tree-structured long short-term memory networks. arXiv preprint arXiv:1503.00075, 2015. ",
+        "bbox": [
+            173,
+            257,
+            821,
+            287
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention is all you need. In Advances in neural information processing systems, pp. 5998–6008, 2017. ",
+        "bbox": [
+            174,
+            295,
+            825,
+            338
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Petar Velickovi ˇ c, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Li ´ o, and Yoshua \\` Bengio. Graph Attention Networks. International Conference on Learning Representations, 2018. URL https://openreview.net/forum?id $=$ rJXMpikCZ. ",
+        "bbox": [
+            173,
+            347,
+            825,
+            390
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Oriol Vinyals, Meire Fortunato, and Navdeep Jaitly. Pointer networks. In Advances in neural information processing systems, pp. 2692–2700, 2015. ",
+        "bbox": [
+            173,
+            398,
+            823,
+            428
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Song Wang, Devin Chollak, Dana Movshovitz-Attias, and Lin Tan. Bugram: Bug detection with n-gram language models. In Proceedings of the 31st IEEE/ACM International Conference on Automated Software Engineering, ASE 2016, pp. 708–719, New York, NY, USA, 2016. Association for Computing Machinery. ISBN 9781450338455. doi: 10.1145/2970276.2970341. URL https://doi.org/10.1145/2970276.2970341. ",
+        "bbox": [
+            173,
+            435,
+            825,
+            507
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka. How powerful are graph neural networks? In International Conference on Learning Representations, 2019. URL https: //openreview.net/forum?id $=$ ryGs6iA5Km. ",
+        "bbox": [
+            174,
+            516,
+            823,
+            559
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Zhilin Yang, Zihang Dai, Yiming Yang, Jaime Carbonell, Russ R Salakhutdinov, and Quoc V Le. Xlnet: Generalized autoregressive pretraining for language understanding. In Advances in neural information processing systems, pp. 5754–5764, 2019. ",
+        "bbox": [
+            176,
+            568,
+            823,
+            611
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Zhitao Ying, Jiaxuan You, Christopher Morris, Xiang Ren, Will Hamilton, and Jure Leskovec. Hierarchical graph representation learning with differentiable pooling. In Advances in neural information processing systems, pp. 4800–4810, 2018. ",
+        "bbox": [
+            173,
+            619,
+            825,
+            662
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Jiaxuan You, Rex Ying, and Jure Leskovec. Position-aware graph neural networks. In Kamalika Chaudhuri and Ruslan Salakhutdinov (eds.), Proceedings of the 36th International Conference on Machine Learning, volume 97 of Proceedings of Machine Learning Research, pp. 7134– 7143. PMLR, 09–15 Jun 2019. URL http://proceedings.mlr.press/v97/you19b. html. ",
+        "bbox": [
+            173,
+            670,
+            825,
+            741
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Muhan Zhang and Yixin Chen. Link prediction based on graph neural networks. In Advances in Neural Information Processing Systems, pp. 5165–5175, 2018. ",
+        "bbox": [
+            176,
+            751,
+            823,
+            779
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/26bec4900b3fdc755545a32837761c235cd99ba3567c283f36c397e15113a344.jpg",
+        "table_caption": [
+            "Table 5: Pairwise cosine similarities of the learned language embeddings of the CODE TRANSFORMER. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Python</td><td>Javascript</td><td>Go</td><td>Ruby</td></tr><tr><td>Python</td><td>1.00</td><td>0.43</td><td>0.42</td><td>0.79</td></tr><tr><td>Javascript</td><td>0.43</td><td>1.00</td><td>0.84</td><td>0.39</td></tr><tr><td>Go</td><td>0.43</td><td>0.84</td><td>1.00</td><td>0.38</td></tr><tr><td>Ruby</td><td>0.79</td><td>0.39</td><td>0.38</td><td>1.00</td></tr></table>",
+        "bbox": [
+            328,
+            101,
+            669,
+            186
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "ACKNOWLEDGEMENTS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            252,
+            367,
+            267
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "We are grateful to Dylan Bourgeois for having paved the way to this research contribution with his thesis work (Bourgeois, 2019). We further thank Simon Geisler for his helpful suggestions and proofreading the paper, as well as the anonymous reviewers for their constructive feedback and fruitful discussions. ",
+        "bbox": [
+            174,
+            282,
+            825,
+            338
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "This research was supported by the TUM International Graduate School of Science and Engineering (IGSSE). Stanford University is supported by DARPA under Nos. N660011924033 (MCS); ARO under Nos. W911NF-16-1- 0342 (MURI), W911NF-16-1-0171 (DURIP); NSF under Nos. OAC1835598 (CINES), OAC-1934578 (HDR), CCF-1918940 (Expeditions), IIS-2030477 (RAPID); Stanford Data Science Initiative, Wu Tsai Neurosciences Institute, Chan Zuckerberg Biohub, Amazon, JPMorgan Chase, Docomo, Hitachi, JD.com, KDDI, NVIDIA, Dell, Toshiba, Intel, and UnitedHealth Group. Jure Leskovec is a Chan Zuckerberg Biohub investigator. ",
+        "bbox": [
+            173,
+            345,
+            825,
+            444
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "A APPENDIX ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            464,
+            299,
+            479
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "A.1 DISTANCE ENCODING FUNCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            496,
+            444,
+            511
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "For encoding scalar relation values via vectors we employ encoding functions $\\phi : \\mathbb { R } \\to \\mathbb { R } ^ { d }$ , where $d$ is the model’s embedding dimension. We choose the popular sinusoidal encoding function presented in Vaswani et al. (2017): ",
+        "bbox": [
+            174,
+            522,
+            825,
+            564
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "equation",
+        "img_path": "images/f46894c730c22bd189c627fee0b9dffb06a45fdfb55c7f527bb4fe0d0c5327e8.jpg",
+        "text": "$$\n\\phi ( r _ { i  j } ) _ { 2 k } = \\sin ( \\frac { r _ { i  j } } { M ^ { 2 k / d } } ) \\qquad \\phi ( r _ { i  j } ) _ { 2 k + 1 } = \\cos ( \\frac { r _ { i  j } } { M ^ { 2 k / d } } ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            258,
+            570,
+            738,
+            598
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "where $1 \\leq k < d / 2$ is the position in the encoding vector and $M$ is some constant; we adopt $M = 1 0 , 0 0 0$ as chosen by (Vaswani et al., 2017). Note that the distance encoding functions have no trainable parameters. ",
+        "bbox": [
+            174,
+            606,
+            825,
+            648
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "A.2 MULTILINGUAL REPRESENTATION ANALYSIS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            666,
+            526,
+            680
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "In Table 5, we show the pairwise cosine similarities of the learned language embeddings of the CODE TRANSFORMER. We can see that the pairs Python-Ruby and Javascript-Go have similar language embeddings. This aligns well with roots of language design and common use cases of the languages. ",
+        "bbox": [
+            173,
+            690,
+            825,
+            748
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Moreover, in Table 6, we show selected snippets starting with is, main, or load (left) and their best embedding matches from other languages (right). ",
+        "bbox": [
+            173,
+            755,
+            823,
+            784
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "A.3 DATA PREPROCESSING ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            800,
+            375,
+            815
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "A.3.1 TEXTUAL CODE SNIPPET PREPROCESSING ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            827,
+            522,
+            842
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "1. Tokenize code snippets with Pygments language-specific tokenizer. ",
+        "bbox": [
+            210,
+            848,
+            676,
+            863
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "2. Remove comments (both multi-line, single-line and doc comments). The comment token types. pygments.token.Comment and pygments.token.Literal.String.Doc that are generated by Pygments are used to identify comments. ",
+        "bbox": [
+            214,
+            867,
+            825,
+            924
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "table",
+        "img_path": "images/dfeb9bd55674c1d88bd8727a7ae6e6c8b0e9d1b458288922467db71461c08de5.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 6: Selected snippets starting with is, main, or load (left) and their best embedding matches from other languages (right). "
+        ],
+        "table_body": "<table><tr><td colspan=\"2\">Published as a conference paper at ICLR 2021</td></tr><tr><td></td><td></td></tr><tr><td>function isEqualArray(a，b){ if (a return true;</td><td></td></tr><tr><td>if ((a === undefined) undefined)）{ return false;</td><td>func areSameFloat32Array(a，b []float32） bool if len(a) != len(b){ return false</td></tr><tr><td>var =a.length; if (i !== b.length){ return false;</td><td>for i := O;i &lt; len(a);i++{ if a[i]!=b[i]{ return false J</td></tr><tr><td>while (i--）{ if(a[i] !== b[i]）{ return false; }</td><td>return true</td></tr><tr><td>return true;</td><td></td></tr><tr><td>function main() var rawData $(&#x27; .HeaderTexture[data-login- user-email]&#x27;) .data() ;</td><td>func TaskSayHello(t *tasking.T){</td></tr><tr><td>if (rawData) 1 me={</td><td>username := t.Flags.String(&quot;name&quot;) if username user, := user.Current ()</td></tr><tr><td>name:rawData.loginUserName, mail: rawData.loginUserEmail }；</td><td>username = user.Name</td></tr><tr><td>getCartId(function (cart）{ me.cart = cart;</td><td>} ift.Flags.Bool(&quot;verbose&quot;)</td></tr><tr><td>injectMenu(); refreshUsers(actions.updateUsers); listenOnChanges(onChange);</td><td>t.Logf(&quot;Hello %s, the time now is %s\\n&quot;, username，time.Now())</td></tr><tr><td>listenonorderConfirm(onConfirm); ）；</td><td>}else{ t.Logf(&quot;Hello %s\\n&quot;,username)</td></tr><tr><td>} else{ caliback(&#x27;no user&#x27;);</td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>func Backup(filename string)error{</td></tr><tr><td></td><td></td></tr><tr><td></td><td>info，err := os.Stat(filename) if err != nil</td></tr><tr><td></td><td>if os.IsNotExist(err）{</td></tr><tr><td></td><td>return nil</td></tr><tr><td></td><td>return err</td></tr><tr><td></td><td></td></tr><tr><td>def _load_rule_file(self, filename):</td><td>if info.Size() == 0{ return nil</td></tr><tr><td>if not (os.path.exists(filename)):</td><td>}</td></tr><tr><td>sys.stderr.write(</td><td>files，err ：= filepath.Glob(</td></tr><tr><td>&quot;rflint: %s: No such file or &quot;directory\\n&quot; % filename</td><td>filename + _BACKUP_SUFFIX</td></tr><tr><td>return</td><td>） if err nil 1</td></tr><tr><td>try:</td><td>return err</td></tr><tr><td>basename = os.path.basename(filename)</td><td>}</td></tr><tr><td>(name，ext）= os.path.splitext(basename) imp.load_source(name,filename)</td><td> numBackup := byte(1)</td></tr><tr><td>except Exception as e: sys.stderr.write(</td><td>if len(files) !=0{</td></tr><tr><td>&quot;rflint: %s: exception while</td><td>lastFile := files[len(files)-1]</td></tr><tr><td>&quot;loading:%s\\n&quot; % (filename, str(e))</td><td>numBackup = lastFile[len(lastFile)-2] + 1</td></tr><tr><td></td><td>if numBackup &gt;</td></tr><tr><td></td><td>numBackup = &#x27;1&#x27;</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>else{</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>&#x27;1&#x27;</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>numBackup =</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>return Copy (filename,</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>fmt.Sprintf(&quot;%s+%s~&quot;,</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>string(numBackup)))</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr></table>",
+        "bbox": [
+            173,
+            15,
+            866,
+            864
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "image",
+        "img_path": "images/e37f9cb44d930542340c5ad3d88619f8535c0f5512daf8c0c8d8a050432bff4b.jpg",
+        "image_caption": [
+            "Figure 6: Example snippet and its corresponding AST obtained from GitHub Semantic. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            300,
+            99,
+            686,
+            333
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "3. Empty lines are removed. ",
+        "bbox": [
+            214,
+            388,
+            405,
+            402
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "4. Hard coded strings and numbers are replaced with a special [MASK STRING] and [MASK NUMBER] token. ",
+        "bbox": [
+            210,
+            411,
+            825,
+            439
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "5. Indentation style of the code snippet is detected and whitespace characters at the beginning of a line are replaced with a single [INDENT] or [DEDENT] token when indentation changes. ",
+        "bbox": [
+            212,
+            446,
+            825,
+            489
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "6. Tokens are further split into sub tokens, e.g., setBottomHeight [‘set’, ‘bottom’, ‘height’]. Throughout our experiments, we use 5 input sub tokens. If a token consists of less than 5 sub tokens, the remaining spaces are filled with a special [PAD] token. ",
+        "bbox": [
+            212,
+            497,
+            825,
+            540
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "7. Any remaining tokens that only consist of white spaces are removed. The only white space characters that are kept are line breaks $^ { \\bullet } \\backslash \\boldsymbol { \\mathrm { n } } ^ { \\prime }$ . ",
+        "bbox": [
+            210,
+            547,
+            821,
+            577
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "8. Any code snippets where the Pygments tokenizer cannot parse a token are discarded. ",
+        "bbox": [
+            207,
+            584,
+            803,
+            599
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "A.3.2 STAGE 1 PREPROCESSING (GENERATION OF ASTS) ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            618,
+            588,
+            633
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "1. Stripped code snippets are used to generate language-specific ASTs. For Java, we use the AST parser from the java-parser project. The ASTs contain node types and source ranges. For Python, JavaScript, Ruby and Go, we use semantic. ",
+        "bbox": [
+            214,
+            645,
+            823,
+            686
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "2. Snippets that lead to an AST parse error are discarded. ",
+        "bbox": [
+            212,
+            695,
+            606,
+            709
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "3. We calculate a mapping between tokens and nodes in the AST. Every token is assigned to the node in the AST with shortest source range that still encompasses the source range of the token. ",
+        "bbox": [
+            210,
+            718,
+            823,
+            758
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "To find such a node, we originally intended to make use of the assumption that source ranges of child nodes do not overlap. Then, one could easily find the node with smallest encompassing source range by greedily selecting at every layer in the AST the child that encompasses the token’s source range (there can only be at most one child that fulfills this). However, this assumption does not hold for all ASTs (see Figure 6 for an example). As a heuristic, we greedily select the child node with the shorter source range in case there were multiple child nodes with encompassing source ranges. This approximation seems to be sufficient in our case, and limits runtime as we do not have to consider multiple paths in the AST. It is also sufficient to stop when no child node encompasses the source range of the token, as in ASTs the source ranges of child nodes are always contained in the source ranges of their parent. ",
+        "bbox": [
+            232,
+            760,
+            825,
+            911
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "1. Tokens are vocabularized. Any token occurring less than 100 times in the training set is replaced by an <unk $>$ token. ",
+        "bbox": [
+            210,
+            125,
+            825,
+            154
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "2. We calculate multiple pair-wise relations between nodes in the AST: ",
+        "bbox": [
+            212,
+            159,
+            689,
+            172
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "• Personalized Page Rank (PPR) We interpret the negative logarithm of PPR as a distance. We use a teleport probability of $\\alpha = 0 . 1 5$ and a threshold of $e ^ { - 5 }$ , i.e., anything with $- \\log P P R > 5$ is considered unreachable   \n• Shortest path length between two nodes   \n• Ancestor shortest paths (bidirectional). That is, the parent has an ancestor shortest path distance of 1 to all its children and the child has a distance of -1 to its parents. We consider nodes that are not ancestors or descendants of a node (i.e. not reachable by following only parent or only child relations) as not connected in the ancestor shortest paths relation. We encode this with a very large value in their distance; we have found a value of $1 , 0 0 0$ to work well in practice.   \n• Next sibling shortest paths (bidirectional, analogous to the ancestor shortest paths) ",
+        "bbox": [
+            251,
+            178,
+            825,
+            354
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "Note that the ancestor shortest paths and next sibling shortest paths are required because treating the AST as a normal graph leads to ambiguity. In a graph, the neighbors of a node have no ordering; however in the AST, the order of the children of a node reflects their order in the code. Therefore, we explicitly include the next sibling shortest paths. The ancestor shortest paths would not be required if we treated the AST as a directed graph; in this case, however, a leaf node could not reach any other node in the AST, and therefore both PPR and shortest path length are not useful in this case. Therefore, we model the AST as undirected and inject the ancestor / child edges to avoid ambiguity. ",
+        "bbox": [
+            232,
+            359,
+            823,
+            470
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "3. Distance values are binned into 32 bins using area-based exponential binning with a growth factor of 1.3, i.e., the area of a bin’s rectangle ( $x$ : bin range, $y$ : number of values in bin) will be approximately 1.3 times bigger for the next bin (going away from the bin that contains the zero value). Additionally, for discrete distance measures (such as sequence distance or shortest path length), we hard-code 9 values around 0 to have their own bins. For instance, on the sequence distance the values $- 4 , - 3 , \\dots , 4$ have their individual bins, and around those values we employ the exponential binning. ",
+        "bbox": [
+            212,
+            476,
+            825,
+            573
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "4. Punctuation tokens (such as points or brackets) are removed from the input sequence, as experiments showed that their presence does not improve performance but slows down training due to bigger input sizes. ",
+        "bbox": [
+            214,
+            579,
+            823,
+            621
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "5. Snippets that are longer than MAX NUM TOKENS after punctuation tokens are removed are discarded from the training set. Throughout our experiments, we use MAX NUM TOKENS $= ~ 5 1 2$ . During evaluation on the test set, we use MAX NUM TOKENS $= ~ 1 0 0 0$ . ",
+        "bbox": [
+            215,
+            626,
+            823,
+            667
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "A.4 INPUT EMBEDDINGS TO THE MODEL ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            686,
+            467,
+            700
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "Besides its five subtokens (e.g., [‘get’, ‘data’, ‘[PAD]’, ‘[PAD]’, ‘[PAD]’]), each input token has a token type (coming from the Pygments tokenizer) and an AST node type. The AST node type is the type of the node assigned to each respective token, as described in Section A.3.2. We concatenate the embeddings of the five subtokens, the token type, and the AST node type. Then, we apply a linear layer (without activation function) to project down to the model’s embedding dimension. ",
+        "bbox": [
+            174,
+            712,
+            825,
+            795
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "A.5 INPUT TO THE GREAT BASELINE",
+        "text_level": 1,
+        "bbox": [
+            176,
+            813,
+            449,
+            828
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "As mentioned in the main text, we also compare with GREAT Hellendoorn et al. (2020). Since their preprocessing pipeline is proprietary and could not be shared with us even after contacting the authors, we provide to GREAT the same AST distances as our model. Since GREAT uses edges instead of distances to encode relations in the Structure, we essentially threshold the ancestor, sibling, and shortest-paths distances and provide the edges where the distances are equal to 1 (including their edge types) to the model. ",
+        "bbox": [
+            174,
+            840,
+            825,
+            922
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "table",
+        "img_path": "images/26b079a48f72f11ac5901761fadc58949615f228994d83e0ca015c1b803de70e.jpg",
+        "table_caption": [
+            "(a) CODE TRANSFORMER ",
+            "Table 7: Code Summarization hyperparameters "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Hyperparameter</td><td>Value</td></tr><tr><td>Activation</td><td>GELU</td></tr><tr><td>Input Nonlinearity</td><td>tanh</td></tr><tr><td>Num. layers</td><td>3</td></tr><tr><td>d</td><td>1024</td></tr><tr><td>dFF</td><td>2048</td></tr><tr><td>Pdropout</td><td>0.2</td></tr><tr><td>Num.heads</td><td>8</td></tr></table>",
+        "bbox": [
+            272,
+            122,
+            483,
+            250
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "table",
+        "img_path": "images/d450c7940cdf06f24a236ed0b2ea7649815a8d485cbb72d5b067d40223c84355.jpg",
+        "table_caption": [
+            "(b) GREAT (Hellendoorn et al., 2020) "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Hyperparameter</td><td>Value</td></tr><tr><td>Activation</td><td>GELU</td></tr><tr><td>Num. layers</td><td>3</td></tr><tr><td>d</td><td>1024</td></tr><tr><td>dFF</td><td>2048</td></tr><tr><td>Pdropout</td><td>0.2</td></tr><tr><td>Num.heads</td><td>8</td></tr></table>",
+        "bbox": [
+            519,
+            136,
+            715,
+            247
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "A.6 EXPERIMENTAL SETUP ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            303,
+            377,
+            316
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "Table 7 shows hyperparameters of our models for code summarization. For all our experiments, we use a Transformer Decoder with one layer and teacher forcing to generate 6 output sub tokens. We also employ label smoothing of 0.1. As optimizer, we use Adam with a learning rate of $8 e ^ { - 5 }$ and weight decay of $3 e ^ { - 5 }$ . Batch size during training is 8 with a simulated batch size of 128 achieved by gradient accumulation. ",
+        "bbox": [
+            173,
+            328,
+            825,
+            398
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "Apart from comparing the CODE TRANSFORMER to baselines, we performed the following hyperparameter comparisons and ablation studies: ",
+        "bbox": [
+            174,
+            419,
+            821,
+            446
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "• CODE TRANSFORMER (structure-only) Using only AST information as input, i.e., masking all tokens that do not correspond to a leaf of the AST, and removing the token distance as a relation to be used by the model. Further, token types are not fed into the model.   \n• CODE TRANSFORMER (context-only) Here, we do not include any information on the AST (i.e. node types and distances on the AST). This is effectively the XLNet backbone plus encoding of the token type returned by the tokenizer.   \n• CODE TRANSFORMER (Max-Dist.) Applying a Max Distance Mask of 5 to the shortest paths distance (i.e., model cannot see a node that is more than 5 hops away no matter how small the other distances are). Early results showed that, as expected, results deteriorate substantially when limiting our model’s receptive field. Hence, we do not include these results in this work.   \n• Using 16 and 64 bins instead of 32 bins. This had no noticeable effect on performance. ",
+        "bbox": [
+            217,
+            460,
+            825,
+            670
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "A.7 CODE SUMMARIZATION EXAMPLES",
+        "text_level": 1,
+        "bbox": [
+            178,
+            686,
+            462,
+            700
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "In the Tables 8, 9, 10, 11, 12, 13, 14 and 15 we present example functions from the Java-small dataset along with the different models’ predictions for the function name. ",
+        "bbox": [
+            173,
+            712,
+            825,
+            741
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "public Summation next() { return parts $[ \\dot { 1 } + + ]$ ; } ",
+        "bbox": [
+            173,
+            118,
+            395,
+            156
+        ],
+        "page_idx": 18
+    },
+    {
+        "type": "table",
+        "img_path": "images/04303ffb667966783611a78b38db4a06a17d54b3303576e3d6f2082eb78c4e3f.jpg",
+        "table_caption": [
+            "Table 8: The CODE TRANSFORMER is the only model to correctly identify the notion of getting the next entry. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td> get x map</td></tr><tr><td>code2seq</td><td> get parts</td></tr><tr><td>Ours w/o structure</td><td>get</td></tr><tr><td>CODE TRANSFORMER</td><td>get next</td></tr><tr><td>Ground Truth</td><td>next</td></tr></table>",
+        "bbox": [
+            377,
+            161,
+            617,
+            258
+        ],
+        "page_idx": 18
+    },
+    {
+        "type": "text",
+        "text": "private Path findCacheFile(Path[] cacheFiles, String fileName) { if (cacheFiles $! =$ null && cacheFiles.length $> 0$ ) { for (Path file : cacheFiles) { if (file.getName().equals(fileName)) { return file; } return null;   \n} ",
+        "bbox": [
+            173,
+            343,
+            740,
+            467
+        ],
+        "page_idx": 18
+    },
+    {
+        "type": "table",
+        "img_path": "images/7fce10876c7dbfae8cd1529bce06e79b9baef638e4b20f560a956fd0593414a7.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td>get path</td></tr><tr><td>code2seq</td><td>find file</td></tr><tr><td>Ours w/o structure</td><td>get file</td></tr><tr><td>CODE TRANSFORMER</td><td>find cache</td></tr><tr><td>Ground Truth</td><td>find cache file</td></tr></table>",
+        "bbox": [
+            367,
+            474,
+            629,
+            573
+        ],
+        "page_idx": 18
+    },
+    {
+        "type": "text",
+        "text": "Table 9: The CODE TRANSFORMER is the only model to both recognize that the task is to find a file as well as the fact that it is about the cache. However, it did not correctly predict the file part of the method name. ",
+        "bbox": [
+            173,
+            583,
+            826,
+            625
+        ],
+        "page_idx": 18
+    },
+    {
+        "type": "text",
+        "text": "public int compare(Pair<LoggedJob, JobTraceReader> p1, Pair<LoggedJob, JobTraceReader> p2) { LoggedJob $\\ j 1 \\ = \\ \\mathtt { p 1 }$ .first(); LoggedJob $\\begin{array} { r } { \\dot { \\bf { \\ j } } 2 { \\bf { \\nu } } = { \\bf { \\ p } } 2 } \\end{array}$ .first(); return (j1.getSubmitTime() $<$ j2.getSubmitTime()) ? -1 : (j1.getSubmitTime() $= =$ j2.getSubmitTime()) ? 0 : 1; } ",
+        "bbox": [
+            173,
+            671,
+            748,
+            758
+        ],
+        "page_idx": 18
+    },
+    {
+        "type": "table",
+        "img_path": "images/fc7647e7d39190fcddd6003a2621a01161522b4db1837436041dcd5808f7523b.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td>run</td></tr><tr><td>code2seq</td><td> get submit time</td></tr><tr><td>Ours w/o structure</td><td>compare</td></tr><tr><td>CODE TRANSFORMER</td><td>compare</td></tr><tr><td>Ground Truth</td><td>compare</td></tr></table>",
+        "bbox": [
+            361,
+            765,
+            633,
+            863
+        ],
+        "page_idx": 18
+    },
+    {
+        "type": "text",
+        "text": "Table 10: The CODE TRANSFORMER and the its context-only variant are the only models correctly recognizing the ‘compare’ template in the method body. ",
+        "bbox": [
+            174,
+            872,
+            823,
+            901
+        ],
+        "page_idx": 18
+    },
+    {
+        "type": "text",
+        "text": "public static MNTPROC fromValue(int value) { if (value $< ~ 0$ || value $> =$ values().length) { return null; } return values()[value];   \n} ",
+        "bbox": [
+            173,
+            116,
+            599,
+            193
+        ],
+        "page_idx": 19
+    },
+    {
+        "type": "table",
+        "img_path": "images/c731fa631d72aabd1f5e32632f679a09b671309e6980e8efeb5fd4f3681003b9.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td> get value</td></tr><tr><td>code2seq</td><td> get value</td></tr><tr><td>Ours w/o structure</td><td>to</td></tr><tr><td>CODE TRANSFORMER</td><td>from value</td></tr><tr><td>Ground Truth</td><td>from value</td></tr></table>",
+        "bbox": [
+            374,
+            196,
+            619,
+            295
+        ],
+        "page_idx": 19
+    },
+    {
+        "type": "text",
+        "text": "Table 11: The CODE TRANSFORMER is the only model to recognize that the snippet is similar to a static factory method which is often preceded with from. ",
+        "bbox": [
+            171,
+            305,
+            825,
+            334
+        ],
+        "page_idx": 19
+    },
+    {
+        "type": "text",
+        "text": "private Iterable<ListBlobItem> listRootBlobs(String aPrefix, ",
+        "bbox": [
+            174,
+            376,
+            700,
+            388
+        ],
+        "page_idx": 19
+    },
+    {
+        "type": "text",
+        "text": "boolean useFlatBlobListing,   \nEnumSet<BlobListingDetails> listingDetails,   \nBlobRequestOptions options,   \nOperationContext opContext) ",
+        "bbox": [
+            565,
+            388,
+            947,
+            439
+        ],
+        "page_idx": 19
+    },
+    {
+        "type": "text",
+        "text": "throws StorageException, URISyntaxException { ",
+        "bbox": [
+            514,
+            440,
+            928,
+            452
+        ],
+        "page_idx": 19
+    },
+    {
+        "type": "text",
+        "text": "CloudBlobDirectoryWrapper directory $=$ this.container.getDirectoryReference(aPrefix); return directory.listBlobs(null, useFlatBlobListing, listingDetails, options, opContext); ",
+        "bbox": [
+            186,
+            453,
+            946,
+            491
+        ],
+        "page_idx": 19
+    },
+    {
+        "type": "text",
+        "text": "} ",
+        "bbox": [
+            174,
+            491,
+            184,
+            502
+        ],
+        "page_idx": 19
+    },
+    {
+        "type": "table",
+        "img_path": "images/4184371f3c5b40e5706dc3536eb808edba7ea9235136630720ca50cbd799e93d.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td>list blobs</td></tr><tr><td>code2seq</td><td>list blobs</td></tr><tr><td>Ours w/o structure</td><td>list blobs</td></tr><tr><td>CODE TRANSFORMER</td><td>list blobs by prefix</td></tr><tr><td>Ground Truth</td><td>list root blobs</td></tr></table>",
+        "bbox": [
+            351,
+            507,
+            643,
+            604
+        ],
+        "page_idx": 19
+    },
+    {
+        "type": "text",
+        "text": "Table 12: All models could correctly identify the listBlobs() call in the return statement. However, the CODE TRANSFORMER additionally comprehended that the specified prefix is quite important. ",
+        "bbox": [
+            171,
+            614,
+            823,
+            643
+        ],
+        "page_idx": 19
+    },
+    {
+        "type": "text",
+        "text": "private static void dumpOpCounts(EnumMap $<$ FSEditLogOpCodes, Holder $<$ <Integer>> opCounts) { StringBuilder sb $=$ new StringBuilder(); sb.append(\"Summary of operations loaded from edit log:\\n \"); Joiner.on(\"\\n \").withKeyValueSeparator(\" $^ { 1 1 } =$ \").appendTo(sb, opCounts); FSImage.LOG.debug(sb.toString());   \n} ",
+        "bbox": [
+            169,
+            685,
+            942,
+            757
+        ],
+        "page_idx": 19
+    },
+    {
+        "type": "table",
+        "img_path": "images/3539e0325fcec95f6f2a244b7e8480d60028213ed3f48a53d7797b35801c9743.jpg",
+        "table_caption": [
+            "Table 13: Only the CODE TRANSFORMER could correctly identify that it is the op counts that should be logged. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td>append</td></tr><tr><td>code2seq</td><td>add</td></tr><tr><td>Ours w/o structure</td><td>log</td></tr><tr><td>CODE TRANSFORMER</td><td>log op counts</td></tr><tr><td>Ground Truth</td><td>dump op counts</td></tr></table>",
+        "bbox": [
+            359,
+            765,
+            633,
+            864
+        ],
+        "page_idx": 19
+    },
+    {
+        "type": "text",
+        "text": "static String execCommand(File f, String... cmd) throws IOException { String[] args $=$ new String[cmd.length $^ +$ 1]; System.arraycopy(cmd, 0, args, 0, cmd.length); args[cmd.length] $=$ f.getCanonicalPath(); String output $=$ Shell.execCommand(args); return output; ",
+        "bbox": [
+            173,
+            190,
+            782,
+            268
+        ],
+        "page_idx": 20
+    },
+    {
+        "type": "table",
+        "img_path": "images/3c5bfe70032cf08db67ee0f3135ec46e80e42b50a65cc9210b7b528695c79ab7.jpg",
+        "table_caption": [
+            "Table 14: Only the CODE TRANSFORMER and code2seq could identify that the relevant part of the method is concerned with executing a command instead of returning something. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td>get canonical path</td></tr><tr><td>code2seq</td><td>exec</td></tr><tr><td>Ours w/o structure</td><td> get output</td></tr><tr><td>CODE TRANSFORMER</td><td>exec command</td></tr><tr><td>Ground Truth</td><td>exec command</td></tr></table>",
+        "bbox": [
+            352,
+            284,
+            642,
+            382
+        ],
+        "page_idx": 20
+    },
+    {
+        "type": "text",
+        "text": "protected void subView(Class<? extends SubView> cls) { ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            612,
+            650,
+            625
+        ],
+        "page_idx": 20
+    },
+    {
+        "type": "text",
+        "text": "indent(of(ENDTAG));   \nsb.setLength(0);   \nout.print(sb.append('[').append(cls.getName()).append(']').toString());   \nout.println(); ",
+        "bbox": [
+            178,
+            621,
+            834,
+            678
+        ],
+        "page_idx": 20
+    },
+    {
+        "type": "table",
+        "img_path": "images/0c4c2219f8a76155c82fd9cf1ddec51733b172b4b12ee945147b97301cb67ad3.jpg",
+        "table_caption": [
+            "Table 15: Only the CODE TRANSFORMER was able to link the print functionality to the object that should be printed, which can only be inferred from the object’s class in the method parameters. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td>print</td></tr><tr><td>code2seq</td><td>print</td></tr><tr><td>Ours w/o structure</td><td>print</td></tr><tr><td>CODE TRANSFORMER</td><td>print sub view</td></tr><tr><td>Ground Truth</td><td>sub view</td></tr></table>",
+        "bbox": [
+            364,
+            691,
+            629,
+            790
+        ],
+        "page_idx": 20
+    },
+    {
+        "type": "image",
+        "img_path": "images/1225dc2212652b0900da96594dc1baedeb731793c2a7f99b2f39f0a306a759b8.jpg",
+        "image_caption": [
+            "Figure 7: Share of tokens in the labels also occurring in the bodies of methods. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            276,
+            106,
+            722,
+            315
+        ],
+        "page_idx": 21
+    },
+    {
+        "type": "table",
+        "img_path": "images/f9846de1ac74fbb68c2e86b16559380e7f8fc1f6b4b397c66475b197f4726324.jpg",
+        "table_caption": [
+            "Table 16: Code summarization results on the CSN dataset (sample-F1). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Model</td><td colspan=\"2\">Python</td><td colspan=\"3\">Javascript</td><td colspan=\"2\"></td><td colspan=\"2\">Ruby</td><td colspan=\"3\">Go</td></tr><tr><td>Prec.</td><td>Rec.</td><td>F1</td><td>Prec.</td><td>Rec.</td><td>F1</td><td>Prec.</td><td>Rec.</td><td>F1</td><td>Prec.</td><td>Rec.</td><td>F1</td></tr><tr><td>code2seq</td><td>1</td><td>1</td><td>1</td><td>-</td><td>1</td><td>1</td><td>=</td><td>1</td><td>1</td><td>1</td><td>1</td><td>-</td></tr><tr><td>GREAT</td><td>34.93</td><td>31.12</td><td>31.61</td><td>29.69</td><td>24.24</td><td>25.55</td><td>25.69</td><td>21.49</td><td>22.18</td><td>48.38</td><td>45.97</td><td>45.71</td></tr><tr><td>Ours w/o structure</td><td>36.87</td><td>32.17</td><td>32.97</td><td>31.30</td><td>25.03</td><td>26.64</td><td>31.43</td><td>25.34</td><td>26.63</td><td>49.78</td><td>46.73</td><td>46.69</td></tr><tr><td>Ours w/o pointer net</td><td>38.77</td><td>31.72</td><td>33.27</td><td>32.70</td><td>25.50</td><td>27.33</td><td>32.12</td><td>30.17</td><td>29.36</td><td>53.09</td><td>48.70</td><td>49.26</td></tr><tr><td>Ours</td><td>36.68</td><td>33.86</td><td>33.84</td><td>33.36</td><td>27.55</td><td>29.02</td><td>31.53</td><td>24.72</td><td>26.43</td><td>52.00</td><td>47.35</td><td>47.93</td></tr><tr><td>code2seq (Multilanguage)</td><td>-</td><td>=</td><td>=</td><td></td><td>=</td><td>=</td><td></td><td></td><td></td><td></td><td></td><td>-</td></tr><tr><td>GREAT (Multilanguage)</td><td>35.73</td><td>30.81</td><td>31.74</td><td>31.49</td><td>26.17</td><td>27.41</td><td>29.72</td><td>24.20</td><td>25.43</td><td>50.32</td><td>47.94</td><td>47.66</td></tr><tr><td>Ours w/o structure (Mult.)</td><td>36.78</td><td>29.92</td><td>31.58</td><td>32.60</td><td>26.02</td><td>27.74</td><td>31.71</td><td>26.07</td><td>27.24</td><td>51.91</td><td>47.58</td><td>48.15</td></tr><tr><td>Ours w/o pointer (Mult.)</td><td>37.18</td><td>30.52</td><td>32.04</td><td>33.95</td><td>25.92</td><td>28.11</td><td>32.76</td><td>25.04</td><td>27.01</td><td>53.50</td><td>48.54</td><td>49.35</td></tr><tr><td>Ours (Multilanguage)</td><td>38.10</td><td>33.32</td><td>34.18</td><td>34.29</td><td>28.69</td><td>30.08</td><td>33.30</td><td>28.33</td><td>29.29</td><td>53.86</td><td>50.46</td><td>50.61</td></tr><tr><td>Ours (Mult. + Finetune)</td><td>38.29</td><td>32.41</td><td>33.65</td><td>34.43</td><td>28.28</td><td>29.91</td><td>32.89</td><td>27.15</td><td>28.49</td><td>53.85</td><td>50.85</td><td></td></tr><tr><td>Ours (Mult.+ LMPretrain)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>50.81</td></tr><tr><td></td><td>38.97</td><td>34.77</td><td>35.34</td><td>35.23</td><td>30.26</td><td>31.38</td><td>33.73</td><td>29.15</td><td>29.94</td><td>55.31</td><td>52.03</td><td>52.13</td></tr></table>",
+        "bbox": [
+            176,
+            361,
+            823,
+            523
+        ],
+        "page_idx": 21
+    },
+    {
+        "type": "text",
+        "text": "A.8 ESTIMATION OF POINTER NETWORK POTENTIAL ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            575,
+            557,
+            590
+        ],
+        "page_idx": 21
+    },
+    {
+        "type": "text",
+        "text": "In Table 2 we observe that the pointer network improves the F1 score for all languages except Go, where counterintuitively it leads to reduced performance as measured by F1 score on the test set (while it improves by about 3 points on validation). To investigate this, in Figure 7 we plot the share of tokens in the labels also occurring in the bodies of methods in the different languages. Intuitively, this gives an indication on how much gain we can expect from using a pointer network. If the share were zero, then no token in the labels ever occur in the bodies of the methods, so the pointer network cannot improve the prediction by pointing at the input. We see that for Go, there is a strong mismatch between the test partition and the train/validation partitions, which much fewer tokens from the labels occurring in the bodies of methods on test compared to train/validation. Thus, we attribute the drop in performance observed by adding a pointer network on Go to this apparent violation of the i.i.d. assumption. ",
+        "bbox": [
+            173,
+            602,
+            825,
+            755
+        ],
+        "page_idx": 21
+    },
+    {
+        "type": "text",
+        "text": "A.9 CODE SUMMARIZATION RESULTS ON THE CSN DATASET (SAMPLE-F1) ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            771,
+            710,
+            786
+        ],
+        "page_idx": 21
+    },
+    {
+        "type": "text",
+        "text": "In Table 16, we present our results on the CSN dataset as measured by the sample-F1 score. ",
+        "bbox": [
+            171,
+            797,
+            771,
+            813
+        ],
+        "page_idx": 21
+    }
+]
\ No newline at end of file
diff --git a/parse/train/Xh5eMZVONGF/Xh5eMZVONGF_middle.json b/parse/train/Xh5eMZVONGF/Xh5eMZVONGF_middle.json
new file mode 100644
index 0000000000000000000000000000000000000000..f2b8b946a678057b9ea2b12f82a1cf15d06d52b6
--- /dev/null
+++ b/parse/train/Xh5eMZVONGF/Xh5eMZVONGF_middle.json
@@ -0,0 +1,53618 @@
+{
+    "pdf_info": [
+        {
+            "preproc_blocks": [
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        79,
+                        504,
+                        116
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                77,
+                                505,
+                                98
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        77,
+                                        505,
+                                        98
+                                    ],
+                                    "score": 1.0,
+                                    "content": "LANGUAGE-AGNOSTIC REPRESENTATION LEARNING",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                98,
+                                495,
+                                118
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        98,
+                                        495,
+                                        118
+                                    ],
+                                    "score": 1.0,
+                                    "content": "OF SOURCE CODE FROM STRUCTURE AND CONTEXT",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        113,
+                        135,
+                        285,
+                        169
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                112,
+                                136,
+                                259,
+                                147
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        112,
+                                        136,
+                                        259,
+                                        147
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Daniel Zugner, Tobias Kirschstein ¨",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                112,
+                                146,
+                                242,
+                                158
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        112,
+                                        146,
+                                        242,
+                                        158
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Technical University of Munich",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                113,
+                                157,
+                                286,
+                                170
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        157,
+                                        286,
+                                        170
+                                    ],
+                                    "score": 1.0,
+                                    "content": "{zuegnerd,kirschto}@in.tum.de",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        365,
+                        135,
+                        498,
+                        168
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                364,
+                                135,
+                                437,
+                                147
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        364,
+                                        135,
+                                        437,
+                                        147
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Michele Catasta",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                364,
+                                145,
+                                446,
+                                158
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        364,
+                                        145,
+                                        446,
+                                        158
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Stanford University",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                364,
+                                158,
+                                498,
+                                168
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        364,
+                                        158,
+                                        498,
+                                        168
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pirroh@cs.stanford.edu",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        113,
+                        186,
+                        234,
+                        218
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                111,
+                                185,
+                                176,
+                                197
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        185,
+                                        176,
+                                        197
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Jure Leskovec",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                111,
+                                195,
+                                194,
+                                209
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        195,
+                                        194,
+                                        209
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Stanford University",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                113,
+                                208,
+                                234,
+                                219
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        208,
+                                        234,
+                                        219
+                                    ],
+                                    "score": 1.0,
+                                    "content": "jure@cs.stanford.edu",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        365,
+                        186,
+                        494,
+                        218
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                365,
+                                186,
+                                458,
+                                197
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        365,
+                                        186,
+                                        458,
+                                        197
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Stephan Gunnemann ¨",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                364,
+                                197,
+                                494,
+                                208
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        364,
+                                        197,
+                                        494,
+                                        208
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Technical University of Munich",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                364,
+                                208,
+                                486,
+                                219
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        364,
+                                        208,
+                                        486,
+                                        219
+                                    ],
+                                    "score": 1.0,
+                                    "content": "guennemann@in.tum.de",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        278,
+                        248,
+                        333,
+                        259
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                276,
+                                246,
+                                336,
+                                262
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        276,
+                                        246,
+                                        336,
+                                        262
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ABSTRACT",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        143,
+                        271,
+                        468,
+                        424
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                142,
+                                271,
+                                470,
+                                283
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        271,
+                                        470,
+                                        283
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Source code (Context) and its parsed abstract syntax tree (AST; Structure) are",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                281,
+                                469,
+                                294
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        281,
+                                        469,
+                                        294
+                                    ],
+                                    "score": 1.0,
+                                    "content": "two complementary representations of the same computer program. Tradition-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                293,
+                                469,
+                                305
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        293,
+                                        469,
+                                        305
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ally, designers of machine learning models have relied predominantly either on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                303,
+                                469,
+                                316
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        303,
+                                        469,
+                                        316
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Structure or Context. We propose a new model, which jointly learns on Context",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                315,
+                                470,
+                                327
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        315,
+                                        470,
+                                        327
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and Structure of source code. In contrast to previous approaches, our model uses",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                325,
+                                470,
+                                339
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        325,
+                                        470,
+                                        339
+                                    ],
+                                    "score": 1.0,
+                                    "content": "only language-agnostic features, i.e., source code and features that can be com-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                337,
+                                470,
+                                349
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        337,
+                                        470,
+                                        349
+                                    ],
+                                    "score": 1.0,
+                                    "content": "puted directly from the AST. Besides obtaining state-of-the-art on monolingual",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                348,
+                                470,
+                                360
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        348,
+                                        470,
+                                        360
+                                    ],
+                                    "score": 1.0,
+                                    "content": "code summarization on all five programming languages considered in this work,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                359,
+                                469,
+                                371
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        359,
+                                        469,
+                                        371
+                                    ],
+                                    "score": 1.0,
+                                    "content": "we propose the first multilingual code summarization model. We show that jointly",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                370,
+                                469,
+                                382
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        370,
+                                        469,
+                                        382
+                                    ],
+                                    "score": 1.0,
+                                    "content": "training on non-parallel data from multiple programming languages improves re-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                380,
+                                470,
+                                393
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        380,
+                                        470,
+                                        393
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sults on all individual languages, where the strongest gains are on low-resource",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                392,
+                                470,
+                                404
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        392,
+                                        470,
+                                        404
+                                    ],
+                                    "score": 1.0,
+                                    "content": "languages. Remarkably, multilingual training only from Context does not lead",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                402,
+                                470,
+                                415
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        402,
+                                        470,
+                                        415
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to the same improvements, highlighting the benefits of combining Structure and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                414,
+                                321,
+                                426
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        414,
+                                        321,
+                                        426
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Context for representation learning on code.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 21.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        443,
+                        206,
+                        456
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                441,
+                                208,
+                                459
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        441,
+                                        208,
+                                        459
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1 INTRODUCTION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 29
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        467,
+                        505,
+                        556
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                468,
+                                505,
+                                480
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        468,
+                                        505,
+                                        480
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Machine learning for code is an active and growing area of research which aims at building models",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                479,
+                                505,
+                                491
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        479,
+                                        505,
+                                        491
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that can learn semantically meaningful representations of programs. These embeddings can be used",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                489,
+                                505,
+                                502
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        489,
+                                        505,
+                                        502
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on downstream tasks, such as code generation, bug detection, or code summarization. We focus",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                500,
+                                506,
+                                514
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        500,
+                                        506,
+                                        514
+                                    ],
+                                    "score": 1.0,
+                                    "content": "our work on two complementary data representations of programs: the source code (referred to as",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                512,
+                                505,
+                                524
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        512,
+                                        505,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Context in this work), and the abstract syntax tree (AST; referred to as Structure). Traditionally,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                523,
+                                505,
+                                535
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        523,
+                                        505,
+                                        535
+                                    ],
+                                    "score": 1.0,
+                                    "content": "researchers and practitioners have decided to predominantly leverage either Structure or Context in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                533,
+                                505,
+                                546
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        533,
+                                        505,
+                                        546
+                                    ],
+                                    "score": 1.0,
+                                    "content": "their machine learning models. In this work, we show that jointly learning on Context and Structure",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                544,
+                                352,
+                                557
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        544,
+                                        352,
+                                        557
+                                    ],
+                                    "score": 1.0,
+                                    "content": "improves representation learning on source code (see Fig. 1).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 33.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        561,
+                        505,
+                        660
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                561,
+                                505,
+                                574
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        561,
+                                        505,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The source code representation naturally lends itself to models from natural language process-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                572,
+                                506,
+                                585
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        572,
+                                        506,
+                                        585
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ing (NLP), e.g., long short-term memory networks (Hochreiter & Schmidhuber, 1997) (LSTM) or",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                582,
+                                505,
+                                596
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        582,
+                                        505,
+                                        596
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Transformers (Vaswani et al., 2017; Radford et al., 2019; Dai et al., 2019; Yang et al., 2019; Shaw",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                594,
+                                506,
+                                607
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        594,
+                                        506,
+                                        607
+                                    ],
+                                    "score": 1.0,
+                                    "content": "et al., 2018). On the other hand, models leveraging the structure representations are typically based",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                604,
+                                506,
+                                618
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        604,
+                                        506,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on graph neural networks (GNNs) (Kipf & Welling, 2017; Xu et al., 2019; Velickovi ˇ c et al., 2018; ´",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                616,
+                                505,
+                                629
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        616,
+                                        505,
+                                        629
+                                    ],
+                                    "score": 1.0,
+                                    "content": "You et al., 2019; Hamilton et al., 2017; Li et al., 2015; Klicpera et al., 2020). While the AST repre-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                627,
+                                505,
+                                639
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        627,
+                                        505,
+                                        639
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sentation makes the highly structured nature of source code explicit to the models, since most GNNs",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                638,
+                                505,
+                                650
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        638,
+                                        505,
+                                        650
+                                    ],
+                                    "score": 1.0,
+                                    "content": "use the message-passing framework, their learned representations are inherently local and struggle",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                649,
+                                250,
+                                662
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        649,
+                                        250,
+                                        662
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to leverage long-range interactions.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        }
+                    ],
+                    "index": 42
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        666,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                665,
+                                505,
+                                678
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        665,
+                                        505,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Recently, Hellendoorn et al. (2020) have explored models that can leverage several representations,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                676,
+                                506,
+                                690
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        676,
+                                        506,
+                                        690
+                                    ],
+                                    "score": 1.0,
+                                    "content": "including both Structure and Context. Their Graph Relational Embedding Attention Transformer",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                687,
+                                505,
+                                700
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        687,
+                                        505,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(GREAT) extends Shaw et al. (2018), which biases the self-attention computation in a localized",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                699,
+                                506,
+                                711
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        699,
+                                        506,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "way given the underlying graph. The language-specific representations used by GREAT include a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                709,
+                                506,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        709,
+                                        506,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "combination of the data flow graph, control flow graph, syntactic edges (inspired by Allamanis et al.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 51
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                720,
+                                459,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        720,
+                                        459,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(2018)), etc. which require specialized pipelines and static analysis tools to be obtained.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 52
+                        }
+                    ],
+                    "index": 49.5
+                }
+            ],
+            "page_idx": 0,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        292,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                25,
+                                293,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        25,
+                                        293,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        303,
+                        751,
+                        308,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                302,
+                                751,
+                                308,
+                                761
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        302,
+                                        751,
+                                        308,
+                                        761
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        79,
+                        504,
+                        116
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                77,
+                                505,
+                                98
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        77,
+                                        505,
+                                        98
+                                    ],
+                                    "score": 1.0,
+                                    "content": "LANGUAGE-AGNOSTIC REPRESENTATION LEARNING",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                98,
+                                495,
+                                118
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        98,
+                                        495,
+                                        118
+                                    ],
+                                    "score": 1.0,
+                                    "content": "OF SOURCE CODE FROM STRUCTURE AND CONTEXT",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        113,
+                        135,
+                        285,
+                        169
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                112,
+                                136,
+                                259,
+                                147
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        112,
+                                        136,
+                                        259,
+                                        147
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Daniel Zugner, Tobias Kirschstein ¨",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                112,
+                                146,
+                                242,
+                                158
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        112,
+                                        146,
+                                        242,
+                                        158
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Technical University of Munich",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                113,
+                                157,
+                                286,
+                                170
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        157,
+                                        286,
+                                        170
+                                    ],
+                                    "score": 1.0,
+                                    "content": "{zuegnerd,kirschto}@in.tum.de",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 4,
+                    "bbox_fs": [
+                        112,
+                        136,
+                        286,
+                        170
+                    ]
+                },
+                {
+                    "type": "list",
+                    "bbox": [
+                        365,
+                        135,
+                        498,
+                        168
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                364,
+                                135,
+                                437,
+                                147
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        364,
+                                        135,
+                                        437,
+                                        147
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Michele Catasta",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                364,
+                                145,
+                                446,
+                                158
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        364,
+                                        145,
+                                        446,
+                                        158
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Stanford University",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                364,
+                                158,
+                                498,
+                                168
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        364,
+                                        158,
+                                        498,
+                                        168
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pirroh@cs.stanford.edu",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7,
+                            "is_list_start_line": true
+                        }
+                    ],
+                    "index": 5,
+                    "bbox_fs": [
+                        364,
+                        135,
+                        498,
+                        168
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        113,
+                        186,
+                        234,
+                        218
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                111,
+                                185,
+                                176,
+                                197
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        185,
+                                        176,
+                                        197
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Jure Leskovec",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                111,
+                                195,
+                                194,
+                                209
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        195,
+                                        194,
+                                        209
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Stanford University",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                113,
+                                208,
+                                234,
+                                219
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        208,
+                                        234,
+                                        219
+                                    ],
+                                    "score": 1.0,
+                                    "content": "jure@cs.stanford.edu",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "index": 10,
+                    "bbox_fs": [
+                        111,
+                        185,
+                        234,
+                        219
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        365,
+                        186,
+                        494,
+                        218
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                365,
+                                186,
+                                458,
+                                197
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        365,
+                                        186,
+                                        458,
+                                        197
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Stephan Gunnemann ¨",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                364,
+                                197,
+                                494,
+                                208
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        364,
+                                        197,
+                                        494,
+                                        208
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Technical University of Munich",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                364,
+                                208,
+                                486,
+                                219
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        364,
+                                        208,
+                                        486,
+                                        219
+                                    ],
+                                    "score": 1.0,
+                                    "content": "guennemann@in.tum.de",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 11,
+                    "bbox_fs": [
+                        364,
+                        186,
+                        494,
+                        219
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        278,
+                        248,
+                        333,
+                        259
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                276,
+                                246,
+                                336,
+                                262
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        276,
+                                        246,
+                                        336,
+                                        262
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ABSTRACT",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        143,
+                        271,
+                        468,
+                        424
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                142,
+                                271,
+                                470,
+                                283
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        271,
+                                        470,
+                                        283
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Source code (Context) and its parsed abstract syntax tree (AST; Structure) are",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                281,
+                                469,
+                                294
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        281,
+                                        469,
+                                        294
+                                    ],
+                                    "score": 1.0,
+                                    "content": "two complementary representations of the same computer program. Tradition-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                293,
+                                469,
+                                305
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        293,
+                                        469,
+                                        305
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ally, designers of machine learning models have relied predominantly either on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                303,
+                                469,
+                                316
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        303,
+                                        469,
+                                        316
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Structure or Context. We propose a new model, which jointly learns on Context",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                315,
+                                470,
+                                327
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        315,
+                                        470,
+                                        327
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and Structure of source code. In contrast to previous approaches, our model uses",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                325,
+                                470,
+                                339
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        325,
+                                        470,
+                                        339
+                                    ],
+                                    "score": 1.0,
+                                    "content": "only language-agnostic features, i.e., source code and features that can be com-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                337,
+                                470,
+                                349
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        337,
+                                        470,
+                                        349
+                                    ],
+                                    "score": 1.0,
+                                    "content": "puted directly from the AST. Besides obtaining state-of-the-art on monolingual",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                348,
+                                470,
+                                360
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        348,
+                                        470,
+                                        360
+                                    ],
+                                    "score": 1.0,
+                                    "content": "code summarization on all five programming languages considered in this work,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                359,
+                                469,
+                                371
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        359,
+                                        469,
+                                        371
+                                    ],
+                                    "score": 1.0,
+                                    "content": "we propose the first multilingual code summarization model. We show that jointly",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                370,
+                                469,
+                                382
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        370,
+                                        469,
+                                        382
+                                    ],
+                                    "score": 1.0,
+                                    "content": "training on non-parallel data from multiple programming languages improves re-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                380,
+                                470,
+                                393
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        380,
+                                        470,
+                                        393
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sults on all individual languages, where the strongest gains are on low-resource",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                392,
+                                470,
+                                404
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        392,
+                                        470,
+                                        404
+                                    ],
+                                    "score": 1.0,
+                                    "content": "languages. Remarkably, multilingual training only from Context does not lead",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                402,
+                                470,
+                                415
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        402,
+                                        470,
+                                        415
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to the same improvements, highlighting the benefits of combining Structure and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                414,
+                                321,
+                                426
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        414,
+                                        321,
+                                        426
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Context for representation learning on code.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 21.5,
+                    "bbox_fs": [
+                        141,
+                        271,
+                        470,
+                        426
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        443,
+                        206,
+                        456
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                441,
+                                208,
+                                459
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        441,
+                                        208,
+                                        459
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1 INTRODUCTION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 29
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        467,
+                        505,
+                        556
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                468,
+                                505,
+                                480
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        468,
+                                        505,
+                                        480
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Machine learning for code is an active and growing area of research which aims at building models",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                479,
+                                505,
+                                491
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        479,
+                                        505,
+                                        491
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that can learn semantically meaningful representations of programs. These embeddings can be used",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                489,
+                                505,
+                                502
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        489,
+                                        505,
+                                        502
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on downstream tasks, such as code generation, bug detection, or code summarization. We focus",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                500,
+                                506,
+                                514
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        500,
+                                        506,
+                                        514
+                                    ],
+                                    "score": 1.0,
+                                    "content": "our work on two complementary data representations of programs: the source code (referred to as",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                512,
+                                505,
+                                524
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        512,
+                                        505,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Context in this work), and the abstract syntax tree (AST; referred to as Structure). Traditionally,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                523,
+                                505,
+                                535
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        523,
+                                        505,
+                                        535
+                                    ],
+                                    "score": 1.0,
+                                    "content": "researchers and practitioners have decided to predominantly leverage either Structure or Context in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                533,
+                                505,
+                                546
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        533,
+                                        505,
+                                        546
+                                    ],
+                                    "score": 1.0,
+                                    "content": "their machine learning models. In this work, we show that jointly learning on Context and Structure",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                544,
+                                352,
+                                557
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        544,
+                                        352,
+                                        557
+                                    ],
+                                    "score": 1.0,
+                                    "content": "improves representation learning on source code (see Fig. 1).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 33.5,
+                    "bbox_fs": [
+                        105,
+                        468,
+                        506,
+                        557
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        561,
+                        505,
+                        660
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                561,
+                                505,
+                                574
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        561,
+                                        505,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The source code representation naturally lends itself to models from natural language process-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                572,
+                                506,
+                                585
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        572,
+                                        506,
+                                        585
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ing (NLP), e.g., long short-term memory networks (Hochreiter & Schmidhuber, 1997) (LSTM) or",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                582,
+                                505,
+                                596
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        582,
+                                        505,
+                                        596
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Transformers (Vaswani et al., 2017; Radford et al., 2019; Dai et al., 2019; Yang et al., 2019; Shaw",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                594,
+                                506,
+                                607
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        594,
+                                        506,
+                                        607
+                                    ],
+                                    "score": 1.0,
+                                    "content": "et al., 2018). On the other hand, models leveraging the structure representations are typically based",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                604,
+                                506,
+                                618
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        604,
+                                        506,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on graph neural networks (GNNs) (Kipf & Welling, 2017; Xu et al., 2019; Velickovi ˇ c et al., 2018; ´",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                616,
+                                505,
+                                629
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        616,
+                                        505,
+                                        629
+                                    ],
+                                    "score": 1.0,
+                                    "content": "You et al., 2019; Hamilton et al., 2017; Li et al., 2015; Klicpera et al., 2020). While the AST repre-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                627,
+                                505,
+                                639
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        627,
+                                        505,
+                                        639
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sentation makes the highly structured nature of source code explicit to the models, since most GNNs",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                638,
+                                505,
+                                650
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        638,
+                                        505,
+                                        650
+                                    ],
+                                    "score": 1.0,
+                                    "content": "use the message-passing framework, their learned representations are inherently local and struggle",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                649,
+                                250,
+                                662
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        649,
+                                        250,
+                                        662
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to leverage long-range interactions.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        }
+                    ],
+                    "index": 42,
+                    "bbox_fs": [
+                        104,
+                        561,
+                        506,
+                        662
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        666,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                665,
+                                505,
+                                678
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        665,
+                                        505,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Recently, Hellendoorn et al. (2020) have explored models that can leverage several representations,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                676,
+                                506,
+                                690
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        676,
+                                        506,
+                                        690
+                                    ],
+                                    "score": 1.0,
+                                    "content": "including both Structure and Context. Their Graph Relational Embedding Attention Transformer",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                687,
+                                505,
+                                700
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        687,
+                                        505,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(GREAT) extends Shaw et al. (2018), which biases the self-attention computation in a localized",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                699,
+                                506,
+                                711
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        699,
+                                        506,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "way given the underlying graph. The language-specific representations used by GREAT include a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                709,
+                                506,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        709,
+                                        506,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "combination of the data flow graph, control flow graph, syntactic edges (inspired by Allamanis et al.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 51
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                720,
+                                459,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        720,
+                                        459,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(2018)), etc. which require specialized pipelines and static analysis tools to be obtained.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 52
+                        }
+                    ],
+                    "index": 49.5,
+                    "bbox_fs": [
+                        105,
+                        665,
+                        506,
+                        732
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "image",
+                    "bbox": [
+                        166,
+                        80,
+                        446,
+                        186
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                166,
+                                80,
+                                446,
+                                186
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        166,
+                                        80,
+                                        446,
+                                        186
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                166,
+                                                80,
+                                                446,
+                                                186
+                                            ],
+                                            "score": 0.923,
+                                            "type": "image",
+                                            "image_path": "7701ebd563c4ccbab0fb3932736f0a3f5ce8408d760ee36d22e78173cbc12d18.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        166,
+                                        80,
+                                        446,
+                                        115.33333333333334
+                                    ],
+                                    "spans": [],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        166,
+                                        115.33333333333334,
+                                        446,
+                                        150.66666666666669
+                                    ],
+                                    "spans": [],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        166,
+                                        150.66666666666669,
+                                        446,
+                                        186.00000000000003
+                                    ],
+                                    "spans": [],
+                                    "index": 2
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                106,
+                                195,
+                                506,
+                                262
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        196,
+                                        505,
+                                        208
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                196,
+                                                505,
+                                                208
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 1: Context and Structure both encapsulate valuable information about source code. In this",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        207,
+                                        505,
+                                        220
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                207,
+                                                505,
+                                                220
+                                            ],
+                                            "score": 1.0,
+                                            "content": "realistic example, token 1 and 4 are distant in the sequence of tokens (Context), but only 5 hops",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        218,
+                                        505,
+                                        230
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                218,
+                                                505,
+                                                230
+                                            ],
+                                            "score": 1.0,
+                                            "content": "away when traversing the Abstract Syntax Tree (Structure). As such, a method that relies only",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 5
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        229,
+                                        505,
+                                        242
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                229,
+                                                505,
+                                                242
+                                            ],
+                                            "score": 1.0,
+                                            "content": "on the sequence of tokens could neglect the relationship between a method name and its return",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 6
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        240,
+                                        505,
+                                        252
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                240,
+                                                505,
+                                                252
+                                            ],
+                                            "score": 1.0,
+                                            "content": "variable. Conversely, token 1 and 2 showcase the opposite setting. Hence, unifying Structure and",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 7
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        251,
+                                        363,
+                                        263
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                251,
+                                                363,
+                                                263
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Context leads to a more powerful representation of source code.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 8
+                                }
+                            ],
+                            "index": 5.5
+                        }
+                    ],
+                    "index": 3.25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        284,
+                        505,
+                        361
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                283,
+                                506,
+                                297
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        283,
+                                        506,
+                                        297
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We propose the CODE TRANSFORMER1, which combines distances computed on Structure and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                294,
+                                505,
+                                307
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        294,
+                                        505,
+                                        307
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Context in the self-attention operation. In contrast to the localized treatment via edges described",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                306,
+                                505,
+                                318
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        306,
+                                        505,
+                                        318
+                                    ],
+                                    "score": 1.0,
+                                    "content": "above, we make the full Structure accessible to the model at each layer by computing pairwise",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                317,
+                                505,
+                                330
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        317,
+                                        505,
+                                        330
+                                    ],
+                                    "score": 1.0,
+                                    "content": "distances on the AST, such as shortest path lengths. To this end, we draw inspiration from the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                328,
+                                505,
+                                340
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        328,
+                                        505,
+                                        340
+                                    ],
+                                    "score": 1.0,
+                                    "content": "XLNet architecture (Yang et al., 2019), which uses relative distances instead of absolute positions",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                339,
+                                505,
+                                352
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        339,
+                                        505,
+                                        352
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in the attention computation. Importantly, all our features are language-agnostic2, i.e., can easily be",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                350,
+                                417,
+                                362
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        350,
+                                        417,
+                                        362
+                                    ],
+                                    "score": 1.0,
+                                    "content": "computed for any programming language based on the source code and AST.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        367,
+                        505,
+                        466
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                366,
+                                505,
+                                380
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        366,
+                                        505,
+                                        380
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We use two datasets comprising 5 different programming languages in total, and evaluate the rep-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                378,
+                                506,
+                                390
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        378,
+                                        506,
+                                        390
+                                    ],
+                                    "score": 1.0,
+                                    "content": "resentations learned by our model on the task of code summarization, where the model predicts a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                389,
+                                505,
+                                401
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        389,
+                                        505,
+                                        401
+                                    ],
+                                    "score": 1.0,
+                                    "content": "method’s name based on its body. Besides setting the state-of-the-art on all five languages for single-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                399,
+                                506,
+                                413
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        399,
+                                        506,
+                                        413
+                                    ],
+                                    "score": 1.0,
+                                    "content": "language training, we also train the first multilingual model for code summarization. This is enabled",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                410,
+                                504,
+                                424
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        410,
+                                        504,
+                                        424
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by the fact that our model uses only language-agnostic features that can easily be obtained for any",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                421,
+                                505,
+                                435
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        421,
+                                        505,
+                                        435
+                                    ],
+                                    "score": 1.0,
+                                    "content": "programming language. Remarkably, training our model on multiple programming languages sub-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                433,
+                                504,
+                                444
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        433,
+                                        504,
+                                        444
+                                    ],
+                                    "score": 1.0,
+                                    "content": "stantially improves the performance on all languages. Moreover, multilingual training only from",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                443,
+                                505,
+                                457
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        443,
+                                        505,
+                                        457
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Context does not lead to the same improvements, highlighting the benefits of combining Structure",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                455,
+                                301,
+                                468
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        455,
+                                        301,
+                                        468
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and Context for representation learning on code.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 20
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        482,
+                        208,
+                        495
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                481,
+                                211,
+                                497
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        481,
+                                        211,
+                                        497
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2 RELATED WORK",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        510,
+                        505,
+                        632
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                509,
+                                505,
+                                523
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        509,
+                                        505,
+                                        523
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Machine Learning for Code. Early research learned language models on raw text data, e.g., (Wang",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                521,
+                                504,
+                                535
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        521,
+                                        504,
+                                        535
+                                    ],
+                                    "score": 1.0,
+                                    "content": "et al., 2016; Raychev et al., 2014; Dam et al., 2016), providing evidence for the naturalness assump-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                532,
+                                505,
+                                545
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        532,
+                                        505,
+                                        545
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tion (Hindle et al., 2012). For example, Allamanis et al. (2015) learned distributed representations",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                545,
+                                505,
+                                556
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        545,
+                                        505,
+                                        556
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of variables and methods, finding that they were indeed able to encode common semantic properties",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                554,
+                                505,
+                                567
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        554,
+                                        505,
+                                        567
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from the regularities present in source code. Alon et al. (2019b) also found evidence of semantic",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                567,
+                                505,
+                                578
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        567,
+                                        505,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arithmetic in their embedding space, dubbed code2vec. These representations—and their variants",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                576,
+                                505,
+                                589
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        576,
+                                        505,
+                                        589
+                                    ],
+                                    "score": 1.0,
+                                    "content": "like (Mou et al., 2016)—can then be used to predict sequences of identifier sub-tokens (Allamanis",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                587,
+                                505,
+                                600
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        587,
+                                        505,
+                                        600
+                                    ],
+                                    "score": 1.0,
+                                    "content": "et al., 2015) or API calls (Acharya et al., 2007; Nguyen et al., 2017). They can be used as advanced",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                598,
+                                505,
+                                611
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        598,
+                                        505,
+                                        611
+                                    ],
+                                    "score": 1.0,
+                                    "content": "auto-completion tools (Hindle et al., 2012; Bhoopchand et al., 2016), including for user-provided",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                609,
+                                506,
+                                622
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        609,
+                                        506,
+                                        622
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tokens like Variable Names (Raychev et al., 2014; Allamanis et al., 2014). These are useful for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                621,
+                                389,
+                                633
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        621,
+                                        389,
+                                        633
+                                    ],
+                                    "score": 1.0,
+                                    "content": "deobfuscating Android applications (Bichsel et al., 2016) for example.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 31
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        637,
+                        505,
+                        681
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                637,
+                                504,
+                                649
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        637,
+                                        504,
+                                        649
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Several works leverage structured graphical models for probabilistic models of source code, usually",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                648,
+                                505,
+                                660
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        648,
+                                        505,
+                                        660
+                                    ],
+                                    "score": 1.0,
+                                    "content": "through parse trees (Maddison & Tarlow, 2014; Bielik et al., 2016). Unlike previous works where",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                659,
+                                505,
+                                672
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        659,
+                                        505,
+                                        672
+                                    ],
+                                    "score": 1.0,
+                                    "content": "hand-crafted features were used as node features (Raychev et al., 2014) or as explicit semantic edges",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                671,
+                                505,
+                                682
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        671,
+                                        505,
+                                        682
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(Allamanis et al., 2018), our work does not augment the existing syntactic relationships between the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        }
+                    ],
+                    "index": 38.5
+                }
+            ],
+            "page_idx": 1,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        106,
+                        690,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                119,
+                                689,
+                                488,
+                                703
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        119,
+                                        689,
+                                        488,
+                                        703
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1Code at www.daml.in.tum.de/code-transformer, demo at code-transformer.org.",
+                                    "type": "text"
+                                }
+                            ]
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                698,
+                                506,
+                                716
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        698,
+                                        506,
+                                        716
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2We use the term language-agnostic to highlight that our model does not rely on language-specific features",
+                                    "type": "text"
+                                }
+                            ]
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                711,
+                                505,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        711,
+                                        505,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(e.g., program analysis edges), thus facilitating multi-language training, as it is possible to generate unified",
+                                    "type": "text"
+                                }
+                            ]
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                720,
+                                320,
+                                734
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        720,
+                                        320,
+                                        734
+                                    ],
+                                    "score": 1.0,
+                                    "content": "AST representations for different programming languages.",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        292,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                293,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        293,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        752,
+                        308,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                302,
+                                750,
+                                310,
+                                763
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        302,
+                                        750,
+                                        310,
+                                        763
+                                    ],
+                                    "score": 1.0,
+                                    "content": "",
+                                    "type": "text",
+                                    "height": 13,
+                                    "width": 8
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "image",
+                    "bbox": [
+                        166,
+                        80,
+                        446,
+                        186
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                166,
+                                80,
+                                446,
+                                186
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        166,
+                                        80,
+                                        446,
+                                        186
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                166,
+                                                80,
+                                                446,
+                                                186
+                                            ],
+                                            "score": 0.923,
+                                            "type": "image",
+                                            "image_path": "7701ebd563c4ccbab0fb3932736f0a3f5ce8408d760ee36d22e78173cbc12d18.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        166,
+                                        80,
+                                        446,
+                                        115.33333333333334
+                                    ],
+                                    "spans": [],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        166,
+                                        115.33333333333334,
+                                        446,
+                                        150.66666666666669
+                                    ],
+                                    "spans": [],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        166,
+                                        150.66666666666669,
+                                        446,
+                                        186.00000000000003
+                                    ],
+                                    "spans": [],
+                                    "index": 2
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                106,
+                                195,
+                                506,
+                                262
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        196,
+                                        505,
+                                        208
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                196,
+                                                505,
+                                                208
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 1: Context and Structure both encapsulate valuable information about source code. In this",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        207,
+                                        505,
+                                        220
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                207,
+                                                505,
+                                                220
+                                            ],
+                                            "score": 1.0,
+                                            "content": "realistic example, token 1 and 4 are distant in the sequence of tokens (Context), but only 5 hops",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        218,
+                                        505,
+                                        230
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                218,
+                                                505,
+                                                230
+                                            ],
+                                            "score": 1.0,
+                                            "content": "away when traversing the Abstract Syntax Tree (Structure). As such, a method that relies only",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 5
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        229,
+                                        505,
+                                        242
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                229,
+                                                505,
+                                                242
+                                            ],
+                                            "score": 1.0,
+                                            "content": "on the sequence of tokens could neglect the relationship between a method name and its return",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 6
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        240,
+                                        505,
+                                        252
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                240,
+                                                505,
+                                                252
+                                            ],
+                                            "score": 1.0,
+                                            "content": "variable. Conversely, token 1 and 2 showcase the opposite setting. Hence, unifying Structure and",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 7
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        251,
+                                        363,
+                                        263
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                251,
+                                                363,
+                                                263
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Context leads to a more powerful representation of source code.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 8
+                                }
+                            ],
+                            "index": 5.5
+                        }
+                    ],
+                    "index": 3.25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        284,
+                        505,
+                        361
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                283,
+                                506,
+                                297
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        283,
+                                        506,
+                                        297
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We propose the CODE TRANSFORMER1, which combines distances computed on Structure and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                294,
+                                505,
+                                307
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        294,
+                                        505,
+                                        307
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Context in the self-attention operation. In contrast to the localized treatment via edges described",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                306,
+                                505,
+                                318
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        306,
+                                        505,
+                                        318
+                                    ],
+                                    "score": 1.0,
+                                    "content": "above, we make the full Structure accessible to the model at each layer by computing pairwise",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                317,
+                                505,
+                                330
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        317,
+                                        505,
+                                        330
+                                    ],
+                                    "score": 1.0,
+                                    "content": "distances on the AST, such as shortest path lengths. To this end, we draw inspiration from the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                328,
+                                505,
+                                340
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        328,
+                                        505,
+                                        340
+                                    ],
+                                    "score": 1.0,
+                                    "content": "XLNet architecture (Yang et al., 2019), which uses relative distances instead of absolute positions",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                339,
+                                505,
+                                352
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        339,
+                                        505,
+                                        352
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in the attention computation. Importantly, all our features are language-agnostic2, i.e., can easily be",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                350,
+                                417,
+                                362
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        350,
+                                        417,
+                                        362
+                                    ],
+                                    "score": 1.0,
+                                    "content": "computed for any programming language based on the source code and AST.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 12,
+                    "bbox_fs": [
+                        105,
+                        283,
+                        506,
+                        362
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        367,
+                        505,
+                        466
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                366,
+                                505,
+                                380
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        366,
+                                        505,
+                                        380
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We use two datasets comprising 5 different programming languages in total, and evaluate the rep-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                378,
+                                506,
+                                390
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        378,
+                                        506,
+                                        390
+                                    ],
+                                    "score": 1.0,
+                                    "content": "resentations learned by our model on the task of code summarization, where the model predicts a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                389,
+                                505,
+                                401
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        389,
+                                        505,
+                                        401
+                                    ],
+                                    "score": 1.0,
+                                    "content": "method’s name based on its body. Besides setting the state-of-the-art on all five languages for single-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                399,
+                                506,
+                                413
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        399,
+                                        506,
+                                        413
+                                    ],
+                                    "score": 1.0,
+                                    "content": "language training, we also train the first multilingual model for code summarization. This is enabled",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                410,
+                                504,
+                                424
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        410,
+                                        504,
+                                        424
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by the fact that our model uses only language-agnostic features that can easily be obtained for any",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                421,
+                                505,
+                                435
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        421,
+                                        505,
+                                        435
+                                    ],
+                                    "score": 1.0,
+                                    "content": "programming language. Remarkably, training our model on multiple programming languages sub-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                433,
+                                504,
+                                444
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        433,
+                                        504,
+                                        444
+                                    ],
+                                    "score": 1.0,
+                                    "content": "stantially improves the performance on all languages. Moreover, multilingual training only from",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                443,
+                                505,
+                                457
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        443,
+                                        505,
+                                        457
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Context does not lead to the same improvements, highlighting the benefits of combining Structure",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                455,
+                                301,
+                                468
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        455,
+                                        301,
+                                        468
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and Context for representation learning on code.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 20,
+                    "bbox_fs": [
+                        105,
+                        366,
+                        506,
+                        468
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        482,
+                        208,
+                        495
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                481,
+                                211,
+                                497
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        481,
+                                        211,
+                                        497
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2 RELATED WORK",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        510,
+                        505,
+                        632
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                509,
+                                505,
+                                523
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        509,
+                                        505,
+                                        523
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Machine Learning for Code. Early research learned language models on raw text data, e.g., (Wang",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                521,
+                                504,
+                                535
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        521,
+                                        504,
+                                        535
+                                    ],
+                                    "score": 1.0,
+                                    "content": "et al., 2016; Raychev et al., 2014; Dam et al., 2016), providing evidence for the naturalness assump-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                532,
+                                505,
+                                545
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        532,
+                                        505,
+                                        545
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tion (Hindle et al., 2012). For example, Allamanis et al. (2015) learned distributed representations",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                545,
+                                505,
+                                556
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        545,
+                                        505,
+                                        556
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of variables and methods, finding that they were indeed able to encode common semantic properties",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                554,
+                                505,
+                                567
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        554,
+                                        505,
+                                        567
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from the regularities present in source code. Alon et al. (2019b) also found evidence of semantic",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                567,
+                                505,
+                                578
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        567,
+                                        505,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arithmetic in their embedding space, dubbed code2vec. These representations—and their variants",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                576,
+                                505,
+                                589
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        576,
+                                        505,
+                                        589
+                                    ],
+                                    "score": 1.0,
+                                    "content": "like (Mou et al., 2016)—can then be used to predict sequences of identifier sub-tokens (Allamanis",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                587,
+                                505,
+                                600
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        587,
+                                        505,
+                                        600
+                                    ],
+                                    "score": 1.0,
+                                    "content": "et al., 2015) or API calls (Acharya et al., 2007; Nguyen et al., 2017). They can be used as advanced",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                598,
+                                505,
+                                611
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        598,
+                                        505,
+                                        611
+                                    ],
+                                    "score": 1.0,
+                                    "content": "auto-completion tools (Hindle et al., 2012; Bhoopchand et al., 2016), including for user-provided",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                609,
+                                506,
+                                622
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        609,
+                                        506,
+                                        622
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tokens like Variable Names (Raychev et al., 2014; Allamanis et al., 2014). These are useful for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                621,
+                                389,
+                                633
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        621,
+                                        389,
+                                        633
+                                    ],
+                                    "score": 1.0,
+                                    "content": "deobfuscating Android applications (Bichsel et al., 2016) for example.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 31,
+                    "bbox_fs": [
+                        105,
+                        509,
+                        506,
+                        633
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        637,
+                        505,
+                        681
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                637,
+                                504,
+                                649
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        637,
+                                        504,
+                                        649
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Several works leverage structured graphical models for probabilistic models of source code, usually",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                648,
+                                505,
+                                660
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        648,
+                                        505,
+                                        660
+                                    ],
+                                    "score": 1.0,
+                                    "content": "through parse trees (Maddison & Tarlow, 2014; Bielik et al., 2016). Unlike previous works where",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                659,
+                                505,
+                                672
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        659,
+                                        505,
+                                        672
+                                    ],
+                                    "score": 1.0,
+                                    "content": "hand-crafted features were used as node features (Raychev et al., 2014) or as explicit semantic edges",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                671,
+                                505,
+                                682
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        671,
+                                        505,
+                                        682
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(Allamanis et al., 2018), our work does not augment the existing syntactic relationships between the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                82,
+                                504,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        82,
+                                        504,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "different elements to enhance the predictive capabilities of the model. Other approaches (Alon et al.,",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                93,
+                                498,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        93,
+                                        498,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2018; Li et al., 2017) also leverage the AST structure, but linearize the graph by first traversing it.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 38.5,
+                    "bbox_fs": [
+                        105,
+                        637,
+                        505,
+                        682
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        82,
+                        503,
+                        105
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                82,
+                                504,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        82,
+                                        504,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "different elements to enhance the predictive capabilities of the model. Other approaches (Alon et al.,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                93,
+                                498,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        93,
+                                        498,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2018; Li et al., 2017) also leverage the AST structure, but linearize the graph by first traversing it.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        113,
+                        505,
+                        245
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                113,
+                                505,
+                                127
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        113,
+                                        505,
+                                        127
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Learning representations of structured languages. While models of language have dramatically",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                124,
+                                506,
+                                137
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        124,
+                                        506,
+                                        137
+                                    ],
+                                    "score": 1.0,
+                                    "content": "improved in their ability to learn structure (syntax) and semantics from scratch, it can be argued that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                135,
+                                505,
+                                148
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        135,
+                                        505,
+                                        148
+                                    ],
+                                    "score": 1.0,
+                                    "content": "directly providing the model with the underlying structure of the language can help with generaliza-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                145,
+                                505,
+                                160
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        145,
+                                        505,
+                                        160
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tion (Battaglia et al., 2018), managing long-ranging dependencies (Tai et al., 2015), or representing",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                158,
+                                505,
+                                170
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        158,
+                                        505,
+                                        170
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the compositional aspect of natural language (Socher et al., 2013). Notably, tree structures have",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                168,
+                                505,
+                                181
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        168,
+                                        505,
+                                        181
+                                    ],
+                                    "score": 1.0,
+                                    "content": "shown promising results and inspired new architectures (Shen et al., 2019), including in the domain",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                180,
+                                505,
+                                192
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        180,
+                                        505,
+                                        192
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of source code (Fernandes et al., 2019), where the underlying syntax is directly available. Our work",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                190,
+                                506,
+                                204
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        190,
+                                        506,
+                                        204
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pursues this line of research, showing the benefits of explicitly integrating structural information as",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                200,
+                                506,
+                                214
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        200,
+                                        506,
+                                        214
+                                    ],
+                                    "score": 1.0,
+                                    "content": "an inductive bias. Shiv & Quirk (2019) propose positional encodings for nodes on trees; however,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                211,
+                                505,
+                                225
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        211,
+                                        505,
+                                        225
+                                    ],
+                                    "score": 1.0,
+                                    "content": "their approach assumes regular trees, which is an unrealistic assumption when working with Ab-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                223,
+                                506,
+                                236
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        223,
+                                        506,
+                                        236
+                                    ],
+                                    "score": 1.0,
+                                    "content": "stract Syntax Trees, as an AST node can have arbitrarily many children, e.g., the arguments of a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                233,
+                                145,
+                                246
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        233,
+                                        145,
+                                        246
+                                    ],
+                                    "score": 1.0,
+                                    "content": "function.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 7.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        253,
+                        505,
+                        353
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                254,
+                                505,
+                                266
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        254,
+                                        505,
+                                        266
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Graph Neural Networks. GNNs provide a powerful tool for machine learning on graphs, thanks to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                265,
+                                505,
+                                277
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        265,
+                                        505,
+                                        277
+                                    ],
+                                    "score": 1.0,
+                                    "content": "their ability to recursively incorporate information from neighboring nodes in the network (Battaglia",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                275,
+                                505,
+                                288
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        275,
+                                        505,
+                                        288
+                                    ],
+                                    "score": 1.0,
+                                    "content": "et al., 2018), naturally capturing the graph structure simultaneously with the nodes’ features. (Gori",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                286,
+                                506,
+                                299
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        286,
+                                        506,
+                                        299
+                                    ],
+                                    "score": 1.0,
+                                    "content": "et al., 2005; Scarselli et al., 2008) are able to learn vector representations of nodes and graphs in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                297,
+                                506,
+                                311
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        297,
+                                        506,
+                                        311
+                                    ],
+                                    "score": 1.0,
+                                    "content": "an end-to-end fashion, encoding structural and feature information in the embedding space. Under",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                307,
+                                506,
+                                321
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        307,
+                                        506,
+                                        321
+                                    ],
+                                    "score": 1.0,
+                                    "content": "this model, GNNs have achieved state-of-the-art performance across a variety of tasks, such as node",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                320,
+                                505,
+                                331
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        320,
+                                        505,
+                                        331
+                                    ],
+                                    "score": 1.0,
+                                    "content": "classification (Kipf & Welling, 2017; Hamilton et al., 2017; Klicpera et al., 2019a), link prediction",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                329,
+                                506,
+                                344
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        329,
+                                        506,
+                                        344
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(Zhang & Chen, 2018; Schlichtkrull et al., 2018), graph clustering (Defferrard et al., 2016; Ying",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                341,
+                                484,
+                                354
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        341,
+                                        484,
+                                        354
+                                    ],
+                                    "score": 1.0,
+                                    "content": "et al., 2018) or graph classification (Ying et al., 2018; Dai et al., 2016; Duvenaud et al., 2015).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        104,
+                        368,
+                        493,
+                        382
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                367,
+                                495,
+                                383
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        367,
+                                        495,
+                                        383
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3 INTEGRATING STRUCTURE AND CONTEXT IN THE CODE TRANSFORMER",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 23
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        392,
+                        504,
+                        416
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                392,
+                                505,
+                                406
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        392,
+                                        505,
+                                        406
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Self-attention is the core operation powering the Transformer. It enables the model to selectively",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                405,
+                                491,
+                                416
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        405,
+                                        491,
+                                        416
+                                    ],
+                                    "score": 1.0,
+                                    "content": "focus on relevant parts of the input. The matrix form equation for attention with a single head is",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 24.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        209,
+                        419,
+                        400,
+                        447
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                209,
+                                419,
+                                400,
+                                447
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        209,
+                                        419,
+                                        400,
+                                        447
+                                    ],
+                                    "score": 0.94,
+                                    "content": "{ \\mathrm { A t t e n t i o n } } ( Q , K , V ) = { \\mathrm { s o f t m a x } } \\left( { \\frac { Q K ^ { T } } { \\sqrt { d _ { k } } } } \\right) V ,",
+                                    "type": "interline_equation",
+                                    "image_path": "bf5062f76acf55f459a4ae89adb1abed3d6a40f640c4bd316cd5ed6cd5cde38d.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 26.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                209,
+                                419,
+                                400,
+                                433.0
+                            ],
+                            "spans": [],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                209,
+                                433.0,
+                                400,
+                                447.0
+                            ],
+                            "spans": [],
+                            "index": 27
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        450,
+                        505,
+                        484
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                448,
+                                505,
+                                464
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        448,
+                                        134,
+                                        464
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        134,
+                                        450,
+                                        201,
+                                        462
+                                    ],
+                                    "score": 0.91,
+                                    "content": "Q , K \\in \\mathbb { R } ^ { N \\times d _ { k } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        201,
+                                        448,
+                                        219,
+                                        464
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        220,
+                                        450,
+                                        272,
+                                        461
+                                    ],
+                                    "score": 0.9,
+                                    "content": "V \\in \\mathbb { R } ^ { N \\times d _ { v } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        272,
+                                        448,
+                                        278,
+                                        464
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        278,
+                                        451,
+                                        289,
+                                        461
+                                    ],
+                                    "score": 0.76,
+                                    "content": "N",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        448,
+                                        413,
+                                        464
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the number of input tokens,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        414,
+                                        451,
+                                        425,
+                                        462
+                                    ],
+                                    "score": 0.89,
+                                    "content": "d _ { k }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        425,
+                                        448,
+                                        505,
+                                        464
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the key dimension,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                461,
+                                505,
+                                475
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        461,
+                                        123,
+                                        475
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        124,
+                                        462,
+                                        135,
+                                        473
+                                    ],
+                                    "score": 0.88,
+                                    "content": "d _ { v }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        135,
+                                        461,
+                                        296,
+                                        475
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the value dimension (typically we have",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        462,
+                                        332,
+                                        473
+                                    ],
+                                    "score": 0.92,
+                                    "content": "d _ { k } = d _ { v }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        332,
+                                        461,
+                                        456,
+                                        475
+                                    ],
+                                    "score": 1.0,
+                                    "content": "). The attention score of query",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        457,
+                                        462,
+                                        470,
+                                        474
+                                    ],
+                                    "score": 0.89,
+                                    "content": "Q _ { i }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        470,
+                                        461,
+                                        505,
+                                        475
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and key",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                473,
+                                195,
+                                486
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        473,
+                                        121,
+                                        486
+                                    ],
+                                    "score": 0.89,
+                                    "content": "K _ { j }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        122,
+                                        473,
+                                        195,
+                                        485
+                                    ],
+                                    "score": 1.0,
+                                    "content": "before softmax is",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 29
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        236,
+                        483,
+                        374,
+                        500
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                236,
+                                483,
+                                374,
+                                500
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        236,
+                                        483,
+                                        374,
+                                        500
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\pmb { A } _ { i j } = \\pmb { Q } _ { i } ^ { T } \\pmb { K } _ { j } = \\pmb { E } _ { i } ^ { T } \\pmb { W } _ { q } ^ { T } \\pmb { W } _ { k } \\pmb { E } _ { j } ,",
+                                    "type": "interline_equation",
+                                    "image_path": "a084e175bb3c6930841d0180a4202d6eff0f84ecb6a8a9cc250c5cd2833a474e.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 31,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                236,
+                                483,
+                                374,
+                                500
+                            ],
+                            "spans": [],
+                            "index": 31
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        502,
+                        504,
+                        524
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                498,
+                                507,
+                                516
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        498,
+                                        133,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        134,
+                                        501,
+                                        186,
+                                        514
+                                    ],
+                                    "score": 0.93,
+                                    "content": "E _ { i } , E _ { j } \\in \\mathbb { R } ^ { d }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        187,
+                                        498,
+                                        216,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "are the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        217,
+                                        502,
+                                        223,
+                                        512
+                                    ],
+                                    "score": 0.82,
+                                    "content": "d",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        223,
+                                        498,
+                                        365,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-dimensional embeddings of tokens",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        365,
+                                        503,
+                                        370,
+                                        512
+                                    ],
+                                    "score": 0.79,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        370,
+                                        498,
+                                        387,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        388,
+                                        502,
+                                        393,
+                                        514
+                                    ],
+                                    "score": 0.78,
+                                    "content": "j",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        394,
+                                        498,
+                                        414,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        414,
+                                        502,
+                                        430,
+                                        514
+                                    ],
+                                    "score": 0.63,
+                                    "content": "W _ { q }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        430,
+                                        498,
+                                        433,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        433,
+                                        501,
+                                        489,
+                                        514
+                                    ],
+                                    "score": 0.61,
+                                    "content": "W _ { k } \\in \\mathbb { R } ^ { d _ { k } \\times d }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        489,
+                                        498,
+                                        507,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "are",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                513,
+                                313,
+                                525
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        513,
+                                        313,
+                                        525
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the query and key projection matrices, respectively.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 32.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        529,
+                        505,
+                        585
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                530,
+                                505,
+                                542
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        530,
+                                        505,
+                                        542
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Observe that Eq. (2) contains no assumption about potential structure in the input domain: in the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                539,
+                                505,
+                                554
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        539,
+                                        505,
+                                        554
+                                    ],
+                                    "score": 1.0,
+                                    "content": "attention operation we compute all dot products of query and key vectors equally, effectively viewing",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                552,
+                                505,
+                                564
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        552,
+                                        505,
+                                        564
+                                    ],
+                                    "score": 1.0,
+                                    "content": "them as unordered sets of vectors. This means, however, that the model is oblivious to structured",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                562,
+                                506,
+                                576
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        562,
+                                        506,
+                                        576
+                                    ],
+                                    "score": 1.0,
+                                    "content": "inputs (such as text or graphs) and therefore is unable to distinguish, for example, a variable name",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                574,
+                                371,
+                                586
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        574,
+                                        371,
+                                        586
+                                    ],
+                                    "score": 1.0,
+                                    "content": "occurring as an argument and in the return statement of a method.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        }
+                    ],
+                    "index": 36
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        590,
+                        505,
+                        635
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                589,
+                                505,
+                                604
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        589,
+                                        505,
+                                        604
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In NLP, it is common to bias Transformers towards sequential inputs by adding positional encodings",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                601,
+                                505,
+                                614
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        601,
+                                        505,
+                                        614
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to the token embeddings. These positional encodings are obtained by applying an encoding function",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                612,
+                                505,
+                                625
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        612,
+                                        156,
+                                        624
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\phi : \\mathbb { R } \\to \\mathbb { R } ^ { d }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        157,
+                                        612,
+                                        253,
+                                        625
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to each token’s position",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        254,
+                                        614,
+                                        263,
+                                        624
+                                    ],
+                                    "score": 0.84,
+                                    "content": "p _ { i }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        263,
+                                        612,
+                                        505,
+                                        625
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". These positional encodings make the information about the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                623,
+                                349,
+                                636
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        623,
+                                        349,
+                                        636
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sequence of tokens available to the model. Eq. (2) becomes:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        }
+                    ],
+                    "index": 40.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        211,
+                        637,
+                        398,
+                        654
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                211,
+                                637,
+                                398,
+                                654
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        211,
+                                        637,
+                                        398,
+                                        654
+                                    ],
+                                    "score": 0.92,
+                                    "content": "A _ { i j } = ( E _ { i } + \\phi ( p _ { i } ) ) ^ { T } W _ { q } ^ { T } W _ { k } ( E _ { j } + \\phi ( p _ { j } ) ) , ,",
+                                    "type": "interline_equation",
+                                    "image_path": "b96beefee59c632a287223572ec7702368e163a81b493e1a921e5c4d74a409f9.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 43,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                211,
+                                637,
+                                398,
+                                654
+                            ],
+                            "spans": [],
+                            "index": 43
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        656,
+                        192,
+                        667
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                656,
+                                192,
+                                667
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        656,
+                                        192,
+                                        667
+                                    ],
+                                    "score": 1.0,
+                                    "content": "which factorizes into",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        }
+                    ],
+                    "index": 44
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        118,
+                        669,
+                        482,
+                        704
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                118,
+                                669,
+                                482,
+                                704
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        118,
+                                        669,
+                                        482,
+                                        704
+                                    ],
+                                    "score": 0.94,
+                                    "content": "A _ { i j } = \\underbrace { { E } _ { i } ^ { T } W _ { q } ^ { T } W _ { k } } _ { ( \\mathrm { u } ) { A } _ { i j } ^ { \\mathrm { c e } } } { + \\underbrace { { E } _ { i } ^ { T } W _ { q } ^ { T } W _ { k } { \\phi } ( p _ { j } ) } _ { ( \\mathrm { b } ) { A } _ { i j } ^ { \\mathrm { c p } } } } + \\underbrace { { \\phi } ( p _ { i } ) ^ { T } W _ { q } ^ { T } W _ { k } { E } _ { j } } _ { ( \\mathrm { c } ) { A } _ { i j } ^ { \\mathrm { c e } } } { + \\underbrace { { { \\phi } ( p _ { i } ) } ^ { T } W _ { q } ^ { T } W _ { k } { \\phi } ( p _ { j } ) } _ { ( \\mathrm { d } ) { A } _ { i j } ^ { \\mathrm { p } } } } .",
+                                    "type": "interline_equation",
+                                    "image_path": "df07c855af71840c08fb5fcac8d0a6450e30cf45761ee10da8da265d06d28ade.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 46,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                118,
+                                669,
+                                482,
+                                680.6666666666666
+                            ],
+                            "spans": [],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                118,
+                                680.6666666666666,
+                                482,
+                                692.3333333333333
+                            ],
+                            "spans": [],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                118,
+                                692.3333333333333,
+                                482,
+                                703.9999999999999
+                            ],
+                            "spans": [],
+                            "index": 47
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        707,
+                        505,
+                        734
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                707,
+                                505,
+                                721
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        707,
+                                        304,
+                                        721
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We can interpret the terms (a)-(d) as follows. (a)",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        708,
+                                        321,
+                                        721
+                                    ],
+                                    "score": 0.91,
+                                    "content": "{ \\cal { A } } _ { i j } ^ { \\mathrm { c c } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        322,
+                                        707,
+                                        505,
+                                        721
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the contribution from the ‘match’ between",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                719,
+                                505,
+                                734
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        719,
+                                        240,
+                                        734
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the content embeddings of tokens",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        241,
+                                        721,
+                                        245,
+                                        730
+                                    ],
+                                    "score": 0.79,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        246,
+                                        719,
+                                        262,
+                                        734
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        263,
+                                        721,
+                                        268,
+                                        732
+                                    ],
+                                    "score": 0.77,
+                                    "content": "j",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        269,
+                                        719,
+                                        286,
+                                        734
+                                    ],
+                                    "score": 1.0,
+                                    "content": "; (b)",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        286,
+                                        720,
+                                        303,
+                                        734
+                                    ],
+                                    "score": 0.9,
+                                    "content": "A _ { i j } ^ { \\mathrm { c p } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        719,
+                                        505,
+                                        734
+                                    ],
+                                    "score": 1.0,
+                                    "content": "steers the attention towards certain positions based",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        }
+                    ],
+                    "index": 48.5
+                }
+            ],
+            "page_idx": 2,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        108,
+                        27,
+                        292,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                293,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        293,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        751,
+                        309,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                301,
+                                750,
+                                310,
+                                762
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        301,
+                                        750,
+                                        310,
+                                        762
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        82,
+                        503,
+                        105
+                    ],
+                    "lines": [],
+                    "index": 0.5,
+                    "bbox_fs": [
+                        106,
+                        82,
+                        504,
+                        106
+                    ],
+                    "lines_deleted": true
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        113,
+                        505,
+                        245
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                113,
+                                505,
+                                127
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        113,
+                                        505,
+                                        127
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Learning representations of structured languages. While models of language have dramatically",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                124,
+                                506,
+                                137
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        124,
+                                        506,
+                                        137
+                                    ],
+                                    "score": 1.0,
+                                    "content": "improved in their ability to learn structure (syntax) and semantics from scratch, it can be argued that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                135,
+                                505,
+                                148
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        135,
+                                        505,
+                                        148
+                                    ],
+                                    "score": 1.0,
+                                    "content": "directly providing the model with the underlying structure of the language can help with generaliza-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                145,
+                                505,
+                                160
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        145,
+                                        505,
+                                        160
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tion (Battaglia et al., 2018), managing long-ranging dependencies (Tai et al., 2015), or representing",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                158,
+                                505,
+                                170
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        158,
+                                        505,
+                                        170
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the compositional aspect of natural language (Socher et al., 2013). Notably, tree structures have",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                168,
+                                505,
+                                181
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        168,
+                                        505,
+                                        181
+                                    ],
+                                    "score": 1.0,
+                                    "content": "shown promising results and inspired new architectures (Shen et al., 2019), including in the domain",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                180,
+                                505,
+                                192
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        180,
+                                        505,
+                                        192
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of source code (Fernandes et al., 2019), where the underlying syntax is directly available. Our work",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                190,
+                                506,
+                                204
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        190,
+                                        506,
+                                        204
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pursues this line of research, showing the benefits of explicitly integrating structural information as",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                200,
+                                506,
+                                214
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        200,
+                                        506,
+                                        214
+                                    ],
+                                    "score": 1.0,
+                                    "content": "an inductive bias. Shiv & Quirk (2019) propose positional encodings for nodes on trees; however,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                211,
+                                505,
+                                225
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        211,
+                                        505,
+                                        225
+                                    ],
+                                    "score": 1.0,
+                                    "content": "their approach assumes regular trees, which is an unrealistic assumption when working with Ab-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                223,
+                                506,
+                                236
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        223,
+                                        506,
+                                        236
+                                    ],
+                                    "score": 1.0,
+                                    "content": "stract Syntax Trees, as an AST node can have arbitrarily many children, e.g., the arguments of a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                233,
+                                145,
+                                246
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        233,
+                                        145,
+                                        246
+                                    ],
+                                    "score": 1.0,
+                                    "content": "function.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 7.5,
+                    "bbox_fs": [
+                        104,
+                        113,
+                        506,
+                        246
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        253,
+                        505,
+                        353
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                254,
+                                505,
+                                266
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        254,
+                                        505,
+                                        266
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Graph Neural Networks. GNNs provide a powerful tool for machine learning on graphs, thanks to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                265,
+                                505,
+                                277
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        265,
+                                        505,
+                                        277
+                                    ],
+                                    "score": 1.0,
+                                    "content": "their ability to recursively incorporate information from neighboring nodes in the network (Battaglia",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                275,
+                                505,
+                                288
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        275,
+                                        505,
+                                        288
+                                    ],
+                                    "score": 1.0,
+                                    "content": "et al., 2018), naturally capturing the graph structure simultaneously with the nodes’ features. (Gori",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                286,
+                                506,
+                                299
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        286,
+                                        506,
+                                        299
+                                    ],
+                                    "score": 1.0,
+                                    "content": "et al., 2005; Scarselli et al., 2008) are able to learn vector representations of nodes and graphs in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                297,
+                                506,
+                                311
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        297,
+                                        506,
+                                        311
+                                    ],
+                                    "score": 1.0,
+                                    "content": "an end-to-end fashion, encoding structural and feature information in the embedding space. Under",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                307,
+                                506,
+                                321
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        307,
+                                        506,
+                                        321
+                                    ],
+                                    "score": 1.0,
+                                    "content": "this model, GNNs have achieved state-of-the-art performance across a variety of tasks, such as node",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                320,
+                                505,
+                                331
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        320,
+                                        505,
+                                        331
+                                    ],
+                                    "score": 1.0,
+                                    "content": "classification (Kipf & Welling, 2017; Hamilton et al., 2017; Klicpera et al., 2019a), link prediction",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                329,
+                                506,
+                                344
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        329,
+                                        506,
+                                        344
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(Zhang & Chen, 2018; Schlichtkrull et al., 2018), graph clustering (Defferrard et al., 2016; Ying",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                341,
+                                484,
+                                354
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        341,
+                                        484,
+                                        354
+                                    ],
+                                    "score": 1.0,
+                                    "content": "et al., 2018) or graph classification (Ying et al., 2018; Dai et al., 2016; Duvenaud et al., 2015).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 18,
+                    "bbox_fs": [
+                        105,
+                        254,
+                        506,
+                        354
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        104,
+                        368,
+                        493,
+                        382
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                367,
+                                495,
+                                383
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        367,
+                                        495,
+                                        383
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3 INTEGRATING STRUCTURE AND CONTEXT IN THE CODE TRANSFORMER",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 23
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        392,
+                        504,
+                        416
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                392,
+                                505,
+                                406
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        392,
+                                        505,
+                                        406
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Self-attention is the core operation powering the Transformer. It enables the model to selectively",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                405,
+                                491,
+                                416
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        405,
+                                        491,
+                                        416
+                                    ],
+                                    "score": 1.0,
+                                    "content": "focus on relevant parts of the input. The matrix form equation for attention with a single head is",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 24.5,
+                    "bbox_fs": [
+                        105,
+                        392,
+                        505,
+                        416
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        209,
+                        419,
+                        400,
+                        447
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                209,
+                                419,
+                                400,
+                                447
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        209,
+                                        419,
+                                        400,
+                                        447
+                                    ],
+                                    "score": 0.94,
+                                    "content": "{ \\mathrm { A t t e n t i o n } } ( Q , K , V ) = { \\mathrm { s o f t m a x } } \\left( { \\frac { Q K ^ { T } } { \\sqrt { d _ { k } } } } \\right) V ,",
+                                    "type": "interline_equation",
+                                    "image_path": "bf5062f76acf55f459a4ae89adb1abed3d6a40f640c4bd316cd5ed6cd5cde38d.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 26.5,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                209,
+                                419,
+                                400,
+                                433.0
+                            ],
+                            "spans": [],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                209,
+                                433.0,
+                                400,
+                                447.0
+                            ],
+                            "spans": [],
+                            "index": 27
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        450,
+                        505,
+                        484
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                448,
+                                505,
+                                464
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        448,
+                                        134,
+                                        464
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        134,
+                                        450,
+                                        201,
+                                        462
+                                    ],
+                                    "score": 0.91,
+                                    "content": "Q , K \\in \\mathbb { R } ^ { N \\times d _ { k } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        201,
+                                        448,
+                                        219,
+                                        464
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        220,
+                                        450,
+                                        272,
+                                        461
+                                    ],
+                                    "score": 0.9,
+                                    "content": "V \\in \\mathbb { R } ^ { N \\times d _ { v } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        272,
+                                        448,
+                                        278,
+                                        464
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        278,
+                                        451,
+                                        289,
+                                        461
+                                    ],
+                                    "score": 0.76,
+                                    "content": "N",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        448,
+                                        413,
+                                        464
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the number of input tokens,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        414,
+                                        451,
+                                        425,
+                                        462
+                                    ],
+                                    "score": 0.89,
+                                    "content": "d _ { k }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        425,
+                                        448,
+                                        505,
+                                        464
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the key dimension,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                461,
+                                505,
+                                475
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        461,
+                                        123,
+                                        475
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        124,
+                                        462,
+                                        135,
+                                        473
+                                    ],
+                                    "score": 0.88,
+                                    "content": "d _ { v }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        135,
+                                        461,
+                                        296,
+                                        475
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the value dimension (typically we have",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        462,
+                                        332,
+                                        473
+                                    ],
+                                    "score": 0.92,
+                                    "content": "d _ { k } = d _ { v }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        332,
+                                        461,
+                                        456,
+                                        475
+                                    ],
+                                    "score": 1.0,
+                                    "content": "). The attention score of query",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        457,
+                                        462,
+                                        470,
+                                        474
+                                    ],
+                                    "score": 0.89,
+                                    "content": "Q _ { i }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        470,
+                                        461,
+                                        505,
+                                        475
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and key",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                473,
+                                195,
+                                486
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        473,
+                                        121,
+                                        486
+                                    ],
+                                    "score": 0.89,
+                                    "content": "K _ { j }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        122,
+                                        473,
+                                        195,
+                                        485
+                                    ],
+                                    "score": 1.0,
+                                    "content": "before softmax is",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 29,
+                    "bbox_fs": [
+                        105,
+                        448,
+                        505,
+                        486
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        236,
+                        483,
+                        374,
+                        500
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                236,
+                                483,
+                                374,
+                                500
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        236,
+                                        483,
+                                        374,
+                                        500
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\pmb { A } _ { i j } = \\pmb { Q } _ { i } ^ { T } \\pmb { K } _ { j } = \\pmb { E } _ { i } ^ { T } \\pmb { W } _ { q } ^ { T } \\pmb { W } _ { k } \\pmb { E } _ { j } ,",
+                                    "type": "interline_equation",
+                                    "image_path": "a084e175bb3c6930841d0180a4202d6eff0f84ecb6a8a9cc250c5cd2833a474e.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 31,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                236,
+                                483,
+                                374,
+                                500
+                            ],
+                            "spans": [],
+                            "index": 31
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        502,
+                        504,
+                        524
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                498,
+                                507,
+                                516
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        498,
+                                        133,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        134,
+                                        501,
+                                        186,
+                                        514
+                                    ],
+                                    "score": 0.93,
+                                    "content": "E _ { i } , E _ { j } \\in \\mathbb { R } ^ { d }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        187,
+                                        498,
+                                        216,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "are the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        217,
+                                        502,
+                                        223,
+                                        512
+                                    ],
+                                    "score": 0.82,
+                                    "content": "d",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        223,
+                                        498,
+                                        365,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-dimensional embeddings of tokens",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        365,
+                                        503,
+                                        370,
+                                        512
+                                    ],
+                                    "score": 0.79,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        370,
+                                        498,
+                                        387,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        388,
+                                        502,
+                                        393,
+                                        514
+                                    ],
+                                    "score": 0.78,
+                                    "content": "j",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        394,
+                                        498,
+                                        414,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        414,
+                                        502,
+                                        430,
+                                        514
+                                    ],
+                                    "score": 0.63,
+                                    "content": "W _ { q }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        430,
+                                        498,
+                                        433,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        433,
+                                        501,
+                                        489,
+                                        514
+                                    ],
+                                    "score": 0.61,
+                                    "content": "W _ { k } \\in \\mathbb { R } ^ { d _ { k } \\times d }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        489,
+                                        498,
+                                        507,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "are",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                513,
+                                313,
+                                525
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        513,
+                                        313,
+                                        525
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the query and key projection matrices, respectively.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 32.5,
+                    "bbox_fs": [
+                        105,
+                        498,
+                        507,
+                        525
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        529,
+                        505,
+                        585
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                530,
+                                505,
+                                542
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        530,
+                                        505,
+                                        542
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Observe that Eq. (2) contains no assumption about potential structure in the input domain: in the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                539,
+                                505,
+                                554
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        539,
+                                        505,
+                                        554
+                                    ],
+                                    "score": 1.0,
+                                    "content": "attention operation we compute all dot products of query and key vectors equally, effectively viewing",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                552,
+                                505,
+                                564
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        552,
+                                        505,
+                                        564
+                                    ],
+                                    "score": 1.0,
+                                    "content": "them as unordered sets of vectors. This means, however, that the model is oblivious to structured",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                562,
+                                506,
+                                576
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        562,
+                                        506,
+                                        576
+                                    ],
+                                    "score": 1.0,
+                                    "content": "inputs (such as text or graphs) and therefore is unable to distinguish, for example, a variable name",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                574,
+                                371,
+                                586
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        574,
+                                        371,
+                                        586
+                                    ],
+                                    "score": 1.0,
+                                    "content": "occurring as an argument and in the return statement of a method.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        }
+                    ],
+                    "index": 36,
+                    "bbox_fs": [
+                        105,
+                        530,
+                        506,
+                        586
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        590,
+                        505,
+                        635
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                589,
+                                505,
+                                604
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        589,
+                                        505,
+                                        604
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In NLP, it is common to bias Transformers towards sequential inputs by adding positional encodings",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                601,
+                                505,
+                                614
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        601,
+                                        505,
+                                        614
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to the token embeddings. These positional encodings are obtained by applying an encoding function",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                612,
+                                505,
+                                625
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        612,
+                                        156,
+                                        624
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\phi : \\mathbb { R } \\to \\mathbb { R } ^ { d }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        157,
+                                        612,
+                                        253,
+                                        625
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to each token’s position",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        254,
+                                        614,
+                                        263,
+                                        624
+                                    ],
+                                    "score": 0.84,
+                                    "content": "p _ { i }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        263,
+                                        612,
+                                        505,
+                                        625
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". These positional encodings make the information about the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                623,
+                                349,
+                                636
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        623,
+                                        349,
+                                        636
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sequence of tokens available to the model. Eq. (2) becomes:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        }
+                    ],
+                    "index": 40.5,
+                    "bbox_fs": [
+                        105,
+                        589,
+                        505,
+                        636
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        211,
+                        637,
+                        398,
+                        654
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                211,
+                                637,
+                                398,
+                                654
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        211,
+                                        637,
+                                        398,
+                                        654
+                                    ],
+                                    "score": 0.92,
+                                    "content": "A _ { i j } = ( E _ { i } + \\phi ( p _ { i } ) ) ^ { T } W _ { q } ^ { T } W _ { k } ( E _ { j } + \\phi ( p _ { j } ) ) , ,",
+                                    "type": "interline_equation",
+                                    "image_path": "b96beefee59c632a287223572ec7702368e163a81b493e1a921e5c4d74a409f9.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 43,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                211,
+                                637,
+                                398,
+                                654
+                            ],
+                            "spans": [],
+                            "index": 43
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        656,
+                        192,
+                        667
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                656,
+                                192,
+                                667
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        656,
+                                        192,
+                                        667
+                                    ],
+                                    "score": 1.0,
+                                    "content": "which factorizes into",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        }
+                    ],
+                    "index": 44,
+                    "bbox_fs": [
+                        107,
+                        656,
+                        192,
+                        667
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        118,
+                        669,
+                        482,
+                        704
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                118,
+                                669,
+                                482,
+                                704
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        118,
+                                        669,
+                                        482,
+                                        704
+                                    ],
+                                    "score": 0.94,
+                                    "content": "A _ { i j } = \\underbrace { { E } _ { i } ^ { T } W _ { q } ^ { T } W _ { k } } _ { ( \\mathrm { u } ) { A } _ { i j } ^ { \\mathrm { c e } } } { + \\underbrace { { E } _ { i } ^ { T } W _ { q } ^ { T } W _ { k } { \\phi } ( p _ { j } ) } _ { ( \\mathrm { b } ) { A } _ { i j } ^ { \\mathrm { c p } } } } + \\underbrace { { \\phi } ( p _ { i } ) ^ { T } W _ { q } ^ { T } W _ { k } { E } _ { j } } _ { ( \\mathrm { c } ) { A } _ { i j } ^ { \\mathrm { c e } } } { + \\underbrace { { { \\phi } ( p _ { i } ) } ^ { T } W _ { q } ^ { T } W _ { k } { \\phi } ( p _ { j } ) } _ { ( \\mathrm { d } ) { A } _ { i j } ^ { \\mathrm { p } } } } .",
+                                    "type": "interline_equation",
+                                    "image_path": "df07c855af71840c08fb5fcac8d0a6450e30cf45761ee10da8da265d06d28ade.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 46,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                118,
+                                669,
+                                482,
+                                680.6666666666666
+                            ],
+                            "spans": [],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                118,
+                                680.6666666666666,
+                                482,
+                                692.3333333333333
+                            ],
+                            "spans": [],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                118,
+                                692.3333333333333,
+                                482,
+                                703.9999999999999
+                            ],
+                            "spans": [],
+                            "index": 47
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        707,
+                        505,
+                        734
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                707,
+                                505,
+                                721
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        707,
+                                        304,
+                                        721
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We can interpret the terms (a)-(d) as follows. (a)",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        708,
+                                        321,
+                                        721
+                                    ],
+                                    "score": 0.91,
+                                    "content": "{ \\cal { A } } _ { i j } ^ { \\mathrm { c c } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        322,
+                                        707,
+                                        505,
+                                        721
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the contribution from the ‘match’ between",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                719,
+                                505,
+                                734
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        719,
+                                        240,
+                                        734
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the content embeddings of tokens",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        241,
+                                        721,
+                                        245,
+                                        730
+                                    ],
+                                    "score": 0.79,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        246,
+                                        719,
+                                        262,
+                                        734
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        263,
+                                        721,
+                                        268,
+                                        732
+                                    ],
+                                    "score": 0.77,
+                                    "content": "j",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        269,
+                                        719,
+                                        286,
+                                        734
+                                    ],
+                                    "score": 1.0,
+                                    "content": "; (b)",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        286,
+                                        720,
+                                        303,
+                                        734
+                                    ],
+                                    "score": 0.9,
+                                    "content": "A _ { i j } ^ { \\mathrm { c p } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        719,
+                                        505,
+                                        734
+                                    ],
+                                    "score": 1.0,
+                                    "content": "steers the attention towards certain positions based",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        }
+                    ],
+                    "index": 48.5,
+                    "bbox_fs": [
+                        106,
+                        707,
+                        505,
+                        734
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        81,
+                        504,
+                        107
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                80,
+                                506,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        80,
+                                        200,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on the content of token",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        200,
+                                        83,
+                                        205,
+                                        93
+                                    ],
+                                    "score": 0.72,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        205,
+                                        80,
+                                        222,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "; (c)",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        223,
+                                        82,
+                                        239,
+                                        96
+                                    ],
+                                    "score": 0.92,
+                                    "content": "A _ { i j } ^ { \\mathrm { p c } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        240,
+                                        80,
+                                        506,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "biases towards content embeddings based on the position of token",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                94,
+                                405,
+                                110
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        97,
+                                        111,
+                                        106
+                                    ],
+                                    "score": 0.67,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        111,
+                                        94,
+                                        129,
+                                        109
+                                    ],
+                                    "score": 1.0,
+                                    "content": "; (d)",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        129,
+                                        95,
+                                        147,
+                                        110
+                                    ],
+                                    "score": 0.9,
+                                    "content": "A _ { i j } ^ { \\mathrm { p p } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        147,
+                                        94,
+                                        405,
+                                        109
+                                    ],
+                                    "score": 1.0,
+                                    "content": "controls which positions should attend to which other positions.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        112,
+                        505,
+                        135
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                111,
+                                505,
+                                126
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        111,
+                                        505,
+                                        126
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In our model, we adopt the formulation of Dai et al. (2019); Yang et al. (2019). They modify Eq. (4)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                123,
+                                480,
+                                137
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        123,
+                                        287,
+                                        137
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by replacing the absolute position encodings",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        287,
+                                        124,
+                                        310,
+                                        136
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\phi ( p _ { i } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        310,
+                                        123,
+                                        442,
+                                        137
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with relative position encodings",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        442,
+                                        124,
+                                        476,
+                                        136
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\phi ( r _ { i \\to j } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        476,
+                                        123,
+                                        480,
+                                        137
+                                    ],
+                                    "score": 1.0,
+                                    "content": ":",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 2.5
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        145,
+                        139,
+                        465,
+                        155
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                145,
+                                139,
+                                465,
+                                155
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        145,
+                                        139,
+                                        465,
+                                        155
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\begin{array} { r } { A _ { i j } ^ { \\mathrm { r e l } } = \\ E _ { i } ^ { T } W _ { q } ^ { T } W _ { k } E _ { j } + E _ { i } ^ { T } W _ { q } ^ { T } W _ { r } \\phi ( r _ { i  j } ) + u ^ { T } W _ { k } E _ { j } + v ^ { T } W _ { r } \\phi ( r _ { i  j } ) , } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "4abc95bdea1392a92734f005afce75f982c5226661a1db2266b0c52e16c233d4.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                145,
+                                139,
+                                465,
+                                155
+                            ],
+                            "spans": [],
+                            "index": 4
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        160,
+                        505,
+                        238
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                159,
+                                505,
+                                173
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        160,
+                                        133,
+                                        173
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        133,
+                                        163,
+                                        154,
+                                        172
+                                    ],
+                                    "score": 0.9,
+                                    "content": "r _ { i \\to j }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        154,
+                                        160,
+                                        291,
+                                        173
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the relative distance from token",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        291,
+                                        162,
+                                        296,
+                                        170
+                                    ],
+                                    "score": 0.78,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        160,
+                                        331,
+                                        173
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to token",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        331,
+                                        161,
+                                        337,
+                                        172
+                                    ],
+                                    "score": 0.84,
+                                    "content": "j",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        337,
+                                        160,
+                                        403,
+                                        173
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in the sequence,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        404,
+                                        159,
+                                        450,
+                                        171
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\boldsymbol { u } , \\boldsymbol { v } \\in \\mathbb { R } ^ { d _ { k } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        450,
+                                        160,
+                                        505,
+                                        173
+                                    ],
+                                    "score": 1.0,
+                                    "content": "are learnable",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                171,
+                                505,
+                                185
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        171,
+                                        175,
+                                        185
+                                    ],
+                                    "score": 1.0,
+                                    "content": "bias vectors, and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        176,
+                                        171,
+                                        192,
+                                        182
+                                    ],
+                                    "score": 0.9,
+                                    "content": "W _ { r }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        192,
+                                        171,
+                                        505,
+                                        185
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is a key projection matrix for the relative distances. Besides fixing issues with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                182,
+                                506,
+                                196
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        182,
+                                        506,
+                                        196
+                                    ],
+                                    "score": 1.0,
+                                    "content": "absolute position encodings such as ambiguity when processing two sentences at a time, Eq. (5)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                194,
+                                505,
+                                205
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        194,
+                                        505,
+                                        205
+                                    ],
+                                    "score": 1.0,
+                                    "content": "enables native application of the powerful self-attention operation on domains such as graphs, where",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                204,
+                                505,
+                                217
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        204,
+                                        505,
+                                        217
+                                    ],
+                                    "score": 1.0,
+                                    "content": "absolute coordinates are not available. We adopt the (non-trainable) sinusoidal encoding function",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                215,
+                                506,
+                                228
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        215,
+                                        506,
+                                        228
+                                    ],
+                                    "score": 1.0,
+                                    "content": "proposed by (Vaswani et al., 2017) for all relations; see Appendix A.1 for details on the distance",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                227,
+                                183,
+                                239
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        227,
+                                        183,
+                                        239
+                                    ],
+                                    "score": 1.0,
+                                    "content": "encoding function.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        250,
+                        451,
+                        262
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                249,
+                                453,
+                                263
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        249,
+                                        453,
+                                        263
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3.1 INTEGRATING SOURCE CODE AND AST REPRESENTATIONS OF PROGRAMS.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        271,
+                        505,
+                        351
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                270,
+                                505,
+                                284
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        270,
+                                        505,
+                                        284
+                                    ],
+                                    "score": 1.0,
+                                    "content": "To enable the model to integrate information both the Context and Structure of programs, we modify",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                282,
+                                505,
+                                295
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        282,
+                                        505,
+                                        295
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Eq. (5) to be able to incorporate multiple different relations. To this end, we use one key projection",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                102,
+                                292,
+                                505,
+                                311
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        102,
+                                        292,
+                                        164,
+                                        311
+                                    ],
+                                    "score": 1.0,
+                                    "content": "matrix W (s)r",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        160,
+                                        295,
+                                        213,
+                                        308
+                                    ],
+                                    "score": 1.0,
+                                    "content": "per relation",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        213,
+                                        298,
+                                        219,
+                                        306
+                                    ],
+                                    "score": 0.58,
+                                    "content": "s",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        219,
+                                        295,
+                                        505,
+                                        308
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and sum their contributions in the raw attention score. This enables",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                307,
+                                505,
+                                318
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        307,
+                                        505,
+                                        318
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the CODE TRANSFORMER to combine information from multiple relations between tokens in the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                318,
+                                505,
+                                329
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        318,
+                                        505,
+                                        329
+                                    ],
+                                    "score": 1.0,
+                                    "content": "attention computation. Besides the token distance in the Context, we include pairwise relations",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                328,
+                                506,
+                                341
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        328,
+                                        506,
+                                        341
+                                    ],
+                                    "score": 1.0,
+                                    "content": "based on the AST as described in the following. See Fig. 2 for a visualization of the Structure",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                339,
+                                178,
+                                352
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        339,
+                                        178,
+                                        352
+                                    ],
+                                    "score": 1.0,
+                                    "content": "distances we use.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        360,
+                        267,
+                        447
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                359,
+                                268,
+                                371
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        359,
+                                        268,
+                                        371
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Shortest path length. We include the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                370,
+                                268,
+                                382
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        370,
+                                        268,
+                                        382
+                                    ],
+                                    "score": 1.0,
+                                    "content": "number of hops required to reach node",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                382,
+                                268,
+                                393
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        382,
+                                        113,
+                                        393
+                                    ],
+                                    "score": 0.78,
+                                    "content": "j",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        113,
+                                        382,
+                                        195,
+                                        392
+                                    ],
+                                    "score": 1.0,
+                                    "content": "starting from node",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        196,
+                                        382,
+                                        201,
+                                        391
+                                    ],
+                                    "score": 0.7,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        201,
+                                        382,
+                                        268,
+                                        392
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and vice versa.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                392,
+                                268,
+                                403
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        392,
+                                        268,
+                                        403
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Here, we treat the AST as an undirected",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                403,
+                                268,
+                                414
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        403,
+                                        268,
+                                        414
+                                    ],
+                                    "score": 1.0,
+                                    "content": "graph, since otherwise most distances",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                414,
+                                268,
+                                426
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        414,
+                                        268,
+                                        426
+                                    ],
+                                    "score": 1.0,
+                                    "content": "would be undefined: e.g., all other nodes",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                425,
+                                268,
+                                437
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        425,
+                                        268,
+                                        437
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in the AST would be unreachable from",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                435,
+                                151,
+                                448
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        435,
+                                        151,
+                                        448
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the leaves.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 23.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        453,
+                        267,
+                        497
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                452,
+                                268,
+                                464
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        452,
+                                        268,
+                                        464
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Similar to the distance of two tokens on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                464,
+                                268,
+                                475
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        464,
+                                        268,
+                                        475
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the source code sequence, the shortest-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                475,
+                                269,
+                                486
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        475,
+                                        269,
+                                        486
+                                    ],
+                                    "score": 1.0,
+                                    "content": "path length is a global distance. This",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                486,
+                                268,
+                                498
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        486,
+                                        268,
+                                        498
+                                    ],
+                                    "score": 1.0,
+                                    "content": "makes the whole graph structure acces-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        }
+                    ],
+                    "index": 29.5
+                },
+                {
+                    "type": "image",
+                    "bbox": [
+                        278,
+                        372,
+                        502,
+                        469
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                278,
+                                372,
+                                502,
+                                469
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        278,
+                                        372,
+                                        502,
+                                        469
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                278,
+                                                372,
+                                                502,
+                                                469
+                                            ],
+                                            "score": 0.962,
+                                            "type": "image",
+                                            "image_path": "971f2174ff96f3b5b7aea4b5cb4f59f9af4bf791dc6a632edbb218691a5d22cf.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 35,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        278,
+                                        372,
+                                        502,
+                                        385.85714285714283
+                                    ],
+                                    "spans": [],
+                                    "index": 32
+                                },
+                                {
+                                    "bbox": [
+                                        278,
+                                        385.85714285714283,
+                                        502,
+                                        399.71428571428567
+                                    ],
+                                    "spans": [],
+                                    "index": 33
+                                },
+                                {
+                                    "bbox": [
+                                        278,
+                                        399.71428571428567,
+                                        502,
+                                        413.5714285714285
+                                    ],
+                                    "spans": [],
+                                    "index": 34
+                                },
+                                {
+                                    "bbox": [
+                                        278,
+                                        413.5714285714285,
+                                        502,
+                                        427.42857142857133
+                                    ],
+                                    "spans": [],
+                                    "index": 35
+                                },
+                                {
+                                    "bbox": [
+                                        278,
+                                        427.42857142857133,
+                                        502,
+                                        441.28571428571416
+                                    ],
+                                    "spans": [],
+                                    "index": 36
+                                },
+                                {
+                                    "bbox": [
+                                        278,
+                                        441.28571428571416,
+                                        502,
+                                        455.142857142857
+                                    ],
+                                    "spans": [],
+                                    "index": 37
+                                },
+                                {
+                                    "bbox": [
+                                        278,
+                                        455.142857142857,
+                                        502,
+                                        468.99999999999983
+                                    ],
+                                    "spans": [],
+                                    "index": 38
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                293,
+                                478,
+                                487,
+                                489
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        291,
+                                        476,
+                                        488,
+                                        491
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                291,
+                                                476,
+                                                488,
+                                                491
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 2: Structure distances used by our model.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 39
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 37.0
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        497,
+                        505,
+                        563
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                497,
+                                505,
+                                509
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        497,
+                                        505,
+                                        509
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sible to the model at each layer. In contrast, Hellendoorn et al. (2020) add bias terms to the attention",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                508,
+                                505,
+                                520
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        508,
+                                        505,
+                                        520
+                                    ],
+                                    "score": 1.0,
+                                    "content": "computation only for edges (i.e. shortest-path distance of 1), which is a local operation that only",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                518,
+                                506,
+                                532
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        518,
+                                        506,
+                                        532
+                                    ],
+                                    "score": 1.0,
+                                    "content": "exchanges information between immediate neighbors (similar to message passing in GNNs). The",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                530,
+                                505,
+                                542
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        530,
+                                        505,
+                                        542
+                                    ],
+                                    "score": 1.0,
+                                    "content": "equivalent localized operation on the source code sequence would be to treat the sequence as a chain",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                541,
+                                506,
+                                554
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        541,
+                                        506,
+                                        554
+                                    ],
+                                    "score": 1.0,
+                                    "content": "graph and only compute attention terms for neighboring tokens, which in turn highlights the benefit",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                552,
+                                241,
+                                564
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        552,
+                                        241,
+                                        564
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of non-local attention operations.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        }
+                    ],
+                    "index": 42.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        571,
+                        505,
+                        627
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                571,
+                                504,
+                                583
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        571,
+                                        504,
+                                        583
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Ancestor distance. Since we treat the ASTs as undirected for the computation of the shortest-path",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                582,
+                                505,
+                                595
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        582,
+                                        505,
+                                        595
+                                    ],
+                                    "score": 1.0,
+                                    "content": "length, we lose the direction information of the edges. To avoid this, we also include the distance",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                591,
+                                505,
+                                607
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        591,
+                                        505,
+                                        607
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on the ordered set of ancestors and descendants of a node in the AST (red arrow in Fig. 2). Again,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                604,
+                                506,
+                                617
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        604,
+                                        506,
+                                        617
+                                    ],
+                                    "score": 1.0,
+                                    "content": "we include number of (vertical) hops to avoid locality in the attention computation. For example, a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                614,
+                                432,
+                                628
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        614,
+                                        128,
+                                        628
+                                    ],
+                                    "score": 1.0,
+                                    "content": "node",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        128,
+                                        616,
+                                        167,
+                                        628
+                                    ],
+                                    "score": 0.92,
+                                    "content": "r _ { i \\to j } = 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        168,
+                                        614,
+                                        252,
+                                        628
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for “grand-children”",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        253,
+                                        616,
+                                        259,
+                                        627
+                                    ],
+                                    "score": 0.81,
+                                    "content": "j",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        259,
+                                        614,
+                                        270,
+                                        628
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        271,
+                                        616,
+                                        275,
+                                        625
+                                    ],
+                                    "score": 0.76,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        276,
+                                        614,
+                                        295,
+                                        628
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        616,
+                                        343,
+                                        628
+                                    ],
+                                    "score": 0.92,
+                                    "content": "r _ { j  i } = - 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        343,
+                                        614,
+                                        432,
+                                        628
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in the other direction.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50
+                        }
+                    ],
+                    "index": 48
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        635,
+                        505,
+                        690
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                635,
+                                505,
+                                647
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        635,
+                                        505,
+                                        647
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sibling distance. The neighbor sets in graphs are typically considered to be unordered, but in an",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 51
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                646,
+                                505,
+                                658
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        646,
+                                        505,
+                                        658
+                                    ],
+                                    "score": 1.0,
+                                    "content": "AST, the order of children encodes their order of occurrence in the source code. To avoid information",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 52
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                656,
+                                506,
+                                669
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        656,
+                                        473,
+                                        669
+                                    ],
+                                    "score": 1.0,
+                                    "content": "loss when encoding the AST, we further include the distance on the ordered set of siblings",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        474,
+                                        657,
+                                        493,
+                                        669
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\{ v _ { i } \\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        493,
+                                        656,
+                                        506,
+                                        669
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 53
+                        },
+                        {
+                            "bbox": [
+                                103,
+                                666,
+                                507,
+                                683
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        103,
+                                        666,
+                                        432,
+                                        683
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a node, where we again avoid locality by encoding the number of hops, i.e.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        432,
+                                        669,
+                                        486,
+                                        680
+                                    ],
+                                    "score": 0.91,
+                                    "content": "r _ { v _ { 1 }  v _ { 3 } } ~ = ~ 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        486,
+                                        666,
+                                        507,
+                                        683
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 54
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                679,
+                                167,
+                                693
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        679,
+                                        167,
+                                        693
+                                    ],
+                                    "score": 1.0,
+                                    "content": "rv3→v1 = −2.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 55
+                        }
+                    ],
+                    "index": 53
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        698,
+                        504,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                698,
+                                506,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        698,
+                                        506,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Personalized PageRank (Page et al., 1999) (PPR). PPR is a well-studied proximity measure which",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 56
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                709,
+                                505,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        709,
+                                        505,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "has been shown to be very effective in learning with graphs (Klicpera et al., 2019a;b; Bojchevski",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 57
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                720,
+                                506,
+                                734
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        720,
+                                        422,
+                                        734
+                                    ],
+                                    "score": 1.0,
+                                    "content": "et al., 2020). PPR captures the local graph structure around a pair of nodes",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        422,
+                                        721,
+                                        443,
+                                        732
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( i , j )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        443,
+                                        720,
+                                        482,
+                                        734
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". E.g., if",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        482,
+                                        721,
+                                        487,
+                                        730
+                                    ],
+                                    "score": 0.75,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        488,
+                                        720,
+                                        506,
+                                        734
+                                    ],
+                                    "score": 1.0,
+                                    "content": "has",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 58
+                        }
+                    ],
+                    "index": 57
+                }
+            ],
+            "page_idx": 3,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        292,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                293,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        293,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        752,
+                        308,
+                        759
+                    ],
+                    "lines": []
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        81,
+                        504,
+                        107
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                80,
+                                506,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        80,
+                                        200,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on the content of token",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        200,
+                                        83,
+                                        205,
+                                        93
+                                    ],
+                                    "score": 0.72,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        205,
+                                        80,
+                                        222,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "; (c)",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        223,
+                                        82,
+                                        239,
+                                        96
+                                    ],
+                                    "score": 0.92,
+                                    "content": "A _ { i j } ^ { \\mathrm { p c } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        240,
+                                        80,
+                                        506,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "biases towards content embeddings based on the position of token",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                94,
+                                405,
+                                110
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        97,
+                                        111,
+                                        106
+                                    ],
+                                    "score": 0.67,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        111,
+                                        94,
+                                        129,
+                                        109
+                                    ],
+                                    "score": 1.0,
+                                    "content": "; (d)",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        129,
+                                        95,
+                                        147,
+                                        110
+                                    ],
+                                    "score": 0.9,
+                                    "content": "A _ { i j } ^ { \\mathrm { p p } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        147,
+                                        94,
+                                        405,
+                                        109
+                                    ],
+                                    "score": 1.0,
+                                    "content": "controls which positions should attend to which other positions.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5,
+                    "bbox_fs": [
+                        105,
+                        80,
+                        506,
+                        110
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        112,
+                        505,
+                        135
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                111,
+                                505,
+                                126
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        111,
+                                        505,
+                                        126
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In our model, we adopt the formulation of Dai et al. (2019); Yang et al. (2019). They modify Eq. (4)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                123,
+                                480,
+                                137
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        123,
+                                        287,
+                                        137
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by replacing the absolute position encodings",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        287,
+                                        124,
+                                        310,
+                                        136
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\phi ( p _ { i } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        310,
+                                        123,
+                                        442,
+                                        137
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with relative position encodings",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        442,
+                                        124,
+                                        476,
+                                        136
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\phi ( r _ { i \\to j } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        476,
+                                        123,
+                                        480,
+                                        137
+                                    ],
+                                    "score": 1.0,
+                                    "content": ":",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 2.5,
+                    "bbox_fs": [
+                        105,
+                        111,
+                        505,
+                        137
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        145,
+                        139,
+                        465,
+                        155
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                145,
+                                139,
+                                465,
+                                155
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        145,
+                                        139,
+                                        465,
+                                        155
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\begin{array} { r } { A _ { i j } ^ { \\mathrm { r e l } } = \\ E _ { i } ^ { T } W _ { q } ^ { T } W _ { k } E _ { j } + E _ { i } ^ { T } W _ { q } ^ { T } W _ { r } \\phi ( r _ { i  j } ) + u ^ { T } W _ { k } E _ { j } + v ^ { T } W _ { r } \\phi ( r _ { i  j } ) , } \\end{array}",
+                                    "type": "interline_equation",
+                                    "image_path": "4abc95bdea1392a92734f005afce75f982c5226661a1db2266b0c52e16c233d4.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                145,
+                                139,
+                                465,
+                                155
+                            ],
+                            "spans": [],
+                            "index": 4
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        160,
+                        505,
+                        238
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                159,
+                                505,
+                                173
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        160,
+                                        133,
+                                        173
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        133,
+                                        163,
+                                        154,
+                                        172
+                                    ],
+                                    "score": 0.9,
+                                    "content": "r _ { i \\to j }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        154,
+                                        160,
+                                        291,
+                                        173
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the relative distance from token",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        291,
+                                        162,
+                                        296,
+                                        170
+                                    ],
+                                    "score": 0.78,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        160,
+                                        331,
+                                        173
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to token",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        331,
+                                        161,
+                                        337,
+                                        172
+                                    ],
+                                    "score": 0.84,
+                                    "content": "j",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        337,
+                                        160,
+                                        403,
+                                        173
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in the sequence,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        404,
+                                        159,
+                                        450,
+                                        171
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\boldsymbol { u } , \\boldsymbol { v } \\in \\mathbb { R } ^ { d _ { k } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        450,
+                                        160,
+                                        505,
+                                        173
+                                    ],
+                                    "score": 1.0,
+                                    "content": "are learnable",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                171,
+                                505,
+                                185
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        171,
+                                        175,
+                                        185
+                                    ],
+                                    "score": 1.0,
+                                    "content": "bias vectors, and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        176,
+                                        171,
+                                        192,
+                                        182
+                                    ],
+                                    "score": 0.9,
+                                    "content": "W _ { r }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        192,
+                                        171,
+                                        505,
+                                        185
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is a key projection matrix for the relative distances. Besides fixing issues with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                182,
+                                506,
+                                196
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        182,
+                                        506,
+                                        196
+                                    ],
+                                    "score": 1.0,
+                                    "content": "absolute position encodings such as ambiguity when processing two sentences at a time, Eq. (5)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                194,
+                                505,
+                                205
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        194,
+                                        505,
+                                        205
+                                    ],
+                                    "score": 1.0,
+                                    "content": "enables native application of the powerful self-attention operation on domains such as graphs, where",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                204,
+                                505,
+                                217
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        204,
+                                        505,
+                                        217
+                                    ],
+                                    "score": 1.0,
+                                    "content": "absolute coordinates are not available. We adopt the (non-trainable) sinusoidal encoding function",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                215,
+                                506,
+                                228
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        215,
+                                        506,
+                                        228
+                                    ],
+                                    "score": 1.0,
+                                    "content": "proposed by (Vaswani et al., 2017) for all relations; see Appendix A.1 for details on the distance",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                227,
+                                183,
+                                239
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        227,
+                                        183,
+                                        239
+                                    ],
+                                    "score": 1.0,
+                                    "content": "encoding function.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 8,
+                    "bbox_fs": [
+                        105,
+                        159,
+                        506,
+                        239
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        250,
+                        451,
+                        262
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                249,
+                                453,
+                                263
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        249,
+                                        453,
+                                        263
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3.1 INTEGRATING SOURCE CODE AND AST REPRESENTATIONS OF PROGRAMS.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        271,
+                        505,
+                        351
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                270,
+                                505,
+                                284
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        270,
+                                        505,
+                                        284
+                                    ],
+                                    "score": 1.0,
+                                    "content": "To enable the model to integrate information both the Context and Structure of programs, we modify",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                282,
+                                505,
+                                295
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        282,
+                                        505,
+                                        295
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Eq. (5) to be able to incorporate multiple different relations. To this end, we use one key projection",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                102,
+                                292,
+                                505,
+                                311
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        102,
+                                        292,
+                                        164,
+                                        311
+                                    ],
+                                    "score": 1.0,
+                                    "content": "matrix W (s)r",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        160,
+                                        295,
+                                        213,
+                                        308
+                                    ],
+                                    "score": 1.0,
+                                    "content": "per relation",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        213,
+                                        298,
+                                        219,
+                                        306
+                                    ],
+                                    "score": 0.58,
+                                    "content": "s",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        219,
+                                        295,
+                                        505,
+                                        308
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and sum their contributions in the raw attention score. This enables",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                307,
+                                505,
+                                318
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        307,
+                                        505,
+                                        318
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the CODE TRANSFORMER to combine information from multiple relations between tokens in the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                318,
+                                505,
+                                329
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        318,
+                                        505,
+                                        329
+                                    ],
+                                    "score": 1.0,
+                                    "content": "attention computation. Besides the token distance in the Context, we include pairwise relations",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                328,
+                                506,
+                                341
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        328,
+                                        506,
+                                        341
+                                    ],
+                                    "score": 1.0,
+                                    "content": "based on the AST as described in the following. See Fig. 2 for a visualization of the Structure",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                339,
+                                178,
+                                352
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        339,
+                                        178,
+                                        352
+                                    ],
+                                    "score": 1.0,
+                                    "content": "distances we use.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 16,
+                    "bbox_fs": [
+                        102,
+                        270,
+                        506,
+                        352
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        360,
+                        267,
+                        447
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                359,
+                                268,
+                                371
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        359,
+                                        268,
+                                        371
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Shortest path length. We include the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                370,
+                                268,
+                                382
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        370,
+                                        268,
+                                        382
+                                    ],
+                                    "score": 1.0,
+                                    "content": "number of hops required to reach node",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                382,
+                                268,
+                                393
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        382,
+                                        113,
+                                        393
+                                    ],
+                                    "score": 0.78,
+                                    "content": "j",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        113,
+                                        382,
+                                        195,
+                                        392
+                                    ],
+                                    "score": 1.0,
+                                    "content": "starting from node",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        196,
+                                        382,
+                                        201,
+                                        391
+                                    ],
+                                    "score": 0.7,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        201,
+                                        382,
+                                        268,
+                                        392
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and vice versa.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                392,
+                                268,
+                                403
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        392,
+                                        268,
+                                        403
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Here, we treat the AST as an undirected",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                403,
+                                268,
+                                414
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        403,
+                                        268,
+                                        414
+                                    ],
+                                    "score": 1.0,
+                                    "content": "graph, since otherwise most distances",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                414,
+                                268,
+                                426
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        414,
+                                        268,
+                                        426
+                                    ],
+                                    "score": 1.0,
+                                    "content": "would be undefined: e.g., all other nodes",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                425,
+                                268,
+                                437
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        425,
+                                        268,
+                                        437
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in the AST would be unreachable from",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                435,
+                                151,
+                                448
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        435,
+                                        151,
+                                        448
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the leaves.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 23.5,
+                    "bbox_fs": [
+                        105,
+                        359,
+                        268,
+                        448
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        453,
+                        267,
+                        497
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                452,
+                                268,
+                                464
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        452,
+                                        268,
+                                        464
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Similar to the distance of two tokens on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                464,
+                                268,
+                                475
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        464,
+                                        268,
+                                        475
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the source code sequence, the shortest-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                475,
+                                269,
+                                486
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        475,
+                                        269,
+                                        486
+                                    ],
+                                    "score": 1.0,
+                                    "content": "path length is a global distance. This",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                486,
+                                268,
+                                498
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        486,
+                                        268,
+                                        498
+                                    ],
+                                    "score": 1.0,
+                                    "content": "makes the whole graph structure acces-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        }
+                    ],
+                    "index": 29.5,
+                    "bbox_fs": [
+                        105,
+                        452,
+                        269,
+                        498
+                    ]
+                },
+                {
+                    "type": "image",
+                    "bbox": [
+                        278,
+                        372,
+                        502,
+                        469
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                278,
+                                372,
+                                502,
+                                469
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        278,
+                                        372,
+                                        502,
+                                        469
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                278,
+                                                372,
+                                                502,
+                                                469
+                                            ],
+                                            "score": 0.962,
+                                            "type": "image",
+                                            "image_path": "971f2174ff96f3b5b7aea4b5cb4f59f9af4bf791dc6a632edbb218691a5d22cf.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 35,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        278,
+                                        372,
+                                        502,
+                                        385.85714285714283
+                                    ],
+                                    "spans": [],
+                                    "index": 32
+                                },
+                                {
+                                    "bbox": [
+                                        278,
+                                        385.85714285714283,
+                                        502,
+                                        399.71428571428567
+                                    ],
+                                    "spans": [],
+                                    "index": 33
+                                },
+                                {
+                                    "bbox": [
+                                        278,
+                                        399.71428571428567,
+                                        502,
+                                        413.5714285714285
+                                    ],
+                                    "spans": [],
+                                    "index": 34
+                                },
+                                {
+                                    "bbox": [
+                                        278,
+                                        413.5714285714285,
+                                        502,
+                                        427.42857142857133
+                                    ],
+                                    "spans": [],
+                                    "index": 35
+                                },
+                                {
+                                    "bbox": [
+                                        278,
+                                        427.42857142857133,
+                                        502,
+                                        441.28571428571416
+                                    ],
+                                    "spans": [],
+                                    "index": 36
+                                },
+                                {
+                                    "bbox": [
+                                        278,
+                                        441.28571428571416,
+                                        502,
+                                        455.142857142857
+                                    ],
+                                    "spans": [],
+                                    "index": 37
+                                },
+                                {
+                                    "bbox": [
+                                        278,
+                                        455.142857142857,
+                                        502,
+                                        468.99999999999983
+                                    ],
+                                    "spans": [],
+                                    "index": 38
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                293,
+                                478,
+                                487,
+                                489
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        291,
+                                        476,
+                                        488,
+                                        491
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                291,
+                                                476,
+                                                488,
+                                                491
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 2: Structure distances used by our model.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 39
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 37.0
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        497,
+                        505,
+                        563
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                497,
+                                505,
+                                509
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        497,
+                                        505,
+                                        509
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sible to the model at each layer. In contrast, Hellendoorn et al. (2020) add bias terms to the attention",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                508,
+                                505,
+                                520
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        508,
+                                        505,
+                                        520
+                                    ],
+                                    "score": 1.0,
+                                    "content": "computation only for edges (i.e. shortest-path distance of 1), which is a local operation that only",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                518,
+                                506,
+                                532
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        518,
+                                        506,
+                                        532
+                                    ],
+                                    "score": 1.0,
+                                    "content": "exchanges information between immediate neighbors (similar to message passing in GNNs). The",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                530,
+                                505,
+                                542
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        530,
+                                        505,
+                                        542
+                                    ],
+                                    "score": 1.0,
+                                    "content": "equivalent localized operation on the source code sequence would be to treat the sequence as a chain",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                541,
+                                506,
+                                554
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        541,
+                                        506,
+                                        554
+                                    ],
+                                    "score": 1.0,
+                                    "content": "graph and only compute attention terms for neighboring tokens, which in turn highlights the benefit",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                552,
+                                241,
+                                564
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        552,
+                                        241,
+                                        564
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of non-local attention operations.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        }
+                    ],
+                    "index": 42.5,
+                    "bbox_fs": [
+                        105,
+                        497,
+                        506,
+                        564
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        571,
+                        505,
+                        627
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                571,
+                                504,
+                                583
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        571,
+                                        504,
+                                        583
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Ancestor distance. Since we treat the ASTs as undirected for the computation of the shortest-path",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                582,
+                                505,
+                                595
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        582,
+                                        505,
+                                        595
+                                    ],
+                                    "score": 1.0,
+                                    "content": "length, we lose the direction information of the edges. To avoid this, we also include the distance",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                591,
+                                505,
+                                607
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        591,
+                                        505,
+                                        607
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on the ordered set of ancestors and descendants of a node in the AST (red arrow in Fig. 2). Again,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                604,
+                                506,
+                                617
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        604,
+                                        506,
+                                        617
+                                    ],
+                                    "score": 1.0,
+                                    "content": "we include number of (vertical) hops to avoid locality in the attention computation. For example, a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                614,
+                                432,
+                                628
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        614,
+                                        128,
+                                        628
+                                    ],
+                                    "score": 1.0,
+                                    "content": "node",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        128,
+                                        616,
+                                        167,
+                                        628
+                                    ],
+                                    "score": 0.92,
+                                    "content": "r _ { i \\to j } = 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        168,
+                                        614,
+                                        252,
+                                        628
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for “grand-children”",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        253,
+                                        616,
+                                        259,
+                                        627
+                                    ],
+                                    "score": 0.81,
+                                    "content": "j",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        259,
+                                        614,
+                                        270,
+                                        628
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        271,
+                                        616,
+                                        275,
+                                        625
+                                    ],
+                                    "score": 0.76,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        276,
+                                        614,
+                                        295,
+                                        628
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        616,
+                                        343,
+                                        628
+                                    ],
+                                    "score": 0.92,
+                                    "content": "r _ { j  i } = - 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        343,
+                                        614,
+                                        432,
+                                        628
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in the other direction.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50
+                        }
+                    ],
+                    "index": 48,
+                    "bbox_fs": [
+                        104,
+                        571,
+                        506,
+                        628
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        635,
+                        505,
+                        690
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                635,
+                                505,
+                                647
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        635,
+                                        505,
+                                        647
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sibling distance. The neighbor sets in graphs are typically considered to be unordered, but in an",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 51
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                646,
+                                505,
+                                658
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        646,
+                                        505,
+                                        658
+                                    ],
+                                    "score": 1.0,
+                                    "content": "AST, the order of children encodes their order of occurrence in the source code. To avoid information",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 52
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                656,
+                                506,
+                                669
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        656,
+                                        473,
+                                        669
+                                    ],
+                                    "score": 1.0,
+                                    "content": "loss when encoding the AST, we further include the distance on the ordered set of siblings",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        474,
+                                        657,
+                                        493,
+                                        669
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\{ v _ { i } \\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        493,
+                                        656,
+                                        506,
+                                        669
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 53
+                        },
+                        {
+                            "bbox": [
+                                103,
+                                666,
+                                507,
+                                683
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        103,
+                                        666,
+                                        432,
+                                        683
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a node, where we again avoid locality by encoding the number of hops, i.e.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        432,
+                                        669,
+                                        486,
+                                        680
+                                    ],
+                                    "score": 0.91,
+                                    "content": "r _ { v _ { 1 }  v _ { 3 } } ~ = ~ 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        486,
+                                        666,
+                                        507,
+                                        683
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 54
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                679,
+                                167,
+                                693
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        679,
+                                        167,
+                                        693
+                                    ],
+                                    "score": 1.0,
+                                    "content": "rv3→v1 = −2.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 55
+                        }
+                    ],
+                    "index": 53,
+                    "bbox_fs": [
+                        103,
+                        635,
+                        507,
+                        693
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        698,
+                        504,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                698,
+                                506,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        698,
+                                        506,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Personalized PageRank (Page et al., 1999) (PPR). PPR is a well-studied proximity measure which",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 56
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                709,
+                                505,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        709,
+                                        505,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "has been shown to be very effective in learning with graphs (Klicpera et al., 2019a;b; Bojchevski",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 57
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                720,
+                                506,
+                                734
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        720,
+                                        422,
+                                        734
+                                    ],
+                                    "score": 1.0,
+                                    "content": "et al., 2020). PPR captures the local graph structure around a pair of nodes",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        422,
+                                        721,
+                                        443,
+                                        732
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( i , j )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        443,
+                                        720,
+                                        482,
+                                        734
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". E.g., if",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        482,
+                                        721,
+                                        487,
+                                        730
+                                    ],
+                                    "score": 0.75,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        488,
+                                        720,
+                                        506,
+                                        734
+                                    ],
+                                    "score": 1.0,
+                                    "content": "has",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 58
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                352,
+                                505,
+                                365
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        352,
+                                        250,
+                                        365
+                                    ],
+                                    "score": 1.0,
+                                    "content": "many neighbors, its PPR score for",
+                                    "type": "text",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        250,
+                                        353,
+                                        257,
+                                        363
+                                    ],
+                                    "score": 0.84,
+                                    "content": "j",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        257,
+                                        352,
+                                        505,
+                                        365
+                                    ],
+                                    "score": 1.0,
+                                    "content": "will be low even when they are only few hops apart, which",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                363,
+                                357,
+                                375
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        363,
+                                        357,
+                                        375
+                                    ],
+                                    "score": 1.0,
+                                    "content": "complements the purely hop-based distances described above.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 57,
+                    "bbox_fs": [
+                        105,
+                        698,
+                        506,
+                        734
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "image",
+                    "bbox": [
+                        115,
+                        80,
+                        498,
+                        249
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                115,
+                                80,
+                                498,
+                                249
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        80,
+                                        498,
+                                        249
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                115,
+                                                80,
+                                                498,
+                                                249
+                                            ],
+                                            "score": 0.974,
+                                            "type": "image",
+                                            "image_path": "2ae4d77322414ffc49b55c0b5e39c6d3b3d0f5b89a9cfca8c5f81d4390780d66.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        80,
+                                        498,
+                                        136.33333333333334
+                                    ],
+                                    "spans": [],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        115,
+                                        136.33333333333334,
+                                        498,
+                                        192.66666666666669
+                                    ],
+                                    "spans": [],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        115,
+                                        192.66666666666669,
+                                        498,
+                                        249.00000000000003
+                                    ],
+                                    "spans": [],
+                                    "index": 2
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                106,
+                                261,
+                                505,
+                                327
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        261,
+                                        505,
+                                        274
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                261,
+                                                505,
+                                                274
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 3: Left: Sequence (Context) and AST (Structure) representation of an input code snippet.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        271,
+                                        505,
+                                        285
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                271,
+                                                505,
+                                                285
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Center: The CODE TRANSFORMER jointly leverages the sequence of tokens and the Abstract Syn-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        283,
+                                        505,
+                                        296
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                283,
+                                                505,
+                                                296
+                                            ],
+                                            "score": 1.0,
+                                            "content": "tax Tree to learn expressive representations of source code. In addition to the input token and node",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 5
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        293,
+                                        505,
+                                        306
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                293,
+                                                505,
+                                                306
+                                            ],
+                                            "score": 1.0,
+                                            "content": "embeddings the model uses different distances between the tokens, e.g., shortest paths on the AST",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 6
+                                },
+                                {
+                                    "bbox": [
+                                        104,
+                                        304,
+                                        506,
+                                        318
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                104,
+                                                304,
+                                                506,
+                                                318
+                                            ],
+                                            "score": 1.0,
+                                            "content": "or personalized PageRank, to reason about their relative positions. The output embeddings can be",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 7
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        316,
+                                        361,
+                                        328
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                316,
+                                                361,
+                                                328
+                                            ],
+                                            "score": 1.0,
+                                            "content": "used for downstream tasks such as code summarization (right).",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 8
+                                }
+                            ],
+                            "index": 5.5
+                        }
+                    ],
+                    "index": 3.25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        351,
+                        504,
+                        374
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                352,
+                                505,
+                                365
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        352,
+                                        250,
+                                        365
+                                    ],
+                                    "score": 1.0,
+                                    "content": "many neighbors, its PPR score for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        250,
+                                        353,
+                                        257,
+                                        363
+                                    ],
+                                    "score": 0.84,
+                                    "content": "j",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        257,
+                                        352,
+                                        505,
+                                        365
+                                    ],
+                                    "score": 1.0,
+                                    "content": "will be low even when they are only few hops apart, which",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                363,
+                                357,
+                                375
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        363,
+                                        357,
+                                        375
+                                    ],
+                                    "score": 1.0,
+                                    "content": "complements the purely hop-based distances described above.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 9.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        383,
+                        505,
+                        460
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                381,
+                                505,
+                                396
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        381,
+                                        505,
+                                        396
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Input embeddings to the model. To combine the Context and Structure information, we assign",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                394,
+                                505,
+                                406
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        394,
+                                        505,
+                                        406
+                                    ],
+                                    "score": 1.0,
+                                    "content": "each token in the sequence to an AST node by selecting the AST node whose range in the source",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                405,
+                                504,
+                                417
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        405,
+                                        504,
+                                        417
+                                    ],
+                                    "score": 1.0,
+                                    "content": "code is the shortest one containing the token. We concatenate the (sub-) token embeddings with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                416,
+                                505,
+                                428
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        416,
+                                        505,
+                                        428
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the embedding of the token’s assigned AST node type as well as the token type returned by the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                427,
+                                505,
+                                439
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        427,
+                                        505,
+                                        439
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tokenizer. That is, among all the internal nodes, we use as input only those corresponding to a token",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                437,
+                                505,
+                                450
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        437,
+                                        505,
+                                        450
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in the sequence; however, the remaining internal nodes can used by the model since their presence",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                448,
+                                496,
+                                461
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        448,
+                                        496,
+                                        461
+                                    ],
+                                    "score": 1.0,
+                                    "content": "affects the distances between the remaining AST nodes. See Appendices A.3 and A.4 for details.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        477,
+                        338,
+                        488
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                476,
+                                341,
+                                489
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        476,
+                                        341,
+                                        489
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3.2 EFFICIENT RELATIVE ATTENTION COMPUTATION.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        498,
+                        505,
+                        597
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                497,
+                                505,
+                                510
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        497,
+                                        376,
+                                        510
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Na¨ıvely, we need to compute and materialize a tensor of dimension",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        376,
+                                        498,
+                                        425,
+                                        509
+                                    ],
+                                    "score": 0.91,
+                                    "content": "N \\times N \\times d",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        425,
+                                        497,
+                                        505,
+                                        510
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to hold all pairwise",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                509,
+                                505,
+                                523
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        509,
+                                        216,
+                                        523
+                                    ],
+                                    "score": 1.0,
+                                    "content": "relative position encodings",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        217,
+                                        509,
+                                        250,
+                                        522
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\phi ( r _ { i \\to j } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        251,
+                                        509,
+                                        325,
+                                        523
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in Eq. (5) , where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        325,
+                                        510,
+                                        336,
+                                        519
+                                    ],
+                                    "score": 0.81,
+                                    "content": "N",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        336,
+                                        509,
+                                        505,
+                                        523
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the input length. This is prohibitive for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                519,
+                                505,
+                                533
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        519,
+                                        505,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": "fast GPU training. While for discrete distance values (e.g., sequence distance or shortest-path length",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                531,
+                                505,
+                                545
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        531,
+                                        505,
+                                        545
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on a graph) we only need to compute unique distance values occurring in the input, this does not gen-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                542,
+                                505,
+                                556
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        542,
+                                        505,
+                                        556
+                                    ],
+                                    "score": 1.0,
+                                    "content": "eralize to continuous distances such as PPR. Therefore, we propose a constant-time approximation",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                552,
+                                505,
+                                567
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        552,
+                                        373,
+                                        567
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of the relational attention computation by grouping the values into",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        373,
+                                        553,
+                                        409,
+                                        564
+                                    ],
+                                    "score": 0.91,
+                                    "content": "k \\ll N ^ { 2 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        409,
+                                        552,
+                                        505,
+                                        567
+                                    ],
+                                    "score": 1.0,
+                                    "content": "bins. Since closer sam-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                564,
+                                505,
+                                577
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        564,
+                                        505,
+                                        577
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ples are typically more relevant for a query sample, we increase the bin widths exponentially with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                575,
+                                506,
+                                588
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        575,
+                                        506,
+                                        588
+                                    ],
+                                    "score": 1.0,
+                                    "content": "growing distance values. Throughout our experiments we have found the CODE TRANSFORMER to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                586,
+                                450,
+                                599
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        587,
+                                        340,
+                                        599
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be relatively insensitive to the number of bins; we thus set",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        340,
+                                        586,
+                                        370,
+                                        596
+                                    ],
+                                    "score": 0.9,
+                                    "content": "k = 3 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        371,
+                                        587,
+                                        450,
+                                        599
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in our experiments.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 23
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        617,
+                        242,
+                        629
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                616,
+                                244,
+                                631
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        616,
+                                        244,
+                                        631
+                                    ],
+                                    "score": 1.0,
+                                    "content": "4 EXPERIMENTAL SETUP",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 28
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        643,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                643,
+                                505,
+                                656
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        643,
+                                        505,
+                                        656
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Code summarization is one of the most popular tasks in machine learning for code. Given the body",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                654,
+                                505,
+                                667
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        654,
+                                        505,
+                                        667
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of a function, the task is to predict the function’s name. As observed by Alon et al. (2019b) and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                665,
+                                505,
+                                678
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        665,
+                                        505,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Allamanis et al. (2016), this is a useful benchmark as method names in open-source projects tend to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                677,
+                                505,
+                                689
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        677,
+                                        505,
+                                        689
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be precise and descriptive, and functions typically form complete logical units. See Fig. 3 (right) for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                687,
+                                505,
+                                700
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        687,
+                                        505,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a visual overview of the task. We use two complementary representations of programs: the source",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                699,
+                                505,
+                                711
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        699,
+                                        505,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "code as a sequence of tokens (Context) and the AST (Structure). As shown in Fig. 3 (left), tokens",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                710,
+                                505,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        710,
+                                        505,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that are far away on the sequence may be very close on the AST and vice versa. In this task we make",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                720,
+                                505,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        720,
+                                        505,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "use of the CODE TRANSFORMER’s ability jointly leverage both Structure and Context and show that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 32.5
+                }
+            ],
+            "page_idx": 4,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        108,
+                        27,
+                        292,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                293,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        293,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        751,
+                        308,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                302,
+                                750,
+                                309,
+                                763
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        302,
+                                        750,
+                                        309,
+                                        763
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "image",
+                    "bbox": [
+                        115,
+                        80,
+                        498,
+                        249
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                115,
+                                80,
+                                498,
+                                249
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        80,
+                                        498,
+                                        249
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                115,
+                                                80,
+                                                498,
+                                                249
+                                            ],
+                                            "score": 0.974,
+                                            "type": "image",
+                                            "image_path": "2ae4d77322414ffc49b55c0b5e39c6d3b3d0f5b89a9cfca8c5f81d4390780d66.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        80,
+                                        498,
+                                        136.33333333333334
+                                    ],
+                                    "spans": [],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        115,
+                                        136.33333333333334,
+                                        498,
+                                        192.66666666666669
+                                    ],
+                                    "spans": [],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        115,
+                                        192.66666666666669,
+                                        498,
+                                        249.00000000000003
+                                    ],
+                                    "spans": [],
+                                    "index": 2
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                106,
+                                261,
+                                505,
+                                327
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        261,
+                                        505,
+                                        274
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                261,
+                                                505,
+                                                274
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 3: Left: Sequence (Context) and AST (Structure) representation of an input code snippet.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        271,
+                                        505,
+                                        285
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                271,
+                                                505,
+                                                285
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Center: The CODE TRANSFORMER jointly leverages the sequence of tokens and the Abstract Syn-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        283,
+                                        505,
+                                        296
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                283,
+                                                505,
+                                                296
+                                            ],
+                                            "score": 1.0,
+                                            "content": "tax Tree to learn expressive representations of source code. In addition to the input token and node",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 5
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        293,
+                                        505,
+                                        306
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                293,
+                                                505,
+                                                306
+                                            ],
+                                            "score": 1.0,
+                                            "content": "embeddings the model uses different distances between the tokens, e.g., shortest paths on the AST",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 6
+                                },
+                                {
+                                    "bbox": [
+                                        104,
+                                        304,
+                                        506,
+                                        318
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                104,
+                                                304,
+                                                506,
+                                                318
+                                            ],
+                                            "score": 1.0,
+                                            "content": "or personalized PageRank, to reason about their relative positions. The output embeddings can be",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 7
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        316,
+                                        361,
+                                        328
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                316,
+                                                361,
+                                                328
+                                            ],
+                                            "score": 1.0,
+                                            "content": "used for downstream tasks such as code summarization (right).",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 8
+                                }
+                            ],
+                            "index": 5.5
+                        }
+                    ],
+                    "index": 3.25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        351,
+                        504,
+                        374
+                    ],
+                    "lines": [],
+                    "index": 9.5,
+                    "bbox_fs": [
+                        105,
+                        352,
+                        505,
+                        375
+                    ],
+                    "lines_deleted": true
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        383,
+                        505,
+                        460
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                381,
+                                505,
+                                396
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        381,
+                                        505,
+                                        396
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Input embeddings to the model. To combine the Context and Structure information, we assign",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                394,
+                                505,
+                                406
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        394,
+                                        505,
+                                        406
+                                    ],
+                                    "score": 1.0,
+                                    "content": "each token in the sequence to an AST node by selecting the AST node whose range in the source",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                405,
+                                504,
+                                417
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        405,
+                                        504,
+                                        417
+                                    ],
+                                    "score": 1.0,
+                                    "content": "code is the shortest one containing the token. We concatenate the (sub-) token embeddings with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                416,
+                                505,
+                                428
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        416,
+                                        505,
+                                        428
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the embedding of the token’s assigned AST node type as well as the token type returned by the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                427,
+                                505,
+                                439
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        427,
+                                        505,
+                                        439
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tokenizer. That is, among all the internal nodes, we use as input only those corresponding to a token",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                437,
+                                505,
+                                450
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        437,
+                                        505,
+                                        450
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in the sequence; however, the remaining internal nodes can used by the model since their presence",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                448,
+                                496,
+                                461
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        448,
+                                        496,
+                                        461
+                                    ],
+                                    "score": 1.0,
+                                    "content": "affects the distances between the remaining AST nodes. See Appendices A.3 and A.4 for details.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 14,
+                    "bbox_fs": [
+                        105,
+                        381,
+                        505,
+                        461
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        477,
+                        338,
+                        488
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                476,
+                                341,
+                                489
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        476,
+                                        341,
+                                        489
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3.2 EFFICIENT RELATIVE ATTENTION COMPUTATION.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        498,
+                        505,
+                        597
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                497,
+                                505,
+                                510
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        497,
+                                        376,
+                                        510
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Na¨ıvely, we need to compute and materialize a tensor of dimension",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        376,
+                                        498,
+                                        425,
+                                        509
+                                    ],
+                                    "score": 0.91,
+                                    "content": "N \\times N \\times d",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        425,
+                                        497,
+                                        505,
+                                        510
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to hold all pairwise",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                509,
+                                505,
+                                523
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        509,
+                                        216,
+                                        523
+                                    ],
+                                    "score": 1.0,
+                                    "content": "relative position encodings",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        217,
+                                        509,
+                                        250,
+                                        522
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\phi ( r _ { i \\to j } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        251,
+                                        509,
+                                        325,
+                                        523
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in Eq. (5) , where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        325,
+                                        510,
+                                        336,
+                                        519
+                                    ],
+                                    "score": 0.81,
+                                    "content": "N",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        336,
+                                        509,
+                                        505,
+                                        523
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the input length. This is prohibitive for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                519,
+                                505,
+                                533
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        519,
+                                        505,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": "fast GPU training. While for discrete distance values (e.g., sequence distance or shortest-path length",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                531,
+                                505,
+                                545
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        531,
+                                        505,
+                                        545
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on a graph) we only need to compute unique distance values occurring in the input, this does not gen-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                542,
+                                505,
+                                556
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        542,
+                                        505,
+                                        556
+                                    ],
+                                    "score": 1.0,
+                                    "content": "eralize to continuous distances such as PPR. Therefore, we propose a constant-time approximation",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                552,
+                                505,
+                                567
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        552,
+                                        373,
+                                        567
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of the relational attention computation by grouping the values into",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        373,
+                                        553,
+                                        409,
+                                        564
+                                    ],
+                                    "score": 0.91,
+                                    "content": "k \\ll N ^ { 2 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        409,
+                                        552,
+                                        505,
+                                        567
+                                    ],
+                                    "score": 1.0,
+                                    "content": "bins. Since closer sam-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                564,
+                                505,
+                                577
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        564,
+                                        505,
+                                        577
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ples are typically more relevant for a query sample, we increase the bin widths exponentially with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                575,
+                                506,
+                                588
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        575,
+                                        506,
+                                        588
+                                    ],
+                                    "score": 1.0,
+                                    "content": "growing distance values. Throughout our experiments we have found the CODE TRANSFORMER to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                586,
+                                450,
+                                599
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        587,
+                                        340,
+                                        599
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be relatively insensitive to the number of bins; we thus set",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        340,
+                                        586,
+                                        370,
+                                        596
+                                    ],
+                                    "score": 0.9,
+                                    "content": "k = 3 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        371,
+                                        587,
+                                        450,
+                                        599
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in our experiments.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 23,
+                    "bbox_fs": [
+                        105,
+                        497,
+                        506,
+                        599
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        617,
+                        242,
+                        629
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                616,
+                                244,
+                                631
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        616,
+                                        244,
+                                        631
+                                    ],
+                                    "score": 1.0,
+                                    "content": "4 EXPERIMENTAL SETUP",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 28
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        643,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                643,
+                                505,
+                                656
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        643,
+                                        505,
+                                        656
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Code summarization is one of the most popular tasks in machine learning for code. Given the body",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                654,
+                                505,
+                                667
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        654,
+                                        505,
+                                        667
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of a function, the task is to predict the function’s name. As observed by Alon et al. (2019b) and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                665,
+                                505,
+                                678
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        665,
+                                        505,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Allamanis et al. (2016), this is a useful benchmark as method names in open-source projects tend to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                677,
+                                505,
+                                689
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        677,
+                                        505,
+                                        689
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be precise and descriptive, and functions typically form complete logical units. See Fig. 3 (right) for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                687,
+                                505,
+                                700
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        687,
+                                        505,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a visual overview of the task. We use two complementary representations of programs: the source",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                699,
+                                505,
+                                711
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        699,
+                                        505,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "code as a sequence of tokens (Context) and the AST (Structure). As shown in Fig. 3 (left), tokens",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                710,
+                                505,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        710,
+                                        505,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that are far away on the sequence may be very close on the AST and vice versa. In this task we make",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                720,
+                                505,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        720,
+                                        505,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "use of the CODE TRANSFORMER’s ability jointly leverage both Structure and Context and show that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                82,
+                                505,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        82,
+                                        505,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "it improves learning. Further, we show the benefit of using only language-agnostic features in our",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                93,
+                                391,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        93,
+                                        391,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "model by training the first multilingual model for code summarization.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 32.5,
+                    "bbox_fs": [
+                        105,
+                        643,
+                        505,
+                        732
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        82,
+                        504,
+                        105
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                82,
+                                505,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        82,
+                                        505,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "it improves learning. Further, we show the benefit of using only language-agnostic features in our",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                93,
+                                391,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        93,
+                                        391,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "model by training the first multilingual model for code summarization.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        113,
+                        504,
+                        168
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                114,
+                                505,
+                                126
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        114,
+                                        505,
+                                        126
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Datasets. To highlight the benefit of only relying on language-agnostic representations such as",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                124,
+                                504,
+                                137
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        124,
+                                        504,
+                                        137
+                                    ],
+                                    "score": 1.0,
+                                    "content": "source code and abstract syntax trees, we evaluate on challenging datasets in four programming lan-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                134,
+                                506,
+                                149
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        134,
+                                        506,
+                                        149
+                                    ],
+                                    "score": 1.0,
+                                    "content": "guages introduced in the CodeSearchNet (CSN) Challenge (Husain et al., 2019): Python, Javascript,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                146,
+                                505,
+                                159
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        146,
+                                        505,
+                                        159
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Go, and Ruby. Similar to Java-small, the datasets from CodeSearchNet have been carefully dedu-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                157,
+                                495,
+                                170
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        157,
+                                        495,
+                                        170
+                                    ],
+                                    "score": 1.0,
+                                    "content": "plicated by the creators to avoid data leakage from the training set, e.g., via copy-and-paste code.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        174,
+                        324,
+                        299
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                174,
+                                324,
+                                186
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        174,
+                                        324,
+                                        186
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We further evaluate on Java-small (Allamanis et al.,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                185,
+                                325,
+                                198
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        185,
+                                        325,
+                                        198
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2016), a popular and challenging code summarization",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                196,
+                                325,
+                                208
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        196,
+                                        325,
+                                        208
+                                    ],
+                                    "score": 1.0,
+                                    "content": "dataset. It contains 11 open-source Java projects. We",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                207,
+                                325,
+                                218
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        207,
+                                        325,
+                                        218
+                                    ],
+                                    "score": 1.0,
+                                    "content": "use the split as in Alon et al. (2019a), where 9 of these",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                218,
+                                325,
+                                230
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        218,
+                                        325,
+                                        230
+                                    ],
+                                    "score": 1.0,
+                                    "content": "projects are used for training, one for validation, and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                228,
+                                325,
+                                240
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        228,
+                                        325,
+                                        240
+                                    ],
+                                    "score": 1.0,
+                                    "content": "one for test. The dataset contains roughly 700K sam-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                240,
+                                325,
+                                252
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        240,
+                                        325,
+                                        252
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ples (function definitions). Moreover, we also experi-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                251,
+                                325,
+                                263
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        251,
+                                        325,
+                                        263
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ment with pre-training our model on Java-medium and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                262,
+                                325,
+                                275
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        262,
+                                        325,
+                                        275
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Java-large (Alon et al., 2019a) before fine-tuning on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                272,
+                                325,
+                                285
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        272,
+                                        325,
+                                        285
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Java-small, making sure to avoid leakage by removing",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                284,
+                                325,
+                                295
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        284,
+                                        325,
+                                        295
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the test and validation projects of Java-small from the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        334,
+                        187,
+                        505,
+                        269
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                334,
+                                187,
+                                505,
+                                269
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        334,
+                                        187,
+                                        505,
+                                        269
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                334,
+                                                187,
+                                                505,
+                                                269
+                                            ],
+                                            "score": 0.977,
+                                            "html": "<table><tr><td></td><td colspan=\"3\">Samples per partition</td></tr><tr><td>Dataset</td><td>Train</td><td>Val.</td><td>Test</td></tr><tr><td>CSN-Python</td><td>412,178</td><td>23,107</td><td>22,176</td></tr><tr><td>CSN-Javascript</td><td>123,889</td><td>8,253</td><td>6,483</td></tr><tr><td>CSN-Ruby</td><td>48,791</td><td>2,209</td><td>2,279</td></tr><tr><td>CSN-Go</td><td>317,832</td><td>14,242</td><td>14,291</td></tr><tr><td>Java-small</td><td>691,974</td><td>23,844</td><td>57,088</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "b4225af91868e1a8a78db0e52181e077f82a2809a40ec936d5ee0af636f96fb7.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 20.5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        334,
+                                        187,
+                                        505,
+                                        200.66666666666666
+                                    ],
+                                    "spans": [],
+                                    "index": 18
+                                },
+                                {
+                                    "bbox": [
+                                        334,
+                                        200.66666666666666,
+                                        505,
+                                        214.33333333333331
+                                    ],
+                                    "spans": [],
+                                    "index": 19
+                                },
+                                {
+                                    "bbox": [
+                                        334,
+                                        214.33333333333331,
+                                        505,
+                                        227.99999999999997
+                                    ],
+                                    "spans": [],
+                                    "index": 20
+                                },
+                                {
+                                    "bbox": [
+                                        334,
+                                        227.99999999999997,
+                                        505,
+                                        241.66666666666663
+                                    ],
+                                    "spans": [],
+                                    "index": 21
+                                },
+                                {
+                                    "bbox": [
+                                        334,
+                                        241.66666666666663,
+                                        505,
+                                        255.3333333333333
+                                    ],
+                                    "spans": [],
+                                    "index": 22
+                                },
+                                {
+                                    "bbox": [
+                                        334,
+                                        255.3333333333333,
+                                        505,
+                                        268.99999999999994
+                                    ],
+                                    "spans": [],
+                                    "index": 23
+                                }
+                            ]
+                        },
+                        {
+                            "type": "table_footnote",
+                            "bbox": [
+                                366,
+                                277,
+                                471,
+                                288
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        365,
+                                        276,
+                                        472,
+                                        288
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                365,
+                                                276,
+                                                472,
+                                                288
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 1: Dataset statistics.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 24
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 22.25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        295,
+                        439,
+                        306
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                294,
+                                441,
+                                307
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        294,
+                                        441,
+                                        307
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pre-training dataset. See Table 1 for a summary of the datasets we use in this work.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        314,
+                        505,
+                        392
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                313,
+                                505,
+                                328
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        313,
+                                        505,
+                                        328
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Preprocessing. Each token of the source code is split into subtokens respective to code naming",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                324,
+                                505,
+                                339
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        324,
+                                        505,
+                                        339
+                                    ],
+                                    "score": 1.0,
+                                    "content": "conventions, i.e., get TrainingData is converted to [get, training, data]. Following",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                337,
+                                504,
+                                348
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        337,
+                                        504,
+                                        348
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Alon et al. (2019a) we use at most six subtokens for the method names, truncating longer function",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                347,
+                                505,
+                                360
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        347,
+                                        505,
+                                        360
+                                    ],
+                                    "score": 1.0,
+                                    "content": "names if necessary. In addition to the tokenized source code we produce an AST for each method",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                358,
+                                505,
+                                370
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        358,
+                                        505,
+                                        370
+                                    ],
+                                    "score": 1.0,
+                                    "content": "using the open-source AST parser Semantic3. We limit the vocabulary to subtokens with at least 100",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                368,
+                                506,
+                                383
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        368,
+                                        506,
+                                        383
+                                    ],
+                                    "score": 1.0,
+                                    "content": "occurrences in the training set, and only consider snippets with 512 or fewer tokens (after removing",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                379,
+                                484,
+                                394
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        379,
+                                        484,
+                                        394
+                                    ],
+                                    "score": 1.0,
+                                    "content": "punctuation). We refer the reader to the appendix for further details on the data preprocessing.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 29
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        399,
+                        504,
+                        466
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                400,
+                                505,
+                                412
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        400,
+                                        505,
+                                        412
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Pointer network. We add a pointer network (Vinyals et al., 2015) (as described in Fernandes et al.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                411,
+                                505,
+                                423
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        411,
+                                        505,
+                                        423
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(2019)) to the decoders of all Transformer-based models. This enables them to enhance their predic-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                422,
+                                505,
+                                434
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        422,
+                                        505,
+                                        434
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tions by pointing at positions in the input sequence. For instance, when predicting the method name",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                432,
+                                506,
+                                446
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        432,
+                                        506,
+                                        446
+                                    ],
+                                    "score": 1.0,
+                                    "content": "get url, the model can point directly to occurrences of the variable url. This often improves",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                444,
+                                505,
+                                456
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        444,
+                                        505,
+                                        456
+                                    ],
+                                    "score": 1.0,
+                                    "content": "results for less frequent tokens, and even enables the model to predict tokens which are not in the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                455,
+                                320,
+                                468
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        455,
+                                        320,
+                                        468
+                                    ],
+                                    "score": 1.0,
+                                    "content": "vocabulary by pointing at their positions in the input.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        }
+                    ],
+                    "index": 35.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        474,
+                        505,
+                        617
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                474,
+                                505,
+                                487
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        474,
+                                        505,
+                                        487
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Baselines. We compare with code2seq (Alon et al., 2019a), the Graph Relational Embedding At-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                484,
+                                506,
+                                498
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        484,
+                                        432,
+                                        498
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tention Transformer (GREAT) (Hellendoorn et al., 2020), and the BiLSTM+GNN",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        433,
+                                        486,
+                                        442,
+                                        495
+                                    ],
+                                    "score": 0.75,
+                                    "content": "",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        443,
+                                        484,
+                                        506,
+                                        498
+                                    ],
+                                    "score": 1.0,
+                                    "content": "LSTM+Pointer",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                496,
+                                506,
+                                509
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        496,
+                                        506,
+                                        509
+                                    ],
+                                    "score": 1.0,
+                                    "content": "model presented in Fernandes et al. (2019). Code2seq is a non-Transformer model and state of the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                507,
+                                505,
+                                519
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        507,
+                                        505,
+                                        519
+                                    ],
+                                    "score": 1.0,
+                                    "content": "art for code summarization using only AST information. GREAT is a recent Transformer model",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                518,
+                                504,
+                                531
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        518,
+                                        504,
+                                        531
+                                    ],
+                                    "score": 1.0,
+                                    "content": "using the framework presented in (Shaw et al., 2018) to bias the attention via edges. In the origi-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                529,
+                                505,
+                                542
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        529,
+                                        505,
+                                        542
+                                    ],
+                                    "score": 1.0,
+                                    "content": "nal formulation, GREAT additionally uses hand-crafted, language-specific edges such as dataflow,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                540,
+                                506,
+                                554
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        540,
+                                        506,
+                                        554
+                                    ],
+                                    "score": 1.0,
+                                    "content": "‘computed from’, or ‘next lexical use’ edges, which require specialized preprocessing and static",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                550,
+                                506,
+                                565
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        550,
+                                        506,
+                                        565
+                                    ],
+                                    "score": 1.0,
+                                    "content": "analysis tools. While this approach of leveraging language-specific features can certainly improve",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                562,
+                                505,
+                                575
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        562,
+                                        505,
+                                        575
+                                    ],
+                                    "score": 1.0,
+                                    "content": "results on specific tasks and programming languages, our goal is to have a flexible model that can",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                573,
+                                505,
+                                587
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        573,
+                                        505,
+                                        587
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be used on any programming language. Since the specialized preprocessing used by GREAT is pro-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                584,
+                                506,
+                                597
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        584,
+                                        506,
+                                        597
+                                    ],
+                                    "score": 1.0,
+                                    "content": "prietary and not public, we produce the results for GREAT using edges from the AST instead, i.e. it",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                594,
+                                506,
+                                608
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        594,
+                                        506,
+                                        608
+                                    ],
+                                    "score": 1.0,
+                                    "content": "has access to the same information as our proposed model. Note that the preprocessing of Fernandes",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                606,
+                                496,
+                                619
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        606,
+                                        496,
+                                        619
+                                    ],
+                                    "score": 1.0,
+                                    "content": "et al. (2019) is language specific, which is why we only compare with their results on Java-small.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 51
+                        }
+                    ],
+                    "index": 45
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        633,
+                        172,
+                        646
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                632,
+                                174,
+                                649
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        632,
+                                        174,
+                                        649
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5 RESULTS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 52
+                        }
+                    ],
+                    "index": 52
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        109,
+                        659,
+                        300,
+                        669
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                659,
+                                302,
+                                671
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        659,
+                                        302,
+                                        671
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5.1 MONOLINGUAL CODE SUMMARIZATION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 53
+                        }
+                    ],
+                    "index": 53
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        679,
+                        504,
+                        713
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                678,
+                                506,
+                                692
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        678,
+                                        506,
+                                        692
+                                    ],
+                                    "score": 1.0,
+                                    "content": "CSN dataset. First, we study the performance (measured by F1 score) of our model and the base-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 54
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                690,
+                                505,
+                                703
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        690,
+                                        505,
+                                        703
+                                    ],
+                                    "score": 1.0,
+                                    "content": "lines on the traditional setting, where training and evaluation are performed on a single programming",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 55
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                702,
+                                505,
+                                713
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        702,
+                                        505,
+                                        713
+                                    ],
+                                    "score": 1.0,
+                                    "content": "language. The results are shown in the upper part of Table 2. The CODE TRANSFORMER (without",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 56
+                        }
+                    ],
+                    "index": 55
+                }
+            ],
+            "page_idx": 5,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        118,
+                        722,
+                        308,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                119,
+                                720,
+                                308,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        119,
+                                        720,
+                                        308,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3https://github.com/github/semantic",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        108,
+                        27,
+                        292,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                293,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        293,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        752,
+                        308,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                302,
+                                751,
+                                309,
+                                762
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        302,
+                                        751,
+                                        309,
+                                        762
+                                    ],
+                                    "score": 1.0,
+                                    "content": "6",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        82,
+                        504,
+                        105
+                    ],
+                    "lines": [],
+                    "index": 0.5,
+                    "bbox_fs": [
+                        106,
+                        82,
+                        505,
+                        106
+                    ],
+                    "lines_deleted": true
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        113,
+                        504,
+                        168
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                114,
+                                505,
+                                126
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        114,
+                                        505,
+                                        126
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Datasets. To highlight the benefit of only relying on language-agnostic representations such as",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                124,
+                                504,
+                                137
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        124,
+                                        504,
+                                        137
+                                    ],
+                                    "score": 1.0,
+                                    "content": "source code and abstract syntax trees, we evaluate on challenging datasets in four programming lan-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                134,
+                                506,
+                                149
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        134,
+                                        506,
+                                        149
+                                    ],
+                                    "score": 1.0,
+                                    "content": "guages introduced in the CodeSearchNet (CSN) Challenge (Husain et al., 2019): Python, Javascript,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                146,
+                                505,
+                                159
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        146,
+                                        505,
+                                        159
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Go, and Ruby. Similar to Java-small, the datasets from CodeSearchNet have been carefully dedu-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                157,
+                                495,
+                                170
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        157,
+                                        495,
+                                        170
+                                    ],
+                                    "score": 1.0,
+                                    "content": "plicated by the creators to avoid data leakage from the training set, e.g., via copy-and-paste code.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 4,
+                    "bbox_fs": [
+                        105,
+                        114,
+                        506,
+                        170
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        174,
+                        324,
+                        299
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                174,
+                                324,
+                                186
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        174,
+                                        324,
+                                        186
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We further evaluate on Java-small (Allamanis et al.,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                185,
+                                325,
+                                198
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        185,
+                                        325,
+                                        198
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2016), a popular and challenging code summarization",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                196,
+                                325,
+                                208
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        196,
+                                        325,
+                                        208
+                                    ],
+                                    "score": 1.0,
+                                    "content": "dataset. It contains 11 open-source Java projects. We",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                207,
+                                325,
+                                218
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        207,
+                                        325,
+                                        218
+                                    ],
+                                    "score": 1.0,
+                                    "content": "use the split as in Alon et al. (2019a), where 9 of these",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                218,
+                                325,
+                                230
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        218,
+                                        325,
+                                        230
+                                    ],
+                                    "score": 1.0,
+                                    "content": "projects are used for training, one for validation, and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                228,
+                                325,
+                                240
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        228,
+                                        325,
+                                        240
+                                    ],
+                                    "score": 1.0,
+                                    "content": "one for test. The dataset contains roughly 700K sam-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                240,
+                                325,
+                                252
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        240,
+                                        325,
+                                        252
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ples (function definitions). Moreover, we also experi-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                251,
+                                325,
+                                263
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        251,
+                                        325,
+                                        263
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ment with pre-training our model on Java-medium and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                262,
+                                325,
+                                275
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        262,
+                                        325,
+                                        275
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Java-large (Alon et al., 2019a) before fine-tuning on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                272,
+                                325,
+                                285
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        272,
+                                        325,
+                                        285
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Java-small, making sure to avoid leakage by removing",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                284,
+                                325,
+                                295
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        284,
+                                        325,
+                                        295
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the test and validation projects of Java-small from the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                294,
+                                441,
+                                307
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        294,
+                                        441,
+                                        307
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pre-training dataset. See Table 1 for a summary of the datasets we use in this work.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 12,
+                    "bbox_fs": [
+                        105,
+                        174,
+                        325,
+                        295
+                    ]
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        334,
+                        187,
+                        505,
+                        269
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                334,
+                                187,
+                                505,
+                                269
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        334,
+                                        187,
+                                        505,
+                                        269
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                334,
+                                                187,
+                                                505,
+                                                269
+                                            ],
+                                            "score": 0.977,
+                                            "html": "<table><tr><td></td><td colspan=\"3\">Samples per partition</td></tr><tr><td>Dataset</td><td>Train</td><td>Val.</td><td>Test</td></tr><tr><td>CSN-Python</td><td>412,178</td><td>23,107</td><td>22,176</td></tr><tr><td>CSN-Javascript</td><td>123,889</td><td>8,253</td><td>6,483</td></tr><tr><td>CSN-Ruby</td><td>48,791</td><td>2,209</td><td>2,279</td></tr><tr><td>CSN-Go</td><td>317,832</td><td>14,242</td><td>14,291</td></tr><tr><td>Java-small</td><td>691,974</td><td>23,844</td><td>57,088</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "b4225af91868e1a8a78db0e52181e077f82a2809a40ec936d5ee0af636f96fb7.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 20.5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        334,
+                                        187,
+                                        505,
+                                        200.66666666666666
+                                    ],
+                                    "spans": [],
+                                    "index": 18
+                                },
+                                {
+                                    "bbox": [
+                                        334,
+                                        200.66666666666666,
+                                        505,
+                                        214.33333333333331
+                                    ],
+                                    "spans": [],
+                                    "index": 19
+                                },
+                                {
+                                    "bbox": [
+                                        334,
+                                        214.33333333333331,
+                                        505,
+                                        227.99999999999997
+                                    ],
+                                    "spans": [],
+                                    "index": 20
+                                },
+                                {
+                                    "bbox": [
+                                        334,
+                                        227.99999999999997,
+                                        505,
+                                        241.66666666666663
+                                    ],
+                                    "spans": [],
+                                    "index": 21
+                                },
+                                {
+                                    "bbox": [
+                                        334,
+                                        241.66666666666663,
+                                        505,
+                                        255.3333333333333
+                                    ],
+                                    "spans": [],
+                                    "index": 22
+                                },
+                                {
+                                    "bbox": [
+                                        334,
+                                        255.3333333333333,
+                                        505,
+                                        268.99999999999994
+                                    ],
+                                    "spans": [],
+                                    "index": 23
+                                }
+                            ]
+                        },
+                        {
+                            "type": "table_footnote",
+                            "bbox": [
+                                366,
+                                277,
+                                471,
+                                288
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        365,
+                                        276,
+                                        472,
+                                        288
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                365,
+                                                276,
+                                                472,
+                                                288
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 1: Dataset statistics.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 24
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 22.25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        295,
+                        439,
+                        306
+                    ],
+                    "lines": [],
+                    "index": 25,
+                    "bbox_fs": [
+                        105,
+                        294,
+                        441,
+                        307
+                    ],
+                    "lines_deleted": true
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        314,
+                        505,
+                        392
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                313,
+                                505,
+                                328
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        313,
+                                        505,
+                                        328
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Preprocessing. Each token of the source code is split into subtokens respective to code naming",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                324,
+                                505,
+                                339
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        324,
+                                        505,
+                                        339
+                                    ],
+                                    "score": 1.0,
+                                    "content": "conventions, i.e., get TrainingData is converted to [get, training, data]. Following",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                337,
+                                504,
+                                348
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        337,
+                                        504,
+                                        348
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Alon et al. (2019a) we use at most six subtokens for the method names, truncating longer function",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                347,
+                                505,
+                                360
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        347,
+                                        505,
+                                        360
+                                    ],
+                                    "score": 1.0,
+                                    "content": "names if necessary. In addition to the tokenized source code we produce an AST for each method",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                358,
+                                505,
+                                370
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        358,
+                                        505,
+                                        370
+                                    ],
+                                    "score": 1.0,
+                                    "content": "using the open-source AST parser Semantic3. We limit the vocabulary to subtokens with at least 100",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                368,
+                                506,
+                                383
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        368,
+                                        506,
+                                        383
+                                    ],
+                                    "score": 1.0,
+                                    "content": "occurrences in the training set, and only consider snippets with 512 or fewer tokens (after removing",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                379,
+                                484,
+                                394
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        379,
+                                        484,
+                                        394
+                                    ],
+                                    "score": 1.0,
+                                    "content": "punctuation). We refer the reader to the appendix for further details on the data preprocessing.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 29,
+                    "bbox_fs": [
+                        105,
+                        313,
+                        506,
+                        394
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        399,
+                        504,
+                        466
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                400,
+                                505,
+                                412
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        400,
+                                        505,
+                                        412
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Pointer network. We add a pointer network (Vinyals et al., 2015) (as described in Fernandes et al.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                411,
+                                505,
+                                423
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        411,
+                                        505,
+                                        423
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(2019)) to the decoders of all Transformer-based models. This enables them to enhance their predic-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                422,
+                                505,
+                                434
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        422,
+                                        505,
+                                        434
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tions by pointing at positions in the input sequence. For instance, when predicting the method name",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                432,
+                                506,
+                                446
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        432,
+                                        506,
+                                        446
+                                    ],
+                                    "score": 1.0,
+                                    "content": "get url, the model can point directly to occurrences of the variable url. This often improves",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                444,
+                                505,
+                                456
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        444,
+                                        505,
+                                        456
+                                    ],
+                                    "score": 1.0,
+                                    "content": "results for less frequent tokens, and even enables the model to predict tokens which are not in the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                455,
+                                320,
+                                468
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        455,
+                                        320,
+                                        468
+                                    ],
+                                    "score": 1.0,
+                                    "content": "vocabulary by pointing at their positions in the input.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        }
+                    ],
+                    "index": 35.5,
+                    "bbox_fs": [
+                        105,
+                        400,
+                        506,
+                        468
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        474,
+                        505,
+                        617
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                474,
+                                505,
+                                487
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        474,
+                                        505,
+                                        487
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Baselines. We compare with code2seq (Alon et al., 2019a), the Graph Relational Embedding At-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                484,
+                                506,
+                                498
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        484,
+                                        432,
+                                        498
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tention Transformer (GREAT) (Hellendoorn et al., 2020), and the BiLSTM+GNN",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        433,
+                                        486,
+                                        442,
+                                        495
+                                    ],
+                                    "score": 0.75,
+                                    "content": "",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        443,
+                                        484,
+                                        506,
+                                        498
+                                    ],
+                                    "score": 1.0,
+                                    "content": "LSTM+Pointer",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                496,
+                                506,
+                                509
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        496,
+                                        506,
+                                        509
+                                    ],
+                                    "score": 1.0,
+                                    "content": "model presented in Fernandes et al. (2019). Code2seq is a non-Transformer model and state of the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                507,
+                                505,
+                                519
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        507,
+                                        505,
+                                        519
+                                    ],
+                                    "score": 1.0,
+                                    "content": "art for code summarization using only AST information. GREAT is a recent Transformer model",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                518,
+                                504,
+                                531
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        518,
+                                        504,
+                                        531
+                                    ],
+                                    "score": 1.0,
+                                    "content": "using the framework presented in (Shaw et al., 2018) to bias the attention via edges. In the origi-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                529,
+                                505,
+                                542
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        529,
+                                        505,
+                                        542
+                                    ],
+                                    "score": 1.0,
+                                    "content": "nal formulation, GREAT additionally uses hand-crafted, language-specific edges such as dataflow,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                540,
+                                506,
+                                554
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        540,
+                                        506,
+                                        554
+                                    ],
+                                    "score": 1.0,
+                                    "content": "‘computed from’, or ‘next lexical use’ edges, which require specialized preprocessing and static",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                550,
+                                506,
+                                565
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        550,
+                                        506,
+                                        565
+                                    ],
+                                    "score": 1.0,
+                                    "content": "analysis tools. While this approach of leveraging language-specific features can certainly improve",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                562,
+                                505,
+                                575
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        562,
+                                        505,
+                                        575
+                                    ],
+                                    "score": 1.0,
+                                    "content": "results on specific tasks and programming languages, our goal is to have a flexible model that can",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                573,
+                                505,
+                                587
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        573,
+                                        505,
+                                        587
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be used on any programming language. Since the specialized preprocessing used by GREAT is pro-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                584,
+                                506,
+                                597
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        584,
+                                        506,
+                                        597
+                                    ],
+                                    "score": 1.0,
+                                    "content": "prietary and not public, we produce the results for GREAT using edges from the AST instead, i.e. it",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                594,
+                                506,
+                                608
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        594,
+                                        506,
+                                        608
+                                    ],
+                                    "score": 1.0,
+                                    "content": "has access to the same information as our proposed model. Note that the preprocessing of Fernandes",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                606,
+                                496,
+                                619
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        606,
+                                        496,
+                                        619
+                                    ],
+                                    "score": 1.0,
+                                    "content": "et al. (2019) is language specific, which is why we only compare with their results on Java-small.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 51
+                        }
+                    ],
+                    "index": 45,
+                    "bbox_fs": [
+                        105,
+                        474,
+                        506,
+                        619
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        633,
+                        172,
+                        646
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                632,
+                                174,
+                                649
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        632,
+                                        174,
+                                        649
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5 RESULTS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 52
+                        }
+                    ],
+                    "index": 52
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        109,
+                        659,
+                        300,
+                        669
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                659,
+                                302,
+                                671
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        659,
+                                        302,
+                                        671
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5.1 MONOLINGUAL CODE SUMMARIZATION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 53
+                        }
+                    ],
+                    "index": 53
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        679,
+                        504,
+                        713
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                678,
+                                506,
+                                692
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        678,
+                                        506,
+                                        692
+                                    ],
+                                    "score": 1.0,
+                                    "content": "CSN dataset. First, we study the performance (measured by F1 score) of our model and the base-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 54
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                690,
+                                505,
+                                703
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        690,
+                                        505,
+                                        703
+                                    ],
+                                    "score": 1.0,
+                                    "content": "lines on the traditional setting, where training and evaluation are performed on a single programming",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 55
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                702,
+                                505,
+                                713
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        702,
+                                        505,
+                                        713
+                                    ],
+                                    "score": 1.0,
+                                    "content": "language. The results are shown in the upper part of Table 2. The CODE TRANSFORMER (without",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 56
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                234,
+                                504,
+                                246
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        234,
+                                        504,
+                                        246
+                                    ],
+                                    "score": 1.0,
+                                    "content": "multi-language training) substantially outperforms all other models on all but one language, high-",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                244,
+                                505,
+                                258
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        244,
+                                        505,
+                                        258
+                                    ],
+                                    "score": 1.0,
+                                    "content": "lighting the effectiveness of jointly learning from Structure and Context. The only exception is Ruby,",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                255,
+                                506,
+                                269
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        255,
+                                        506,
+                                        269
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where it performs on par with its Context-only variant. We attribute this to the fact that there are",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                266,
+                                505,
+                                279
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        266,
+                                        505,
+                                        279
+                                    ],
+                                    "score": 1.0,
+                                    "content": "relatively few samples in the Ruby dataset, and that Ruby is an dynamically typed language, which",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                278,
+                                505,
+                                289
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        278,
+                                        505,
+                                        289
+                                    ],
+                                    "score": 1.0,
+                                    "content": "could make the Structure less powerful for learning. Interestingly, the Context-only CODE TRANS-",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                288,
+                                505,
+                                301
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        288,
+                                        505,
+                                        301
+                                    ],
+                                    "score": 1.0,
+                                    "content": "FORMER outperforms GREAT on all languages. We attribute this to the fact that GREAT uses the",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                299,
+                                506,
+                                312
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        299,
+                                        506,
+                                        312
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Structure of the programs only in a localized way (see Sec. 3.1). Another noteworthy finding is",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                310,
+                                506,
+                                323
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        310,
+                                        506,
+                                        323
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that code2seq performs comparably to the Transformer-based baselines on Go. We hypothesize that",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                320,
+                                449,
+                                335
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        320,
+                                        449,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ASTs are more informative on Go since it is a compiled and strongly typed language.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "index": 55,
+                    "bbox_fs": [
+                        105,
+                        678,
+                        506,
+                        713
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "table",
+                    "bbox": [
+                        108,
+                        63,
+                        503,
+                        192
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                108,
+                                63,
+                                503,
+                                192
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        108,
+                                        63,
+                                        503,
+                                        192
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                108,
+                                                63,
+                                                503,
+                                                192
+                                            ],
+                                            "score": 0.982,
+                                            "html": "<table><tr><td rowspan=\"2\">Model</td><td colspan=\"3\">Python</td><td colspan=\"3\">Javascript</td><td colspan=\"3\">Ruby</td><td colspan=\"3\">Go</td></tr><tr><td>Prec.</td><td>Rec.</td><td>F1</td><td>Prec.</td><td>Rec.</td><td>F1</td><td>Prec.</td><td>Rec.</td><td>F1</td><td>Prec.</td><td>Rec.</td><td>F1</td></tr><tr><td>code2seq</td><td>35.79</td><td>24.85</td><td>29.34</td><td>30.18</td><td>19.88</td><td>23.97</td><td>23.23</td><td>10.31</td><td>14.28</td><td>52.30</td><td>43.43</td><td>47.45</td></tr><tr><td>GREAT</td><td>35.07</td><td>31.59</td><td>33.24</td><td>31.20</td><td>26.84</td><td>28.86</td><td>24.64</td><td>22.23</td><td>23.38</td><td>50.01</td><td>46.51</td><td>48.20</td></tr><tr><td>Ours w/o structure</td><td>37.38</td><td>31.98</td><td>34.47</td><td>33.17</td><td>26.70</td><td>29.59</td><td>29.85</td><td>25.87</td><td>27.72</td><td>51.78</td><td>47.57</td><td>49.59</td></tr><tr><td>Ours w/o pointer net</td><td>37.74</td><td>31.85</td><td>34.55</td><td>33.12</td><td>28.70</td><td>30.75</td><td>23.32</td><td>25.21</td><td>24.23</td><td>54.31</td><td>50.12</td><td>52.13</td></tr><tr><td>Ours</td><td>36.40</td><td>33.66</td><td>34.97</td><td>35.06</td><td>29.61</td><td>32.11</td><td>31.42</td><td>24.46</td><td>27.50</td><td>55.10</td><td>48.05</td><td>51.34</td></tr><tr><td>code2seq (Multilanguage)</td><td>34.49</td><td>25.49</td><td>29.32</td><td>31.62</td><td>22.16</td><td>26.06</td><td>23.97</td><td>17.06</td><td>19.93</td><td>52.70</td><td>44.36</td><td>48.17</td></tr><tr><td>GREAT (Multilanguage)</td><td>36.75</td><td>31.54</td><td>33.94</td><td>33.58</td><td>27.78</td><td>30.41</td><td>30.05</td><td>24.33</td><td>26.89</td><td>52.65</td><td>48.30</td><td>50.38</td></tr><tr><td>Ours w/o structure (Mult.)</td><td>38.48</td><td>30.14</td><td>33.80</td><td>35.38</td><td>27.41</td><td>30.89</td><td>32.61</td><td>26.76</td><td>29.40</td><td>55.03</td><td>47.34</td><td>50.90</td></tr><tr><td>Ours w/o pointer (Mult.)</td><td>38.91</td><td>33.12</td><td>35.78</td><td>37.21</td><td>29.75</td><td>33.07</td><td>34.52</td><td>27.31</td><td>30.50</td><td>56.07</td><td>50.76</td><td>53.28</td></tr><tr><td>Ours (Multilanguage)</td><td>38.89</td><td>33.82</td><td>36.18</td><td>36.95</td><td>29.98</td><td>33.10</td><td>33.93</td><td>28.94</td><td>31.24</td><td>56.00</td><td>50.44</td><td>53.07</td></tr><tr><td>Ours (Mult.+ Finetune)</td><td>39.85</td><td>32.79</td><td>35.98</td><td>37.00</td><td>29.79</td><td>33.00</td><td>35.85</td><td>27.75</td><td>31.28</td><td>55.63</td><td>51.12</td><td>53.28</td></tr><tr><td>Ours (Mult. + LM Pretrain)</td><td>39.67</td><td>35.29</td><td>37.35</td><td>37.06</td><td>31.94</td><td>34.31</td><td>35.19</td><td>29.36</td><td>32.01</td><td>57.73</td><td>51.89</td><td>54.65</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "6ea8249b1a6b65be5a059f68d87e3dba30b23b79c16802b7d266349476c02871.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        108,
+                                        63,
+                                        503,
+                                        106.0
+                                    ],
+                                    "spans": [],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        108,
+                                        106.0,
+                                        503,
+                                        149.0
+                                    ],
+                                    "spans": [],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        108,
+                                        149.0,
+                                        503,
+                                        192.0
+                                    ],
+                                    "spans": [],
+                                    "index": 2
+                                }
+                            ]
+                        },
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                167,
+                                200,
+                                442,
+                                212
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        167,
+                                        198,
+                                        443,
+                                        213
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                167,
+                                                198,
+                                                443,
+                                                213
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 2: Code summarization results on the CSN dataset (micro F1).",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 2.0
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        233,
+                        505,
+                        333
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                234,
+                                504,
+                                246
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        234,
+                                        504,
+                                        246
+                                    ],
+                                    "score": 1.0,
+                                    "content": "multi-language training) substantially outperforms all other models on all but one language, high-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                244,
+                                505,
+                                258
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        244,
+                                        505,
+                                        258
+                                    ],
+                                    "score": 1.0,
+                                    "content": "lighting the effectiveness of jointly learning from Structure and Context. The only exception is Ruby,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                255,
+                                506,
+                                269
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        255,
+                                        506,
+                                        269
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where it performs on par with its Context-only variant. We attribute this to the fact that there are",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                266,
+                                505,
+                                279
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        266,
+                                        505,
+                                        279
+                                    ],
+                                    "score": 1.0,
+                                    "content": "relatively few samples in the Ruby dataset, and that Ruby is an dynamically typed language, which",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                278,
+                                505,
+                                289
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        278,
+                                        505,
+                                        289
+                                    ],
+                                    "score": 1.0,
+                                    "content": "could make the Structure less powerful for learning. Interestingly, the Context-only CODE TRANS-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                288,
+                                505,
+                                301
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        288,
+                                        505,
+                                        301
+                                    ],
+                                    "score": 1.0,
+                                    "content": "FORMER outperforms GREAT on all languages. We attribute this to the fact that GREAT uses the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                299,
+                                506,
+                                312
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        299,
+                                        506,
+                                        312
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Structure of the programs only in a localized way (see Sec. 3.1). Another noteworthy finding is",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                310,
+                                506,
+                                323
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        310,
+                                        506,
+                                        323
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that code2seq performs comparably to the Transformer-based baselines on Go. We hypothesize that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                320,
+                                449,
+                                335
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        320,
+                                        449,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ASTs are more informative on Go since it is a compiled and strongly typed language.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        345,
+                        505,
+                        422
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                344,
+                                505,
+                                357
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        344,
+                                        505,
+                                        357
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Java-small results. In Table 3 we present code summarization results on the Java-small dataset.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                356,
+                                505,
+                                369
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        356,
+                                        505,
+                                        369
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Among all models equipped with a pointer network, the CODE TRANSFORMER (without pre-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                367,
+                                505,
+                                379
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        367,
+                                        505,
+                                        379
+                                    ],
+                                    "score": 1.0,
+                                    "content": "training) obtains state-of-the-art on code summarization, outperforming all baselines, including the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                377,
+                                506,
+                                392
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        377,
+                                        506,
+                                        392
+                                    ],
+                                    "score": 1.0,
+                                    "content": "previous state-of-the-art on Java-small proposed by Fernandes et al. (2019). Further, pre-training",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                388,
+                                505,
+                                402
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        388,
+                                        505,
+                                        402
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on Java-medium and Java-large on the permutation language modeling objective (Yang et al., 2019)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                399,
+                                505,
+                                413
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        399,
+                                        505,
+                                        413
+                                    ],
+                                    "score": 1.0,
+                                    "content": "substantially improves precision, recall, and F1 score after fine-tuning on Java-small. To avoid leak-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                411,
+                                495,
+                                425
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        411,
+                                        495,
+                                        425
+                                    ],
+                                    "score": 1.0,
+                                    "content": "age, we exclude the projects used in the validation and test splits of Java-small from pre-training.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        434,
+                        504,
+                        457
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                434,
+                                505,
+                                447
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        434,
+                                        505,
+                                        447
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Ablation study. We further perform ablations where we remove our model’s access to the Context",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                446,
+                                263,
+                                457
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        446,
+                                        263,
+                                        457
+                                    ],
+                                    "score": 1.0,
+                                    "content": "or Structure, also presented in Table 3.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 20.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        463,
+                        295,
+                        626
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                462,
+                                296,
+                                474
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        462,
+                                        296,
+                                        474
+                                    ],
+                                    "score": 1.0,
+                                    "content": "With pointer network. We find that both ab-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                473,
+                                297,
+                                485
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        473,
+                                        297,
+                                        485
+                                    ],
+                                    "score": 1.0,
+                                    "content": "lations lead to a substantial drop in perfor-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                484,
+                                297,
+                                497
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        484,
+                                        297,
+                                        497
+                                    ],
+                                    "score": 1.0,
+                                    "content": "mance, highlighting the benefit of learning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                495,
+                                297,
+                                507
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        495,
+                                        297,
+                                        507
+                                    ],
+                                    "score": 1.0,
+                                    "content": "jointly from Structure and Context. Interest-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                506,
+                                297,
+                                518
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        506,
+                                        297,
+                                        518
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ingly, the model without access to the Struc-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                518,
+                                297,
+                                529
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        518,
+                                        297,
+                                        529
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ture performs slightly better than the variant",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                528,
+                                297,
+                                539
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        528,
+                                        297,
+                                        539
+                                    ],
+                                    "score": 1.0,
+                                    "content": "without Context. Note that our model with-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                538,
+                                297,
+                                552
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        538,
+                                        297,
+                                        552
+                                    ],
+                                    "score": 1.0,
+                                    "content": "out Structure is related to the XLNet (Yang",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                550,
+                                297,
+                                562
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        550,
+                                        297,
+                                        562
+                                    ],
+                                    "score": 1.0,
+                                    "content": "et al., 2019) model, where we add a pointer net-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                561,
+                                297,
+                                573
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        561,
+                                        297,
+                                        573
+                                    ],
+                                    "score": 1.0,
+                                    "content": "work to the decoder and concatenate the token",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                572,
+                                297,
+                                585
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        572,
+                                        297,
+                                        585
+                                    ],
+                                    "score": 1.0,
+                                    "content": "types to their respective input tokens (see Ap-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                583,
+                                297,
+                                594
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        583,
+                                        297,
+                                        594
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pendix A.4). Without pointer network. We re-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                595,
+                                297,
+                                606
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        595,
+                                        297,
+                                        606
+                                    ],
+                                    "score": 1.0,
+                                    "content": "peat the ablation on the variants without pointer",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                605,
+                                297,
+                                617
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        605,
+                                        297,
+                                        617
+                                    ],
+                                    "score": 1.0,
+                                    "content": "network. Here, the variant without Context per-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                615,
+                                297,
+                                628
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        615,
+                                        297,
+                                        628
+                                    ],
+                                    "score": 1.0,
+                                    "content": "forms better than the variant without Structure,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 29
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        315,
+                        462,
+                        496,
+                        603
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                315,
+                                462,
+                                496,
+                                603
+                            ],
+                            "group_id": 1,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        315,
+                                        462,
+                                        496,
+                                        603
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                315,
+                                                462,
+                                                496,
+                                                603
+                                            ],
+                                            "score": 0.98,
+                                            "html": "<table><tr><td>Model</td><td>Prec.</td><td>Rec.</td><td>F1</td></tr><tr><td>Without pointer net code2seq Ours w/o structure Ours w/o context</td><td>51.23 50.70 51.81</td><td>37.31 45.49 46.04</td><td>43.18 47.96</td></tr><tr><td>Ours With pointer net</td><td>50.33</td><td>46.80</td><td>48.75 48.50</td></tr><tr><td>Fernandes et al. (2019)</td><td>=</td><td>1</td><td>51.4</td></tr><tr><td>GREAT Ours w/o structure</td><td>53.60</td><td>46.41</td><td>49.75</td></tr><tr><td>Ours w/o context</td><td>55.48</td><td>46.07</td><td>50.34</td></tr><tr><td></td><td>54.45</td><td>45.29</td><td>49.45</td></tr><tr><td>Ours</td><td>54.85</td><td>49.84</td><td>52.22</td></tr><tr><td>Ours + Pretrain</td><td>57.02</td><td>50.87</td><td>53.77</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "93c3db634ac78ceb6a3e42a79f6c881109ae26412d90ebf329ef70021d85d788.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 42,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        315,
+                                        462,
+                                        496,
+                                        474.8181818181818
+                                    ],
+                                    "spans": [],
+                                    "index": 37
+                                },
+                                {
+                                    "bbox": [
+                                        315,
+                                        474.8181818181818,
+                                        496,
+                                        487.6363636363636
+                                    ],
+                                    "spans": [],
+                                    "index": 38
+                                },
+                                {
+                                    "bbox": [
+                                        315,
+                                        487.6363636363636,
+                                        496,
+                                        500.45454545454544
+                                    ],
+                                    "spans": [],
+                                    "index": 39
+                                },
+                                {
+                                    "bbox": [
+                                        315,
+                                        500.45454545454544,
+                                        496,
+                                        513.2727272727273
+                                    ],
+                                    "spans": [],
+                                    "index": 40
+                                },
+                                {
+                                    "bbox": [
+                                        315,
+                                        513.2727272727273,
+                                        496,
+                                        526.0909090909091
+                                    ],
+                                    "spans": [],
+                                    "index": 41
+                                },
+                                {
+                                    "bbox": [
+                                        315,
+                                        526.0909090909091,
+                                        496,
+                                        538.909090909091
+                                    ],
+                                    "spans": [],
+                                    "index": 42
+                                },
+                                {
+                                    "bbox": [
+                                        315,
+                                        538.909090909091,
+                                        496,
+                                        551.7272727272729
+                                    ],
+                                    "spans": [],
+                                    "index": 43
+                                },
+                                {
+                                    "bbox": [
+                                        315,
+                                        551.7272727272729,
+                                        496,
+                                        564.5454545454547
+                                    ],
+                                    "spans": [],
+                                    "index": 44
+                                },
+                                {
+                                    "bbox": [
+                                        315,
+                                        564.5454545454547,
+                                        496,
+                                        577.3636363636366
+                                    ],
+                                    "spans": [],
+                                    "index": 45
+                                },
+                                {
+                                    "bbox": [
+                                        315,
+                                        577.3636363636366,
+                                        496,
+                                        590.1818181818185
+                                    ],
+                                    "spans": [],
+                                    "index": 46
+                                },
+                                {
+                                    "bbox": [
+                                        315,
+                                        590.1818181818185,
+                                        496,
+                                        603.0000000000003
+                                    ],
+                                    "spans": [],
+                                    "index": 47
+                                }
+                            ]
+                        },
+                        {
+                            "type": "table_footnote",
+                            "bbox": [
+                                304,
+                                612,
+                                504,
+                                622
+                            ],
+                            "group_id": 1,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        303,
+                                        610,
+                                        505,
+                                        624
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                303,
+                                                610,
+                                                505,
+                                                624
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 3: Results on Java-small and ablation study.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 48
+                                }
+                            ],
+                            "index": 48
+                        }
+                    ],
+                    "index": 45.0
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        627,
+                        505,
+                        671
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                627,
+                                505,
+                                639
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        627,
+                                        505,
+                                        639
+                                    ],
+                                    "score": 1.0,
+                                    "content": "indicating that the pointer network helps to compensate for the lack of access to Structure. The",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                639,
+                                504,
+                                649
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        639,
+                                        504,
+                                        649
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Structure-only variant (w/o pointer net) of our model even outperforms the full variant in this sce-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                649,
+                                505,
+                                661
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        649,
+                                        505,
+                                        661
+                                    ],
+                                    "score": 1.0,
+                                    "content": "nario. Inspection of the results revealed that the Structure-only variant has better performance on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 51
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                660,
+                                489,
+                                671
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        660,
+                                        489,
+                                        671
+                                    ],
+                                    "score": 1.0,
+                                    "content": "longer method names, which have an outsize influence on the micro-F1 score used in this work.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 52
+                        }
+                    ],
+                    "index": 50.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        677,
+                        504,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                678,
+                                505,
+                                688
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        678,
+                                        505,
+                                        688
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Ablation of the AST-based distances. In Table 4 we compare the performance of our model when",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 53
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                687,
+                                505,
+                                700
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        687,
+                                        505,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "trained with each of the four different AST distances (sibling shortest paths, ancestor shortest paths,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 54
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                699,
+                                505,
+                                711
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        699,
+                                        505,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "shortest paths, personalized PageRank; see Section 3.1). Here, the model is trained on Java-small",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 55
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                710,
+                                505,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        710,
+                                        505,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in the Structure-only setting and without pointer network. For reference, we also show the results",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 56
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                721,
+                                505,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        721,
+                                        505,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of training our model using all four AST distance functions (c.f. Table 3). We find that, while the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 57
+                        }
+                    ],
+                    "index": 55
+                }
+            ],
+            "page_idx": 6,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        108,
+                        27,
+                        292,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                25,
+                                293,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        25,
+                                        293,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        303,
+                        751,
+                        309,
+                        759
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                302,
+                                750,
+                                309,
+                                762
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        302,
+                                        750,
+                                        309,
+                                        762
+                                    ],
+                                    "score": 1.0,
+                                    "content": "7",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "table",
+                    "bbox": [
+                        108,
+                        63,
+                        503,
+                        192
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                108,
+                                63,
+                                503,
+                                192
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        108,
+                                        63,
+                                        503,
+                                        192
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                108,
+                                                63,
+                                                503,
+                                                192
+                                            ],
+                                            "score": 0.982,
+                                            "html": "<table><tr><td rowspan=\"2\">Model</td><td colspan=\"3\">Python</td><td colspan=\"3\">Javascript</td><td colspan=\"3\">Ruby</td><td colspan=\"3\">Go</td></tr><tr><td>Prec.</td><td>Rec.</td><td>F1</td><td>Prec.</td><td>Rec.</td><td>F1</td><td>Prec.</td><td>Rec.</td><td>F1</td><td>Prec.</td><td>Rec.</td><td>F1</td></tr><tr><td>code2seq</td><td>35.79</td><td>24.85</td><td>29.34</td><td>30.18</td><td>19.88</td><td>23.97</td><td>23.23</td><td>10.31</td><td>14.28</td><td>52.30</td><td>43.43</td><td>47.45</td></tr><tr><td>GREAT</td><td>35.07</td><td>31.59</td><td>33.24</td><td>31.20</td><td>26.84</td><td>28.86</td><td>24.64</td><td>22.23</td><td>23.38</td><td>50.01</td><td>46.51</td><td>48.20</td></tr><tr><td>Ours w/o structure</td><td>37.38</td><td>31.98</td><td>34.47</td><td>33.17</td><td>26.70</td><td>29.59</td><td>29.85</td><td>25.87</td><td>27.72</td><td>51.78</td><td>47.57</td><td>49.59</td></tr><tr><td>Ours w/o pointer net</td><td>37.74</td><td>31.85</td><td>34.55</td><td>33.12</td><td>28.70</td><td>30.75</td><td>23.32</td><td>25.21</td><td>24.23</td><td>54.31</td><td>50.12</td><td>52.13</td></tr><tr><td>Ours</td><td>36.40</td><td>33.66</td><td>34.97</td><td>35.06</td><td>29.61</td><td>32.11</td><td>31.42</td><td>24.46</td><td>27.50</td><td>55.10</td><td>48.05</td><td>51.34</td></tr><tr><td>code2seq (Multilanguage)</td><td>34.49</td><td>25.49</td><td>29.32</td><td>31.62</td><td>22.16</td><td>26.06</td><td>23.97</td><td>17.06</td><td>19.93</td><td>52.70</td><td>44.36</td><td>48.17</td></tr><tr><td>GREAT (Multilanguage)</td><td>36.75</td><td>31.54</td><td>33.94</td><td>33.58</td><td>27.78</td><td>30.41</td><td>30.05</td><td>24.33</td><td>26.89</td><td>52.65</td><td>48.30</td><td>50.38</td></tr><tr><td>Ours w/o structure (Mult.)</td><td>38.48</td><td>30.14</td><td>33.80</td><td>35.38</td><td>27.41</td><td>30.89</td><td>32.61</td><td>26.76</td><td>29.40</td><td>55.03</td><td>47.34</td><td>50.90</td></tr><tr><td>Ours w/o pointer (Mult.)</td><td>38.91</td><td>33.12</td><td>35.78</td><td>37.21</td><td>29.75</td><td>33.07</td><td>34.52</td><td>27.31</td><td>30.50</td><td>56.07</td><td>50.76</td><td>53.28</td></tr><tr><td>Ours (Multilanguage)</td><td>38.89</td><td>33.82</td><td>36.18</td><td>36.95</td><td>29.98</td><td>33.10</td><td>33.93</td><td>28.94</td><td>31.24</td><td>56.00</td><td>50.44</td><td>53.07</td></tr><tr><td>Ours (Mult.+ Finetune)</td><td>39.85</td><td>32.79</td><td>35.98</td><td>37.00</td><td>29.79</td><td>33.00</td><td>35.85</td><td>27.75</td><td>31.28</td><td>55.63</td><td>51.12</td><td>53.28</td></tr><tr><td>Ours (Mult. + LM Pretrain)</td><td>39.67</td><td>35.29</td><td>37.35</td><td>37.06</td><td>31.94</td><td>34.31</td><td>35.19</td><td>29.36</td><td>32.01</td><td>57.73</td><td>51.89</td><td>54.65</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "6ea8249b1a6b65be5a059f68d87e3dba30b23b79c16802b7d266349476c02871.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        108,
+                                        63,
+                                        503,
+                                        106.0
+                                    ],
+                                    "spans": [],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        108,
+                                        106.0,
+                                        503,
+                                        149.0
+                                    ],
+                                    "spans": [],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        108,
+                                        149.0,
+                                        503,
+                                        192.0
+                                    ],
+                                    "spans": [],
+                                    "index": 2
+                                }
+                            ]
+                        },
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                167,
+                                200,
+                                442,
+                                212
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        167,
+                                        198,
+                                        443,
+                                        213
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                167,
+                                                198,
+                                                443,
+                                                213
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 2: Code summarization results on the CSN dataset (micro F1).",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 2.0
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        233,
+                        505,
+                        333
+                    ],
+                    "lines": [],
+                    "index": 8,
+                    "bbox_fs": [
+                        105,
+                        234,
+                        506,
+                        335
+                    ],
+                    "lines_deleted": true
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        345,
+                        505,
+                        422
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                344,
+                                505,
+                                357
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        344,
+                                        505,
+                                        357
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Java-small results. In Table 3 we present code summarization results on the Java-small dataset.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                356,
+                                505,
+                                369
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        356,
+                                        505,
+                                        369
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Among all models equipped with a pointer network, the CODE TRANSFORMER (without pre-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                367,
+                                505,
+                                379
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        367,
+                                        505,
+                                        379
+                                    ],
+                                    "score": 1.0,
+                                    "content": "training) obtains state-of-the-art on code summarization, outperforming all baselines, including the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                377,
+                                506,
+                                392
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        377,
+                                        506,
+                                        392
+                                    ],
+                                    "score": 1.0,
+                                    "content": "previous state-of-the-art on Java-small proposed by Fernandes et al. (2019). Further, pre-training",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                388,
+                                505,
+                                402
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        388,
+                                        505,
+                                        402
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on Java-medium and Java-large on the permutation language modeling objective (Yang et al., 2019)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                399,
+                                505,
+                                413
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        399,
+                                        505,
+                                        413
+                                    ],
+                                    "score": 1.0,
+                                    "content": "substantially improves precision, recall, and F1 score after fine-tuning on Java-small. To avoid leak-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                411,
+                                495,
+                                425
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        411,
+                                        495,
+                                        425
+                                    ],
+                                    "score": 1.0,
+                                    "content": "age, we exclude the projects used in the validation and test splits of Java-small from pre-training.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 16,
+                    "bbox_fs": [
+                        105,
+                        344,
+                        506,
+                        425
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        434,
+                        504,
+                        457
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                434,
+                                505,
+                                447
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        434,
+                                        505,
+                                        447
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Ablation study. We further perform ablations where we remove our model’s access to the Context",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                446,
+                                263,
+                                457
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        446,
+                                        263,
+                                        457
+                                    ],
+                                    "score": 1.0,
+                                    "content": "or Structure, also presented in Table 3.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 20.5,
+                    "bbox_fs": [
+                        105,
+                        434,
+                        505,
+                        457
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        463,
+                        295,
+                        626
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                462,
+                                296,
+                                474
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        462,
+                                        296,
+                                        474
+                                    ],
+                                    "score": 1.0,
+                                    "content": "With pointer network. We find that both ab-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                473,
+                                297,
+                                485
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        473,
+                                        297,
+                                        485
+                                    ],
+                                    "score": 1.0,
+                                    "content": "lations lead to a substantial drop in perfor-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                484,
+                                297,
+                                497
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        484,
+                                        297,
+                                        497
+                                    ],
+                                    "score": 1.0,
+                                    "content": "mance, highlighting the benefit of learning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                495,
+                                297,
+                                507
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        495,
+                                        297,
+                                        507
+                                    ],
+                                    "score": 1.0,
+                                    "content": "jointly from Structure and Context. Interest-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                506,
+                                297,
+                                518
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        506,
+                                        297,
+                                        518
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ingly, the model without access to the Struc-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                518,
+                                297,
+                                529
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        518,
+                                        297,
+                                        529
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ture performs slightly better than the variant",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                528,
+                                297,
+                                539
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        528,
+                                        297,
+                                        539
+                                    ],
+                                    "score": 1.0,
+                                    "content": "without Context. Note that our model with-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                538,
+                                297,
+                                552
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        538,
+                                        297,
+                                        552
+                                    ],
+                                    "score": 1.0,
+                                    "content": "out Structure is related to the XLNet (Yang",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                550,
+                                297,
+                                562
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        550,
+                                        297,
+                                        562
+                                    ],
+                                    "score": 1.0,
+                                    "content": "et al., 2019) model, where we add a pointer net-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                561,
+                                297,
+                                573
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        561,
+                                        297,
+                                        573
+                                    ],
+                                    "score": 1.0,
+                                    "content": "work to the decoder and concatenate the token",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                572,
+                                297,
+                                585
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        572,
+                                        297,
+                                        585
+                                    ],
+                                    "score": 1.0,
+                                    "content": "types to their respective input tokens (see Ap-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                583,
+                                297,
+                                594
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        583,
+                                        297,
+                                        594
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pendix A.4). Without pointer network. We re-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                595,
+                                297,
+                                606
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        595,
+                                        297,
+                                        606
+                                    ],
+                                    "score": 1.0,
+                                    "content": "peat the ablation on the variants without pointer",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                605,
+                                297,
+                                617
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        605,
+                                        297,
+                                        617
+                                    ],
+                                    "score": 1.0,
+                                    "content": "network. Here, the variant without Context per-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                615,
+                                297,
+                                628
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        615,
+                                        297,
+                                        628
+                                    ],
+                                    "score": 1.0,
+                                    "content": "forms better than the variant without Structure,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 29,
+                    "bbox_fs": [
+                        105,
+                        462,
+                        297,
+                        628
+                    ]
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        315,
+                        462,
+                        496,
+                        603
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                315,
+                                462,
+                                496,
+                                603
+                            ],
+                            "group_id": 1,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        315,
+                                        462,
+                                        496,
+                                        603
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                315,
+                                                462,
+                                                496,
+                                                603
+                                            ],
+                                            "score": 0.98,
+                                            "html": "<table><tr><td>Model</td><td>Prec.</td><td>Rec.</td><td>F1</td></tr><tr><td>Without pointer net code2seq Ours w/o structure Ours w/o context</td><td>51.23 50.70 51.81</td><td>37.31 45.49 46.04</td><td>43.18 47.96</td></tr><tr><td>Ours With pointer net</td><td>50.33</td><td>46.80</td><td>48.75 48.50</td></tr><tr><td>Fernandes et al. (2019)</td><td>=</td><td>1</td><td>51.4</td></tr><tr><td>GREAT Ours w/o structure</td><td>53.60</td><td>46.41</td><td>49.75</td></tr><tr><td>Ours w/o context</td><td>55.48</td><td>46.07</td><td>50.34</td></tr><tr><td></td><td>54.45</td><td>45.29</td><td>49.45</td></tr><tr><td>Ours</td><td>54.85</td><td>49.84</td><td>52.22</td></tr><tr><td>Ours + Pretrain</td><td>57.02</td><td>50.87</td><td>53.77</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "93c3db634ac78ceb6a3e42a79f6c881109ae26412d90ebf329ef70021d85d788.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 42,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        315,
+                                        462,
+                                        496,
+                                        474.8181818181818
+                                    ],
+                                    "spans": [],
+                                    "index": 37
+                                },
+                                {
+                                    "bbox": [
+                                        315,
+                                        474.8181818181818,
+                                        496,
+                                        487.6363636363636
+                                    ],
+                                    "spans": [],
+                                    "index": 38
+                                },
+                                {
+                                    "bbox": [
+                                        315,
+                                        487.6363636363636,
+                                        496,
+                                        500.45454545454544
+                                    ],
+                                    "spans": [],
+                                    "index": 39
+                                },
+                                {
+                                    "bbox": [
+                                        315,
+                                        500.45454545454544,
+                                        496,
+                                        513.2727272727273
+                                    ],
+                                    "spans": [],
+                                    "index": 40
+                                },
+                                {
+                                    "bbox": [
+                                        315,
+                                        513.2727272727273,
+                                        496,
+                                        526.0909090909091
+                                    ],
+                                    "spans": [],
+                                    "index": 41
+                                },
+                                {
+                                    "bbox": [
+                                        315,
+                                        526.0909090909091,
+                                        496,
+                                        538.909090909091
+                                    ],
+                                    "spans": [],
+                                    "index": 42
+                                },
+                                {
+                                    "bbox": [
+                                        315,
+                                        538.909090909091,
+                                        496,
+                                        551.7272727272729
+                                    ],
+                                    "spans": [],
+                                    "index": 43
+                                },
+                                {
+                                    "bbox": [
+                                        315,
+                                        551.7272727272729,
+                                        496,
+                                        564.5454545454547
+                                    ],
+                                    "spans": [],
+                                    "index": 44
+                                },
+                                {
+                                    "bbox": [
+                                        315,
+                                        564.5454545454547,
+                                        496,
+                                        577.3636363636366
+                                    ],
+                                    "spans": [],
+                                    "index": 45
+                                },
+                                {
+                                    "bbox": [
+                                        315,
+                                        577.3636363636366,
+                                        496,
+                                        590.1818181818185
+                                    ],
+                                    "spans": [],
+                                    "index": 46
+                                },
+                                {
+                                    "bbox": [
+                                        315,
+                                        590.1818181818185,
+                                        496,
+                                        603.0000000000003
+                                    ],
+                                    "spans": [],
+                                    "index": 47
+                                }
+                            ]
+                        },
+                        {
+                            "type": "table_footnote",
+                            "bbox": [
+                                304,
+                                612,
+                                504,
+                                622
+                            ],
+                            "group_id": 1,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        303,
+                                        610,
+                                        505,
+                                        624
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                303,
+                                                610,
+                                                505,
+                                                624
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 3: Results on Java-small and ablation study.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 48
+                                }
+                            ],
+                            "index": 48
+                        }
+                    ],
+                    "index": 45.0
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        627,
+                        505,
+                        671
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                627,
+                                505,
+                                639
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        627,
+                                        505,
+                                        639
+                                    ],
+                                    "score": 1.0,
+                                    "content": "indicating that the pointer network helps to compensate for the lack of access to Structure. The",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                639,
+                                504,
+                                649
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        639,
+                                        504,
+                                        649
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Structure-only variant (w/o pointer net) of our model even outperforms the full variant in this sce-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                649,
+                                505,
+                                661
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        649,
+                                        505,
+                                        661
+                                    ],
+                                    "score": 1.0,
+                                    "content": "nario. Inspection of the results revealed that the Structure-only variant has better performance on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 51
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                660,
+                                489,
+                                671
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        660,
+                                        489,
+                                        671
+                                    ],
+                                    "score": 1.0,
+                                    "content": "longer method names, which have an outsize influence on the micro-F1 score used in this work.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 52
+                        }
+                    ],
+                    "index": 50.5,
+                    "bbox_fs": [
+                        105,
+                        627,
+                        505,
+                        671
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        677,
+                        504,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                678,
+                                505,
+                                688
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        678,
+                                        505,
+                                        688
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Ablation of the AST-based distances. In Table 4 we compare the performance of our model when",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 53
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                687,
+                                505,
+                                700
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        687,
+                                        505,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "trained with each of the four different AST distances (sibling shortest paths, ancestor shortest paths,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 54
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                699,
+                                505,
+                                711
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        699,
+                                        505,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "shortest paths, personalized PageRank; see Section 3.1). Here, the model is trained on Java-small",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 55
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                710,
+                                505,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        710,
+                                        505,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in the Structure-only setting and without pointer network. For reference, we also show the results",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 56
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                721,
+                                505,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        721,
+                                        505,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of training our model using all four AST distance functions (c.f. Table 3). We find that, while the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 57
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                82,
+                                506,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        82,
+                                        506,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "personalized PageRank distance performs best on its own, each of the individual distances on their",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                93,
+                                505,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        93,
+                                        505,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "own performs substantially worse than their combination, highlighting the usefulness of combining",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                104,
+                                370,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        104,
+                                        370,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the distances in our model as well as their complementary nature.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 55,
+                    "bbox_fs": [
+                        105,
+                        678,
+                        505,
+                        732
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        82,
+                        504,
+                        116
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                82,
+                                506,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        82,
+                                        506,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "personalized PageRank distance performs best on its own, each of the individual distances on their",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                93,
+                                505,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        93,
+                                        505,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "own performs substantially worse than their combination, highlighting the usefulness of combining",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                104,
+                                370,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        104,
+                                        370,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the distances in our model as well as their complementary nature.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        129,
+                        300,
+                        140
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                128,
+                                302,
+                                141
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        128,
+                                        302,
+                                        141
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5.2 MULTILINGUAL CODE SUMMARIZATION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        149,
+                        338,
+                        237
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                149,
+                                339,
+                                161
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        149,
+                                        339,
+                                        161
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Setup. A key contribution of our proposed architecture",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                160,
+                                339,
+                                173
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        160,
+                                        339,
+                                        173
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is that it only uses language-agnostic features, i.e. the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                171,
+                                339,
+                                183
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        171,
+                                        339,
+                                        183
+                                    ],
+                                    "score": 1.0,
+                                    "content": "source code and features that can be directly computed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                182,
+                                339,
+                                194
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        182,
+                                        339,
+                                        194
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from the AST. We use this fact to study the first multi-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                194,
+                                339,
+                                205
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        194,
+                                        339,
+                                        205
+                                    ],
+                                    "score": 1.0,
+                                    "content": "language code summarization model. We train our model",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                205,
+                                340,
+                                216
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        205,
+                                        340,
+                                        216
+                                    ],
+                                    "score": 1.0,
+                                    "content": "jointly on Python, Javascript, Ruby, and Go. The shared",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                215,
+                                339,
+                                227
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        215,
+                                        339,
+                                        227
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sub-token vocabulary is the union of the individual vocab-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                227,
+                                340,
+                                239
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        227,
+                                        340,
+                                        239
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ularies, enabling us to evaluate the multi-language model",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 7.5
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        354,
+                        146,
+                        496,
+                        212
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                354,
+                                146,
+                                496,
+                                212
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        354,
+                                        146,
+                                        496,
+                                        212
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                354,
+                                                146,
+                                                496,
+                                                212
+                                            ],
+                                            "score": 0.971,
+                                            "html": "<table><tr><td>AST distance</td><td>F1 score</td></tr><tr><td>Sibling shortest paths</td><td>46.17</td></tr><tr><td>Ancestor shortest paths</td><td>47.89</td></tr><tr><td>Shortest paths</td><td>47.76</td></tr><tr><td>Personalized PageRank</td><td>48.47</td></tr><tr><td>All the above (c.f. Table 3)</td><td>48.75</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "44d93ce3802abbb255784a0d5f66ef881ac7c557a4abf8c4d5752cc699deb37d.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 12.5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        354,
+                                        146,
+                                        496,
+                                        179.0
+                                    ],
+                                    "spans": [],
+                                    "index": 12
+                                },
+                                {
+                                    "bbox": [
+                                        354,
+                                        179.0,
+                                        496,
+                                        212.0
+                                    ],
+                                    "spans": [],
+                                    "index": 13
+                                }
+                            ]
+                        },
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                351,
+                                221,
+                                501,
+                                232
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        349,
+                                        218,
+                                        501,
+                                        234
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                349,
+                                                218,
+                                                501,
+                                                234
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 4: AST distance ablation study.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 14
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 13.25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        238,
+                        505,
+                        259
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                236,
+                                505,
+                                250
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        236,
+                                        505,
+                                        250
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on the individual languages and compare with the single-language models. As proposed by Conneau",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                246,
+                                439,
+                                262
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        246,
+                                        439,
+                                        262
+                                    ],
+                                    "score": 1.0,
+                                    "content": "& Lample (2019), we add a learned language embedding to each input embedding.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 15.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        271,
+                        505,
+                        360
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                271,
+                                505,
+                                284
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        271,
+                                        505,
+                                        284
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Results. In the lower part of Table 2 we can see the results of training our CODE TRANSFORMER",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                283,
+                                505,
+                                295
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        283,
+                                        505,
+                                        295
+                                    ],
+                                    "score": 1.0,
+                                    "content": "jointly on all four programming languages. Our multi-lingual variants substantially outperform",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                293,
+                                506,
+                                306
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        293,
+                                        506,
+                                        306
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the mono-lingual models on all languages. The strongest improvement is on Ruby, which is also",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                304,
+                                506,
+                                318
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        304,
+                                        506,
+                                        318
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the programming language with the smallest number of samples in the dataset. Fine-tuning on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                315,
+                                506,
+                                328
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        315,
+                                        506,
+                                        328
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the individual languages after joint training on code summarization only has a marginal effect on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                325,
+                                506,
+                                340
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        325,
+                                        506,
+                                        340
+                                    ],
+                                    "score": 1.0,
+                                    "content": "performance, indicating that the multilingual objective is well-aligned with the individual languages.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                337,
+                                506,
+                                351
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        337,
+                                        506,
+                                        351
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In the last row, we have a variant of our model where we pre-train on the multi-lingual masked",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                348,
+                                505,
+                                362
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        348,
+                                        505,
+                                        362
+                                    ],
+                                    "score": 1.0,
+                                    "content": "language modeling task, followed by finetuning on code summarization on the individual languages.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 20.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        365,
+                        505,
+                        442
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                364,
+                                505,
+                                378
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        364,
+                                        505,
+                                        378
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Further, we observe that similar to the results on Java-small, removing the pointer network generally",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                377,
+                                505,
+                                388
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        377,
+                                        505,
+                                        388
+                                    ],
+                                    "score": 1.0,
+                                    "content": "leads to weaker performance. One notable exception is Go, where the variant without the pointer",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                387,
+                                505,
+                                399
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        387,
+                                        505,
+                                        399
+                                    ],
+                                    "score": 1.0,
+                                    "content": "network performs better in terms of F1 score. Our investigation revealed that there seems to be some",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                398,
+                                505,
+                                411
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        398,
+                                        505,
+                                        411
+                                    ],
+                                    "score": 1.0,
+                                    "content": "violation of the i.i.d. assumption in the split provided by the creators of the dataset. In Figure 7 we",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                408,
+                                506,
+                                422
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        408,
+                                        506,
+                                        422
+                                    ],
+                                    "score": 1.0,
+                                    "content": "show that in the test partition of the Go dataset, the share of tokens from the labels also occurring in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                420,
+                                505,
+                                432
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        420,
+                                        505,
+                                        432
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the methods’ bodies – exactly the scenario where the pointer network can improve predictions – is",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                431,
+                                357,
+                                443
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        431,
+                                        357,
+                                        443
+                                    ],
+                                    "score": 1.0,
+                                    "content": "substantially lower compared to the train/validation partitions.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        }
+                    ],
+                    "index": 28
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        448,
+                        505,
+                        514
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                448,
+                                505,
+                                460
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        448,
+                                        505,
+                                        460
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Remarkably, the multi-language Context-only variant (i.e. without access to the Structure) performs",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                459,
+                                505,
+                                470
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        459,
+                                        505,
+                                        470
+                                    ],
+                                    "score": 1.0,
+                                    "content": "substantially worse than the full multi-language variant. This highlights that Structure is crucial to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                469,
+                                505,
+                                483
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        469,
+                                        505,
+                                        483
+                                    ],
+                                    "score": 1.0,
+                                    "content": "exploit the commonalities of different programming languages. Also notably, the GREAT baseline’s",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                480,
+                                505,
+                                493
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        480,
+                                        505,
+                                        493
+                                    ],
+                                    "score": 1.0,
+                                    "content": "results also improve substantially when trained in the multi-language setting, though it is still outper-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                491,
+                                506,
+                                505
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        491,
+                                        506,
+                                        505
+                                    ],
+                                    "score": 1.0,
+                                    "content": "formed by our model. However, our results indicate that any representation learning model for code",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                502,
+                                495,
+                                516
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        502,
+                                        495,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "can benefit from multi-language training, especially when evaluating on low-resource languages.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 34.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        519,
+                        504,
+                        553
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                520,
+                                505,
+                                532
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        520,
+                                        505,
+                                        532
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In Table 16 we present results using the sample-F1 score. At the time of submission, our mono-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                530,
+                                506,
+                                543
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        530,
+                                        422,
+                                        543
+                                    ],
+                                    "score": 1.0,
+                                    "content": "lingual model on Python outperforms the state of the art on the ogbg-code",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        422,
+                                        530,
+                                        433,
+                                        541
+                                    ],
+                                    "score": 0.67,
+                                    "content": "2 ^ { 4 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        433,
+                                        530,
+                                        506,
+                                        543
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(Hu et al., 2020)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                542,
+                                503,
+                                554
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        542,
+                                        169,
+                                        554
+                                    ],
+                                    "score": 1.0,
+                                    "content": "leaderboard by",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        169,
+                                        542,
+                                        193,
+                                        552
+                                    ],
+                                    "score": 0.86,
+                                    "content": "112 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        193,
+                                        542,
+                                        474,
+                                        554
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and our multilanguage variant with LM pretraining outperforms it by",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        475,
+                                        542,
+                                        499,
+                                        552
+                                    ],
+                                    "score": 0.9,
+                                    "content": "122 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        499,
+                                        542,
+                                        503,
+                                        554
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        }
+                    ],
+                    "index": 39
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        565,
+                        505,
+                        664
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                564,
+                                505,
+                                578
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        564,
+                                        505,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Qualitative analysis of multilingual representations. Learning the CODE TRANSFORMER on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                576,
+                                505,
+                                588
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        576,
+                                        505,
+                                        588
+                                    ],
+                                    "score": 1.0,
+                                    "content": "multiple programming languages jointly provides us with embeddings in a shared representation",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                586,
+                                506,
+                                600
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        586,
+                                        506,
+                                        600
+                                    ],
+                                    "score": 1.0,
+                                    "content": "space. In Fig. 4 we show a t-SNE (Maaten & Hinton, 2008) visualization of the ca. 40,000 snippets",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                596,
+                                506,
+                                612
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        596,
+                                        506,
+                                        612
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from the validation sets of four programming languages from the CSN dataset. For the embedding",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                609,
+                                506,
+                                622
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        609,
+                                        506,
+                                        622
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of a snippet, we use the representation of the method name in the final layer of the encoder. Note",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                619,
+                                506,
+                                632
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        619,
+                                        506,
+                                        632
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that the true method names are masked, i.e., inaccessible to the model. Further, note that in contrast",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                630,
+                                506,
+                                644
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        630,
+                                        506,
+                                        644
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to the monolingual embeddings learned by Kanade et al. (2020), the embeddings we evaluate are",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                640,
+                                505,
+                                655
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        640,
+                                        505,
+                                        655
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learned on the task of code summarization (though a similar study could be performed by using our",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                652,
+                                505,
+                                666
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        652,
+                                        505,
+                                        666
+                                    ],
+                                    "score": 1.0,
+                                    "content": "model that was trained on the traditional language modeling pretraining task on multiple languages).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        }
+                    ],
+                    "index": 45
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        669,
+                        504,
+                        714
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                669,
+                                506,
+                                682
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        669,
+                                        506,
+                                        682
+                                    ],
+                                    "score": 1.0,
+                                    "content": "While snippets from the same language tend to be grouped together, there are interesting intersec-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                680,
+                                506,
+                                694
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        680,
+                                        506,
+                                        694
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tions of the different programming languages. For example, we highlight all methods whose names",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 51
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                692,
+                                505,
+                                704
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        692,
+                                        505,
+                                        704
+                                    ],
+                                    "score": 1.0,
+                                    "content": "start with the subtoken parse or main. We see that snippets starting with parse are predom-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 52
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                703,
+                                505,
+                                715
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        703,
+                                        505,
+                                        715
+                                    ],
+                                    "score": 1.0,
+                                    "content": "inantly in an intersection region of Python and Javascript. From these snippets, we display the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 53
+                        }
+                    ],
+                    "index": 51.5
+                }
+            ],
+            "page_idx": 7,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        117,
+                        722,
+                        399,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                118,
+                                719,
+                                400,
+                                734
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        118,
+                                        719,
+                                        400,
+                                        734
+                                    ],
+                                    "score": 1.0,
+                                    "content": "4https://ogb.stanford.edu/docs/graphprop/#ogbg-code2",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        108,
+                        27,
+                        292,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                293,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        293,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        752,
+                        308,
+                        759
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                302,
+                                750,
+                                309,
+                                761
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        302,
+                                        750,
+                                        309,
+                                        761
+                                    ],
+                                    "score": 1.0,
+                                    "content": "8",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        82,
+                        504,
+                        116
+                    ],
+                    "lines": [],
+                    "index": 1,
+                    "bbox_fs": [
+                        105,
+                        82,
+                        506,
+                        117
+                    ],
+                    "lines_deleted": true
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        129,
+                        300,
+                        140
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                128,
+                                302,
+                                141
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        128,
+                                        302,
+                                        141
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5.2 MULTILINGUAL CODE SUMMARIZATION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        149,
+                        338,
+                        237
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                149,
+                                339,
+                                161
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        149,
+                                        339,
+                                        161
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Setup. A key contribution of our proposed architecture",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                160,
+                                339,
+                                173
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        160,
+                                        339,
+                                        173
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is that it only uses language-agnostic features, i.e. the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                171,
+                                339,
+                                183
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        171,
+                                        339,
+                                        183
+                                    ],
+                                    "score": 1.0,
+                                    "content": "source code and features that can be directly computed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                182,
+                                339,
+                                194
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        182,
+                                        339,
+                                        194
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from the AST. We use this fact to study the first multi-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                194,
+                                339,
+                                205
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        194,
+                                        339,
+                                        205
+                                    ],
+                                    "score": 1.0,
+                                    "content": "language code summarization model. We train our model",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                205,
+                                340,
+                                216
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        205,
+                                        340,
+                                        216
+                                    ],
+                                    "score": 1.0,
+                                    "content": "jointly on Python, Javascript, Ruby, and Go. The shared",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                215,
+                                339,
+                                227
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        215,
+                                        339,
+                                        227
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sub-token vocabulary is the union of the individual vocab-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                227,
+                                340,
+                                239
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        227,
+                                        340,
+                                        239
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ularies, enabling us to evaluate the multi-language model",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                236,
+                                505,
+                                250
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        236,
+                                        505,
+                                        250
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on the individual languages and compare with the single-language models. As proposed by Conneau",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                246,
+                                439,
+                                262
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        246,
+                                        439,
+                                        262
+                                    ],
+                                    "score": 1.0,
+                                    "content": "& Lample (2019), we add a learned language embedding to each input embedding.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 7.5,
+                    "bbox_fs": [
+                        105,
+                        149,
+                        340,
+                        239
+                    ]
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        354,
+                        146,
+                        496,
+                        212
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                354,
+                                146,
+                                496,
+                                212
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        354,
+                                        146,
+                                        496,
+                                        212
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                354,
+                                                146,
+                                                496,
+                                                212
+                                            ],
+                                            "score": 0.971,
+                                            "html": "<table><tr><td>AST distance</td><td>F1 score</td></tr><tr><td>Sibling shortest paths</td><td>46.17</td></tr><tr><td>Ancestor shortest paths</td><td>47.89</td></tr><tr><td>Shortest paths</td><td>47.76</td></tr><tr><td>Personalized PageRank</td><td>48.47</td></tr><tr><td>All the above (c.f. Table 3)</td><td>48.75</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "44d93ce3802abbb255784a0d5f66ef881ac7c557a4abf8c4d5752cc699deb37d.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 12.5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        354,
+                                        146,
+                                        496,
+                                        179.0
+                                    ],
+                                    "spans": [],
+                                    "index": 12
+                                },
+                                {
+                                    "bbox": [
+                                        354,
+                                        179.0,
+                                        496,
+                                        212.0
+                                    ],
+                                    "spans": [],
+                                    "index": 13
+                                }
+                            ]
+                        },
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                351,
+                                221,
+                                501,
+                                232
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        349,
+                                        218,
+                                        501,
+                                        234
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                349,
+                                                218,
+                                                501,
+                                                234
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 4: AST distance ablation study.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 14
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 13.25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        238,
+                        505,
+                        259
+                    ],
+                    "lines": [],
+                    "index": 15.5,
+                    "bbox_fs": [
+                        105,
+                        236,
+                        505,
+                        262
+                    ],
+                    "lines_deleted": true
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        271,
+                        505,
+                        360
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                271,
+                                505,
+                                284
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        271,
+                                        505,
+                                        284
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Results. In the lower part of Table 2 we can see the results of training our CODE TRANSFORMER",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                283,
+                                505,
+                                295
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        283,
+                                        505,
+                                        295
+                                    ],
+                                    "score": 1.0,
+                                    "content": "jointly on all four programming languages. Our multi-lingual variants substantially outperform",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                293,
+                                506,
+                                306
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        293,
+                                        506,
+                                        306
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the mono-lingual models on all languages. The strongest improvement is on Ruby, which is also",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                304,
+                                506,
+                                318
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        304,
+                                        506,
+                                        318
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the programming language with the smallest number of samples in the dataset. Fine-tuning on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                315,
+                                506,
+                                328
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        315,
+                                        506,
+                                        328
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the individual languages after joint training on code summarization only has a marginal effect on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                325,
+                                506,
+                                340
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        325,
+                                        506,
+                                        340
+                                    ],
+                                    "score": 1.0,
+                                    "content": "performance, indicating that the multilingual objective is well-aligned with the individual languages.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                337,
+                                506,
+                                351
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        337,
+                                        506,
+                                        351
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In the last row, we have a variant of our model where we pre-train on the multi-lingual masked",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                348,
+                                505,
+                                362
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        348,
+                                        505,
+                                        362
+                                    ],
+                                    "score": 1.0,
+                                    "content": "language modeling task, followed by finetuning on code summarization on the individual languages.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 20.5,
+                    "bbox_fs": [
+                        105,
+                        271,
+                        506,
+                        362
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        365,
+                        505,
+                        442
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                364,
+                                505,
+                                378
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        364,
+                                        505,
+                                        378
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Further, we observe that similar to the results on Java-small, removing the pointer network generally",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                377,
+                                505,
+                                388
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        377,
+                                        505,
+                                        388
+                                    ],
+                                    "score": 1.0,
+                                    "content": "leads to weaker performance. One notable exception is Go, where the variant without the pointer",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                387,
+                                505,
+                                399
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        387,
+                                        505,
+                                        399
+                                    ],
+                                    "score": 1.0,
+                                    "content": "network performs better in terms of F1 score. Our investigation revealed that there seems to be some",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                398,
+                                505,
+                                411
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        398,
+                                        505,
+                                        411
+                                    ],
+                                    "score": 1.0,
+                                    "content": "violation of the i.i.d. assumption in the split provided by the creators of the dataset. In Figure 7 we",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                408,
+                                506,
+                                422
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        408,
+                                        506,
+                                        422
+                                    ],
+                                    "score": 1.0,
+                                    "content": "show that in the test partition of the Go dataset, the share of tokens from the labels also occurring in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                420,
+                                505,
+                                432
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        420,
+                                        505,
+                                        432
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the methods’ bodies – exactly the scenario where the pointer network can improve predictions – is",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                431,
+                                357,
+                                443
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        431,
+                                        357,
+                                        443
+                                    ],
+                                    "score": 1.0,
+                                    "content": "substantially lower compared to the train/validation partitions.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        }
+                    ],
+                    "index": 28,
+                    "bbox_fs": [
+                        105,
+                        364,
+                        506,
+                        443
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        448,
+                        505,
+                        514
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                448,
+                                505,
+                                460
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        448,
+                                        505,
+                                        460
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Remarkably, the multi-language Context-only variant (i.e. without access to the Structure) performs",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                459,
+                                505,
+                                470
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        459,
+                                        505,
+                                        470
+                                    ],
+                                    "score": 1.0,
+                                    "content": "substantially worse than the full multi-language variant. This highlights that Structure is crucial to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                469,
+                                505,
+                                483
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        469,
+                                        505,
+                                        483
+                                    ],
+                                    "score": 1.0,
+                                    "content": "exploit the commonalities of different programming languages. Also notably, the GREAT baseline’s",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                480,
+                                505,
+                                493
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        480,
+                                        505,
+                                        493
+                                    ],
+                                    "score": 1.0,
+                                    "content": "results also improve substantially when trained in the multi-language setting, though it is still outper-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                491,
+                                506,
+                                505
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        491,
+                                        506,
+                                        505
+                                    ],
+                                    "score": 1.0,
+                                    "content": "formed by our model. However, our results indicate that any representation learning model for code",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                502,
+                                495,
+                                516
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        502,
+                                        495,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "can benefit from multi-language training, especially when evaluating on low-resource languages.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 34.5,
+                    "bbox_fs": [
+                        105,
+                        448,
+                        506,
+                        516
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        519,
+                        504,
+                        553
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                520,
+                                505,
+                                532
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        520,
+                                        505,
+                                        532
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In Table 16 we present results using the sample-F1 score. At the time of submission, our mono-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                530,
+                                506,
+                                543
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        530,
+                                        422,
+                                        543
+                                    ],
+                                    "score": 1.0,
+                                    "content": "lingual model on Python outperforms the state of the art on the ogbg-code",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        422,
+                                        530,
+                                        433,
+                                        541
+                                    ],
+                                    "score": 0.67,
+                                    "content": "2 ^ { 4 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        433,
+                                        530,
+                                        506,
+                                        543
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(Hu et al., 2020)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                542,
+                                503,
+                                554
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        542,
+                                        169,
+                                        554
+                                    ],
+                                    "score": 1.0,
+                                    "content": "leaderboard by",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        169,
+                                        542,
+                                        193,
+                                        552
+                                    ],
+                                    "score": 0.86,
+                                    "content": "112 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        193,
+                                        542,
+                                        474,
+                                        554
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and our multilanguage variant with LM pretraining outperforms it by",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        475,
+                                        542,
+                                        499,
+                                        552
+                                    ],
+                                    "score": 0.9,
+                                    "content": "122 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        499,
+                                        542,
+                                        503,
+                                        554
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        }
+                    ],
+                    "index": 39,
+                    "bbox_fs": [
+                        105,
+                        520,
+                        506,
+                        554
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        565,
+                        505,
+                        664
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                564,
+                                505,
+                                578
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        564,
+                                        505,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Qualitative analysis of multilingual representations. Learning the CODE TRANSFORMER on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                576,
+                                505,
+                                588
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        576,
+                                        505,
+                                        588
+                                    ],
+                                    "score": 1.0,
+                                    "content": "multiple programming languages jointly provides us with embeddings in a shared representation",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                586,
+                                506,
+                                600
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        586,
+                                        506,
+                                        600
+                                    ],
+                                    "score": 1.0,
+                                    "content": "space. In Fig. 4 we show a t-SNE (Maaten & Hinton, 2008) visualization of the ca. 40,000 snippets",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                596,
+                                506,
+                                612
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        596,
+                                        506,
+                                        612
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from the validation sets of four programming languages from the CSN dataset. For the embedding",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                609,
+                                506,
+                                622
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        609,
+                                        506,
+                                        622
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of a snippet, we use the representation of the method name in the final layer of the encoder. Note",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                619,
+                                506,
+                                632
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        619,
+                                        506,
+                                        632
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that the true method names are masked, i.e., inaccessible to the model. Further, note that in contrast",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                630,
+                                506,
+                                644
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        630,
+                                        506,
+                                        644
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to the monolingual embeddings learned by Kanade et al. (2020), the embeddings we evaluate are",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                640,
+                                505,
+                                655
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        640,
+                                        505,
+                                        655
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learned on the task of code summarization (though a similar study could be performed by using our",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                652,
+                                505,
+                                666
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        652,
+                                        505,
+                                        666
+                                    ],
+                                    "score": 1.0,
+                                    "content": "model that was trained on the traditional language modeling pretraining task on multiple languages).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        }
+                    ],
+                    "index": 45,
+                    "bbox_fs": [
+                        104,
+                        564,
+                        506,
+                        666
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        669,
+                        504,
+                        714
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                669,
+                                506,
+                                682
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        669,
+                                        506,
+                                        682
+                                    ],
+                                    "score": 1.0,
+                                    "content": "While snippets from the same language tend to be grouped together, there are interesting intersec-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                680,
+                                506,
+                                694
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        680,
+                                        506,
+                                        694
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tions of the different programming languages. For example, we highlight all methods whose names",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 51
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                692,
+                                505,
+                                704
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        692,
+                                        505,
+                                        704
+                                    ],
+                                    "score": 1.0,
+                                    "content": "start with the subtoken parse or main. We see that snippets starting with parse are predom-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 52
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                703,
+                                505,
+                                715
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        703,
+                                        505,
+                                        715
+                                    ],
+                                    "score": 1.0,
+                                    "content": "inantly in an intersection region of Python and Javascript. From these snippets, we display the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 53
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                422,
+                                505,
+                                437
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        422,
+                                        505,
+                                        437
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cross-language pair with smallest Euclidean embedding distance in Fig. 5. Remarkably, both snip-",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                434,
+                                506,
+                                447
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        434,
+                                        506,
+                                        447
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pets are effectively the same method in Javascript and Python – it is worth reminding that the model",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                445,
+                                505,
+                                458
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        445,
+                                        505,
+                                        458
+                                    ],
+                                    "score": 1.0,
+                                    "content": "has never seen any parallel data during training. On the other hand, snippets starting with main tend",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                457,
+                                505,
+                                468
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        457,
+                                        505,
+                                        468
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to lie at an intersectional region of Python, Javascript, and Go. In Table 6 in the appendix we show",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                467,
+                                505,
+                                480
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        467,
+                                        505,
+                                        480
+                                    ],
+                                    "score": 1.0,
+                                    "content": "additional cross-lingual pairs with similar embeddings, including a failure case of a main function,",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                478,
+                                506,
+                                491
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        478,
+                                        506,
+                                        491
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where embedding distance is not representative of semantic similarity. We attribute this to the fact",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                489,
+                                505,
+                                502
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        489,
+                                        505,
+                                        502
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that we used the encoder output embedding of the masked method name – the representation used",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                500,
+                                505,
+                                513
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        500,
+                                        505,
+                                        513
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by the decoder to predict the method name – as a snippet’s representation. Thus, snippets with com-",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                510,
+                                506,
+                                524
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        510,
+                                        506,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pletely different semantics (as is to be expected for very generic method names starting with main)",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                522,
+                                416,
+                                534
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        522,
+                                        416,
+                                        534
+                                    ],
+                                    "score": 1.0,
+                                    "content": "have similar representations because they are predictive of the method name.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 51.5,
+                    "bbox_fs": [
+                        106,
+                        669,
+                        506,
+                        715
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "image",
+                    "bbox": [
+                        137,
+                        64,
+                        474,
+                        241
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                137,
+                                64,
+                                474,
+                                241
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        137,
+                                        64,
+                                        474,
+                                        241
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                137,
+                                                64,
+                                                474,
+                                                241
+                                            ],
+                                            "score": 0.972,
+                                            "type": "image",
+                                            "image_path": "e875f6f92fb5baf876c7eada99cff2f2f6a1ae4c2907de273c6e3de07dd8a6a8.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        137,
+                                        64,
+                                        474,
+                                        123.0
+                                    ],
+                                    "spans": [],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        137,
+                                        123.0,
+                                        474,
+                                        182.0
+                                    ],
+                                    "spans": [],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        137,
+                                        182.0,
+                                        474,
+                                        241.0
+                                    ],
+                                    "spans": [],
+                                    "index": 2
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                106,
+                                247,
+                                502,
+                                259
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        246,
+                                        504,
+                                        261
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                246,
+                                                504,
+                                                261
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 4: t-SNE visualization of the CODE TRANSFORMER’s learned multilingual representations.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 2.0
+                },
+                {
+                    "type": "image",
+                    "bbox": [
+                        125,
+                        270,
+                        475,
+                        349
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                125,
+                                270,
+                                475,
+                                349
+                            ],
+                            "group_id": 1,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        125,
+                                        270,
+                                        475,
+                                        348
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                125,
+                                                270,
+                                                475,
+                                                348
+                                            ],
+                                            "score": 0.771,
+                                            "type": "image",
+                                            "image_path": "b4f73ecaf41d7a935e9b22345a3d4464c58d6b6b17f19a5180425db1c0483a08.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        125,
+                                        270,
+                                        475,
+                                        296.3333333333333
+                                    ],
+                                    "spans": [],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        125,
+                                        296.3333333333333,
+                                        475,
+                                        322.66666666666663
+                                    ],
+                                    "spans": [],
+                                    "index": 5
+                                },
+                                {
+                                    "bbox": [
+                                        125,
+                                        322.66666666666663,
+                                        475,
+                                        348.99999999999994
+                                    ],
+                                    "spans": [],
+                                    "index": 6
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                106,
+                                357,
+                                505,
+                                401
+                            ],
+                            "group_id": 1,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        357,
+                                        506,
+                                        370
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                357,
+                                                506,
+                                                370
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 5: Example snippet starting with parse (left) and its best embedding match from other",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 7
+                                },
+                                {
+                                    "bbox": [
+                                        104,
+                                        367,
+                                        506,
+                                        381
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                104,
+                                                367,
+                                                506,
+                                                381
+                                            ],
+                                            "score": 1.0,
+                                            "content": "languages (right). Both methods parse an input string to convert it into a boolean value. Note",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 8
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        379,
+                                        506,
+                                        392
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                379,
+                                                506,
+                                                392
+                                            ],
+                                            "score": 1.0,
+                                            "content": "that even though they are semantically very similar, their method names are not; nonetheless, their",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 9
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        390,
+                                        452,
+                                        403
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                390,
+                                                452,
+                                                403
+                                            ],
+                                            "score": 1.0,
+                                            "content": "representations in the CODE TRANSFORMER encoder reflect their semantic similarity.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 10
+                                }
+                            ],
+                            "index": 8.5
+                        }
+                    ],
+                    "index": 6.75
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        423,
+                        505,
+                        533
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                422,
+                                505,
+                                437
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        422,
+                                        505,
+                                        437
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cross-language pair with smallest Euclidean embedding distance in Fig. 5. Remarkably, both snip-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                434,
+                                506,
+                                447
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        434,
+                                        506,
+                                        447
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pets are effectively the same method in Javascript and Python – it is worth reminding that the model",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                445,
+                                505,
+                                458
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        445,
+                                        505,
+                                        458
+                                    ],
+                                    "score": 1.0,
+                                    "content": "has never seen any parallel data during training. On the other hand, snippets starting with main tend",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                457,
+                                505,
+                                468
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        457,
+                                        505,
+                                        468
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to lie at an intersectional region of Python, Javascript, and Go. In Table 6 in the appendix we show",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                467,
+                                505,
+                                480
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        467,
+                                        505,
+                                        480
+                                    ],
+                                    "score": 1.0,
+                                    "content": "additional cross-lingual pairs with similar embeddings, including a failure case of a main function,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                478,
+                                506,
+                                491
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        478,
+                                        506,
+                                        491
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where embedding distance is not representative of semantic similarity. We attribute this to the fact",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                489,
+                                505,
+                                502
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        489,
+                                        505,
+                                        502
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that we used the encoder output embedding of the masked method name – the representation used",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                500,
+                                505,
+                                513
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        500,
+                                        505,
+                                        513
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by the decoder to predict the method name – as a snippet’s representation. Thus, snippets with com-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                510,
+                                506,
+                                524
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        510,
+                                        506,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pletely different semantics (as is to be expected for very generic method names starting with main)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                522,
+                                416,
+                                534
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        522,
+                                        416,
+                                        534
+                                    ],
+                                    "score": 1.0,
+                                    "content": "have similar representations because they are predictive of the method name.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 15.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        538,
+                        504,
+                        572
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                537,
+                                505,
+                                552
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        537,
+                                        505,
+                                        552
+                                    ],
+                                    "score": 1.0,
+                                    "content": "As another qualitative insight into the representations learned by the CODE TRANSFORMER we have",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                550,
+                                505,
+                                563
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        550,
+                                        505,
+                                        563
+                                    ],
+                                    "score": 1.0,
+                                    "content": "found that the language embeddings of languages with similar roots in language design are close;",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                560,
+                                501,
+                                574
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        560,
+                                        501,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": "see Table 5 in the appendix for the pairwise similarity matrix of the learned language embeddings.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 22
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        588,
+                        195,
+                        601
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                586,
+                                197,
+                                604
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        586,
+                                        197,
+                                        604
+                                    ],
+                                    "score": 1.0,
+                                    "content": "6 CONCLUSION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 24
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        613,
+                        505,
+                        723
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                613,
+                                505,
+                                626
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        613,
+                                        505,
+                                        626
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We present the CODE TRANSFORMER, which learns jointly from Structure and Context of programs",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                624,
+                                505,
+                                637
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        624,
+                                        505,
+                                        637
+                                    ],
+                                    "score": 1.0,
+                                    "content": "while only relying on language-agnostic features. Our model obtains state-of-the-art performance",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                635,
+                                505,
+                                648
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        635,
+                                        505,
+                                        648
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on code summarization on five different programming languages. Besides these results for train-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                646,
+                                505,
+                                659
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        646,
+                                        505,
+                                        659
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ing on individual languages, the language-agnostic nature of our model allows us to train it jointly",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                657,
+                                505,
+                                670
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        657,
+                                        505,
+                                        670
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on multiple programming languages. The resulting multilingual model substantially outperforms",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                668,
+                                505,
+                                680
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        668,
+                                        505,
+                                        680
+                                    ],
+                                    "score": 1.0,
+                                    "content": "its mono-lingual variant on all programming languages, setting the state of the art on each lan-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                678,
+                                506,
+                                693
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        678,
+                                        506,
+                                        693
+                                    ],
+                                    "score": 1.0,
+                                    "content": "guage. We observe the largest improvement from multilingual training on the language with fewest",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                690,
+                                505,
+                                703
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        690,
+                                        505,
+                                        703
+                                    ],
+                                    "score": 1.0,
+                                    "content": "resources, indicating that multilingual training can improve learning for less widely used program-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                701,
+                                505,
+                                714
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        701,
+                                        505,
+                                        714
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ming languages. Remarkably, multilingual training only from Context does not lead to the same",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                712,
+                                416,
+                                725
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        712,
+                                        416,
+                                        725
+                                    ],
+                                    "score": 1.0,
+                                    "content": "improvements, highlighting the benefits of combining Structure and Context.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        }
+                    ],
+                    "index": 29.5
+                }
+            ],
+            "page_idx": 8,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        292,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                293,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        293,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        751,
+                        308,
+                        759
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                302,
+                                751,
+                                309,
+                                762
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        302,
+                                        751,
+                                        309,
+                                        762
+                                    ],
+                                    "score": 1.0,
+                                    "content": "9",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "image",
+                    "bbox": [
+                        137,
+                        64,
+                        474,
+                        241
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                137,
+                                64,
+                                474,
+                                241
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        137,
+                                        64,
+                                        474,
+                                        241
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                137,
+                                                64,
+                                                474,
+                                                241
+                                            ],
+                                            "score": 0.972,
+                                            "type": "image",
+                                            "image_path": "e875f6f92fb5baf876c7eada99cff2f2f6a1ae4c2907de273c6e3de07dd8a6a8.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        137,
+                                        64,
+                                        474,
+                                        123.0
+                                    ],
+                                    "spans": [],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        137,
+                                        123.0,
+                                        474,
+                                        182.0
+                                    ],
+                                    "spans": [],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        137,
+                                        182.0,
+                                        474,
+                                        241.0
+                                    ],
+                                    "spans": [],
+                                    "index": 2
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                106,
+                                247,
+                                502,
+                                259
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        246,
+                                        504,
+                                        261
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                246,
+                                                504,
+                                                261
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 4: t-SNE visualization of the CODE TRANSFORMER’s learned multilingual representations.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 2.0
+                },
+                {
+                    "type": "image",
+                    "bbox": [
+                        125,
+                        270,
+                        475,
+                        349
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                125,
+                                270,
+                                475,
+                                349
+                            ],
+                            "group_id": 1,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        125,
+                                        270,
+                                        475,
+                                        348
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                125,
+                                                270,
+                                                475,
+                                                348
+                                            ],
+                                            "score": 0.771,
+                                            "type": "image",
+                                            "image_path": "b4f73ecaf41d7a935e9b22345a3d4464c58d6b6b17f19a5180425db1c0483a08.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        125,
+                                        270,
+                                        475,
+                                        296.3333333333333
+                                    ],
+                                    "spans": [],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        125,
+                                        296.3333333333333,
+                                        475,
+                                        322.66666666666663
+                                    ],
+                                    "spans": [],
+                                    "index": 5
+                                },
+                                {
+                                    "bbox": [
+                                        125,
+                                        322.66666666666663,
+                                        475,
+                                        348.99999999999994
+                                    ],
+                                    "spans": [],
+                                    "index": 6
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                106,
+                                357,
+                                505,
+                                401
+                            ],
+                            "group_id": 1,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        357,
+                                        506,
+                                        370
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                357,
+                                                506,
+                                                370
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 5: Example snippet starting with parse (left) and its best embedding match from other",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 7
+                                },
+                                {
+                                    "bbox": [
+                                        104,
+                                        367,
+                                        506,
+                                        381
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                104,
+                                                367,
+                                                506,
+                                                381
+                                            ],
+                                            "score": 1.0,
+                                            "content": "languages (right). Both methods parse an input string to convert it into a boolean value. Note",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 8
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        379,
+                                        506,
+                                        392
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                379,
+                                                506,
+                                                392
+                                            ],
+                                            "score": 1.0,
+                                            "content": "that even though they are semantically very similar, their method names are not; nonetheless, their",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 9
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        390,
+                                        452,
+                                        403
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                390,
+                                                452,
+                                                403
+                                            ],
+                                            "score": 1.0,
+                                            "content": "representations in the CODE TRANSFORMER encoder reflect their semantic similarity.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 10
+                                }
+                            ],
+                            "index": 8.5
+                        }
+                    ],
+                    "index": 6.75
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        423,
+                        505,
+                        533
+                    ],
+                    "lines": [],
+                    "index": 15.5,
+                    "bbox_fs": [
+                        104,
+                        422,
+                        506,
+                        534
+                    ],
+                    "lines_deleted": true
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        538,
+                        504,
+                        572
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                537,
+                                505,
+                                552
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        537,
+                                        505,
+                                        552
+                                    ],
+                                    "score": 1.0,
+                                    "content": "As another qualitative insight into the representations learned by the CODE TRANSFORMER we have",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                550,
+                                505,
+                                563
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        550,
+                                        505,
+                                        563
+                                    ],
+                                    "score": 1.0,
+                                    "content": "found that the language embeddings of languages with similar roots in language design are close;",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                560,
+                                501,
+                                574
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        560,
+                                        501,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": "see Table 5 in the appendix for the pairwise similarity matrix of the learned language embeddings.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 22,
+                    "bbox_fs": [
+                        106,
+                        537,
+                        505,
+                        574
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        588,
+                        195,
+                        601
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                586,
+                                197,
+                                604
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        586,
+                                        197,
+                                        604
+                                    ],
+                                    "score": 1.0,
+                                    "content": "6 CONCLUSION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 24
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        613,
+                        505,
+                        723
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                613,
+                                505,
+                                626
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        613,
+                                        505,
+                                        626
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We present the CODE TRANSFORMER, which learns jointly from Structure and Context of programs",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                624,
+                                505,
+                                637
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        624,
+                                        505,
+                                        637
+                                    ],
+                                    "score": 1.0,
+                                    "content": "while only relying on language-agnostic features. Our model obtains state-of-the-art performance",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                635,
+                                505,
+                                648
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        635,
+                                        505,
+                                        648
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on code summarization on five different programming languages. Besides these results for train-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                646,
+                                505,
+                                659
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        646,
+                                        505,
+                                        659
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ing on individual languages, the language-agnostic nature of our model allows us to train it jointly",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                657,
+                                505,
+                                670
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        657,
+                                        505,
+                                        670
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on multiple programming languages. The resulting multilingual model substantially outperforms",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                668,
+                                505,
+                                680
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        668,
+                                        505,
+                                        680
+                                    ],
+                                    "score": 1.0,
+                                    "content": "its mono-lingual variant on all programming languages, setting the state of the art on each lan-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                678,
+                                506,
+                                693
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        678,
+                                        506,
+                                        693
+                                    ],
+                                    "score": 1.0,
+                                    "content": "guage. We observe the largest improvement from multilingual training on the language with fewest",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                690,
+                                505,
+                                703
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        690,
+                                        505,
+                                        703
+                                    ],
+                                    "score": 1.0,
+                                    "content": "resources, indicating that multilingual training can improve learning for less widely used program-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                701,
+                                505,
+                                714
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        701,
+                                        505,
+                                        714
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ming languages. Remarkably, multilingual training only from Context does not lead to the same",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                712,
+                                416,
+                                725
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        712,
+                                        416,
+                                        725
+                                    ],
+                                    "score": 1.0,
+                                    "content": "improvements, highlighting the benefits of combining Structure and Context.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        }
+                    ],
+                    "index": 29.5,
+                    "bbox_fs": [
+                        104,
+                        613,
+                        506,
+                        725
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        82,
+                        175,
+                        93
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                81,
+                                176,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        81,
+                                        176,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "REFERENCES",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        100,
+                        505,
+                        166
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                99,
+                                505,
+                                113
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        99,
+                                        505,
+                                        113
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Mithun Acharya, Tao Xie, Jian Pei, and Jun Xu. Mining api patterns as partial orders from source",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                111,
+                                504,
+                                123
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        111,
+                                        504,
+                                        123
+                                    ],
+                                    "score": 1.0,
+                                    "content": "code: From usage scenarios to specifications. In Proceedings of the the 6th Joint Meeting of the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                122,
+                                505,
+                                135
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        122,
+                                        505,
+                                        135
+                                    ],
+                                    "score": 1.0,
+                                    "content": "European Software Engineering Conference and the ACM SIGSOFT Symposium on The Founda-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                132,
+                                505,
+                                146
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        132,
+                                        505,
+                                        146
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tions of Software Engineering, ESEC-FSE ’07, pp. 25–34, New York, NY, USA, 2007. Associ-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                144,
+                                506,
+                                156
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        144,
+                                        506,
+                                        156
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ation for Computing Machinery. ISBN 9781595938114. doi: 10.1145/1287624.1287630. URL",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                155,
+                                354,
+                                167
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        155,
+                                        354,
+                                        167
+                                    ],
+                                    "score": 1.0,
+                                    "content": "https://doi.org/10.1145/1287624.1287630.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 3.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        173,
+                        505,
+                        229
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                172,
+                                506,
+                                188
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        172,
+                                        506,
+                                        188
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Miltiadis Allamanis, Earl T. Barr, Christian Bird, and Charles Sutton. Learning natural coding",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                185,
+                                505,
+                                198
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        185,
+                                        505,
+                                        198
+                                    ],
+                                    "score": 1.0,
+                                    "content": "conventions. In Proceedings of the 22nd ACM SIGSOFT International Symposium on Founda-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                195,
+                                505,
+                                208
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        195,
+                                        505,
+                                        208
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tions of Software Engineering, FSE 2014, pp. 281–293, New York, NY, USA, 2014. Associa-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                207,
+                                506,
+                                219
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        207,
+                                        506,
+                                        219
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tion for Computing Machinery. ISBN 9781450330565. doi: 10.1145/2635868.2635883. URL",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                217,
+                                355,
+                                230
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        217,
+                                        355,
+                                        230
+                                    ],
+                                    "score": 1.0,
+                                    "content": "https://doi.org/10.1145/2635868.2635883.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        236,
+                        505,
+                        291
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                236,
+                                505,
+                                249
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        236,
+                                        505,
+                                        249
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Miltiadis Allamanis, Earl T. Barr, Christian Bird, and Charles Sutton. Suggesting accurate method",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                247,
+                                505,
+                                261
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        247,
+                                        505,
+                                        261
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and class names. In Proceedings of the 2015 10th Joint Meeting on Foundations of Software",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                256,
+                                506,
+                                273
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        256,
+                                        506,
+                                        273
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Engineering, ESEC/FSE 2015, pp. 38–49, New York, NY, USA, 2015. Association for Computing",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                268,
+                                504,
+                                282
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        268,
+                                        504,
+                                        282
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Machinery. ISBN 9781450336758. doi: 10.1145/2786805.2786849. URL https://doi.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                280,
+                                284,
+                                293
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        280,
+                                        284,
+                                        293
+                                    ],
+                                    "score": 1.0,
+                                    "content": "org/10.1145/2786805.2786849.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        299,
+                        503,
+                        332
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                298,
+                                505,
+                                312
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        298,
+                                        505,
+                                        312
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Miltiadis Allamanis, Hao Peng, and Charles Sutton. A convolutional attention network for extreme",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                310,
+                                505,
+                                322
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        310,
+                                        505,
+                                        322
+                                    ],
+                                    "score": 1.0,
+                                    "content": "summarization of source code. In International conference on machine learning, pp. 2091–2100,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                319,
+                                143,
+                                333
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        319,
+                                        143,
+                                        333
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        339,
+                        504,
+                        374
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                338,
+                                505,
+                                353
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        338,
+                                        505,
+                                        353
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Miltiadis Allamanis, Marc Brockschmidt, and Mahmoud Khademi. Learning to represent programs",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                351,
+                                504,
+                                363
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        351,
+                                        504,
+                                        363
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with graphs. In International Conference on Learning Representations, 2018. URL https:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                362,
+                                332,
+                                374
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        362,
+                                        266,
+                                        374
+                                    ],
+                                    "score": 1.0,
+                                    "content": "//openreview.net/forum?id",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        267,
+                                        363,
+                                        273,
+                                        371
+                                    ],
+                                    "score": 0.52,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        273,
+                                        362,
+                                        332,
+                                        374
+                                    ],
+                                    "score": 1.0,
+                                    "content": "BJOFETxR-.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 21
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        380,
+                        505,
+                        436
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                381,
+                                504,
+                                393
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        381,
+                                        504,
+                                        393
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Uri Alon, Meital Zilberstein, Omer Levy, and Eran Yahav. A general path-based representa-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                391,
+                                505,
+                                405
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        391,
+                                        505,
+                                        405
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tion for predicting program properties. In Proceedings of the 39th ACM SIGPLAN Confer-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                403,
+                                505,
+                                415
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        403,
+                                        505,
+                                        415
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ence on Programming Language Design and Implementation, PLDI 2018, pp. 404–419, New",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                413,
+                                505,
+                                426
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        413,
+                                        505,
+                                        426
+                                    ],
+                                    "score": 1.0,
+                                    "content": "York, NY, USA, 2018. Association for Computing Machinery. ISBN 9781450356985. doi:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                424,
+                                491,
+                                437
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        424,
+                                        491,
+                                        437
+                                    ],
+                                    "score": 1.0,
+                                    "content": "10.1145/3192366.3192412. URL https://doi.org/10.1145/3192366.3192412.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        443,
+                        505,
+                        477
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                442,
+                                505,
+                                457
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        442,
+                                        505,
+                                        457
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Uri Alon, Shaked Brody, Omer Levy, and Eran Yahav. code2seq: Generating sequences from struc-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                454,
+                                505,
+                                466
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        454,
+                                        505,
+                                        466
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tured representations of code. In International Conference on Learning Representations, 2019a.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                464,
+                                396,
+                                479
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        464,
+                                        325,
+                                        479
+                                    ],
+                                    "score": 1.0,
+                                    "content": "URL https://openreview.net/forum?id",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        325,
+                                        466,
+                                        331,
+                                        474
+                                    ],
+                                    "score": 0.47,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        332,
+                                        464,
+                                        396,
+                                        479
+                                    ],
+                                    "score": 1.0,
+                                    "content": "H1gKYo09tX.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 29
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        483,
+                        504,
+                        507
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                483,
+                                505,
+                                496
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        483,
+                                        505,
+                                        496
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Uri Alon, Meital Zilberstein, Omer Levy, and Eran Yahav. code2vec: Learning distributed repre-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                494,
+                                505,
+                                508
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        494,
+                                        505,
+                                        508
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sentations of code. Proceedings of the ACM on Programming Languages, 3(POPL):1–29, 2019b.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 31.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        513,
+                        505,
+                        558
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                514,
+                                505,
+                                525
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        514,
+                                        505,
+                                        525
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Peter W Battaglia, Jessica B Hamrick, Victor Bapst, Alvaro Sanchez-Gonzalez, Vinicius Zambaldi,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                524,
+                                505,
+                                536
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        524,
+                                        505,
+                                        536
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Mateusz Malinowski, Andrea Tacchetti, David Raposo, Adam Santoro, Ryan Faulkner, et al.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                535,
+                                506,
+                                549
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        535,
+                                        506,
+                                        549
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Relational inductive biases, deep learning, and graph networks. arXiv preprint arXiv:1806.01261,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                545,
+                                143,
+                                559
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        545,
+                                        143,
+                                        559
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 34.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        565,
+                        505,
+                        588
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                565,
+                                505,
+                                578
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        565,
+                                        505,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Avishkar Bhoopchand, Tim Rocktaschel, Earl Barr, and Sebastian Riedel. Learning python code ¨",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                577,
+                                448,
+                                588
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        577,
+                                        448,
+                                        588
+                                    ],
+                                    "score": 1.0,
+                                    "content": "suggestion with a sparse pointer network. arXiv preprint arXiv:1611.08307, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        }
+                    ],
+                    "index": 37.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        595,
+                        505,
+                        650
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                595,
+                                505,
+                                608
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        595,
+                                        505,
+                                        608
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Benjamin Bichsel, Veselin Raychev, Petar Tsankov, and Martin Vechev. Statistical deobfuscation",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                606,
+                                506,
+                                620
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        606,
+                                        506,
+                                        620
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of android applications. In Proceedings of the 2016 ACM SIGSAC Conference on Computer and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                617,
+                                506,
+                                631
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        617,
+                                        506,
+                                        631
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Communications Security, CCS ’16, pp. 343–355, New York, NY, USA, 2016. Association for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                627,
+                                505,
+                                642
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        627,
+                                        505,
+                                        642
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Computing Machinery. ISBN 9781450341394. doi: 10.1145/2976749.2978422. URL https:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                639,
+                                318,
+                                651
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        639,
+                                        318,
+                                        651
+                                    ],
+                                    "score": 1.0,
+                                    "content": "//doi.org/10.1145/2976749.2978422.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        }
+                    ],
+                    "index": 41
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        657,
+                        504,
+                        681
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                657,
+                                505,
+                                671
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        657,
+                                        505,
+                                        671
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Pavol Bielik, Veselin Raychev, and Martin Vechev. Phog: probabilistic model for code. In Interna-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                669,
+                                371,
+                                681
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        669,
+                                        371,
+                                        681
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tional Conference on Machine Learning, pp. 2933–2942, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        }
+                    ],
+                    "index": 44.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        687,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                687,
+                                506,
+                                700
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        687,
+                                        506,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Aleksandar Bojchevski, Johannes Klicpera, Bryan Perozzi, Amol Kapoor, Martin Blais, Benedek",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                699,
+                                505,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        699,
+                                        505,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Rozemberczki, Michal Lukasik, and Stephan G ´ unnemann. Scaling graph neural networks with ¨",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                710,
+                                505,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        710,
+                                        505,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "approximate pagerank. In Proceedings of the 26th ACM SIGKDD International Conference on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                720,
+                                505,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        720,
+                                        505,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Knowledge Discovery amp; Data Mining, KDD ’20, pp. 2464–2473, New York, NY, USA, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        }
+                    ],
+                    "index": 47.5
+                }
+            ],
+            "page_idx": 9,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        108,
+                        27,
+                        292,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                25,
+                                293,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        25,
+                                        293,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        311,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                313,
+                                764
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        313,
+                                        764
+                                    ],
+                                    "score": 1.0,
+                                    "content": "10",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        82,
+                        175,
+                        93
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                81,
+                                176,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        81,
+                                        176,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "REFERENCES",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        100,
+                        505,
+                        166
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                99,
+                                505,
+                                113
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        99,
+                                        505,
+                                        113
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Mithun Acharya, Tao Xie, Jian Pei, and Jun Xu. Mining api patterns as partial orders from source",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                111,
+                                504,
+                                123
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        111,
+                                        504,
+                                        123
+                                    ],
+                                    "score": 1.0,
+                                    "content": "code: From usage scenarios to specifications. In Proceedings of the the 6th Joint Meeting of the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                122,
+                                505,
+                                135
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        122,
+                                        505,
+                                        135
+                                    ],
+                                    "score": 1.0,
+                                    "content": "European Software Engineering Conference and the ACM SIGSOFT Symposium on The Founda-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                132,
+                                505,
+                                146
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        132,
+                                        505,
+                                        146
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tions of Software Engineering, ESEC-FSE ’07, pp. 25–34, New York, NY, USA, 2007. Associ-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                144,
+                                506,
+                                156
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        144,
+                                        506,
+                                        156
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ation for Computing Machinery. ISBN 9781595938114. doi: 10.1145/1287624.1287630. URL",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                155,
+                                354,
+                                167
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        155,
+                                        354,
+                                        167
+                                    ],
+                                    "score": 1.0,
+                                    "content": "https://doi.org/10.1145/1287624.1287630.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 3.5,
+                    "bbox_fs": [
+                        105,
+                        99,
+                        506,
+                        167
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        173,
+                        505,
+                        229
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                172,
+                                506,
+                                188
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        172,
+                                        506,
+                                        188
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Miltiadis Allamanis, Earl T. Barr, Christian Bird, and Charles Sutton. Learning natural coding",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                185,
+                                505,
+                                198
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        185,
+                                        505,
+                                        198
+                                    ],
+                                    "score": 1.0,
+                                    "content": "conventions. In Proceedings of the 22nd ACM SIGSOFT International Symposium on Founda-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                195,
+                                505,
+                                208
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        195,
+                                        505,
+                                        208
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tions of Software Engineering, FSE 2014, pp. 281–293, New York, NY, USA, 2014. Associa-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                207,
+                                506,
+                                219
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        207,
+                                        506,
+                                        219
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tion for Computing Machinery. ISBN 9781450330565. doi: 10.1145/2635868.2635883. URL",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                217,
+                                355,
+                                230
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        217,
+                                        355,
+                                        230
+                                    ],
+                                    "score": 1.0,
+                                    "content": "https://doi.org/10.1145/2635868.2635883.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 9,
+                    "bbox_fs": [
+                        105,
+                        172,
+                        506,
+                        230
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        236,
+                        505,
+                        291
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                236,
+                                505,
+                                249
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        236,
+                                        505,
+                                        249
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Miltiadis Allamanis, Earl T. Barr, Christian Bird, and Charles Sutton. Suggesting accurate method",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                247,
+                                505,
+                                261
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        247,
+                                        505,
+                                        261
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and class names. In Proceedings of the 2015 10th Joint Meeting on Foundations of Software",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                256,
+                                506,
+                                273
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        256,
+                                        506,
+                                        273
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Engineering, ESEC/FSE 2015, pp. 38–49, New York, NY, USA, 2015. Association for Computing",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                268,
+                                504,
+                                282
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        268,
+                                        504,
+                                        282
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Machinery. ISBN 9781450336758. doi: 10.1145/2786805.2786849. URL https://doi.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                280,
+                                284,
+                                293
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        280,
+                                        284,
+                                        293
+                                    ],
+                                    "score": 1.0,
+                                    "content": "org/10.1145/2786805.2786849.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 14,
+                    "bbox_fs": [
+                        105,
+                        236,
+                        506,
+                        293
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        299,
+                        503,
+                        332
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                298,
+                                505,
+                                312
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        298,
+                                        505,
+                                        312
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Miltiadis Allamanis, Hao Peng, and Charles Sutton. A convolutional attention network for extreme",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                310,
+                                505,
+                                322
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        310,
+                                        505,
+                                        322
+                                    ],
+                                    "score": 1.0,
+                                    "content": "summarization of source code. In International conference on machine learning, pp. 2091–2100,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                319,
+                                143,
+                                333
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        319,
+                                        143,
+                                        333
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 18,
+                    "bbox_fs": [
+                        105,
+                        298,
+                        505,
+                        333
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        339,
+                        504,
+                        374
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                338,
+                                505,
+                                353
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        338,
+                                        505,
+                                        353
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Miltiadis Allamanis, Marc Brockschmidt, and Mahmoud Khademi. Learning to represent programs",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                351,
+                                504,
+                                363
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        351,
+                                        504,
+                                        363
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with graphs. In International Conference on Learning Representations, 2018. URL https:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                362,
+                                332,
+                                374
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        362,
+                                        266,
+                                        374
+                                    ],
+                                    "score": 1.0,
+                                    "content": "//openreview.net/forum?id",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        267,
+                                        363,
+                                        273,
+                                        371
+                                    ],
+                                    "score": 0.52,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        273,
+                                        362,
+                                        332,
+                                        374
+                                    ],
+                                    "score": 1.0,
+                                    "content": "BJOFETxR-.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 21,
+                    "bbox_fs": [
+                        105,
+                        338,
+                        505,
+                        374
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        380,
+                        505,
+                        436
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                381,
+                                504,
+                                393
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        381,
+                                        504,
+                                        393
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Uri Alon, Meital Zilberstein, Omer Levy, and Eran Yahav. A general path-based representa-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                391,
+                                505,
+                                405
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        391,
+                                        505,
+                                        405
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tion for predicting program properties. In Proceedings of the 39th ACM SIGPLAN Confer-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                403,
+                                505,
+                                415
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        403,
+                                        505,
+                                        415
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ence on Programming Language Design and Implementation, PLDI 2018, pp. 404–419, New",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                413,
+                                505,
+                                426
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        413,
+                                        505,
+                                        426
+                                    ],
+                                    "score": 1.0,
+                                    "content": "York, NY, USA, 2018. Association for Computing Machinery. ISBN 9781450356985. doi:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                424,
+                                491,
+                                437
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        424,
+                                        491,
+                                        437
+                                    ],
+                                    "score": 1.0,
+                                    "content": "10.1145/3192366.3192412. URL https://doi.org/10.1145/3192366.3192412.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 25,
+                    "bbox_fs": [
+                        106,
+                        381,
+                        505,
+                        437
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        443,
+                        505,
+                        477
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                442,
+                                505,
+                                457
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        442,
+                                        505,
+                                        457
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Uri Alon, Shaked Brody, Omer Levy, and Eran Yahav. code2seq: Generating sequences from struc-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                454,
+                                505,
+                                466
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        454,
+                                        505,
+                                        466
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tured representations of code. In International Conference on Learning Representations, 2019a.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                464,
+                                396,
+                                479
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        464,
+                                        325,
+                                        479
+                                    ],
+                                    "score": 1.0,
+                                    "content": "URL https://openreview.net/forum?id",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        325,
+                                        466,
+                                        331,
+                                        474
+                                    ],
+                                    "score": 0.47,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        332,
+                                        464,
+                                        396,
+                                        479
+                                    ],
+                                    "score": 1.0,
+                                    "content": "H1gKYo09tX.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 29,
+                    "bbox_fs": [
+                        106,
+                        442,
+                        505,
+                        479
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        483,
+                        504,
+                        507
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                483,
+                                505,
+                                496
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        483,
+                                        505,
+                                        496
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Uri Alon, Meital Zilberstein, Omer Levy, and Eran Yahav. code2vec: Learning distributed repre-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                494,
+                                505,
+                                508
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        494,
+                                        505,
+                                        508
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sentations of code. Proceedings of the ACM on Programming Languages, 3(POPL):1–29, 2019b.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 31.5,
+                    "bbox_fs": [
+                        106,
+                        483,
+                        505,
+                        508
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        513,
+                        505,
+                        558
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                514,
+                                505,
+                                525
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        514,
+                                        505,
+                                        525
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Peter W Battaglia, Jessica B Hamrick, Victor Bapst, Alvaro Sanchez-Gonzalez, Vinicius Zambaldi,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                524,
+                                505,
+                                536
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        524,
+                                        505,
+                                        536
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Mateusz Malinowski, Andrea Tacchetti, David Raposo, Adam Santoro, Ryan Faulkner, et al.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                535,
+                                506,
+                                549
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        535,
+                                        506,
+                                        549
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Relational inductive biases, deep learning, and graph networks. arXiv preprint arXiv:1806.01261,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                545,
+                                143,
+                                559
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        545,
+                                        143,
+                                        559
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 34.5,
+                    "bbox_fs": [
+                        105,
+                        514,
+                        506,
+                        559
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        565,
+                        505,
+                        588
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                565,
+                                505,
+                                578
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        565,
+                                        505,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Avishkar Bhoopchand, Tim Rocktaschel, Earl Barr, and Sebastian Riedel. Learning python code ¨",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                577,
+                                448,
+                                588
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        577,
+                                        448,
+                                        588
+                                    ],
+                                    "score": 1.0,
+                                    "content": "suggestion with a sparse pointer network. arXiv preprint arXiv:1611.08307, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        }
+                    ],
+                    "index": 37.5,
+                    "bbox_fs": [
+                        106,
+                        565,
+                        505,
+                        588
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        595,
+                        505,
+                        650
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                595,
+                                505,
+                                608
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        595,
+                                        505,
+                                        608
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Benjamin Bichsel, Veselin Raychev, Petar Tsankov, and Martin Vechev. Statistical deobfuscation",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                606,
+                                506,
+                                620
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        606,
+                                        506,
+                                        620
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of android applications. In Proceedings of the 2016 ACM SIGSAC Conference on Computer and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                617,
+                                506,
+                                631
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        617,
+                                        506,
+                                        631
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Communications Security, CCS ’16, pp. 343–355, New York, NY, USA, 2016. Association for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                627,
+                                505,
+                                642
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        627,
+                                        505,
+                                        642
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Computing Machinery. ISBN 9781450341394. doi: 10.1145/2976749.2978422. URL https:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                639,
+                                318,
+                                651
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        639,
+                                        318,
+                                        651
+                                    ],
+                                    "score": 1.0,
+                                    "content": "//doi.org/10.1145/2976749.2978422.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        }
+                    ],
+                    "index": 41,
+                    "bbox_fs": [
+                        106,
+                        595,
+                        506,
+                        651
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        657,
+                        504,
+                        681
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                657,
+                                505,
+                                671
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        657,
+                                        505,
+                                        671
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Pavol Bielik, Veselin Raychev, and Martin Vechev. Phog: probabilistic model for code. In Interna-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                669,
+                                371,
+                                681
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        669,
+                                        371,
+                                        681
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tional Conference on Machine Learning, pp. 2933–2942, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        }
+                    ],
+                    "index": 44.5,
+                    "bbox_fs": [
+                        105,
+                        657,
+                        505,
+                        681
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        687,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                687,
+                                506,
+                                700
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        687,
+                                        506,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Aleksandar Bojchevski, Johannes Klicpera, Bryan Perozzi, Amol Kapoor, Martin Blais, Benedek",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                699,
+                                505,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        699,
+                                        505,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Rozemberczki, Michal Lukasik, and Stephan G ´ unnemann. Scaling graph neural networks with ¨",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                710,
+                                505,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        710,
+                                        505,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "approximate pagerank. In Proceedings of the 26th ACM SIGKDD International Conference on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                720,
+                                505,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        720,
+                                        505,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Knowledge Discovery amp; Data Mining, KDD ’20, pp. 2464–2473, New York, NY, USA, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        }
+                    ],
+                    "index": 47.5,
+                    "bbox_fs": [
+                        106,
+                        687,
+                        506,
+                        733
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        112,
+                        82,
+                        503,
+                        105
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                116,
+                                82,
+                                505,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        82,
+                                        505,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Association for Computing Machinery. ISBN 9781450379984. doi: 10.1145/3394486.3403296.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                94,
+                                377,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        94,
+                                        377,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "URL https://doi.org/10.1145/3394486.3403296.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        113,
+                        504,
+                        135
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                112,
+                                505,
+                                125
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        112,
+                                        505,
+                                        125
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Dylan Bourgeois. Learning representations of source code from structure and context. 2019. URL",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                124,
+                                361,
+                                135
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        124,
+                                        361,
+                                        135
+                                    ],
+                                    "score": 1.0,
+                                    "content": "http://infoscience.epfl.ch/record/277163.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 2.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        142,
+                        505,
+                        198
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                142,
+                                505,
+                                155
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        142,
+                                        299,
+                                        154
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Alexis Conneau and Guillaume Lample.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        324,
+                                        142,
+                                        505,
+                                        155
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Cross-lingual language model pretrain-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                152,
+                                505,
+                                166
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        154,
+                                        136,
+                                        166
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ing.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        147,
+                                        152,
+                                        505,
+                                        166
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In H. Wallach, H. Larochelle, A. Beygelzimer, F. d'Alche-Buc, E. Fox, and ´",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                164,
+                                506,
+                                177
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        164,
+                                        506,
+                                        177
+                                    ],
+                                    "score": 1.0,
+                                    "content": "R. Garnett (eds.), Advances in Neural Information Processing Systems 32, pp. 7059–",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                174,
+                                505,
+                                189
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        174,
+                                        291,
+                                        188
+                                    ],
+                                    "score": 1.0,
+                                    "content": "7069. Curran Associates, Inc., 2019.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        174,
+                                        505,
+                                        189
+                                    ],
+                                    "score": 1.0,
+                                    "content": "URL http://papers.nips.cc/paper/",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                186,
+                                417,
+                                200
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        186,
+                                        417,
+                                        200
+                                    ],
+                                    "score": 1.0,
+                                    "content": "8928-cross-lingual-language-model-pretraining.pdf.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        205,
+                        503,
+                        229
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                206,
+                                504,
+                                217
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        206,
+                                        504,
+                                        217
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Hanjun Dai, Bo Dai, and Le Song. Discriminative embeddings of latent variable models for struc-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                216,
+                                451,
+                                230
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        216,
+                                        451,
+                                        230
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tured data. In International conference on machine learning, pp. 2702–2711, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 9.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        235,
+                        504,
+                        269
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                235,
+                                504,
+                                248
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        235,
+                                        504,
+                                        248
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Zihang Dai, Zhilin Yang, Yiming Yang, Jaime Carbonell, Quoc V Le, and Ruslan Salakhutdi-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                247,
+                                505,
+                                259
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        247,
+                                        505,
+                                        259
+                                    ],
+                                    "score": 1.0,
+                                    "content": "nov. Transformer-xl: Attentive language models beyond a fixed-length context. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                257,
+                                219,
+                                269
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        257,
+                                        219,
+                                        269
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1901.02860, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        276,
+                        505,
+                        310
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                276,
+                                505,
+                                290
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        276,
+                                        505,
+                                        290
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Hoa Khanh Dam, Truyen Tran, and Trang Pham. A deep language model for software code. In",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                288,
+                                505,
+                                300
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        288,
+                                        505,
+                                        300
+                                    ],
+                                    "score": 1.0,
+                                    "content": "FSE 2016: Proceedings of the Foundations Software Engineering International Symposium [The",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                299,
+                                196,
+                                312
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        299,
+                                        196,
+                                        312
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Conference], 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        317,
+                        504,
+                        351
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                317,
+                                505,
+                                330
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        317,
+                                        505,
+                                        330
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Michael Defferrard, Xavier Bresson, and Pierre Vandergheynst. Convolutional neural networks on ¨",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                329,
+                                506,
+                                343
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        329,
+                                        506,
+                                        343
+                                    ],
+                                    "score": 1.0,
+                                    "content": "graphs with fast localized spectral filtering. In Advances in neural information processing systems,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                339,
+                                207,
+                                352
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        339,
+                                        207,
+                                        352
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pp. 3844–3852, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        358,
+                        503,
+                        393
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                358,
+                                505,
+                                372
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        358,
+                                        505,
+                                        372
+                                    ],
+                                    "score": 1.0,
+                                    "content": "David K Duvenaud, Dougal Maclaurin, Jorge Iparraguirre, Rafael Bombarell, Timothy Hirzel, Alan´",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                370,
+                                505,
+                                383
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        370,
+                                        505,
+                                        383
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Aspuru-Guzik, and Ryan P Adams. Convolutional networks on graphs for learning molecular",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                380,
+                                479,
+                                394
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        380,
+                                        479,
+                                        394
+                                    ],
+                                    "score": 1.0,
+                                    "content": "fingerprints. In Advances in neural information processing systems, pp. 2224–2232, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 21
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        399,
+                        502,
+                        434
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                399,
+                                504,
+                                412
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        399,
+                                        504,
+                                        412
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Patrick Fernandes, Miltiadis Allamanis, and Marc Brockschmidt. Structured neural summa-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                411,
+                                504,
+                                424
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        411,
+                                        504,
+                                        424
+                                    ],
+                                    "score": 1.0,
+                                    "content": "rization. In International Conference on Learning Representations, 2019. URL https:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                422,
+                                336,
+                                434
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        422,
+                                        266,
+                                        434
+                                    ],
+                                    "score": 1.0,
+                                    "content": "//openreview.net/forum?id",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        267,
+                                        424,
+                                        273,
+                                        431
+                                    ],
+                                    "score": 0.51,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        273,
+                                        422,
+                                        336,
+                                        434
+                                    ],
+                                    "score": 1.0,
+                                    "content": "H1ersoRqtm.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 24
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        441,
+                        504,
+                        474
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                440,
+                                504,
+                                453
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        440,
+                                        504,
+                                        453
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Marco Gori, Gabriele Monfardini, and Franco Scarselli. A new model for learning in graph domains.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                452,
+                                505,
+                                464
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        452,
+                                        505,
+                                        464
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In Proceedings. 2005 IEEE International Joint Conference on Neural Networks, 2005., volume 2,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                463,
+                                223,
+                                474
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        463,
+                                        223,
+                                        474
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pp. 729–734. IEEE, 2005.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 27
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        482,
+                        503,
+                        505
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                480,
+                                505,
+                                496
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        480,
+                                        505,
+                                        496
+                                    ],
+                                    "score": 1.0,
+                                    "content": "William L. Hamilton, Rex Ying, and Jure Leskovec. Inductive representation learning on large",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                493,
+                                212,
+                                505
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        493,
+                                        212,
+                                        505
+                                    ],
+                                    "score": 1.0,
+                                    "content": "graphs. In NIPS, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 29.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        511,
+                        505,
+                        546
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                512,
+                                505,
+                                524
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        512,
+                                        505,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Vincent J. Hellendoorn, Charles Sutton, Rishabh Singh, Petros Maniatis, and David Bieber. Global",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                523,
+                                505,
+                                536
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        523,
+                                        505,
+                                        536
+                                    ],
+                                    "score": 1.0,
+                                    "content": "relational models of source code. In International Conference on Learning Representations, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                533,
+                                396,
+                                548
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        533,
+                                        325,
+                                        548
+                                    ],
+                                    "score": 1.0,
+                                    "content": "URL https://openreview.net/forum?id",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        325,
+                                        536,
+                                        331,
+                                        544
+                                    ],
+                                    "score": 0.44,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        331,
+                                        533,
+                                        396,
+                                        548
+                                    ],
+                                    "score": 1.0,
+                                    "content": "B1lnbRNtwr.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 32
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        553,
+                        505,
+                        587
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                553,
+                                504,
+                                565
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        553,
+                                        504,
+                                        565
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Abram Hindle, Earl T. Barr, Zhendong Su, Mark Gabel, and Premkumar Devanbu. On the natural-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                564,
+                                505,
+                                578
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        564,
+                                        505,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ness of software. In Proceedings of the 34th International Conference on Software Engineering,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                576,
+                                385,
+                                588
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        576,
+                                        385,
+                                        588
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ICSE ’12, pp. 837–847. IEEE Press, 2012. ISBN 9781467310673.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 35
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        594,
+                        503,
+                        617
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                594,
+                                505,
+                                608
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        594,
+                                        505,
+                                        608
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sepp Hochreiter and Jurgen Schmidhuber. Long short-term memory. ¨ Neural computation, 9(8):",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                605,
+                                191,
+                                617
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        605,
+                                        191,
+                                        617
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1735–1780, 1997.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        }
+                    ],
+                    "index": 37.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        624,
+                        505,
+                        691
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                624,
+                                506,
+                                637
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        624,
+                                        506,
+                                        637
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Weihua Hu, Matthias Fey, Marinka Zitnik, Yuxiao Dong, Hongyu Ren, Bowen Liu, Michele",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                635,
+                                505,
+                                648
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        635,
+                                        505,
+                                        648
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Catasta, and Jure Leskovec. Open graph benchmark: Datasets for machine learning on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                646,
+                                505,
+                                659
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        646,
+                                        505,
+                                        659
+                                    ],
+                                    "score": 1.0,
+                                    "content": "graphs. In H. Larochelle, M. Ranzato, R. Hadsell, M. F. Balcan, and H. Lin (eds.), Ad-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                658,
+                                504,
+                                669
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        658,
+                                        504,
+                                        669
+                                    ],
+                                    "score": 1.0,
+                                    "content": "vances in Neural Information Processing Systems, volume 33, pp. 22118–22133. Curran As-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                668,
+                                505,
+                                681
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        668,
+                                        505,
+                                        681
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sociates, Inc., 2020. URL https://proceedings.neurips.cc/paper/2020/file/",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                678,
+                                373,
+                                692
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        678,
+                                        373,
+                                        692
+                                    ],
+                                    "score": 1.0,
+                                    "content": "fb60d411a5c5b72b2e7d3527cfc84fd0-Paper.pdf.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        }
+                    ],
+                    "index": 41.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        699,
+                        504,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                698,
+                                504,
+                                711
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        698,
+                                        504,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Hamel Husain, Ho-Hsiang Wu, Tiferet Gazit, Miltiadis Allamanis, and Marc Brockschmidt.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                709,
+                                505,
+                                721
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        709,
+                                        505,
+                                        721
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Codesearchnet challenge: Evaluating the state of semantic code search. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                720,
+                                220,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        720,
+                                        220,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1909.09436, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        }
+                    ],
+                    "index": 46
+                }
+            ],
+            "page_idx": 10,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        108,
+                        27,
+                        292,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                293,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        293,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        310,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                312,
+                                765
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        312,
+                                        765
+                                    ],
+                                    "score": 1.0,
+                                    "content": "",
+                                    "type": "text",
+                                    "height": 15,
+                                    "width": 13
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "list",
+                    "bbox": [
+                        112,
+                        82,
+                        503,
+                        105
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                116,
+                                82,
+                                505,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        82,
+                                        505,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Association for Computing Machinery. ISBN 9781450379984. doi: 10.1145/3394486.3403296.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                94,
+                                377,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        94,
+                                        377,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "URL https://doi.org/10.1145/3394486.3403296.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1,
+                            "is_list_start_line": true,
+                            "is_list_end_line": true
+                        }
+                    ],
+                    "index": 0.5,
+                    "bbox_fs": [
+                        116,
+                        82,
+                        505,
+                        106
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        113,
+                        504,
+                        135
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                112,
+                                505,
+                                125
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        112,
+                                        505,
+                                        125
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Dylan Bourgeois. Learning representations of source code from structure and context. 2019. URL",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                124,
+                                361,
+                                135
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        124,
+                                        361,
+                                        135
+                                    ],
+                                    "score": 1.0,
+                                    "content": "http://infoscience.epfl.ch/record/277163.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 2.5,
+                    "bbox_fs": [
+                        106,
+                        112,
+                        505,
+                        135
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        142,
+                        505,
+                        198
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                142,
+                                505,
+                                155
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        142,
+                                        299,
+                                        154
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Alexis Conneau and Guillaume Lample.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        324,
+                                        142,
+                                        505,
+                                        155
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Cross-lingual language model pretrain-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                152,
+                                505,
+                                166
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        154,
+                                        136,
+                                        166
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ing.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        147,
+                                        152,
+                                        505,
+                                        166
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In H. Wallach, H. Larochelle, A. Beygelzimer, F. d'Alche-Buc, E. Fox, and ´",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                164,
+                                506,
+                                177
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        164,
+                                        506,
+                                        177
+                                    ],
+                                    "score": 1.0,
+                                    "content": "R. Garnett (eds.), Advances in Neural Information Processing Systems 32, pp. 7059–",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                174,
+                                505,
+                                189
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        174,
+                                        291,
+                                        188
+                                    ],
+                                    "score": 1.0,
+                                    "content": "7069. Curran Associates, Inc., 2019.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        174,
+                                        505,
+                                        189
+                                    ],
+                                    "score": 1.0,
+                                    "content": "URL http://papers.nips.cc/paper/",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                186,
+                                417,
+                                200
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        186,
+                                        417,
+                                        200
+                                    ],
+                                    "score": 1.0,
+                                    "content": "8928-cross-lingual-language-model-pretraining.pdf.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 6,
+                    "bbox_fs": [
+                        106,
+                        142,
+                        506,
+                        200
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        205,
+                        503,
+                        229
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                206,
+                                504,
+                                217
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        206,
+                                        504,
+                                        217
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Hanjun Dai, Bo Dai, and Le Song. Discriminative embeddings of latent variable models for struc-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                216,
+                                451,
+                                230
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        216,
+                                        451,
+                                        230
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tured data. In International conference on machine learning, pp. 2702–2711, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 9.5,
+                    "bbox_fs": [
+                        106,
+                        206,
+                        504,
+                        230
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        235,
+                        504,
+                        269
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                235,
+                                504,
+                                248
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        235,
+                                        504,
+                                        248
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Zihang Dai, Zhilin Yang, Yiming Yang, Jaime Carbonell, Quoc V Le, and Ruslan Salakhutdi-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                247,
+                                505,
+                                259
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        247,
+                                        505,
+                                        259
+                                    ],
+                                    "score": 1.0,
+                                    "content": "nov. Transformer-xl: Attentive language models beyond a fixed-length context. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                257,
+                                219,
+                                269
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        257,
+                                        219,
+                                        269
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1901.02860, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 12,
+                    "bbox_fs": [
+                        106,
+                        235,
+                        505,
+                        269
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        276,
+                        505,
+                        310
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                276,
+                                505,
+                                290
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        276,
+                                        505,
+                                        290
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Hoa Khanh Dam, Truyen Tran, and Trang Pham. A deep language model for software code. In",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                288,
+                                505,
+                                300
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        288,
+                                        505,
+                                        300
+                                    ],
+                                    "score": 1.0,
+                                    "content": "FSE 2016: Proceedings of the Foundations Software Engineering International Symposium [The",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                299,
+                                196,
+                                312
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        299,
+                                        196,
+                                        312
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Conference], 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 15,
+                    "bbox_fs": [
+                        105,
+                        276,
+                        505,
+                        312
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        317,
+                        504,
+                        351
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                317,
+                                505,
+                                330
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        317,
+                                        505,
+                                        330
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Michael Defferrard, Xavier Bresson, and Pierre Vandergheynst. Convolutional neural networks on ¨",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                329,
+                                506,
+                                343
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        329,
+                                        506,
+                                        343
+                                    ],
+                                    "score": 1.0,
+                                    "content": "graphs with fast localized spectral filtering. In Advances in neural information processing systems,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                339,
+                                207,
+                                352
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        339,
+                                        207,
+                                        352
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pp. 3844–3852, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 18,
+                    "bbox_fs": [
+                        105,
+                        317,
+                        506,
+                        352
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        358,
+                        503,
+                        393
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                358,
+                                505,
+                                372
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        358,
+                                        505,
+                                        372
+                                    ],
+                                    "score": 1.0,
+                                    "content": "David K Duvenaud, Dougal Maclaurin, Jorge Iparraguirre, Rafael Bombarell, Timothy Hirzel, Alan´",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                370,
+                                505,
+                                383
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        370,
+                                        505,
+                                        383
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Aspuru-Guzik, and Ryan P Adams. Convolutional networks on graphs for learning molecular",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                380,
+                                479,
+                                394
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        380,
+                                        479,
+                                        394
+                                    ],
+                                    "score": 1.0,
+                                    "content": "fingerprints. In Advances in neural information processing systems, pp. 2224–2232, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 21,
+                    "bbox_fs": [
+                        106,
+                        358,
+                        505,
+                        394
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        399,
+                        502,
+                        434
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                399,
+                                504,
+                                412
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        399,
+                                        504,
+                                        412
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Patrick Fernandes, Miltiadis Allamanis, and Marc Brockschmidt. Structured neural summa-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                411,
+                                504,
+                                424
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        411,
+                                        504,
+                                        424
+                                    ],
+                                    "score": 1.0,
+                                    "content": "rization. In International Conference on Learning Representations, 2019. URL https:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                422,
+                                336,
+                                434
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        422,
+                                        266,
+                                        434
+                                    ],
+                                    "score": 1.0,
+                                    "content": "//openreview.net/forum?id",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        267,
+                                        424,
+                                        273,
+                                        431
+                                    ],
+                                    "score": 0.51,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        273,
+                                        422,
+                                        336,
+                                        434
+                                    ],
+                                    "score": 1.0,
+                                    "content": "H1ersoRqtm.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 24,
+                    "bbox_fs": [
+                        105,
+                        399,
+                        504,
+                        434
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        441,
+                        504,
+                        474
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                440,
+                                504,
+                                453
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        440,
+                                        504,
+                                        453
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Marco Gori, Gabriele Monfardini, and Franco Scarselli. A new model for learning in graph domains.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                452,
+                                505,
+                                464
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        452,
+                                        505,
+                                        464
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In Proceedings. 2005 IEEE International Joint Conference on Neural Networks, 2005., volume 2,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                463,
+                                223,
+                                474
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        463,
+                                        223,
+                                        474
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pp. 729–734. IEEE, 2005.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 27,
+                    "bbox_fs": [
+                        105,
+                        440,
+                        505,
+                        474
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        482,
+                        503,
+                        505
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                480,
+                                505,
+                                496
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        480,
+                                        505,
+                                        496
+                                    ],
+                                    "score": 1.0,
+                                    "content": "William L. Hamilton, Rex Ying, and Jure Leskovec. Inductive representation learning on large",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                493,
+                                212,
+                                505
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        493,
+                                        212,
+                                        505
+                                    ],
+                                    "score": 1.0,
+                                    "content": "graphs. In NIPS, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 29.5,
+                    "bbox_fs": [
+                        105,
+                        480,
+                        505,
+                        505
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        511,
+                        505,
+                        546
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                512,
+                                505,
+                                524
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        512,
+                                        505,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Vincent J. Hellendoorn, Charles Sutton, Rishabh Singh, Petros Maniatis, and David Bieber. Global",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                523,
+                                505,
+                                536
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        523,
+                                        505,
+                                        536
+                                    ],
+                                    "score": 1.0,
+                                    "content": "relational models of source code. In International Conference on Learning Representations, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                533,
+                                396,
+                                548
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        533,
+                                        325,
+                                        548
+                                    ],
+                                    "score": 1.0,
+                                    "content": "URL https://openreview.net/forum?id",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        325,
+                                        536,
+                                        331,
+                                        544
+                                    ],
+                                    "score": 0.44,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        331,
+                                        533,
+                                        396,
+                                        548
+                                    ],
+                                    "score": 1.0,
+                                    "content": "B1lnbRNtwr.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 32,
+                    "bbox_fs": [
+                        106,
+                        512,
+                        505,
+                        548
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        553,
+                        505,
+                        587
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                553,
+                                504,
+                                565
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        553,
+                                        504,
+                                        565
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Abram Hindle, Earl T. Barr, Zhendong Su, Mark Gabel, and Premkumar Devanbu. On the natural-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                564,
+                                505,
+                                578
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        564,
+                                        505,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ness of software. In Proceedings of the 34th International Conference on Software Engineering,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                576,
+                                385,
+                                588
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        576,
+                                        385,
+                                        588
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ICSE ’12, pp. 837–847. IEEE Press, 2012. ISBN 9781467310673.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 35,
+                    "bbox_fs": [
+                        106,
+                        553,
+                        505,
+                        588
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        594,
+                        503,
+                        617
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                594,
+                                505,
+                                608
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        594,
+                                        505,
+                                        608
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sepp Hochreiter and Jurgen Schmidhuber. Long short-term memory. ¨ Neural computation, 9(8):",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                605,
+                                191,
+                                617
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        605,
+                                        191,
+                                        617
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1735–1780, 1997.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        }
+                    ],
+                    "index": 37.5,
+                    "bbox_fs": [
+                        105,
+                        594,
+                        505,
+                        617
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        624,
+                        505,
+                        691
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                624,
+                                506,
+                                637
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        624,
+                                        506,
+                                        637
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Weihua Hu, Matthias Fey, Marinka Zitnik, Yuxiao Dong, Hongyu Ren, Bowen Liu, Michele",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                635,
+                                505,
+                                648
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        635,
+                                        505,
+                                        648
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Catasta, and Jure Leskovec. Open graph benchmark: Datasets for machine learning on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                646,
+                                505,
+                                659
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        646,
+                                        505,
+                                        659
+                                    ],
+                                    "score": 1.0,
+                                    "content": "graphs. In H. Larochelle, M. Ranzato, R. Hadsell, M. F. Balcan, and H. Lin (eds.), Ad-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                658,
+                                504,
+                                669
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        658,
+                                        504,
+                                        669
+                                    ],
+                                    "score": 1.0,
+                                    "content": "vances in Neural Information Processing Systems, volume 33, pp. 22118–22133. Curran As-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                668,
+                                505,
+                                681
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        668,
+                                        505,
+                                        681
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sociates, Inc., 2020. URL https://proceedings.neurips.cc/paper/2020/file/",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                678,
+                                373,
+                                692
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        678,
+                                        373,
+                                        692
+                                    ],
+                                    "score": 1.0,
+                                    "content": "fb60d411a5c5b72b2e7d3527cfc84fd0-Paper.pdf.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        }
+                    ],
+                    "index": 41.5,
+                    "bbox_fs": [
+                        106,
+                        624,
+                        506,
+                        692
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        699,
+                        504,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                698,
+                                504,
+                                711
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        698,
+                                        504,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Hamel Husain, Ho-Hsiang Wu, Tiferet Gazit, Miltiadis Allamanis, and Marc Brockschmidt.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                709,
+                                505,
+                                721
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        709,
+                                        505,
+                                        721
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Codesearchnet challenge: Evaluating the state of semantic code search. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                720,
+                                220,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        720,
+                                        220,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1909.09436, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        }
+                    ],
+                    "index": 46,
+                    "bbox_fs": [
+                        106,
+                        698,
+                        505,
+                        732
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        82,
+                        503,
+                        116
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                81,
+                                505,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        81,
+                                        505,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Aditya Kanade, Petros Maniatis, Gogul Balakrishnan, and Kensen Shi. Learning and evaluating",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                93,
+                                505,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        93,
+                                        505,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "contextual embedding of source code. In Proceedings of the 37th International Conference on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                104,
+                                220,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        104,
+                                        220,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Machine Learning, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        123,
+                        503,
+                        146
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                123,
+                                504,
+                                136
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        123,
+                                        504,
+                                        136
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Thomas N. Kipf and Max Welling. Semi-supervised classification with graph convolutional net-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                134,
+                                437,
+                                146
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        134,
+                                        437,
+                                        146
+                                    ],
+                                    "score": 1.0,
+                                    "content": "works. In International Conference on Learning Representations (ICLR), 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 3.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        152,
+                        504,
+                        186
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                151,
+                                505,
+                                165
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        151,
+                                        505,
+                                        165
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Johannes Klicpera, Aleksandar Bojchevski, and Stephan Gunnemann. Predict then propagate: ¨",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                163,
+                                505,
+                                177
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        163,
+                                        505,
+                                        177
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Graph neural networks meet personalized pagerank. In International Conference on Learning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                175,
+                                245,
+                                187
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        175,
+                                        245,
+                                        187
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Representations (ICLR), 2019a.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        192,
+                        504,
+                        216
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                193,
+                                504,
+                                206
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        193,
+                                        504,
+                                        206
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Johannes Klicpera, Stefan Weißenberger, and Stephan Gunnemann. Diffusion improves graph learn-¨",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                204,
+                                443,
+                                216
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        204,
+                                        443,
+                                        216
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ing. In Conference on Neural Information Processing Systems (NeurIPS), 2019b.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 8.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        222,
+                        504,
+                        245
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                223,
+                                505,
+                                236
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        223,
+                                        505,
+                                        236
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Johannes Klicpera, Janek Groß, and Stephan Gunnemann. Directional message passing for molec- ¨",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                233,
+                                457,
+                                246
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        233,
+                                        457,
+                                        246
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ular graphs. In International Conference on Learning Representations (ICLR), 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 10.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        252,
+                        504,
+                        275
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                252,
+                                505,
+                                265
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        252,
+                                        505,
+                                        265
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Jian Li, Yue Wang, Michael R Lyu, and Irwin King. Code completion with neural attention and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                264,
+                                352,
+                                275
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        264,
+                                        352,
+                                        275
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pointer networks. arXiv preprint arXiv:1711.09573, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 12.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        281,
+                        504,
+                        305
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                281,
+                                505,
+                                294
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        281,
+                                        505,
+                                        294
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Yujia Li, Daniel Tarlow, Marc Brockschmidt, and Richard Zemel. Gated graph sequence neural",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                293,
+                                321,
+                                305
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        293,
+                                        321,
+                                        305
+                                    ],
+                                    "score": 1.0,
+                                    "content": "networks. arXiv preprint arXiv:1511.05493, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 14.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        311,
+                        504,
+                        334
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                311,
+                                505,
+                                324
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        311,
+                                        505,
+                                        324
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Laurens van der Maaten and Geoffrey Hinton. Visualizing data using t-sne. Journal of machine",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                322,
+                                298,
+                                335
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        322,
+                                        298,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning research, 9(Nov):2579–2605, 2008.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 16.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        341,
+                        503,
+                        364
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                341,
+                                505,
+                                354
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        341,
+                                        505,
+                                        354
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Chris Maddison and Daniel Tarlow. Structured generative models of natural source code. In Inter-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                352,
+                                371,
+                                364
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        352,
+                                        371,
+                                        364
+                                    ],
+                                    "score": 1.0,
+                                    "content": "national Conference on Machine Learning, pp. 649–657, 2014.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 18.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        370,
+                        504,
+                        405
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                370,
+                                504,
+                                384
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        370,
+                                        504,
+                                        384
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lili Mou, Ge Li, Lu Zhang, Tao Wang, and Zhi Jin. Convolutional neural networks over tree struc-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                382,
+                                505,
+                                395
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        382,
+                                        505,
+                                        395
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tures for programming language processing. In Proceedings of the Thirtieth AAAI Conference on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                393,
+                                393,
+                                405
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        393,
+                                        393,
+                                        405
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Artificial Intelligence, AAAI’16, pp. 1287–1293. AAAI Press, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 21
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        411,
+                        505,
+                        456
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                410,
+                                506,
+                                425
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        410,
+                                        506,
+                                        425
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Trong Duc Nguyen, Anh Tuan Nguyen, Hung Dang Phan, and Tien N. Nguyen. Exploring api",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                423,
+                                506,
+                                435
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        423,
+                                        506,
+                                        435
+                                    ],
+                                    "score": 1.0,
+                                    "content": "embedding for api usages and applications. In Proceedings of the 39th International Conference",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                434,
+                                505,
+                                445
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        434,
+                                        505,
+                                        445
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on Software Engineering, ICSE ’17, pp. 438–449. IEEE Press, 2017. ISBN 9781538638682. doi:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                444,
+                                457,
+                                456
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        444,
+                                        457,
+                                        456
+                                    ],
+                                    "score": 1.0,
+                                    "content": "10.1109/ICSE.2017.47. URL https://doi.org/10.1109/ICSE.2017.47.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 24.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        462,
+                        504,
+                        486
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                461,
+                                505,
+                                477
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        461,
+                                        505,
+                                        477
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lawrence Page, Sergey Brin, Rajeev Motwani, and Terry Winograd. The pagerank citation ranking:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                474,
+                                394,
+                                487
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        474,
+                                        394,
+                                        487
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Bringing order to the web. Technical report, Stanford InfoLab, 1999.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 27.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        492,
+                        504,
+                        515
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                490,
+                                505,
+                                507
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        490,
+                                        505,
+                                        507
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Alec Radford, Jeffrey Wu, Rewon Child, David Luan, Dario Amodei, and Ilya Sutskever. Language",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                503,
+                                407,
+                                516
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        503,
+                                        407,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "models are unsupervised multitask learners. OpenAI Blog, 1(8):9, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 29.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        522,
+                        505,
+                        578
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                522,
+                                504,
+                                534
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        522,
+                                        504,
+                                        534
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Veselin Raychev, Martin Vechev, and Eran Yahav. Code completion with statistical language models.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                533,
+                                505,
+                                546
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        533,
+                                        505,
+                                        546
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In Proceedings of the 35th ACM SIGPLAN Conference on Programming Language Design and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                542,
+                                505,
+                                559
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        542,
+                                        505,
+                                        559
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Implementation, PLDI ’14, pp. 419–428, New York, NY, USA, 2014. Association for Computing",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                554,
+                                504,
+                                568
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        554,
+                                        504,
+                                        568
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Machinery. ISBN 9781450327848. doi: 10.1145/2594291.2594321. URL https://doi.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                566,
+                                284,
+                                578
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        566,
+                                        284,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": "org/10.1145/2594291.2594321.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        }
+                    ],
+                    "index": 33
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        584,
+                        503,
+                        607
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                584,
+                                505,
+                                597
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        584,
+                                        505,
+                                        597
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Franco Scarselli, Marco Gori, Ah Chung Tsoi, Markus Hagenbuchner, and Gabriele Monfardini.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                595,
+                                495,
+                                608
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        595,
+                                        495,
+                                        608
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The graph neural network model. IEEE Transactions on Neural Networks, 20(1):61–80, 2008.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 36.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        614,
+                        505,
+                        669
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                613,
+                                505,
+                                627
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        613,
+                                        505,
+                                        627
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Michael Schlichtkrull, Thomas N. Kipf, Peter Bloem, Rianne van den Berg, Ivan Titov, and Max",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                624,
+                                506,
+                                638
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        624,
+                                        506,
+                                        638
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Welling. Modeling relational data with graph convolutional networks. In Aldo Gangemi, Roberto",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                636,
+                                505,
+                                649
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        636,
+                                        505,
+                                        649
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Navigli, Maria-Esther Vidal, Pascal Hitzler, Raphael Troncy, Laura Hollink, Anna Tordai, and ¨",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                645,
+                                505,
+                                660
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        645,
+                                        505,
+                                        660
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Mehwish Alam (eds.), The Semantic Web, pp. 593–607, Cham, 2018. Springer International Pub-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                658,
+                                258,
+                                671
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        658,
+                                        258,
+                                        671
+                                    ],
+                                    "score": 1.0,
+                                    "content": "lishing. ISBN 978-3-319-93417-4.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        }
+                    ],
+                    "index": 40
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        676,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                676,
+                                505,
+                                689
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        676,
+                                        505,
+                                        689
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Peter Shaw, Jakob Uszkoreit, and Ashish Vaswani. Self-attention with relative position representa-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                687,
+                                505,
+                                701
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        687,
+                                        505,
+                                        701
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tions. In Proceedings of the 2018 Conference of the North American Chapter of the Association",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                697,
+                                505,
+                                713
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        697,
+                                        505,
+                                        713
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for Computational Linguistics: Human Language Technologies, Volume 2 (Short Papers), pp.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                708,
+                                505,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        708,
+                                        505,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "464–468, New Orleans, Louisiana, June 2018. Association for Computational Linguistics. doi:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                719,
+                                489,
+                                734
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        719,
+                                        489,
+                                        734
+                                    ],
+                                    "score": 1.0,
+                                    "content": "10.18653/v1/N18-2074. URL https://www.aclweb.org/anthology/N18-2074.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        }
+                    ],
+                    "index": 45
+                }
+            ],
+            "page_idx": 11,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        108,
+                        27,
+                        292,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                293,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        293,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        311,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                313,
+                                764
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        313,
+                                        764
+                                    ],
+                                    "score": 1.0,
+                                    "content": "12",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        82,
+                        503,
+                        116
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                81,
+                                505,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        81,
+                                        505,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Aditya Kanade, Petros Maniatis, Gogul Balakrishnan, and Kensen Shi. Learning and evaluating",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                93,
+                                505,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        93,
+                                        505,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "contextual embedding of source code. In Proceedings of the 37th International Conference on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                104,
+                                220,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        104,
+                                        220,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Machine Learning, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1,
+                    "bbox_fs": [
+                        105,
+                        81,
+                        505,
+                        117
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        123,
+                        503,
+                        146
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                123,
+                                504,
+                                136
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        123,
+                                        504,
+                                        136
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Thomas N. Kipf and Max Welling. Semi-supervised classification with graph convolutional net-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                134,
+                                437,
+                                146
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        134,
+                                        437,
+                                        146
+                                    ],
+                                    "score": 1.0,
+                                    "content": "works. In International Conference on Learning Representations (ICLR), 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 3.5,
+                    "bbox_fs": [
+                        106,
+                        123,
+                        504,
+                        146
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        152,
+                        504,
+                        186
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                151,
+                                505,
+                                165
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        151,
+                                        505,
+                                        165
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Johannes Klicpera, Aleksandar Bojchevski, and Stephan Gunnemann. Predict then propagate: ¨",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                163,
+                                505,
+                                177
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        163,
+                                        505,
+                                        177
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Graph neural networks meet personalized pagerank. In International Conference on Learning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                175,
+                                245,
+                                187
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        175,
+                                        245,
+                                        187
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Representations (ICLR), 2019a.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 6,
+                    "bbox_fs": [
+                        105,
+                        151,
+                        505,
+                        187
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        192,
+                        504,
+                        216
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                193,
+                                504,
+                                206
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        193,
+                                        504,
+                                        206
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Johannes Klicpera, Stefan Weißenberger, and Stephan Gunnemann. Diffusion improves graph learn-¨",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                204,
+                                443,
+                                216
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        204,
+                                        443,
+                                        216
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ing. In Conference on Neural Information Processing Systems (NeurIPS), 2019b.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 8.5,
+                    "bbox_fs": [
+                        105,
+                        193,
+                        504,
+                        216
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        222,
+                        504,
+                        245
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                223,
+                                505,
+                                236
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        223,
+                                        505,
+                                        236
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Johannes Klicpera, Janek Groß, and Stephan Gunnemann. Directional message passing for molec- ¨",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                233,
+                                457,
+                                246
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        233,
+                                        457,
+                                        246
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ular graphs. In International Conference on Learning Representations (ICLR), 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 10.5,
+                    "bbox_fs": [
+                        106,
+                        223,
+                        505,
+                        246
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        252,
+                        504,
+                        275
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                252,
+                                505,
+                                265
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        252,
+                                        505,
+                                        265
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Jian Li, Yue Wang, Michael R Lyu, and Irwin King. Code completion with neural attention and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                264,
+                                352,
+                                275
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        264,
+                                        352,
+                                        275
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pointer networks. arXiv preprint arXiv:1711.09573, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 12.5,
+                    "bbox_fs": [
+                        106,
+                        252,
+                        505,
+                        275
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        281,
+                        504,
+                        305
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                281,
+                                505,
+                                294
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        281,
+                                        505,
+                                        294
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Yujia Li, Daniel Tarlow, Marc Brockschmidt, and Richard Zemel. Gated graph sequence neural",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                293,
+                                321,
+                                305
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        293,
+                                        321,
+                                        305
+                                    ],
+                                    "score": 1.0,
+                                    "content": "networks. arXiv preprint arXiv:1511.05493, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 14.5,
+                    "bbox_fs": [
+                        106,
+                        281,
+                        505,
+                        305
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        311,
+                        504,
+                        334
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                311,
+                                505,
+                                324
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        311,
+                                        505,
+                                        324
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Laurens van der Maaten and Geoffrey Hinton. Visualizing data using t-sne. Journal of machine",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                322,
+                                298,
+                                335
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        322,
+                                        298,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning research, 9(Nov):2579–2605, 2008.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 16.5,
+                    "bbox_fs": [
+                        106,
+                        311,
+                        505,
+                        335
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        341,
+                        503,
+                        364
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                341,
+                                505,
+                                354
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        341,
+                                        505,
+                                        354
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Chris Maddison and Daniel Tarlow. Structured generative models of natural source code. In Inter-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                352,
+                                371,
+                                364
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        352,
+                                        371,
+                                        364
+                                    ],
+                                    "score": 1.0,
+                                    "content": "national Conference on Machine Learning, pp. 649–657, 2014.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 18.5,
+                    "bbox_fs": [
+                        106,
+                        341,
+                        505,
+                        364
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        370,
+                        504,
+                        405
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                370,
+                                504,
+                                384
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        370,
+                                        504,
+                                        384
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lili Mou, Ge Li, Lu Zhang, Tao Wang, and Zhi Jin. Convolutional neural networks over tree struc-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                382,
+                                505,
+                                395
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        382,
+                                        505,
+                                        395
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tures for programming language processing. In Proceedings of the Thirtieth AAAI Conference on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                393,
+                                393,
+                                405
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        393,
+                                        393,
+                                        405
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Artificial Intelligence, AAAI’16, pp. 1287–1293. AAAI Press, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 21,
+                    "bbox_fs": [
+                        105,
+                        370,
+                        505,
+                        405
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        411,
+                        505,
+                        456
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                410,
+                                506,
+                                425
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        410,
+                                        506,
+                                        425
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Trong Duc Nguyen, Anh Tuan Nguyen, Hung Dang Phan, and Tien N. Nguyen. Exploring api",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                423,
+                                506,
+                                435
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        423,
+                                        506,
+                                        435
+                                    ],
+                                    "score": 1.0,
+                                    "content": "embedding for api usages and applications. In Proceedings of the 39th International Conference",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                434,
+                                505,
+                                445
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        434,
+                                        505,
+                                        445
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on Software Engineering, ICSE ’17, pp. 438–449. IEEE Press, 2017. ISBN 9781538638682. doi:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                444,
+                                457,
+                                456
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        444,
+                                        457,
+                                        456
+                                    ],
+                                    "score": 1.0,
+                                    "content": "10.1109/ICSE.2017.47. URL https://doi.org/10.1109/ICSE.2017.47.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 24.5,
+                    "bbox_fs": [
+                        105,
+                        410,
+                        506,
+                        456
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        462,
+                        504,
+                        486
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                461,
+                                505,
+                                477
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        461,
+                                        505,
+                                        477
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lawrence Page, Sergey Brin, Rajeev Motwani, and Terry Winograd. The pagerank citation ranking:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                474,
+                                394,
+                                487
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        474,
+                                        394,
+                                        487
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Bringing order to the web. Technical report, Stanford InfoLab, 1999.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 27.5,
+                    "bbox_fs": [
+                        105,
+                        461,
+                        505,
+                        487
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        492,
+                        504,
+                        515
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                490,
+                                505,
+                                507
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        490,
+                                        505,
+                                        507
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Alec Radford, Jeffrey Wu, Rewon Child, David Luan, Dario Amodei, and Ilya Sutskever. Language",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                503,
+                                407,
+                                516
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        503,
+                                        407,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "models are unsupervised multitask learners. OpenAI Blog, 1(8):9, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 29.5,
+                    "bbox_fs": [
+                        105,
+                        490,
+                        505,
+                        516
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        522,
+                        505,
+                        578
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                522,
+                                504,
+                                534
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        522,
+                                        504,
+                                        534
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Veselin Raychev, Martin Vechev, and Eran Yahav. Code completion with statistical language models.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                533,
+                                505,
+                                546
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        533,
+                                        505,
+                                        546
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In Proceedings of the 35th ACM SIGPLAN Conference on Programming Language Design and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                542,
+                                505,
+                                559
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        542,
+                                        505,
+                                        559
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Implementation, PLDI ’14, pp. 419–428, New York, NY, USA, 2014. Association for Computing",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                554,
+                                504,
+                                568
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        554,
+                                        504,
+                                        568
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Machinery. ISBN 9781450327848. doi: 10.1145/2594291.2594321. URL https://doi.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                566,
+                                284,
+                                578
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        566,
+                                        284,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": "org/10.1145/2594291.2594321.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        }
+                    ],
+                    "index": 33,
+                    "bbox_fs": [
+                        106,
+                        522,
+                        505,
+                        578
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        584,
+                        503,
+                        607
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                584,
+                                505,
+                                597
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        584,
+                                        505,
+                                        597
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Franco Scarselli, Marco Gori, Ah Chung Tsoi, Markus Hagenbuchner, and Gabriele Monfardini.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                595,
+                                495,
+                                608
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        595,
+                                        495,
+                                        608
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The graph neural network model. IEEE Transactions on Neural Networks, 20(1):61–80, 2008.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 36.5,
+                    "bbox_fs": [
+                        106,
+                        584,
+                        505,
+                        608
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        614,
+                        505,
+                        669
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                613,
+                                505,
+                                627
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        613,
+                                        505,
+                                        627
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Michael Schlichtkrull, Thomas N. Kipf, Peter Bloem, Rianne van den Berg, Ivan Titov, and Max",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                624,
+                                506,
+                                638
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        624,
+                                        506,
+                                        638
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Welling. Modeling relational data with graph convolutional networks. In Aldo Gangemi, Roberto",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                636,
+                                505,
+                                649
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        636,
+                                        505,
+                                        649
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Navigli, Maria-Esther Vidal, Pascal Hitzler, Raphael Troncy, Laura Hollink, Anna Tordai, and ¨",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                645,
+                                505,
+                                660
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        645,
+                                        505,
+                                        660
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Mehwish Alam (eds.), The Semantic Web, pp. 593–607, Cham, 2018. Springer International Pub-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                658,
+                                258,
+                                671
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        658,
+                                        258,
+                                        671
+                                    ],
+                                    "score": 1.0,
+                                    "content": "lishing. ISBN 978-3-319-93417-4.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        }
+                    ],
+                    "index": 40,
+                    "bbox_fs": [
+                        106,
+                        613,
+                        506,
+                        671
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        676,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                676,
+                                505,
+                                689
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        676,
+                                        505,
+                                        689
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Peter Shaw, Jakob Uszkoreit, and Ashish Vaswani. Self-attention with relative position representa-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                687,
+                                505,
+                                701
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        687,
+                                        505,
+                                        701
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tions. In Proceedings of the 2018 Conference of the North American Chapter of the Association",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                697,
+                                505,
+                                713
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        697,
+                                        505,
+                                        713
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for Computational Linguistics: Human Language Technologies, Volume 2 (Short Papers), pp.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                708,
+                                505,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        708,
+                                        505,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "464–468, New Orleans, Louisiana, June 2018. Association for Computational Linguistics. doi:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                719,
+                                489,
+                                734
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        719,
+                                        489,
+                                        734
+                                    ],
+                                    "score": 1.0,
+                                    "content": "10.18653/v1/N18-2074. URL https://www.aclweb.org/anthology/N18-2074.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        }
+                    ],
+                    "index": 45,
+                    "bbox_fs": [
+                        105,
+                        676,
+                        505,
+                        734
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        109,
+                        82,
+                        504,
+                        116
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                80,
+                                505,
+                                97
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        80,
+                                        505,
+                                        97
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Yikang Shen, Shawn Tan, Alessandro Sordoni, and Aaron Courville. Ordered neurons: Integrating",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                93,
+                                505,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        93,
+                                        505,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tree structures into recurrent neural networks. In International Conference on Learning Repre-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                104,
+                                467,
+                                118
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        104,
+                                        396,
+                                        118
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sentations, 2019. URL https://openreview.net/forum?id",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        396,
+                                        106,
+                                        402,
+                                        114
+                                    ],
+                                    "score": 0.4,
+                                    "content": "{ . } =",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        403,
+                                        104,
+                                        467,
+                                        118
+                                    ],
+                                    "score": 1.0,
+                                    "content": "B1l6qiR5F7.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        123,
+                        504,
+                        146
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                123,
+                                505,
+                                136
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        123,
+                                        505,
+                                        136
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Vighnesh Shiv and Chris Quirk. Novel positional encodings to enable tree-based transformers. In",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                134,
+                                430,
+                                147
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        134,
+                                        430,
+                                        147
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Advances in Neural Information Processing Systems, pp. 12081–12091, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 3.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        153,
+                        505,
+                        198
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                152,
+                                505,
+                                167
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        152,
+                                        505,
+                                        167
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Richard Socher, Alex Perelygin, Jean Wu, Jason Chuang, Christopher D Manning, Andrew Y Ng,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                164,
+                                505,
+                                177
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        164,
+                                        505,
+                                        177
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and Christopher Potts. Recursive deep models for semantic compositionality over a sentiment",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                175,
+                                505,
+                                188
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        175,
+                                        505,
+                                        188
+                                    ],
+                                    "score": 1.0,
+                                    "content": "treebank. In Proceedings of the 2013 conference on empirical methods in natural language pro-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                187,
+                                240,
+                                198
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        187,
+                                        240,
+                                        198
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cessing, pp. 1631–1642, 2013.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 6.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        204,
+                        503,
+                        228
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                204,
+                                505,
+                                217
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        204,
+                                        505,
+                                        217
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Kai Sheng Tai, Richard Socher, and Christopher D Manning. Improved semantic representations",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                216,
+                                504,
+                                228
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        216,
+                                        504,
+                                        228
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from tree-structured long short-term memory networks. arXiv preprint arXiv:1503.00075, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 9.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        234,
+                        505,
+                        268
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                233,
+                                505,
+                                248
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        233,
+                                        505,
+                                        248
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                245,
+                                505,
+                                258
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        245,
+                                        505,
+                                        258
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Łukasz Kaiser, and Illia Polosukhin. Attention is all you need. In Advances in neural information",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                257,
+                                287,
+                                268
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        257,
+                                        287,
+                                        268
+                                    ],
+                                    "score": 1.0,
+                                    "content": "processing systems, pp. 5998–6008, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        275,
+                        505,
+                        309
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                275,
+                                505,
+                                288
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        275,
+                                        505,
+                                        288
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Petar Velickovi ˇ c, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Li ´ o, and Yoshua `",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                286,
+                                505,
+                                300
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        286,
+                                        505,
+                                        300
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Bengio. Graph Attention Networks. International Conference on Learning Representations,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                297,
+                                416,
+                                311
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        297,
+                                        351,
+                                        311
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2018. URL https://openreview.net/forum?id",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        351,
+                                        299,
+                                        357,
+                                        307
+                                    ],
+                                    "score": 0.44,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        358,
+                                        297,
+                                        416,
+                                        311
+                                    ],
+                                    "score": 1.0,
+                                    "content": "rJXMpikCZ.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        316,
+                        504,
+                        339
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                315,
+                                506,
+                                329
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        315,
+                                        506,
+                                        329
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Oriol Vinyals, Meire Fortunato, and Navdeep Jaitly. Pointer networks. In Advances in neural",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                327,
+                                336,
+                                340
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        327,
+                                        336,
+                                        340
+                                    ],
+                                    "score": 1.0,
+                                    "content": "information processing systems, pp. 2692–2700, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 17.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        345,
+                        505,
+                        402
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                347,
+                                504,
+                                359
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        347,
+                                        504,
+                                        359
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Song Wang, Devin Chollak, Dana Movshovitz-Attias, and Lin Tan. Bugram: Bug detection with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                357,
+                                506,
+                                372
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        357,
+                                        506,
+                                        372
+                                    ],
+                                    "score": 1.0,
+                                    "content": "n-gram language models. In Proceedings of the 31st IEEE/ACM International Conference on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                368,
+                                506,
+                                381
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        368,
+                                        506,
+                                        381
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Automated Software Engineering, ASE 2016, pp. 708–719, New York, NY, USA, 2016. Associ-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                379,
+                                506,
+                                392
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        379,
+                                        506,
+                                        392
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ation for Computing Machinery. ISBN 9781450338455. doi: 10.1145/2970276.2970341. URL",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                390,
+                                355,
+                                403
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        390,
+                                        355,
+                                        403
+                                    ],
+                                    "score": 1.0,
+                                    "content": "https://doi.org/10.1145/2970276.2970341.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 21
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        409,
+                        504,
+                        443
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                409,
+                                505,
+                                421
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        409,
+                                        505,
+                                        421
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka. How powerful are graph neural",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                419,
+                                505,
+                                433
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        419,
+                                        505,
+                                        433
+                                    ],
+                                    "score": 1.0,
+                                    "content": "networks? In International Conference on Learning Representations, 2019. URL https:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                432,
+                                337,
+                                444
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        432,
+                                        266,
+                                        444
+                                    ],
+                                    "score": 1.0,
+                                    "content": "//openreview.net/forum?id",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        267,
+                                        433,
+                                        273,
+                                        441
+                                    ],
+                                    "score": 0.66,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        273,
+                                        432,
+                                        337,
+                                        444
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ryGs6iA5Km.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        450,
+                        504,
+                        484
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                449,
+                                505,
+                                463
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        449,
+                                        505,
+                                        463
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Zhilin Yang, Zihang Dai, Yiming Yang, Jaime Carbonell, Russ R Salakhutdinov, and Quoc V Le.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                461,
+                                506,
+                                474
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        461,
+                                        506,
+                                        474
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Xlnet: Generalized autoregressive pretraining for language understanding. In Advances in neural",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                472,
+                                336,
+                                484
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        472,
+                                        336,
+                                        484
+                                    ],
+                                    "score": 1.0,
+                                    "content": "information processing systems, pp. 5754–5764, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 28
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        491,
+                        505,
+                        525
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                490,
+                                505,
+                                504
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        490,
+                                        505,
+                                        504
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Zhitao Ying, Jiaxuan You, Christopher Morris, Xiang Ren, Will Hamilton, and Jure Leskovec. Hi-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                501,
+                                505,
+                                515
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        501,
+                                        505,
+                                        515
+                                    ],
+                                    "score": 1.0,
+                                    "content": "erarchical graph representation learning with differentiable pooling. In Advances in neural infor-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                513,
+                                317,
+                                525
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        513,
+                                        317,
+                                        525
+                                    ],
+                                    "score": 1.0,
+                                    "content": "mation processing systems, pp. 4800–4810, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 31
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        531,
+                        505,
+                        587
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                532,
+                                505,
+                                544
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        532,
+                                        505,
+                                        544
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Jiaxuan You, Rex Ying, and Jure Leskovec. Position-aware graph neural networks. In Kamalika",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                542,
+                                506,
+                                556
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        542,
+                                        506,
+                                        556
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Chaudhuri and Ruslan Salakhutdinov (eds.), Proceedings of the 36th International Conference",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                554,
+                                504,
+                                567
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        554,
+                                        504,
+                                        567
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on Machine Learning, volume 97 of Proceedings of Machine Learning Research, pp. 7134–",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                563,
+                                504,
+                                578
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        563,
+                                        504,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": "7143. PMLR, 09–15 Jun 2019. URL http://proceedings.mlr.press/v97/you19b.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                576,
+                                146,
+                                588
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        576,
+                                        146,
+                                        588
+                                    ],
+                                    "score": 1.0,
+                                    "content": "html.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 35
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        595,
+                        504,
+                        617
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                595,
+                                506,
+                                607
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        595,
+                                        506,
+                                        607
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Muhan Zhang and Yixin Chen. Link prediction based on graph neural networks. In Advances in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                605,
+                                369,
+                                618
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        605,
+                                        369,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Neural Information Processing Systems, pp. 5165–5175, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 38.5
+                }
+            ],
+            "page_idx": 12,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        108,
+                        27,
+                        292,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                293,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        293,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        311,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                313,
+                                764
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        313,
+                                        764
+                                    ],
+                                    "score": 1.0,
+                                    "content": "13",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        109,
+                        82,
+                        504,
+                        116
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                80,
+                                505,
+                                97
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        80,
+                                        505,
+                                        97
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Yikang Shen, Shawn Tan, Alessandro Sordoni, and Aaron Courville. Ordered neurons: Integrating",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                93,
+                                505,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        93,
+                                        505,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tree structures into recurrent neural networks. In International Conference on Learning Repre-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                104,
+                                467,
+                                118
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        104,
+                                        396,
+                                        118
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sentations, 2019. URL https://openreview.net/forum?id",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        396,
+                                        106,
+                                        402,
+                                        114
+                                    ],
+                                    "score": 0.4,
+                                    "content": "{ . } =",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        403,
+                                        104,
+                                        467,
+                                        118
+                                    ],
+                                    "score": 1.0,
+                                    "content": "B1l6qiR5F7.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1,
+                    "bbox_fs": [
+                        105,
+                        80,
+                        505,
+                        118
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        123,
+                        504,
+                        146
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                123,
+                                505,
+                                136
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        123,
+                                        505,
+                                        136
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Vighnesh Shiv and Chris Quirk. Novel positional encodings to enable tree-based transformers. In",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                134,
+                                430,
+                                147
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        134,
+                                        430,
+                                        147
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Advances in Neural Information Processing Systems, pp. 12081–12091, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 3.5,
+                    "bbox_fs": [
+                        106,
+                        123,
+                        505,
+                        147
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        153,
+                        505,
+                        198
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                152,
+                                505,
+                                167
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        152,
+                                        505,
+                                        167
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Richard Socher, Alex Perelygin, Jean Wu, Jason Chuang, Christopher D Manning, Andrew Y Ng,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                164,
+                                505,
+                                177
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        164,
+                                        505,
+                                        177
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and Christopher Potts. Recursive deep models for semantic compositionality over a sentiment",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                175,
+                                505,
+                                188
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        175,
+                                        505,
+                                        188
+                                    ],
+                                    "score": 1.0,
+                                    "content": "treebank. In Proceedings of the 2013 conference on empirical methods in natural language pro-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                187,
+                                240,
+                                198
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        187,
+                                        240,
+                                        198
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cessing, pp. 1631–1642, 2013.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 6.5,
+                    "bbox_fs": [
+                        105,
+                        152,
+                        505,
+                        198
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        204,
+                        503,
+                        228
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                204,
+                                505,
+                                217
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        204,
+                                        505,
+                                        217
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Kai Sheng Tai, Richard Socher, and Christopher D Manning. Improved semantic representations",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                216,
+                                504,
+                                228
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        216,
+                                        504,
+                                        228
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from tree-structured long short-term memory networks. arXiv preprint arXiv:1503.00075, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 9.5,
+                    "bbox_fs": [
+                        105,
+                        204,
+                        505,
+                        228
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        234,
+                        505,
+                        268
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                233,
+                                505,
+                                248
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        233,
+                                        505,
+                                        248
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                245,
+                                505,
+                                258
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        245,
+                                        505,
+                                        258
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Łukasz Kaiser, and Illia Polosukhin. Attention is all you need. In Advances in neural information",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                257,
+                                287,
+                                268
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        257,
+                                        287,
+                                        268
+                                    ],
+                                    "score": 1.0,
+                                    "content": "processing systems, pp. 5998–6008, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 12,
+                    "bbox_fs": [
+                        105,
+                        233,
+                        505,
+                        268
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        275,
+                        505,
+                        309
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                275,
+                                505,
+                                288
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        275,
+                                        505,
+                                        288
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Petar Velickovi ˇ c, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Li ´ o, and Yoshua `",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                286,
+                                505,
+                                300
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        286,
+                                        505,
+                                        300
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Bengio. Graph Attention Networks. International Conference on Learning Representations,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                297,
+                                416,
+                                311
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        297,
+                                        351,
+                                        311
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2018. URL https://openreview.net/forum?id",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        351,
+                                        299,
+                                        357,
+                                        307
+                                    ],
+                                    "score": 0.44,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        358,
+                                        297,
+                                        416,
+                                        311
+                                    ],
+                                    "score": 1.0,
+                                    "content": "rJXMpikCZ.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 15,
+                    "bbox_fs": [
+                        106,
+                        275,
+                        505,
+                        311
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        316,
+                        504,
+                        339
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                315,
+                                506,
+                                329
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        315,
+                                        506,
+                                        329
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Oriol Vinyals, Meire Fortunato, and Navdeep Jaitly. Pointer networks. In Advances in neural",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                327,
+                                336,
+                                340
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        327,
+                                        336,
+                                        340
+                                    ],
+                                    "score": 1.0,
+                                    "content": "information processing systems, pp. 2692–2700, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 17.5,
+                    "bbox_fs": [
+                        106,
+                        315,
+                        506,
+                        340
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        345,
+                        505,
+                        402
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                347,
+                                504,
+                                359
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        347,
+                                        504,
+                                        359
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Song Wang, Devin Chollak, Dana Movshovitz-Attias, and Lin Tan. Bugram: Bug detection with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                357,
+                                506,
+                                372
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        357,
+                                        506,
+                                        372
+                                    ],
+                                    "score": 1.0,
+                                    "content": "n-gram language models. In Proceedings of the 31st IEEE/ACM International Conference on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                368,
+                                506,
+                                381
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        368,
+                                        506,
+                                        381
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Automated Software Engineering, ASE 2016, pp. 708–719, New York, NY, USA, 2016. Associ-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                379,
+                                506,
+                                392
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        379,
+                                        506,
+                                        392
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ation for Computing Machinery. ISBN 9781450338455. doi: 10.1145/2970276.2970341. URL",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                390,
+                                355,
+                                403
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        390,
+                                        355,
+                                        403
+                                    ],
+                                    "score": 1.0,
+                                    "content": "https://doi.org/10.1145/2970276.2970341.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 21,
+                    "bbox_fs": [
+                        106,
+                        347,
+                        506,
+                        403
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        409,
+                        504,
+                        443
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                409,
+                                505,
+                                421
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        409,
+                                        505,
+                                        421
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka. How powerful are graph neural",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                419,
+                                505,
+                                433
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        419,
+                                        505,
+                                        433
+                                    ],
+                                    "score": 1.0,
+                                    "content": "networks? In International Conference on Learning Representations, 2019. URL https:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                432,
+                                337,
+                                444
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        432,
+                                        266,
+                                        444
+                                    ],
+                                    "score": 1.0,
+                                    "content": "//openreview.net/forum?id",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        267,
+                                        433,
+                                        273,
+                                        441
+                                    ],
+                                    "score": 0.66,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        273,
+                                        432,
+                                        337,
+                                        444
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ryGs6iA5Km.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 25,
+                    "bbox_fs": [
+                        106,
+                        409,
+                        505,
+                        444
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        450,
+                        504,
+                        484
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                449,
+                                505,
+                                463
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        449,
+                                        505,
+                                        463
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Zhilin Yang, Zihang Dai, Yiming Yang, Jaime Carbonell, Russ R Salakhutdinov, and Quoc V Le.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                461,
+                                506,
+                                474
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        461,
+                                        506,
+                                        474
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Xlnet: Generalized autoregressive pretraining for language understanding. In Advances in neural",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                472,
+                                336,
+                                484
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        472,
+                                        336,
+                                        484
+                                    ],
+                                    "score": 1.0,
+                                    "content": "information processing systems, pp. 5754–5764, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 28,
+                    "bbox_fs": [
+                        105,
+                        449,
+                        506,
+                        484
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        491,
+                        505,
+                        525
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                490,
+                                505,
+                                504
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        490,
+                                        505,
+                                        504
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Zhitao Ying, Jiaxuan You, Christopher Morris, Xiang Ren, Will Hamilton, and Jure Leskovec. Hi-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                501,
+                                505,
+                                515
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        501,
+                                        505,
+                                        515
+                                    ],
+                                    "score": 1.0,
+                                    "content": "erarchical graph representation learning with differentiable pooling. In Advances in neural infor-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                513,
+                                317,
+                                525
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        513,
+                                        317,
+                                        525
+                                    ],
+                                    "score": 1.0,
+                                    "content": "mation processing systems, pp. 4800–4810, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 31,
+                    "bbox_fs": [
+                        106,
+                        490,
+                        505,
+                        525
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        531,
+                        505,
+                        587
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                532,
+                                505,
+                                544
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        532,
+                                        505,
+                                        544
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Jiaxuan You, Rex Ying, and Jure Leskovec. Position-aware graph neural networks. In Kamalika",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                542,
+                                506,
+                                556
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        542,
+                                        506,
+                                        556
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Chaudhuri and Ruslan Salakhutdinov (eds.), Proceedings of the 36th International Conference",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                554,
+                                504,
+                                567
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        554,
+                                        504,
+                                        567
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on Machine Learning, volume 97 of Proceedings of Machine Learning Research, pp. 7134–",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                563,
+                                504,
+                                578
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        563,
+                                        504,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": "7143. PMLR, 09–15 Jun 2019. URL http://proceedings.mlr.press/v97/you19b.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                576,
+                                146,
+                                588
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        576,
+                                        146,
+                                        588
+                                    ],
+                                    "score": 1.0,
+                                    "content": "html.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 35,
+                    "bbox_fs": [
+                        106,
+                        532,
+                        506,
+                        588
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        595,
+                        504,
+                        617
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                595,
+                                506,
+                                607
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        595,
+                                        506,
+                                        607
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Muhan Zhang and Yixin Chen. Link prediction based on graph neural networks. In Advances in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                605,
+                                369,
+                                618
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        605,
+                                        369,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Neural Information Processing Systems, pp. 5165–5175, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 38.5,
+                    "bbox_fs": [
+                        106,
+                        595,
+                        506,
+                        618
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "table",
+                    "bbox": [
+                        201,
+                        80,
+                        410,
+                        148
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                201,
+                                80,
+                                410,
+                                148
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        201,
+                                        80,
+                                        410,
+                                        148
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                201,
+                                                80,
+                                                410,
+                                                148
+                                            ],
+                                            "score": 0.975,
+                                            "html": "<table><tr><td></td><td>Python</td><td>Javascript</td><td>Go</td><td>Ruby</td></tr><tr><td>Python</td><td>1.00</td><td>0.43</td><td>0.42</td><td>0.79</td></tr><tr><td>Javascript</td><td>0.43</td><td>1.00</td><td>0.84</td><td>0.39</td></tr><tr><td>Go</td><td>0.43</td><td>0.84</td><td>1.00</td><td>0.38</td></tr><tr><td>Ruby</td><td>0.79</td><td>0.39</td><td>0.38</td><td>1.00</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "26bec4900b3fdc755545a32837761c235cd99ba3567c283f36c397e15113a344.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 2,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        201,
+                                        80,
+                                        410,
+                                        93.6
+                                    ],
+                                    "spans": [],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        201,
+                                        93.6,
+                                        410,
+                                        107.19999999999999
+                                    ],
+                                    "spans": [],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        201,
+                                        107.19999999999999,
+                                        410,
+                                        120.79999999999998
+                                    ],
+                                    "spans": [],
+                                    "index": 2
+                                },
+                                {
+                                    "bbox": [
+                                        201,
+                                        120.79999999999998,
+                                        410,
+                                        134.39999999999998
+                                    ],
+                                    "spans": [],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        201,
+                                        134.39999999999998,
+                                        410,
+                                        147.99999999999997
+                                    ],
+                                    "spans": [],
+                                    "index": 4
+                                }
+                            ]
+                        },
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                107,
+                                156,
+                                503,
+                                178
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        155,
+                                        505,
+                                        168
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                155,
+                                                505,
+                                                168
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 5: Pairwise cosine similarities of the learned language embeddings of the CODE TRANS-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 5
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        168,
+                                        147,
+                                        178
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                168,
+                                                147,
+                                                178
+                                            ],
+                                            "score": 1.0,
+                                            "content": "FORMER.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 6
+                                }
+                            ],
+                            "index": 5.5
+                        }
+                    ],
+                    "index": 3.75
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        200,
+                        225,
+                        212
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                200,
+                                226,
+                                213
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        200,
+                                        226,
+                                        213
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ACKNOWLEDGEMENTS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        224,
+                        505,
+                        268
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                225,
+                                505,
+                                237
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        225,
+                                        505,
+                                        237
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We are grateful to Dylan Bourgeois for having paved the way to this research contribution with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                236,
+                                505,
+                                247
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        236,
+                                        505,
+                                        247
+                                    ],
+                                    "score": 1.0,
+                                    "content": "his thesis work (Bourgeois, 2019). We further thank Simon Geisler for his helpful suggestions and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                246,
+                                505,
+                                259
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        246,
+                                        505,
+                                        259
+                                    ],
+                                    "score": 1.0,
+                                    "content": "proofreading the paper, as well as the anonymous reviewers for their constructive feedback and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                257,
+                                187,
+                                269
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        257,
+                                        187,
+                                        269
+                                    ],
+                                    "score": 1.0,
+                                    "content": "fruitful discussions.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 9.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        274,
+                        505,
+                        352
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                273,
+                                505,
+                                288
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        273,
+                                        505,
+                                        288
+                                    ],
+                                    "score": 1.0,
+                                    "content": "This research was supported by the TUM International Graduate School of Science and Engineering",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                284,
+                                505,
+                                298
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        284,
+                                        505,
+                                        298
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(IGSSE). Stanford University is supported by DARPA under Nos. N660011924033 (MCS); ARO",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                297,
+                                505,
+                                309
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        297,
+                                        505,
+                                        309
+                                    ],
+                                    "score": 1.0,
+                                    "content": "under Nos. W911NF-16-1- 0342 (MURI), W911NF-16-1-0171 (DURIP); NSF under Nos. OAC-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                306,
+                                505,
+                                321
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        306,
+                                        505,
+                                        321
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1835598 (CINES), OAC-1934578 (HDR), CCF-1918940 (Expeditions), IIS-2030477 (RAPID);",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                318,
+                                505,
+                                331
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        318,
+                                        505,
+                                        331
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Stanford Data Science Initiative, Wu Tsai Neurosciences Institute, Chan Zuckerberg Biohub, Ama-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                329,
+                                505,
+                                342
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        329,
+                                        505,
+                                        342
+                                    ],
+                                    "score": 1.0,
+                                    "content": "zon, JPMorgan Chase, Docomo, Hitachi, JD.com, KDDI, NVIDIA, Dell, Toshiba, Intel, and Unit-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                340,
+                                406,
+                                355
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        340,
+                                        406,
+                                        355
+                                    ],
+                                    "score": 1.0,
+                                    "content": "edHealth Group. Jure Leskovec is a Chan Zuckerberg Biohub investigator.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        368,
+                        183,
+                        380
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                366,
+                                184,
+                                383
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        366,
+                                        184,
+                                        383
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A APPENDIX",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 19
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        393,
+                        272,
+                        405
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                393,
+                                274,
+                                406
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        393,
+                                        274,
+                                        406
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.1 DISTANCE ENCODING FUNCTION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 20
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        414,
+                        505,
+                        447
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                413,
+                                504,
+                                426
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        413,
+                                        417,
+                                        426
+                                    ],
+                                    "score": 1.0,
+                                    "content": "For encoding scalar relation values via vectors we employ encoding functions",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        417,
+                                        413,
+                                        467,
+                                        425
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\phi : \\mathbb { R } \\to \\mathbb { R } ^ { d }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        467,
+                                        413,
+                                        497,
+                                        426
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        497,
+                                        415,
+                                        504,
+                                        424
+                                    ],
+                                    "score": 0.78,
+                                    "content": "d",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                425,
+                                505,
+                                437
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        425,
+                                        505,
+                                        437
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the model’s embedding dimension. We choose the popular sinusoidal encoding function presented",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                436,
+                                207,
+                                448
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        436,
+                                        207,
+                                        448
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in Vaswani et al. (2017):",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 22
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        158,
+                        452,
+                        452,
+                        474
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                158,
+                                452,
+                                452,
+                                474
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        158,
+                                        452,
+                                        452,
+                                        474
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\phi ( r _ { i  j } ) _ { 2 k } = \\sin ( \\frac { r _ { i  j } } { M ^ { 2 k / d } } ) \\qquad \\phi ( r _ { i  j } ) _ { 2 k + 1 } = \\cos ( \\frac { r _ { i  j } } { M ^ { 2 k / d } } ) ,",
+                                    "type": "interline_equation",
+                                    "image_path": "f46894c730c22bd189c627fee0b9dffb06a45fdfb55c7f527bb4fe0d0c5327e8.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 24,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                158,
+                                452,
+                                452,
+                                474
+                            ],
+                            "spans": [],
+                            "index": 24
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        480,
+                        505,
+                        514
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                479,
+                                505,
+                                493
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        479,
+                                        134,
+                                        493
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        135,
+                                        480,
+                                        197,
+                                        492
+                                    ],
+                                    "score": 0.92,
+                                    "content": "1 \\leq k < d / 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        198,
+                                        479,
+                                        375,
+                                        493
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the position in the encoding vector and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        375,
+                                        480,
+                                        388,
+                                        490
+                                    ],
+                                    "score": 0.84,
+                                    "content": "M",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        388,
+                                        479,
+                                        505,
+                                        493
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is some constant; we adopt",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                491,
+                                505,
+                                504
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        492,
+                                        163,
+                                        503
+                                    ],
+                                    "score": 0.86,
+                                    "content": "M = 1 0 , 0 0 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        163,
+                                        491,
+                                        505,
+                                        504
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as chosen by (Vaswani et al., 2017). Note that the distance encoding functions have",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                502,
+                                206,
+                                515
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        502,
+                                        206,
+                                        515
+                                    ],
+                                    "score": 1.0,
+                                    "content": "no trainable parameters.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 26
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        528,
+                        322,
+                        539
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                528,
+                                325,
+                                540
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        528,
+                                        325,
+                                        540
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.2 MULTILINGUAL REPRESENTATION ANALYSIS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 28
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        547,
+                        505,
+                        593
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                548,
+                                505,
+                                560
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        548,
+                                        505,
+                                        560
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In Table 5, we show the pairwise cosine similarities of the learned language embeddings of the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                559,
+                                505,
+                                572
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        559,
+                                        505,
+                                        572
+                                    ],
+                                    "score": 1.0,
+                                    "content": "CODE TRANSFORMER. We can see that the pairs Python-Ruby and Javascript-Go have similar",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                569,
+                                506,
+                                583
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        569,
+                                        506,
+                                        583
+                                    ],
+                                    "score": 1.0,
+                                    "content": "language embeddings. This aligns well with roots of language design and common use cases of the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                580,
+                                153,
+                                596
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        580,
+                                        153,
+                                        596
+                                    ],
+                                    "score": 1.0,
+                                    "content": "languages.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 30.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        598,
+                        504,
+                        621
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                597,
+                                505,
+                                610
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        597,
+                                        505,
+                                        610
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Moreover, in Table 6, we show selected snippets starting with is, main, or load (left) and their",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                610,
+                                324,
+                                621
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        610,
+                                        324,
+                                        621
+                                    ],
+                                    "score": 1.0,
+                                    "content": "best embedding matches from other languages (right).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        }
+                    ],
+                    "index": 33.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        634,
+                        230,
+                        646
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                635,
+                                230,
+                                646
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        635,
+                                        230,
+                                        646
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.3 DATA PREPROCESSING",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        }
+                    ],
+                    "index": 35
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        655,
+                        320,
+                        667
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                655,
+                                320,
+                                668
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        655,
+                                        320,
+                                        668
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.3.1 TEXTUAL CODE SNIPPET PREPROCESSING",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 36
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        129,
+                        672,
+                        414,
+                        684
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                130,
+                                671,
+                                414,
+                                686
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        130,
+                                        671,
+                                        414,
+                                        686
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1. Tokenize code snippets with Pygments language-specific tokenizer.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 37
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        131,
+                        687,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                128,
+                                687,
+                                505,
+                                700
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        687,
+                                        329,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2. Remove comments (both multi-line,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        340,
+                                        687,
+                                        505,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "single-line and doc comments).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                698,
+                                505,
+                                711
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        698,
+                                        162,
+                                        710
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        174,
+                                        700,
+                                        217,
+                                        710
+                                    ],
+                                    "score": 1.0,
+                                    "content": "comment",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        226,
+                                        699,
+                                        295,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "token types.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        338,
+                                        700,
+                                        505,
+                                        710
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pygments.token.Comment and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                710,
+                                506,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        710,
+                                        506,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pygments.token.Literal.String.Doc that are generated by Pygments are",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                721,
+                                253,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        721,
+                                        253,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "used to identify comments.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        }
+                    ],
+                    "index": 39.5
+                }
+            ],
+            "page_idx": 13,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        292,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                293,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        293,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        311,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                313,
+                                764
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        313,
+                                        764
+                                    ],
+                                    "score": 1.0,
+                                    "content": "14",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "table",
+                    "bbox": [
+                        201,
+                        80,
+                        410,
+                        148
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                201,
+                                80,
+                                410,
+                                148
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        201,
+                                        80,
+                                        410,
+                                        148
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                201,
+                                                80,
+                                                410,
+                                                148
+                                            ],
+                                            "score": 0.975,
+                                            "html": "<table><tr><td></td><td>Python</td><td>Javascript</td><td>Go</td><td>Ruby</td></tr><tr><td>Python</td><td>1.00</td><td>0.43</td><td>0.42</td><td>0.79</td></tr><tr><td>Javascript</td><td>0.43</td><td>1.00</td><td>0.84</td><td>0.39</td></tr><tr><td>Go</td><td>0.43</td><td>0.84</td><td>1.00</td><td>0.38</td></tr><tr><td>Ruby</td><td>0.79</td><td>0.39</td><td>0.38</td><td>1.00</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "26bec4900b3fdc755545a32837761c235cd99ba3567c283f36c397e15113a344.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 2,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        201,
+                                        80,
+                                        410,
+                                        93.6
+                                    ],
+                                    "spans": [],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        201,
+                                        93.6,
+                                        410,
+                                        107.19999999999999
+                                    ],
+                                    "spans": [],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        201,
+                                        107.19999999999999,
+                                        410,
+                                        120.79999999999998
+                                    ],
+                                    "spans": [],
+                                    "index": 2
+                                },
+                                {
+                                    "bbox": [
+                                        201,
+                                        120.79999999999998,
+                                        410,
+                                        134.39999999999998
+                                    ],
+                                    "spans": [],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        201,
+                                        134.39999999999998,
+                                        410,
+                                        147.99999999999997
+                                    ],
+                                    "spans": [],
+                                    "index": 4
+                                }
+                            ]
+                        },
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                107,
+                                156,
+                                503,
+                                178
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        155,
+                                        505,
+                                        168
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                155,
+                                                505,
+                                                168
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 5: Pairwise cosine similarities of the learned language embeddings of the CODE TRANS-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 5
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        168,
+                                        147,
+                                        178
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                168,
+                                                147,
+                                                178
+                                            ],
+                                            "score": 1.0,
+                                            "content": "FORMER.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 6
+                                }
+                            ],
+                            "index": 5.5
+                        }
+                    ],
+                    "index": 3.75
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        200,
+                        225,
+                        212
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                200,
+                                226,
+                                213
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        200,
+                                        226,
+                                        213
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ACKNOWLEDGEMENTS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        224,
+                        505,
+                        268
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                225,
+                                505,
+                                237
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        225,
+                                        505,
+                                        237
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We are grateful to Dylan Bourgeois for having paved the way to this research contribution with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                236,
+                                505,
+                                247
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        236,
+                                        505,
+                                        247
+                                    ],
+                                    "score": 1.0,
+                                    "content": "his thesis work (Bourgeois, 2019). We further thank Simon Geisler for his helpful suggestions and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                246,
+                                505,
+                                259
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        246,
+                                        505,
+                                        259
+                                    ],
+                                    "score": 1.0,
+                                    "content": "proofreading the paper, as well as the anonymous reviewers for their constructive feedback and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                257,
+                                187,
+                                269
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        257,
+                                        187,
+                                        269
+                                    ],
+                                    "score": 1.0,
+                                    "content": "fruitful discussions.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 9.5,
+                    "bbox_fs": [
+                        105,
+                        225,
+                        505,
+                        269
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        274,
+                        505,
+                        352
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                273,
+                                505,
+                                288
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        273,
+                                        505,
+                                        288
+                                    ],
+                                    "score": 1.0,
+                                    "content": "This research was supported by the TUM International Graduate School of Science and Engineering",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                284,
+                                505,
+                                298
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        284,
+                                        505,
+                                        298
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(IGSSE). Stanford University is supported by DARPA under Nos. N660011924033 (MCS); ARO",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                297,
+                                505,
+                                309
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        297,
+                                        505,
+                                        309
+                                    ],
+                                    "score": 1.0,
+                                    "content": "under Nos. W911NF-16-1- 0342 (MURI), W911NF-16-1-0171 (DURIP); NSF under Nos. OAC-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                306,
+                                505,
+                                321
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        306,
+                                        505,
+                                        321
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1835598 (CINES), OAC-1934578 (HDR), CCF-1918940 (Expeditions), IIS-2030477 (RAPID);",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                318,
+                                505,
+                                331
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        318,
+                                        505,
+                                        331
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Stanford Data Science Initiative, Wu Tsai Neurosciences Institute, Chan Zuckerberg Biohub, Ama-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                329,
+                                505,
+                                342
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        329,
+                                        505,
+                                        342
+                                    ],
+                                    "score": 1.0,
+                                    "content": "zon, JPMorgan Chase, Docomo, Hitachi, JD.com, KDDI, NVIDIA, Dell, Toshiba, Intel, and Unit-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                340,
+                                406,
+                                355
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        340,
+                                        406,
+                                        355
+                                    ],
+                                    "score": 1.0,
+                                    "content": "edHealth Group. Jure Leskovec is a Chan Zuckerberg Biohub investigator.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 15,
+                    "bbox_fs": [
+                        105,
+                        273,
+                        505,
+                        355
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        368,
+                        183,
+                        380
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                366,
+                                184,
+                                383
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        366,
+                                        184,
+                                        383
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A APPENDIX",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 19
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        393,
+                        272,
+                        405
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                393,
+                                274,
+                                406
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        393,
+                                        274,
+                                        406
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.1 DISTANCE ENCODING FUNCTION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 20
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        414,
+                        505,
+                        447
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                413,
+                                504,
+                                426
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        413,
+                                        417,
+                                        426
+                                    ],
+                                    "score": 1.0,
+                                    "content": "For encoding scalar relation values via vectors we employ encoding functions",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        417,
+                                        413,
+                                        467,
+                                        425
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\phi : \\mathbb { R } \\to \\mathbb { R } ^ { d }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        467,
+                                        413,
+                                        497,
+                                        426
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        497,
+                                        415,
+                                        504,
+                                        424
+                                    ],
+                                    "score": 0.78,
+                                    "content": "d",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                425,
+                                505,
+                                437
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        425,
+                                        505,
+                                        437
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the model’s embedding dimension. We choose the popular sinusoidal encoding function presented",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                436,
+                                207,
+                                448
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        436,
+                                        207,
+                                        448
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in Vaswani et al. (2017):",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 22,
+                    "bbox_fs": [
+                        105,
+                        413,
+                        505,
+                        448
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        158,
+                        452,
+                        452,
+                        474
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                158,
+                                452,
+                                452,
+                                474
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        158,
+                                        452,
+                                        452,
+                                        474
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\phi ( r _ { i  j } ) _ { 2 k } = \\sin ( \\frac { r _ { i  j } } { M ^ { 2 k / d } } ) \\qquad \\phi ( r _ { i  j } ) _ { 2 k + 1 } = \\cos ( \\frac { r _ { i  j } } { M ^ { 2 k / d } } ) ,",
+                                    "type": "interline_equation",
+                                    "image_path": "f46894c730c22bd189c627fee0b9dffb06a45fdfb55c7f527bb4fe0d0c5327e8.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 24,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                158,
+                                452,
+                                452,
+                                474
+                            ],
+                            "spans": [],
+                            "index": 24
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        480,
+                        505,
+                        514
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                479,
+                                505,
+                                493
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        479,
+                                        134,
+                                        493
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        135,
+                                        480,
+                                        197,
+                                        492
+                                    ],
+                                    "score": 0.92,
+                                    "content": "1 \\leq k < d / 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        198,
+                                        479,
+                                        375,
+                                        493
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the position in the encoding vector and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        375,
+                                        480,
+                                        388,
+                                        490
+                                    ],
+                                    "score": 0.84,
+                                    "content": "M",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        388,
+                                        479,
+                                        505,
+                                        493
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is some constant; we adopt",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                491,
+                                505,
+                                504
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        492,
+                                        163,
+                                        503
+                                    ],
+                                    "score": 0.86,
+                                    "content": "M = 1 0 , 0 0 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        163,
+                                        491,
+                                        505,
+                                        504
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as chosen by (Vaswani et al., 2017). Note that the distance encoding functions have",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                502,
+                                206,
+                                515
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        502,
+                                        206,
+                                        515
+                                    ],
+                                    "score": 1.0,
+                                    "content": "no trainable parameters.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 26,
+                    "bbox_fs": [
+                        105,
+                        479,
+                        505,
+                        515
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        528,
+                        322,
+                        539
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                528,
+                                325,
+                                540
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        528,
+                                        325,
+                                        540
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.2 MULTILINGUAL REPRESENTATION ANALYSIS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 28
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        547,
+                        505,
+                        593
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                548,
+                                505,
+                                560
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        548,
+                                        505,
+                                        560
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In Table 5, we show the pairwise cosine similarities of the learned language embeddings of the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                559,
+                                505,
+                                572
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        559,
+                                        505,
+                                        572
+                                    ],
+                                    "score": 1.0,
+                                    "content": "CODE TRANSFORMER. We can see that the pairs Python-Ruby and Javascript-Go have similar",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                569,
+                                506,
+                                583
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        569,
+                                        506,
+                                        583
+                                    ],
+                                    "score": 1.0,
+                                    "content": "language embeddings. This aligns well with roots of language design and common use cases of the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                580,
+                                153,
+                                596
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        580,
+                                        153,
+                                        596
+                                    ],
+                                    "score": 1.0,
+                                    "content": "languages.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 30.5,
+                    "bbox_fs": [
+                        104,
+                        548,
+                        506,
+                        596
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        598,
+                        504,
+                        621
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                597,
+                                505,
+                                610
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        597,
+                                        505,
+                                        610
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Moreover, in Table 6, we show selected snippets starting with is, main, or load (left) and their",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                610,
+                                324,
+                                621
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        610,
+                                        324,
+                                        621
+                                    ],
+                                    "score": 1.0,
+                                    "content": "best embedding matches from other languages (right).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        }
+                    ],
+                    "index": 33.5,
+                    "bbox_fs": [
+                        106,
+                        597,
+                        505,
+                        621
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        634,
+                        230,
+                        646
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                635,
+                                230,
+                                646
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        635,
+                                        230,
+                                        646
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.3 DATA PREPROCESSING",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        }
+                    ],
+                    "index": 35
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        655,
+                        320,
+                        667
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                655,
+                                320,
+                                668
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        655,
+                                        320,
+                                        668
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.3.1 TEXTUAL CODE SNIPPET PREPROCESSING",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 36
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        129,
+                        672,
+                        414,
+                        684
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                130,
+                                671,
+                                414,
+                                686
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        130,
+                                        671,
+                                        414,
+                                        686
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1. Tokenize code snippets with Pygments language-specific tokenizer.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 37,
+                    "bbox_fs": [
+                        130,
+                        671,
+                        414,
+                        686
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        131,
+                        687,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                128,
+                                687,
+                                505,
+                                700
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        687,
+                                        329,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2. Remove comments (both multi-line,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        340,
+                                        687,
+                                        505,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "single-line and doc comments).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                698,
+                                505,
+                                711
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        698,
+                                        162,
+                                        710
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        174,
+                                        700,
+                                        217,
+                                        710
+                                    ],
+                                    "score": 1.0,
+                                    "content": "comment",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        226,
+                                        699,
+                                        295,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "token types.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        338,
+                                        700,
+                                        505,
+                                        710
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pygments.token.Comment and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                710,
+                                506,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        710,
+                                        506,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pygments.token.Literal.String.Doc that are generated by Pygments are",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                721,
+                                253,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        721,
+                                        253,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "used to identify comments.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        }
+                    ],
+                    "index": 39.5,
+                    "bbox_fs": [
+                        128,
+                        687,
+                        506,
+                        732
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "table",
+                    "bbox": [
+                        106,
+                        12,
+                        530,
+                        685
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                106,
+                                12,
+                                530,
+                                685
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        12,
+                                        530,
+                                        685
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                12,
+                                                530,
+                                                685
+                                            ],
+                                            "score": 0.422,
+                                            "html": "<table><tr><td colspan=\"2\">Published as a conference paper at ICLR 2021</td></tr><tr><td></td><td></td></tr><tr><td>function isEqualArray(a，b){ if (a return true;</td><td></td></tr><tr><td>if ((a === undefined) undefined)）{ return false;</td><td>func areSameFloat32Array(a，b []float32） bool if len(a) != len(b){ return false</td></tr><tr><td>var =a.length; if (i !== b.length){ return false;</td><td>for i := O;i &lt; len(a);i++{ if a[i]!=b[i]{ return false J</td></tr><tr><td>while (i--）{ if(a[i] !== b[i]）{ return false; }</td><td>return true</td></tr><tr><td>return true;</td><td></td></tr><tr><td>function main() var rawData $(&#x27; .HeaderTexture[data-login- user-email]&#x27;) .data() ;</td><td>func TaskSayHello(t *tasking.T){</td></tr><tr><td>if (rawData) 1 me={</td><td>username := t.Flags.String(&quot;name&quot;) if username user, := user.Current ()</td></tr><tr><td>name:rawData.loginUserName, mail: rawData.loginUserEmail }；</td><td>username = user.Name</td></tr><tr><td>getCartId(function (cart）{ me.cart = cart;</td><td>} ift.Flags.Bool(&quot;verbose&quot;)</td></tr><tr><td>injectMenu(); refreshUsers(actions.updateUsers); listenOnChanges(onChange);</td><td>t.Logf(&quot;Hello %s, the time now is %s\\n&quot;, username，time.Now())</td></tr><tr><td>listenonorderConfirm(onConfirm); ）；</td><td>}else{ t.Logf(&quot;Hello %s\\n&quot;,username)</td></tr><tr><td>} else{ caliback(&#x27;no user&#x27;);</td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>func Backup(filename string)error{</td></tr><tr><td></td><td></td></tr><tr><td></td><td>info，err := os.Stat(filename) if err != nil</td></tr><tr><td></td><td>if os.IsNotExist(err）{</td></tr><tr><td></td><td>return nil</td></tr><tr><td></td><td>return err</td></tr><tr><td></td><td></td></tr><tr><td>def _load_rule_file(self, filename):</td><td>if info.Size() == 0{ return nil</td></tr><tr><td>if not (os.path.exists(filename)):</td><td>}</td></tr><tr><td>sys.stderr.write(</td><td>files，err ：= filepath.Glob(</td></tr><tr><td>&quot;rflint: %s: No such file or &quot;directory\\n&quot; % filename</td><td>filename + _BACKUP_SUFFIX</td></tr><tr><td>return</td><td>） if err nil 1</td></tr><tr><td>try:</td><td>return err</td></tr><tr><td>basename = os.path.basename(filename)</td><td>}</td></tr><tr><td>(name，ext）= os.path.splitext(basename) imp.load_source(name,filename)</td><td> numBackup := byte(1)</td></tr><tr><td>except Exception as e: sys.stderr.write(</td><td>if len(files) !=0{</td></tr><tr><td>&quot;rflint: %s: exception while</td><td>lastFile := files[len(files)-1]</td></tr><tr><td>&quot;loading:%s\\n&quot; % (filename, str(e))</td><td>numBackup = lastFile[len(lastFile)-2] + 1</td></tr><tr><td></td><td>if numBackup &gt;</td></tr><tr><td></td><td>numBackup = &#x27;1&#x27;</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>else{</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>&#x27;1&#x27;</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>numBackup =</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>return Copy (filename,</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>fmt.Sprintf(&quot;%s+%s~&quot;,</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>string(numBackup)))</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "dfeb9bd55674c1d88bd8727a7ae6e6c8b0e9d1b458288922467db71461c08de5.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        12,
+                                        530,
+                                        236.33333333333334
+                                    ],
+                                    "spans": [],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        236.33333333333334,
+                                        530,
+                                        460.6666666666667
+                                    ],
+                                    "spans": [],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        460.6666666666667,
+                                        530,
+                                        685.0
+                                    ],
+                                    "spans": [],
+                                    "index": 2
+                                }
+                            ]
+                        },
+                        {
+                            "type": "table_footnote",
+                            "bbox": [
+                                107,
+                                685,
+                                505,
+                                708
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        683,
+                                        505,
+                                        697
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                683,
+                                                505,
+                                                697
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 6: Selected snippets starting with is, main, or load (left) and their best embedding matches",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        694,
+                                        224,
+                                        709
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                694,
+                                                224,
+                                                709
+                                            ],
+                                            "score": 1.0,
+                                            "content": "from other languages (right).",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 4
+                                }
+                            ],
+                            "index": 3.5
+                        }
+                    ],
+                    "index": 2.25
+                }
+            ],
+            "page_idx": 14,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        108,
+                        27,
+                        292,
+                        37
+                    ],
+                    "lines": []
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        311,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                313,
+                                764
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        313,
+                                        764
+                                    ],
+                                    "score": 1.0,
+                                    "content": "15",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "table",
+                    "bbox": [
+                        106,
+                        12,
+                        530,
+                        685
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                106,
+                                12,
+                                530,
+                                685
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        12,
+                                        530,
+                                        685
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                12,
+                                                530,
+                                                685
+                                            ],
+                                            "score": 0.422,
+                                            "html": "<table><tr><td colspan=\"2\">Published as a conference paper at ICLR 2021</td></tr><tr><td></td><td></td></tr><tr><td>function isEqualArray(a，b){ if (a return true;</td><td></td></tr><tr><td>if ((a === undefined) undefined)）{ return false;</td><td>func areSameFloat32Array(a，b []float32） bool if len(a) != len(b){ return false</td></tr><tr><td>var =a.length; if (i !== b.length){ return false;</td><td>for i := O;i &lt; len(a);i++{ if a[i]!=b[i]{ return false J</td></tr><tr><td>while (i--）{ if(a[i] !== b[i]）{ return false; }</td><td>return true</td></tr><tr><td>return true;</td><td></td></tr><tr><td>function main() var rawData $(&#x27; .HeaderTexture[data-login- user-email]&#x27;) .data() ;</td><td>func TaskSayHello(t *tasking.T){</td></tr><tr><td>if (rawData) 1 me={</td><td>username := t.Flags.String(&quot;name&quot;) if username user, := user.Current ()</td></tr><tr><td>name:rawData.loginUserName, mail: rawData.loginUserEmail }；</td><td>username = user.Name</td></tr><tr><td>getCartId(function (cart）{ me.cart = cart;</td><td>} ift.Flags.Bool(&quot;verbose&quot;)</td></tr><tr><td>injectMenu(); refreshUsers(actions.updateUsers); listenOnChanges(onChange);</td><td>t.Logf(&quot;Hello %s, the time now is %s\\n&quot;, username，time.Now())</td></tr><tr><td>listenonorderConfirm(onConfirm); ）；</td><td>}else{ t.Logf(&quot;Hello %s\\n&quot;,username)</td></tr><tr><td>} else{ caliback(&#x27;no user&#x27;);</td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>func Backup(filename string)error{</td></tr><tr><td></td><td></td></tr><tr><td></td><td>info，err := os.Stat(filename) if err != nil</td></tr><tr><td></td><td>if os.IsNotExist(err）{</td></tr><tr><td></td><td>return nil</td></tr><tr><td></td><td>return err</td></tr><tr><td></td><td></td></tr><tr><td>def _load_rule_file(self, filename):</td><td>if info.Size() == 0{ return nil</td></tr><tr><td>if not (os.path.exists(filename)):</td><td>}</td></tr><tr><td>sys.stderr.write(</td><td>files，err ：= filepath.Glob(</td></tr><tr><td>&quot;rflint: %s: No such file or &quot;directory\\n&quot; % filename</td><td>filename + _BACKUP_SUFFIX</td></tr><tr><td>return</td><td>） if err nil 1</td></tr><tr><td>try:</td><td>return err</td></tr><tr><td>basename = os.path.basename(filename)</td><td>}</td></tr><tr><td>(name，ext）= os.path.splitext(basename) imp.load_source(name,filename)</td><td> numBackup := byte(1)</td></tr><tr><td>except Exception as e: sys.stderr.write(</td><td>if len(files) !=0{</td></tr><tr><td>&quot;rflint: %s: exception while</td><td>lastFile := files[len(files)-1]</td></tr><tr><td>&quot;loading:%s\\n&quot; % (filename, str(e))</td><td>numBackup = lastFile[len(lastFile)-2] + 1</td></tr><tr><td></td><td>if numBackup &gt;</td></tr><tr><td></td><td>numBackup = &#x27;1&#x27;</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>else{</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>&#x27;1&#x27;</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>numBackup =</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>return Copy (filename,</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>fmt.Sprintf(&quot;%s+%s~&quot;,</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>string(numBackup)))</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "dfeb9bd55674c1d88bd8727a7ae6e6c8b0e9d1b458288922467db71461c08de5.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        12,
+                                        530,
+                                        236.33333333333334
+                                    ],
+                                    "spans": [],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        236.33333333333334,
+                                        530,
+                                        460.6666666666667
+                                    ],
+                                    "spans": [],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        460.6666666666667,
+                                        530,
+                                        685.0
+                                    ],
+                                    "spans": [],
+                                    "index": 2
+                                }
+                            ]
+                        },
+                        {
+                            "type": "table_footnote",
+                            "bbox": [
+                                107,
+                                685,
+                                505,
+                                708
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        683,
+                                        505,
+                                        697
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                683,
+                                                505,
+                                                697
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 6: Selected snippets starting with is, main, or load (left) and their best embedding matches",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        694,
+                                        224,
+                                        709
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                694,
+                                                224,
+                                                709
+                                            ],
+                                            "score": 1.0,
+                                            "content": "from other languages (right).",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 4
+                                }
+                            ],
+                            "index": 3.5
+                        }
+                    ],
+                    "index": 2.25
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "image",
+                    "bbox": [
+                        184,
+                        79,
+                        420,
+                        264
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                184,
+                                79,
+                                420,
+                                264
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        184,
+                                        79,
+                                        420,
+                                        264
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                184,
+                                                79,
+                                                420,
+                                                264
+                                            ],
+                                            "score": 0.967,
+                                            "type": "image",
+                                            "image_path": "e37f9cb44d930542340c5ad3d88619f8535c0f5512daf8c0c8d8a050432bff4b.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 6.5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        184,
+                                        79,
+                                        420,
+                                        92.21428571428571
+                                    ],
+                                    "spans": [],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        92.21428571428571,
+                                        420,
+                                        105.42857142857142
+                                    ],
+                                    "spans": [],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        105.42857142857142,
+                                        420,
+                                        118.64285714285712
+                                    ],
+                                    "spans": [],
+                                    "index": 2
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        118.64285714285712,
+                                        420,
+                                        131.85714285714283
+                                    ],
+                                    "spans": [],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        131.85714285714283,
+                                        420,
+                                        145.07142857142856
+                                    ],
+                                    "spans": [],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        145.07142857142856,
+                                        420,
+                                        158.28571428571428
+                                    ],
+                                    "spans": [],
+                                    "index": 5
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        158.28571428571428,
+                                        420,
+                                        171.5
+                                    ],
+                                    "spans": [],
+                                    "index": 6
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        171.5,
+                                        420,
+                                        184.71428571428572
+                                    ],
+                                    "spans": [],
+                                    "index": 7
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        184.71428571428572,
+                                        420,
+                                        197.92857142857144
+                                    ],
+                                    "spans": [],
+                                    "index": 8
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        197.92857142857144,
+                                        420,
+                                        211.14285714285717
+                                    ],
+                                    "spans": [],
+                                    "index": 9
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        211.14285714285717,
+                                        420,
+                                        224.3571428571429
+                                    ],
+                                    "spans": [],
+                                    "index": 10
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        224.3571428571429,
+                                        420,
+                                        237.5714285714286
+                                    ],
+                                    "spans": [],
+                                    "index": 11
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        237.5714285714286,
+                                        420,
+                                        250.78571428571433
+                                    ],
+                                    "spans": [],
+                                    "index": 12
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        250.78571428571433,
+                                        420,
+                                        264.00000000000006
+                                    ],
+                                    "spans": [],
+                                    "index": 13
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                131,
+                                271,
+                                480,
+                                284
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        129,
+                                        271,
+                                        481,
+                                        285
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                129,
+                                                271,
+                                                481,
+                                                285
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 6: Example snippet and its corresponding AST obtained from GitHub Semantic.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 14
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 10.25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        131,
+                        308,
+                        248,
+                        319
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                129,
+                                307,
+                                250,
+                                321
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        129,
+                                        307,
+                                        250,
+                                        321
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3. Empty lines are removed.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        129,
+                        326,
+                        505,
+                        348
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                129,
+                                325,
+                                505,
+                                338
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        129,
+                                        325,
+                                        505,
+                                        338
+                                    ],
+                                    "score": 1.0,
+                                    "content": "4. Hard coded strings and numbers are replaced with a special [MASK STRING] and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                144,
+                                337,
+                                247,
+                                348
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        144,
+                                        337,
+                                        247,
+                                        348
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[MASK NUMBER] token.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 16.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        130,
+                        354,
+                        505,
+                        388
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                128,
+                                353,
+                                505,
+                                368
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        353,
+                                        505,
+                                        368
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5. Indentation style of the code snippet is detected and whitespace characters at the beginning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                365,
+                                505,
+                                378
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        365,
+                                        505,
+                                        378
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of a line are replaced with a single [INDENT] or [DEDENT] token when indentation",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                140,
+                                374,
+                                181,
+                                391
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        140,
+                                        374,
+                                        181,
+                                        391
+                                    ],
+                                    "score": 1.0,
+                                    "content": "changes.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 19
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        130,
+                        394,
+                        505,
+                        428
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                129,
+                                394,
+                                505,
+                                407
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        129,
+                                        394,
+                                        420,
+                                        407
+                                    ],
+                                    "score": 1.0,
+                                    "content": "6. Tokens are further split into sub tokens, e.g., setBottomHeight",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        420,
+                                        396,
+                                        434,
+                                        405
+                                    ],
+                                    "score": 0.6,
+                                    "content": "",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        434,
+                                        394,
+                                        505,
+                                        407
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[‘set’, ‘bottom’,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                143,
+                                406,
+                                505,
+                                418
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        143,
+                                        406,
+                                        505,
+                                        418
+                                    ],
+                                    "score": 1.0,
+                                    "content": "‘height’]. Throughout our experiments, we use 5 input sub tokens. If a token consists",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                415,
+                                484,
+                                430
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        415,
+                                        484,
+                                        430
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of less than 5 sub tokens, the remaining spaces are filled with a special [PAD] token.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 22
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        129,
+                        434,
+                        503,
+                        457
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                129,
+                                433,
+                                505,
+                                447
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        129,
+                                        433,
+                                        505,
+                                        447
+                                    ],
+                                    "score": 1.0,
+                                    "content": "7. Any remaining tokens that only consist of white spaces are removed. The only white",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                445,
+                                344,
+                                458
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        445,
+                                        322,
+                                        458
+                                    ],
+                                    "score": 1.0,
+                                    "content": "space characters that are kept are line breaks",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        323,
+                                        445,
+                                        339,
+                                        457
+                                    ],
+                                    "score": 0.85,
+                                    "content": "^ { \\bullet } \\backslash \\boldsymbol { \\mathrm { n } } ^ { \\prime }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        340,
+                                        445,
+                                        344,
+                                        458
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 24.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        127,
+                        463,
+                        492,
+                        475
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                128,
+                                463,
+                                492,
+                                476
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        463,
+                                        492,
+                                        476
+                                    ],
+                                    "score": 1.0,
+                                    "content": "8. Any code snippets where the Pygments tokenizer cannot parse a token are discarded.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 26
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        490,
+                        360,
+                        502
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                488,
+                                361,
+                                504
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        488,
+                                        361,
+                                        504
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.3.2 STAGE 1 PREPROCESSING (GENERATION OF ASTS)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 27
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        131,
+                        511,
+                        504,
+                        544
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                129,
+                                510,
+                                505,
+                                524
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        129,
+                                        510,
+                                        505,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1. Stripped code snippets are used to generate language-specific ASTs. For Java, we use the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                521,
+                                505,
+                                535
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        521,
+                                        505,
+                                        535
+                                    ],
+                                    "score": 1.0,
+                                    "content": "AST parser from the java-parser project. The ASTs contain node types and source ranges.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                532,
+                                368,
+                                545
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        532,
+                                        368,
+                                        545
+                                    ],
+                                    "score": 1.0,
+                                    "content": "For Python, JavaScript, Ruby and Go, we use semantic.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 29
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        130,
+                        551,
+                        371,
+                        562
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                129,
+                                550,
+                                372,
+                                564
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        129,
+                                        550,
+                                        372,
+                                        564
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2. Snippets that lead to an AST parse error are discarded.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        }
+                    ],
+                    "index": 31
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        129,
+                        569,
+                        504,
+                        601
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                129,
+                                569,
+                                505,
+                                581
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        129,
+                                        569,
+                                        505,
+                                        581
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3. We calculate a mapping between tokens and nodes in the AST. Every token is assigned",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                579,
+                                505,
+                                592
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        579,
+                                        505,
+                                        592
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to the node in the AST with shortest source range that still encompasses the source range",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                589,
+                                195,
+                                603
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        589,
+                                        195,
+                                        603
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of the token.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        }
+                    ],
+                    "index": 33
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        142,
+                        602,
+                        505,
+                        722
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                141,
+                                601,
+                                506,
+                                614
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        601,
+                                        506,
+                                        614
+                                    ],
+                                    "score": 1.0,
+                                    "content": "To find such a node, we originally intended to make use of the assumption that source",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                613,
+                                506,
+                                624
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        613,
+                                        506,
+                                        624
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ranges of child nodes do not overlap. Then, one could easily find the node with smallest",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                624,
+                                506,
+                                636
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        624,
+                                        506,
+                                        636
+                                    ],
+                                    "score": 1.0,
+                                    "content": "encompassing source range by greedily selecting at every layer in the AST the child that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                634,
+                                505,
+                                646
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        634,
+                                        505,
+                                        646
+                                    ],
+                                    "score": 1.0,
+                                    "content": "encompasses the token’s source range (there can only be at most one child that fulfills this).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                645,
+                                506,
+                                658
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        645,
+                                        506,
+                                        658
+                                    ],
+                                    "score": 1.0,
+                                    "content": "However, this assumption does not hold for all ASTs (see Figure 6 for an example). As a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                656,
+                                506,
+                                669
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        656,
+                                        506,
+                                        669
+                                    ],
+                                    "score": 1.0,
+                                    "content": "heuristic, we greedily select the child node with the shorter source range in case there were",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                668,
+                                506,
+                                680
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        668,
+                                        506,
+                                        680
+                                    ],
+                                    "score": 1.0,
+                                    "content": "multiple child nodes with encompassing source ranges. This approximation seems to be",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                678,
+                                505,
+                                690
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        678,
+                                        505,
+                                        690
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sufficient in our case, and limits runtime as we do not have to consider multiple paths in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                688,
+                                506,
+                                702
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        688,
+                                        506,
+                                        702
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the AST. It is also sufficient to stop when no child node encompasses the source range of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                700,
+                                505,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        700,
+                                        505,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the token, as in ASTs the source ranges of child nodes are always contained in the source",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                712,
+                                232,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        712,
+                                        232,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ranges of their parent.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        }
+                    ],
+                    "index": 40
+                }
+            ],
+            "page_idx": 15,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        292,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                293,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        293,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        311,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                313,
+                                764
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        313,
+                                        764
+                                    ],
+                                    "score": 1.0,
+                                    "content": "16",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "image",
+                    "bbox": [
+                        184,
+                        79,
+                        420,
+                        264
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                184,
+                                79,
+                                420,
+                                264
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        184,
+                                        79,
+                                        420,
+                                        264
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                184,
+                                                79,
+                                                420,
+                                                264
+                                            ],
+                                            "score": 0.967,
+                                            "type": "image",
+                                            "image_path": "e37f9cb44d930542340c5ad3d88619f8535c0f5512daf8c0c8d8a050432bff4b.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 6.5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        184,
+                                        79,
+                                        420,
+                                        92.21428571428571
+                                    ],
+                                    "spans": [],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        92.21428571428571,
+                                        420,
+                                        105.42857142857142
+                                    ],
+                                    "spans": [],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        105.42857142857142,
+                                        420,
+                                        118.64285714285712
+                                    ],
+                                    "spans": [],
+                                    "index": 2
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        118.64285714285712,
+                                        420,
+                                        131.85714285714283
+                                    ],
+                                    "spans": [],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        131.85714285714283,
+                                        420,
+                                        145.07142857142856
+                                    ],
+                                    "spans": [],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        145.07142857142856,
+                                        420,
+                                        158.28571428571428
+                                    ],
+                                    "spans": [],
+                                    "index": 5
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        158.28571428571428,
+                                        420,
+                                        171.5
+                                    ],
+                                    "spans": [],
+                                    "index": 6
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        171.5,
+                                        420,
+                                        184.71428571428572
+                                    ],
+                                    "spans": [],
+                                    "index": 7
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        184.71428571428572,
+                                        420,
+                                        197.92857142857144
+                                    ],
+                                    "spans": [],
+                                    "index": 8
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        197.92857142857144,
+                                        420,
+                                        211.14285714285717
+                                    ],
+                                    "spans": [],
+                                    "index": 9
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        211.14285714285717,
+                                        420,
+                                        224.3571428571429
+                                    ],
+                                    "spans": [],
+                                    "index": 10
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        224.3571428571429,
+                                        420,
+                                        237.5714285714286
+                                    ],
+                                    "spans": [],
+                                    "index": 11
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        237.5714285714286,
+                                        420,
+                                        250.78571428571433
+                                    ],
+                                    "spans": [],
+                                    "index": 12
+                                },
+                                {
+                                    "bbox": [
+                                        184,
+                                        250.78571428571433,
+                                        420,
+                                        264.00000000000006
+                                    ],
+                                    "spans": [],
+                                    "index": 13
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                131,
+                                271,
+                                480,
+                                284
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        129,
+                                        271,
+                                        481,
+                                        285
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                129,
+                                                271,
+                                                481,
+                                                285
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 6: Example snippet and its corresponding AST obtained from GitHub Semantic.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 14
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 10.25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        131,
+                        308,
+                        248,
+                        319
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                129,
+                                307,
+                                250,
+                                321
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        129,
+                                        307,
+                                        250,
+                                        321
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3. Empty lines are removed.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 15,
+                    "bbox_fs": [
+                        129,
+                        307,
+                        250,
+                        321
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        129,
+                        326,
+                        505,
+                        348
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                129,
+                                325,
+                                505,
+                                338
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        129,
+                                        325,
+                                        505,
+                                        338
+                                    ],
+                                    "score": 1.0,
+                                    "content": "4. Hard coded strings and numbers are replaced with a special [MASK STRING] and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                144,
+                                337,
+                                247,
+                                348
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        144,
+                                        337,
+                                        247,
+                                        348
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[MASK NUMBER] token.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 16.5,
+                    "bbox_fs": [
+                        129,
+                        325,
+                        505,
+                        348
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        130,
+                        354,
+                        505,
+                        388
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                128,
+                                353,
+                                505,
+                                368
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        353,
+                                        505,
+                                        368
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5. Indentation style of the code snippet is detected and whitespace characters at the beginning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                365,
+                                505,
+                                378
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        365,
+                                        505,
+                                        378
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of a line are replaced with a single [INDENT] or [DEDENT] token when indentation",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                140,
+                                374,
+                                181,
+                                391
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        140,
+                                        374,
+                                        181,
+                                        391
+                                    ],
+                                    "score": 1.0,
+                                    "content": "changes.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 19,
+                    "bbox_fs": [
+                        128,
+                        353,
+                        505,
+                        391
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        130,
+                        394,
+                        505,
+                        428
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                129,
+                                394,
+                                505,
+                                407
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        129,
+                                        394,
+                                        420,
+                                        407
+                                    ],
+                                    "score": 1.0,
+                                    "content": "6. Tokens are further split into sub tokens, e.g., setBottomHeight",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        420,
+                                        396,
+                                        434,
+                                        405
+                                    ],
+                                    "score": 0.6,
+                                    "content": "",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        434,
+                                        394,
+                                        505,
+                                        407
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[‘set’, ‘bottom’,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                143,
+                                406,
+                                505,
+                                418
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        143,
+                                        406,
+                                        505,
+                                        418
+                                    ],
+                                    "score": 1.0,
+                                    "content": "‘height’]. Throughout our experiments, we use 5 input sub tokens. If a token consists",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                415,
+                                484,
+                                430
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        415,
+                                        484,
+                                        430
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of less than 5 sub tokens, the remaining spaces are filled with a special [PAD] token.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 22,
+                    "bbox_fs": [
+                        129,
+                        394,
+                        505,
+                        430
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        129,
+                        434,
+                        503,
+                        457
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                129,
+                                433,
+                                505,
+                                447
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        129,
+                                        433,
+                                        505,
+                                        447
+                                    ],
+                                    "score": 1.0,
+                                    "content": "7. Any remaining tokens that only consist of white spaces are removed. The only white",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                445,
+                                344,
+                                458
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        445,
+                                        322,
+                                        458
+                                    ],
+                                    "score": 1.0,
+                                    "content": "space characters that are kept are line breaks",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        323,
+                                        445,
+                                        339,
+                                        457
+                                    ],
+                                    "score": 0.85,
+                                    "content": "^ { \\bullet } \\backslash \\boldsymbol { \\mathrm { n } } ^ { \\prime }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        340,
+                                        445,
+                                        344,
+                                        458
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 24.5,
+                    "bbox_fs": [
+                        129,
+                        433,
+                        505,
+                        458
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        127,
+                        463,
+                        492,
+                        475
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                128,
+                                463,
+                                492,
+                                476
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        463,
+                                        492,
+                                        476
+                                    ],
+                                    "score": 1.0,
+                                    "content": "8. Any code snippets where the Pygments tokenizer cannot parse a token are discarded.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 26,
+                    "bbox_fs": [
+                        128,
+                        463,
+                        492,
+                        476
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        490,
+                        360,
+                        502
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                488,
+                                361,
+                                504
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        488,
+                                        361,
+                                        504
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.3.2 STAGE 1 PREPROCESSING (GENERATION OF ASTS)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 27
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        131,
+                        511,
+                        504,
+                        544
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                129,
+                                510,
+                                505,
+                                524
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        129,
+                                        510,
+                                        505,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1. Stripped code snippets are used to generate language-specific ASTs. For Java, we use the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                521,
+                                505,
+                                535
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        521,
+                                        505,
+                                        535
+                                    ],
+                                    "score": 1.0,
+                                    "content": "AST parser from the java-parser project. The ASTs contain node types and source ranges.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                532,
+                                368,
+                                545
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        532,
+                                        368,
+                                        545
+                                    ],
+                                    "score": 1.0,
+                                    "content": "For Python, JavaScript, Ruby and Go, we use semantic.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 29,
+                    "bbox_fs": [
+                        129,
+                        510,
+                        505,
+                        545
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        130,
+                        551,
+                        371,
+                        562
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                129,
+                                550,
+                                372,
+                                564
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        129,
+                                        550,
+                                        372,
+                                        564
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2. Snippets that lead to an AST parse error are discarded.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        }
+                    ],
+                    "index": 31,
+                    "bbox_fs": [
+                        129,
+                        550,
+                        372,
+                        564
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        129,
+                        569,
+                        504,
+                        601
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                129,
+                                569,
+                                505,
+                                581
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        129,
+                                        569,
+                                        505,
+                                        581
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3. We calculate a mapping between tokens and nodes in the AST. Every token is assigned",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                579,
+                                505,
+                                592
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        579,
+                                        505,
+                                        592
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to the node in the AST with shortest source range that still encompasses the source range",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                589,
+                                195,
+                                603
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        589,
+                                        195,
+                                        603
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of the token.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        }
+                    ],
+                    "index": 33,
+                    "bbox_fs": [
+                        129,
+                        569,
+                        505,
+                        603
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        142,
+                        602,
+                        505,
+                        722
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                141,
+                                601,
+                                506,
+                                614
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        601,
+                                        506,
+                                        614
+                                    ],
+                                    "score": 1.0,
+                                    "content": "To find such a node, we originally intended to make use of the assumption that source",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                613,
+                                506,
+                                624
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        613,
+                                        506,
+                                        624
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ranges of child nodes do not overlap. Then, one could easily find the node with smallest",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                624,
+                                506,
+                                636
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        624,
+                                        506,
+                                        636
+                                    ],
+                                    "score": 1.0,
+                                    "content": "encompassing source range by greedily selecting at every layer in the AST the child that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                634,
+                                505,
+                                646
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        634,
+                                        505,
+                                        646
+                                    ],
+                                    "score": 1.0,
+                                    "content": "encompasses the token’s source range (there can only be at most one child that fulfills this).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                645,
+                                506,
+                                658
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        645,
+                                        506,
+                                        658
+                                    ],
+                                    "score": 1.0,
+                                    "content": "However, this assumption does not hold for all ASTs (see Figure 6 for an example). As a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                656,
+                                506,
+                                669
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        656,
+                                        506,
+                                        669
+                                    ],
+                                    "score": 1.0,
+                                    "content": "heuristic, we greedily select the child node with the shorter source range in case there were",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                668,
+                                506,
+                                680
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        668,
+                                        506,
+                                        680
+                                    ],
+                                    "score": 1.0,
+                                    "content": "multiple child nodes with encompassing source ranges. This approximation seems to be",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                678,
+                                505,
+                                690
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        678,
+                                        505,
+                                        690
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sufficient in our case, and limits runtime as we do not have to consider multiple paths in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                688,
+                                506,
+                                702
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        688,
+                                        506,
+                                        702
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the AST. It is also sufficient to stop when no child node encompasses the source range of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                700,
+                                505,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        700,
+                                        505,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the token, as in ASTs the source ranges of child nodes are always contained in the source",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                712,
+                                232,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        712,
+                                        232,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ranges of their parent.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        }
+                    ],
+                    "index": 40,
+                    "bbox_fs": [
+                        141,
+                        601,
+                        506,
+                        723
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        129,
+                        99,
+                        505,
+                        122
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                129,
+                                98,
+                                505,
+                                112
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        129,
+                                        98,
+                                        505,
+                                        112
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1. Tokens are vocabularized. Any token occurring less than 100 times in the training set is",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                111,
+                                267,
+                                123
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        111,
+                                        231,
+                                        123
+                                    ],
+                                    "score": 1.0,
+                                    "content": "replaced by an <unk",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        231,
+                                        112,
+                                        239,
+                                        121
+                                    ],
+                                    "score": 0.45,
+                                    "content": ">",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        239,
+                                        111,
+                                        267,
+                                        123
+                                    ],
+                                    "score": 1.0,
+                                    "content": "token.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        130,
+                        126,
+                        422,
+                        137
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                129,
+                                125,
+                                422,
+                                139
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        129,
+                                        125,
+                                        422,
+                                        139
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2. We calculate multiple pair-wise relations between nodes in the AST:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        154,
+                        141,
+                        505,
+                        281
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                153,
+                                141,
+                                288,
+                                154
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        153,
+                                        141,
+                                        288,
+                                        154
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• Personalized Page Rank (PPR)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                161,
+                                152,
+                                504,
+                                165
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        161,
+                                        152,
+                                        504,
+                                        165
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We interpret the negative logarithm of PPR as a distance. We use a teleport probability",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                161,
+                                163,
+                                505,
+                                176
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        161,
+                                        163,
+                                        173,
+                                        176
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        173,
+                                        164,
+                                        212,
+                                        174
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\alpha = 0 . 1 5",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        212,
+                                        163,
+                                        287,
+                                        176
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and a threshold of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        288,
+                                        163,
+                                        303,
+                                        174
+                                    ],
+                                    "score": 0.89,
+                                    "content": "e ^ { - 5 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        163,
+                                        381,
+                                        176
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", i.e., anything with",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        382,
+                                        164,
+                                        449,
+                                        175
+                                    ],
+                                    "score": 0.89,
+                                    "content": "- \\log P P R > 5",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        450,
+                                        163,
+                                        505,
+                                        176
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is considered",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                162,
+                                176,
+                                213,
+                                185
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        162,
+                                        176,
+                                        213,
+                                        185
+                                    ],
+                                    "score": 1.0,
+                                    "content": "unreachable",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                155,
+                                188,
+                                323,
+                                199
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        155,
+                                        188,
+                                        323,
+                                        199
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• Shortest path length between two nodes",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                154,
+                                201,
+                                505,
+                                213
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        154,
+                                        201,
+                                        505,
+                                        213
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• Ancestor shortest paths (bidirectional). That is, the parent has an ancestor shortest",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                161,
+                                212,
+                                506,
+                                223
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        161,
+                                        212,
+                                        506,
+                                        223
+                                    ],
+                                    "score": 1.0,
+                                    "content": "path distance of 1 to all its children and the child has a distance of -1 to its parents. We",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                161,
+                                223,
+                                505,
+                                235
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        161,
+                                        223,
+                                        505,
+                                        235
+                                    ],
+                                    "score": 1.0,
+                                    "content": "consider nodes that are not ancestors or descendants of a node (i.e. not reachable by",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                162,
+                                234,
+                                506,
+                                246
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        162,
+                                        234,
+                                        506,
+                                        246
+                                    ],
+                                    "score": 1.0,
+                                    "content": "following only parent or only child relations) as not connected in the ancestor shortest",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                160,
+                                245,
+                                505,
+                                257
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        160,
+                                        245,
+                                        505,
+                                        257
+                                    ],
+                                    "score": 1.0,
+                                    "content": "paths relation. We encode this with a very large value in their distance; we have found",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                161,
+                                256,
+                                330,
+                                268
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        161,
+                                        257,
+                                        204,
+                                        268
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a value of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        204,
+                                        256,
+                                        230,
+                                        267
+                                    ],
+                                    "score": 0.25,
+                                    "content": "1 , 0 0 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        230,
+                                        257,
+                                        330,
+                                        268
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to work well in practice.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                154,
+                                268,
+                                493,
+                                281
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        154,
+                                        268,
+                                        493,
+                                        281
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• Next sibling shortest paths (bidirectional, analogous to the ancestor shortest paths)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 8.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        142,
+                        285,
+                        504,
+                        373
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                141,
+                                284,
+                                505,
+                                297
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        284,
+                                        505,
+                                        297
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Note that the ancestor shortest paths and next sibling shortest paths are required because",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                295,
+                                506,
+                                309
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        295,
+                                        506,
+                                        309
+                                    ],
+                                    "score": 1.0,
+                                    "content": "treating the AST as a normal graph leads to ambiguity. In a graph, the neighbors of a node",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                307,
+                                505,
+                                319
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        307,
+                                        505,
+                                        319
+                                    ],
+                                    "score": 1.0,
+                                    "content": "have no ordering; however in the AST, the order of the children of a node reflects their",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                318,
+                                506,
+                                330
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        318,
+                                        506,
+                                        330
+                                    ],
+                                    "score": 1.0,
+                                    "content": "order in the code. Therefore, we explicitly include the next sibling shortest paths. The",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                329,
+                                505,
+                                341
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        329,
+                                        505,
+                                        341
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ancestor shortest paths would not be required if we treated the AST as a directed graph; in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                340,
+                                505,
+                                352
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        340,
+                                        505,
+                                        352
+                                    ],
+                                    "score": 1.0,
+                                    "content": "this case, however, a leaf node could not reach any other node in the AST, and therefore",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                350,
+                                506,
+                                363
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        350,
+                                        506,
+                                        363
+                                    ],
+                                    "score": 1.0,
+                                    "content": "both PPR and shortest path length are not useful in this case. Therefore, we model the AST",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                361,
+                                421,
+                                375
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        361,
+                                        421,
+                                        375
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as undirected and inject the ancestor / child edges to avoid ambiguity.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 18.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        130,
+                        377,
+                        505,
+                        454
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                128,
+                                376,
+                                506,
+                                389
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        376,
+                                        506,
+                                        389
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3. Distance values are binned into 32 bins using area-based exponential binning with a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                388,
+                                505,
+                                401
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        388,
+                                        371,
+                                        401
+                                    ],
+                                    "score": 1.0,
+                                    "content": "growth factor of 1.3, i.e., the area of a bin’s rectangle (",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        371,
+                                        390,
+                                        378,
+                                        398
+                                    ],
+                                    "score": 0.48,
+                                    "content": "x",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        378,
+                                        388,
+                                        428,
+                                        401
+                                    ],
+                                    "score": 1.0,
+                                    "content": ": bin range,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        429,
+                                        390,
+                                        435,
+                                        400
+                                    ],
+                                    "score": 0.62,
+                                    "content": "y",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        435,
+                                        388,
+                                        505,
+                                        401
+                                    ],
+                                    "score": 1.0,
+                                    "content": ": number of val-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                399,
+                                505,
+                                411
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        399,
+                                        505,
+                                        411
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ues in bin) will be approximately 1.3 times bigger for the next bin (going away from the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                410,
+                                505,
+                                423
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        410,
+                                        505,
+                                        423
+                                    ],
+                                    "score": 1.0,
+                                    "content": "bin that contains the zero value). Additionally, for discrete distance measures (such as se-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                421,
+                                505,
+                                433
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        421,
+                                        505,
+                                        433
+                                    ],
+                                    "score": 1.0,
+                                    "content": "quence distance or shortest path length), we hard-code 9 values around 0 to have their own",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                432,
+                                505,
+                                444
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        432,
+                                        361,
+                                        444
+                                    ],
+                                    "score": 1.0,
+                                    "content": "bins. For instance, on the sequence distance the values",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        362,
+                                        432,
+                                        420,
+                                        443
+                                    ],
+                                    "score": 0.9,
+                                    "content": "- 4 , - 3 , \\dots , 4",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        420,
+                                        432,
+                                        505,
+                                        444
+                                    ],
+                                    "score": 1.0,
+                                    "content": "have their individual",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                441,
+                                407,
+                                457
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        441,
+                                        407,
+                                        457
+                                    ],
+                                    "score": 1.0,
+                                    "content": "bins, and around those values we employ the exponential binning.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 26
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        131,
+                        459,
+                        504,
+                        492
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                128,
+                                457,
+                                505,
+                                471
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        457,
+                                        505,
+                                        471
+                                    ],
+                                    "score": 1.0,
+                                    "content": "4. Punctuation tokens (such as points or brackets) are removed from the input sequence, as",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                469,
+                                505,
+                                483
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        469,
+                                        505,
+                                        483
+                                    ],
+                                    "score": 1.0,
+                                    "content": "experiments showed that their presence does not improve performance but slows down",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                480,
+                                278,
+                                493
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        480,
+                                        278,
+                                        493
+                                    ],
+                                    "score": 1.0,
+                                    "content": "training due to bigger input sizes.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 31
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        132,
+                        496,
+                        504,
+                        529
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                129,
+                                495,
+                                505,
+                                509
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        129,
+                                        495,
+                                        505,
+                                        509
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5. Snippets that are longer than MAX NUM TOKENS after punctuation tokens are removed are",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                507,
+                                505,
+                                519
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        507,
+                                        505,
+                                        519
+                                    ],
+                                    "score": 1.0,
+                                    "content": "discarded from the training set. Throughout our experiments, we use MAX NUM TOKENS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                518,
+                                468,
+                                529
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        518,
+                                        173,
+                                        529
+                                    ],
+                                    "score": 0.76,
+                                    "content": "= ~ 5 1 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        173,
+                                        518,
+                                        424,
+                                        529
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". During evaluation on the test set, we use MAX NUM TOKENS",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        424,
+                                        518,
+                                        464,
+                                        528
+                                    ],
+                                    "score": 0.76,
+                                    "content": "= ~ 1 0 0 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        464,
+                                        518,
+                                        468,
+                                        529
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        }
+                    ],
+                    "index": 34
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        544,
+                        286,
+                        555
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                543,
+                                288,
+                                556
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        543,
+                                        288,
+                                        556
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.4 INPUT EMBEDDINGS TO THE MODEL",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 36
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        564,
+                        505,
+                        630
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                564,
+                                506,
+                                578
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        564,
+                                        506,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Besides its five subtokens (e.g., [‘get’, ‘data’, ‘[PAD]’, ‘[PAD]’, ‘[PAD]’]),",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                574,
+                                505,
+                                589
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        574,
+                                        505,
+                                        589
+                                    ],
+                                    "score": 1.0,
+                                    "content": "each input token has a token type (coming from the Pygments tokenizer) and an AST node type.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                586,
+                                505,
+                                599
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        586,
+                                        505,
+                                        599
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The AST node type is the type of the node assigned to each respective token, as described in Section",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                596,
+                                505,
+                                610
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        596,
+                                        505,
+                                        610
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.3.2. We concatenate the embeddings of the five subtokens, the token type, and the AST node",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                608,
+                                506,
+                                621
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        608,
+                                        506,
+                                        621
+                                    ],
+                                    "score": 1.0,
+                                    "content": "type. Then, we apply a linear layer (without activation function) to project down to the model’s",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                619,
+                                200,
+                                632
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        619,
+                                        200,
+                                        632
+                                    ],
+                                    "score": 1.0,
+                                    "content": "embedding dimension.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        }
+                    ],
+                    "index": 39.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        644,
+                        275,
+                        656
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                644,
+                                277,
+                                657
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        644,
+                                        277,
+                                        657
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.5 INPUT TO THE GREAT BASELINE",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        }
+                    ],
+                    "index": 43
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        666,
+                        505,
+                        731
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                665,
+                                505,
+                                678
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        665,
+                                        505,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "As mentioned in the main text, we also compare with GREAT Hellendoorn et al. (2020). Since",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                676,
+                                505,
+                                689
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        676,
+                                        505,
+                                        689
+                                    ],
+                                    "score": 1.0,
+                                    "content": "their preprocessing pipeline is proprietary and could not be shared with us even after contacting the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                687,
+                                505,
+                                700
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        687,
+                                        505,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "authors, we provide to GREAT the same AST distances as our model. Since GREAT uses edges in-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                698,
+                                505,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        698,
+                                        505,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "stead of distances to encode relations in the Structure, we essentially threshold the ancestor, sibling,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                709,
+                                505,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        709,
+                                        505,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and shortest-paths distances and provide the edges where the distances are equal to 1 (including their",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                720,
+                                210,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        720,
+                                        210,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "edge types) to the model.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        }
+                    ],
+                    "index": 46.5
+                }
+            ],
+            "page_idx": 16,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        108,
+                        27,
+                        292,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                25,
+                                293,
+                                39
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        25,
+                                        293,
+                                        39
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        311,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                312,
+                                764
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        312,
+                                        764
+                                    ],
+                                    "score": 1.0,
+                                    "content": "17",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        82,
+                        429,
+                        94
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                81,
+                                430,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        81,
+                                        430,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.3.3 STAGE 2 PREPROCESSING (CALCULATION OF DISTANCE MATRICES)",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        129,
+                        99,
+                        505,
+                        122
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                129,
+                                98,
+                                505,
+                                112
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        129,
+                                        98,
+                                        505,
+                                        112
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1. Tokens are vocabularized. Any token occurring less than 100 times in the training set is",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                111,
+                                267,
+                                123
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        111,
+                                        231,
+                                        123
+                                    ],
+                                    "score": 1.0,
+                                    "content": "replaced by an <unk",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        231,
+                                        112,
+                                        239,
+                                        121
+                                    ],
+                                    "score": 0.45,
+                                    "content": ">",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        239,
+                                        111,
+                                        267,
+                                        123
+                                    ],
+                                    "score": 1.0,
+                                    "content": "token.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5,
+                    "bbox_fs": [
+                        129,
+                        98,
+                        505,
+                        123
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        130,
+                        126,
+                        422,
+                        137
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                129,
+                                125,
+                                422,
+                                139
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        129,
+                                        125,
+                                        422,
+                                        139
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2. We calculate multiple pair-wise relations between nodes in the AST:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 2,
+                    "bbox_fs": [
+                        129,
+                        125,
+                        422,
+                        139
+                    ]
+                },
+                {
+                    "type": "list",
+                    "bbox": [
+                        154,
+                        141,
+                        505,
+                        281
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                153,
+                                141,
+                                288,
+                                154
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        153,
+                                        141,
+                                        288,
+                                        154
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• Personalized Page Rank (PPR)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3,
+                            "is_list_start_line": true,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                161,
+                                152,
+                                504,
+                                165
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        161,
+                                        152,
+                                        504,
+                                        165
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We interpret the negative logarithm of PPR as a distance. We use a teleport probability",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                161,
+                                163,
+                                505,
+                                176
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        161,
+                                        163,
+                                        173,
+                                        176
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        173,
+                                        164,
+                                        212,
+                                        174
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\alpha = 0 . 1 5",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        212,
+                                        163,
+                                        287,
+                                        176
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and a threshold of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        288,
+                                        163,
+                                        303,
+                                        174
+                                    ],
+                                    "score": 0.89,
+                                    "content": "e ^ { - 5 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        163,
+                                        381,
+                                        176
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", i.e., anything with",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        382,
+                                        164,
+                                        449,
+                                        175
+                                    ],
+                                    "score": 0.89,
+                                    "content": "- \\log P P R > 5",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        450,
+                                        163,
+                                        505,
+                                        176
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is considered",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                162,
+                                176,
+                                213,
+                                185
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        162,
+                                        176,
+                                        213,
+                                        185
+                                    ],
+                                    "score": 1.0,
+                                    "content": "unreachable",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                155,
+                                188,
+                                323,
+                                199
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        155,
+                                        188,
+                                        323,
+                                        199
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• Shortest path length between two nodes",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7,
+                            "is_list_start_line": true,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                154,
+                                201,
+                                505,
+                                213
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        154,
+                                        201,
+                                        505,
+                                        213
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• Ancestor shortest paths (bidirectional). That is, the parent has an ancestor shortest",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                161,
+                                212,
+                                506,
+                                223
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        161,
+                                        212,
+                                        506,
+                                        223
+                                    ],
+                                    "score": 1.0,
+                                    "content": "path distance of 1 to all its children and the child has a distance of -1 to its parents. We",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                161,
+                                223,
+                                505,
+                                235
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        161,
+                                        223,
+                                        505,
+                                        235
+                                    ],
+                                    "score": 1.0,
+                                    "content": "consider nodes that are not ancestors or descendants of a node (i.e. not reachable by",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                162,
+                                234,
+                                506,
+                                246
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        162,
+                                        234,
+                                        506,
+                                        246
+                                    ],
+                                    "score": 1.0,
+                                    "content": "following only parent or only child relations) as not connected in the ancestor shortest",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                160,
+                                245,
+                                505,
+                                257
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        160,
+                                        245,
+                                        505,
+                                        257
+                                    ],
+                                    "score": 1.0,
+                                    "content": "paths relation. We encode this with a very large value in their distance; we have found",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                161,
+                                256,
+                                330,
+                                268
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        161,
+                                        257,
+                                        204,
+                                        268
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a value of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        204,
+                                        256,
+                                        230,
+                                        267
+                                    ],
+                                    "score": 0.25,
+                                    "content": "1 , 0 0 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        230,
+                                        257,
+                                        330,
+                                        268
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to work well in practice.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                154,
+                                268,
+                                493,
+                                281
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        154,
+                                        268,
+                                        493,
+                                        281
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• Next sibling shortest paths (bidirectional, analogous to the ancestor shortest paths)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14,
+                            "is_list_start_line": true
+                        }
+                    ],
+                    "index": 8.5,
+                    "bbox_fs": [
+                        153,
+                        141,
+                        506,
+                        281
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        142,
+                        285,
+                        504,
+                        373
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                141,
+                                284,
+                                505,
+                                297
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        284,
+                                        505,
+                                        297
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Note that the ancestor shortest paths and next sibling shortest paths are required because",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                295,
+                                506,
+                                309
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        295,
+                                        506,
+                                        309
+                                    ],
+                                    "score": 1.0,
+                                    "content": "treating the AST as a normal graph leads to ambiguity. In a graph, the neighbors of a node",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                307,
+                                505,
+                                319
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        307,
+                                        505,
+                                        319
+                                    ],
+                                    "score": 1.0,
+                                    "content": "have no ordering; however in the AST, the order of the children of a node reflects their",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                318,
+                                506,
+                                330
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        318,
+                                        506,
+                                        330
+                                    ],
+                                    "score": 1.0,
+                                    "content": "order in the code. Therefore, we explicitly include the next sibling shortest paths. The",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                329,
+                                505,
+                                341
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        329,
+                                        505,
+                                        341
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ancestor shortest paths would not be required if we treated the AST as a directed graph; in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                340,
+                                505,
+                                352
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        340,
+                                        505,
+                                        352
+                                    ],
+                                    "score": 1.0,
+                                    "content": "this case, however, a leaf node could not reach any other node in the AST, and therefore",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                350,
+                                506,
+                                363
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        350,
+                                        506,
+                                        363
+                                    ],
+                                    "score": 1.0,
+                                    "content": "both PPR and shortest path length are not useful in this case. Therefore, we model the AST",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                361,
+                                421,
+                                375
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        361,
+                                        421,
+                                        375
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as undirected and inject the ancestor / child edges to avoid ambiguity.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 18.5,
+                    "bbox_fs": [
+                        141,
+                        284,
+                        506,
+                        375
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        130,
+                        377,
+                        505,
+                        454
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                128,
+                                376,
+                                506,
+                                389
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        376,
+                                        506,
+                                        389
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3. Distance values are binned into 32 bins using area-based exponential binning with a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                388,
+                                505,
+                                401
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        388,
+                                        371,
+                                        401
+                                    ],
+                                    "score": 1.0,
+                                    "content": "growth factor of 1.3, i.e., the area of a bin’s rectangle (",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        371,
+                                        390,
+                                        378,
+                                        398
+                                    ],
+                                    "score": 0.48,
+                                    "content": "x",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        378,
+                                        388,
+                                        428,
+                                        401
+                                    ],
+                                    "score": 1.0,
+                                    "content": ": bin range,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        429,
+                                        390,
+                                        435,
+                                        400
+                                    ],
+                                    "score": 0.62,
+                                    "content": "y",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        435,
+                                        388,
+                                        505,
+                                        401
+                                    ],
+                                    "score": 1.0,
+                                    "content": ": number of val-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                399,
+                                505,
+                                411
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        399,
+                                        505,
+                                        411
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ues in bin) will be approximately 1.3 times bigger for the next bin (going away from the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                410,
+                                505,
+                                423
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        410,
+                                        505,
+                                        423
+                                    ],
+                                    "score": 1.0,
+                                    "content": "bin that contains the zero value). Additionally, for discrete distance measures (such as se-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                421,
+                                505,
+                                433
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        421,
+                                        505,
+                                        433
+                                    ],
+                                    "score": 1.0,
+                                    "content": "quence distance or shortest path length), we hard-code 9 values around 0 to have their own",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                432,
+                                505,
+                                444
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        432,
+                                        361,
+                                        444
+                                    ],
+                                    "score": 1.0,
+                                    "content": "bins. For instance, on the sequence distance the values",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        362,
+                                        432,
+                                        420,
+                                        443
+                                    ],
+                                    "score": 0.9,
+                                    "content": "- 4 , - 3 , \\dots , 4",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        420,
+                                        432,
+                                        505,
+                                        444
+                                    ],
+                                    "score": 1.0,
+                                    "content": "have their individual",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                441,
+                                407,
+                                457
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        441,
+                                        407,
+                                        457
+                                    ],
+                                    "score": 1.0,
+                                    "content": "bins, and around those values we employ the exponential binning.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 26,
+                    "bbox_fs": [
+                        128,
+                        376,
+                        506,
+                        457
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        131,
+                        459,
+                        504,
+                        492
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                128,
+                                457,
+                                505,
+                                471
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        457,
+                                        505,
+                                        471
+                                    ],
+                                    "score": 1.0,
+                                    "content": "4. Punctuation tokens (such as points or brackets) are removed from the input sequence, as",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                469,
+                                505,
+                                483
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        469,
+                                        505,
+                                        483
+                                    ],
+                                    "score": 1.0,
+                                    "content": "experiments showed that their presence does not improve performance but slows down",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                480,
+                                278,
+                                493
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        480,
+                                        278,
+                                        493
+                                    ],
+                                    "score": 1.0,
+                                    "content": "training due to bigger input sizes.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 31,
+                    "bbox_fs": [
+                        128,
+                        457,
+                        505,
+                        493
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        132,
+                        496,
+                        504,
+                        529
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                129,
+                                495,
+                                505,
+                                509
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        129,
+                                        495,
+                                        505,
+                                        509
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5. Snippets that are longer than MAX NUM TOKENS after punctuation tokens are removed are",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                507,
+                                505,
+                                519
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        507,
+                                        505,
+                                        519
+                                    ],
+                                    "score": 1.0,
+                                    "content": "discarded from the training set. Throughout our experiments, we use MAX NUM TOKENS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                518,
+                                468,
+                                529
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        518,
+                                        173,
+                                        529
+                                    ],
+                                    "score": 0.76,
+                                    "content": "= ~ 5 1 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        173,
+                                        518,
+                                        424,
+                                        529
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". During evaluation on the test set, we use MAX NUM TOKENS",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        424,
+                                        518,
+                                        464,
+                                        528
+                                    ],
+                                    "score": 0.76,
+                                    "content": "= ~ 1 0 0 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        464,
+                                        518,
+                                        468,
+                                        529
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        }
+                    ],
+                    "index": 34,
+                    "bbox_fs": [
+                        129,
+                        495,
+                        505,
+                        529
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        544,
+                        286,
+                        555
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                543,
+                                288,
+                                556
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        543,
+                                        288,
+                                        556
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.4 INPUT EMBEDDINGS TO THE MODEL",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 36
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        564,
+                        505,
+                        630
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                564,
+                                506,
+                                578
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        564,
+                                        506,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Besides its five subtokens (e.g., [‘get’, ‘data’, ‘[PAD]’, ‘[PAD]’, ‘[PAD]’]),",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                574,
+                                505,
+                                589
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        574,
+                                        505,
+                                        589
+                                    ],
+                                    "score": 1.0,
+                                    "content": "each input token has a token type (coming from the Pygments tokenizer) and an AST node type.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                586,
+                                505,
+                                599
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        586,
+                                        505,
+                                        599
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The AST node type is the type of the node assigned to each respective token, as described in Section",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                596,
+                                505,
+                                610
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        596,
+                                        505,
+                                        610
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.3.2. We concatenate the embeddings of the five subtokens, the token type, and the AST node",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                608,
+                                506,
+                                621
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        608,
+                                        506,
+                                        621
+                                    ],
+                                    "score": 1.0,
+                                    "content": "type. Then, we apply a linear layer (without activation function) to project down to the model’s",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                619,
+                                200,
+                                632
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        619,
+                                        200,
+                                        632
+                                    ],
+                                    "score": 1.0,
+                                    "content": "embedding dimension.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        }
+                    ],
+                    "index": 39.5,
+                    "bbox_fs": [
+                        105,
+                        564,
+                        506,
+                        632
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        644,
+                        275,
+                        656
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                644,
+                                277,
+                                657
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        644,
+                                        277,
+                                        657
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.5 INPUT TO THE GREAT BASELINE",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        }
+                    ],
+                    "index": 43
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        666,
+                        505,
+                        731
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                665,
+                                505,
+                                678
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        665,
+                                        505,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "As mentioned in the main text, we also compare with GREAT Hellendoorn et al. (2020). Since",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                676,
+                                505,
+                                689
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        676,
+                                        505,
+                                        689
+                                    ],
+                                    "score": 1.0,
+                                    "content": "their preprocessing pipeline is proprietary and could not be shared with us even after contacting the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                687,
+                                505,
+                                700
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        687,
+                                        505,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "authors, we provide to GREAT the same AST distances as our model. Since GREAT uses edges in-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                698,
+                                505,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        698,
+                                        505,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "stead of distances to encode relations in the Structure, we essentially threshold the ancestor, sibling,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                709,
+                                505,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        709,
+                                        505,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and shortest-paths distances and provide the edges where the distances are equal to 1 (including their",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                720,
+                                210,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        720,
+                                        210,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "edge types) to the model.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        }
+                    ],
+                    "index": 46.5,
+                    "bbox_fs": [
+                        105,
+                        665,
+                        505,
+                        733
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "table",
+                    "bbox": [
+                        167,
+                        97,
+                        296,
+                        198
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                182,
+                                86,
+                                280,
+                                96
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        182,
+                                        86,
+                                        281,
+                                        97
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                182,
+                                                86,
+                                                281,
+                                                97
+                                            ],
+                                            "score": 1.0,
+                                            "content": "(a) CODE TRANSFORMER",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 0
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                167,
+                                97,
+                                296,
+                                198
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        167,
+                                        97,
+                                        296,
+                                        198
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                167,
+                                                97,
+                                                296,
+                                                198
+                                            ],
+                                            "score": 0.968,
+                                            "html": "<table><tr><td>Hyperparameter</td><td>Value</td></tr><tr><td>Activation</td><td>GELU</td></tr><tr><td>Input Nonlinearity</td><td>tanh</td></tr><tr><td>Num. layers</td><td>3</td></tr><tr><td>d</td><td>1024</td></tr><tr><td>dFF</td><td>2048</td></tr><tr><td>Pdropout</td><td>0.2</td></tr><tr><td>Num.heads</td><td>8</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "26b079a48f72f11ac5901761fadc58949615f228994d83e0ca015c1b803de70e.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 3.5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        167,
+                                        97,
+                                        296,
+                                        147.5
+                                    ],
+                                    "spans": [],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        167,
+                                        147.5,
+                                        296,
+                                        198.0
+                                    ],
+                                    "spans": [],
+                                    "index": 4
+                                }
+                            ]
+                        },
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                210,
+                                207,
+                                401,
+                                219
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        209,
+                                        204,
+                                        401,
+                                        222
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                209,
+                                                204,
+                                                401,
+                                                222
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 7: Code Summarization hyperparameters",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 7
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 3.5
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        318,
+                        108,
+                        438,
+                        196
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                313,
+                                86,
+                                444,
+                                106
+                            ],
+                            "group_id": 1,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        312,
+                                        85,
+                                        446,
+                                        98
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                312,
+                                                85,
+                                                446,
+                                                98
+                                            ],
+                                            "score": 1.0,
+                                            "content": "(b) GREAT (Hellendoorn et al.,",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        311,
+                                        95,
+                                        338,
+                                        108
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                311,
+                                                95,
+                                                338,
+                                                108
+                                            ],
+                                            "score": 1.0,
+                                            "content": "2020)",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 2
+                                }
+                            ],
+                            "index": 1.5
+                        },
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                318,
+                                108,
+                                438,
+                                196
+                            ],
+                            "group_id": 1,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        318,
+                                        108,
+                                        438,
+                                        196
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                318,
+                                                108,
+                                                438,
+                                                196
+                                            ],
+                                            "score": 0.969,
+                                            "html": "<table><tr><td>Hyperparameter</td><td>Value</td></tr><tr><td>Activation</td><td>GELU</td></tr><tr><td>Num. layers</td><td>3</td></tr><tr><td>d</td><td>1024</td></tr><tr><td>dFF</td><td>2048</td></tr><tr><td>Pdropout</td><td>0.2</td></tr><tr><td>Num.heads</td><td>8</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "d450c7940cdf06f24a236ed0b2ea7649815a8d485cbb72d5b067d40223c84355.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 5.5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        318,
+                                        108,
+                                        438,
+                                        152.0
+                                    ],
+                                    "spans": [],
+                                    "index": 5
+                                },
+                                {
+                                    "bbox": [
+                                        318,
+                                        152.0,
+                                        438,
+                                        196.0
+                                    ],
+                                    "spans": [],
+                                    "index": 6
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        240,
+                        231,
+                        251
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                240,
+                                232,
+                                252
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        240,
+                                        232,
+                                        252
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.6 EXPERIMENTAL SETUP",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        260,
+                        505,
+                        316
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                260,
+                                505,
+                                273
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        260,
+                                        505,
+                                        273
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Table 7 shows hyperparameters of our models for code summarization. For all our experiments, we",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                271,
+                                505,
+                                284
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        271,
+                                        505,
+                                        284
+                                    ],
+                                    "score": 1.0,
+                                    "content": "use a Transformer Decoder with one layer and teacher forcing to generate 6 output sub tokens. We",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                282,
+                                506,
+                                295
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        282,
+                                        465,
+                                        295
+                                    ],
+                                    "score": 1.0,
+                                    "content": "also employ label smoothing of 0.1. As optimizer, we use Adam with a learning rate of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        465,
+                                        282,
+                                        487,
+                                        293
+                                    ],
+                                    "score": 0.9,
+                                    "content": "8 e ^ { - 5 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        487,
+                                        282,
+                                        506,
+                                        295
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                292,
+                                506,
+                                307
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        292,
+                                        174,
+                                        307
+                                    ],
+                                    "score": 1.0,
+                                    "content": "weight decay of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        174,
+                                        293,
+                                        195,
+                                        304
+                                    ],
+                                    "score": 0.9,
+                                    "content": "3 e ^ { - 5 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        195,
+                                        292,
+                                        506,
+                                        307
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Batch size during training is 8 with a simulated batch size of 128 achieved",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                305,
+                                212,
+                                316
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        305,
+                                        212,
+                                        316
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by gradient accumulation.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        332,
+                        503,
+                        354
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                331,
+                                505,
+                                345
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        331,
+                                        505,
+                                        345
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Apart from comparing the CODE TRANSFORMER to baselines, we performed the following hyper-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                344,
+                                285,
+                                356
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        344,
+                                        285,
+                                        356
+                                    ],
+                                    "score": 1.0,
+                                    "content": "parameter comparisons and ablation studies:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 14.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        133,
+                        365,
+                        505,
+                        531
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                136,
+                                364,
+                                303,
+                                376
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        136,
+                                        364,
+                                        303,
+                                        376
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• CODE TRANSFORMER (structure-only)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                375,
+                                506,
+                                387
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        375,
+                                        506,
+                                        387
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Using only AST information as input, i.e., masking all tokens that do not correspond to a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                387,
+                                505,
+                                398
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        387,
+                                        505,
+                                        398
+                                    ],
+                                    "score": 1.0,
+                                    "content": "leaf of the AST, and removing the token distance as a relation to be used by the model.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                397,
+                                332,
+                                409
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        397,
+                                        332,
+                                        409
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Further, token types are not fed into the model.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                136,
+                                411,
+                                297,
+                                424
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        136,
+                                        411,
+                                        297,
+                                        424
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• CODE TRANSFORMER (context-only)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                423,
+                                505,
+                                434
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        423,
+                                        505,
+                                        434
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Here, we do not include any information on the AST (i.e. node types and distances on the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                433,
+                                505,
+                                447
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        433,
+                                        505,
+                                        447
+                                    ],
+                                    "score": 1.0,
+                                    "content": "AST). This is effectively the XLNet backbone plus encoding of the token type returned by",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                445,
+                                198,
+                                457
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        445,
+                                        198,
+                                        457
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the tokenizer.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                136,
+                                459,
+                                288,
+                                472
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        136,
+                                        459,
+                                        288,
+                                        472
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• CODE TRANSFORMER (Max-Dist.)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                471,
+                                506,
+                                483
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        471,
+                                        506,
+                                        483
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Applying a Max Distance Mask of 5 to the shortest paths distance (i.e., model cannot see",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                140,
+                                481,
+                                505,
+                                495
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        140,
+                                        481,
+                                        505,
+                                        495
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a node that is more than 5 hops away no matter how small the other distances are). Early",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                494,
+                                505,
+                                504
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        494,
+                                        505,
+                                        504
+                                    ],
+                                    "score": 1.0,
+                                    "content": "results showed that, as expected, results deteriorate substantially when limiting our model’s",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                504,
+                                412,
+                                515
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        504,
+                                        412,
+                                        515
+                                    ],
+                                    "score": 1.0,
+                                    "content": "receptive field. Hence, we do not include these results in this work.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                132,
+                                518,
+                                492,
+                                532
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        132,
+                                        518,
+                                        492,
+                                        532
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• Using 16 and 64 bins instead of 32 bins. This had no noticeable effect on performance.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 22.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        109,
+                        544,
+                        283,
+                        555
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                543,
+                                284,
+                                556
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        543,
+                                        284,
+                                        556
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.7 CODE SUMMARIZATION EXAMPLES",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 30
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        564,
+                        505,
+                        587
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                564,
+                                504,
+                                576
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        564,
+                                        504,
+                                        576
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In the Tables 8, 9, 10, 11, 12, 13, 14 and 15 we present example functions from the Java-small",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                574,
+                                405,
+                                588
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        574,
+                                        405,
+                                        588
+                                    ],
+                                    "score": 1.0,
+                                    "content": "dataset along with the different models’ predictions for the function name.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 31.5
+                }
+            ],
+            "page_idx": 17,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        292,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                293,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        293,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        311,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                313,
+                                763
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        313,
+                                        763
+                                    ],
+                                    "score": 1.0,
+                                    "content": "18",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "table",
+                    "bbox": [
+                        167,
+                        97,
+                        296,
+                        198
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                182,
+                                86,
+                                280,
+                                96
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        182,
+                                        86,
+                                        281,
+                                        97
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                182,
+                                                86,
+                                                281,
+                                                97
+                                            ],
+                                            "score": 1.0,
+                                            "content": "(a) CODE TRANSFORMER",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 0
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                167,
+                                97,
+                                296,
+                                198
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        167,
+                                        97,
+                                        296,
+                                        198
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                167,
+                                                97,
+                                                296,
+                                                198
+                                            ],
+                                            "score": 0.968,
+                                            "html": "<table><tr><td>Hyperparameter</td><td>Value</td></tr><tr><td>Activation</td><td>GELU</td></tr><tr><td>Input Nonlinearity</td><td>tanh</td></tr><tr><td>Num. layers</td><td>3</td></tr><tr><td>d</td><td>1024</td></tr><tr><td>dFF</td><td>2048</td></tr><tr><td>Pdropout</td><td>0.2</td></tr><tr><td>Num.heads</td><td>8</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "26b079a48f72f11ac5901761fadc58949615f228994d83e0ca015c1b803de70e.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 3.5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        167,
+                                        97,
+                                        296,
+                                        147.5
+                                    ],
+                                    "spans": [],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        167,
+                                        147.5,
+                                        296,
+                                        198.0
+                                    ],
+                                    "spans": [],
+                                    "index": 4
+                                }
+                            ]
+                        },
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                210,
+                                207,
+                                401,
+                                219
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        209,
+                                        204,
+                                        401,
+                                        222
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                209,
+                                                204,
+                                                401,
+                                                222
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 7: Code Summarization hyperparameters",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 7
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 3.5
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        318,
+                        108,
+                        438,
+                        196
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                313,
+                                86,
+                                444,
+                                106
+                            ],
+                            "group_id": 1,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        312,
+                                        85,
+                                        446,
+                                        98
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                312,
+                                                85,
+                                                446,
+                                                98
+                                            ],
+                                            "score": 1.0,
+                                            "content": "(b) GREAT (Hellendoorn et al.,",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        311,
+                                        95,
+                                        338,
+                                        108
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                311,
+                                                95,
+                                                338,
+                                                108
+                                            ],
+                                            "score": 1.0,
+                                            "content": "2020)",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 2
+                                }
+                            ],
+                            "index": 1.5
+                        },
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                318,
+                                108,
+                                438,
+                                196
+                            ],
+                            "group_id": 1,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        318,
+                                        108,
+                                        438,
+                                        196
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                318,
+                                                108,
+                                                438,
+                                                196
+                                            ],
+                                            "score": 0.969,
+                                            "html": "<table><tr><td>Hyperparameter</td><td>Value</td></tr><tr><td>Activation</td><td>GELU</td></tr><tr><td>Num. layers</td><td>3</td></tr><tr><td>d</td><td>1024</td></tr><tr><td>dFF</td><td>2048</td></tr><tr><td>Pdropout</td><td>0.2</td></tr><tr><td>Num.heads</td><td>8</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "d450c7940cdf06f24a236ed0b2ea7649815a8d485cbb72d5b067d40223c84355.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 5.5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        318,
+                                        108,
+                                        438,
+                                        152.0
+                                    ],
+                                    "spans": [],
+                                    "index": 5
+                                },
+                                {
+                                    "bbox": [
+                                        318,
+                                        152.0,
+                                        438,
+                                        196.0
+                                    ],
+                                    "spans": [],
+                                    "index": 6
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        240,
+                        231,
+                        251
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                240,
+                                232,
+                                252
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        240,
+                                        232,
+                                        252
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.6 EXPERIMENTAL SETUP",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        260,
+                        505,
+                        316
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                260,
+                                505,
+                                273
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        260,
+                                        505,
+                                        273
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Table 7 shows hyperparameters of our models for code summarization. For all our experiments, we",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                271,
+                                505,
+                                284
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        271,
+                                        505,
+                                        284
+                                    ],
+                                    "score": 1.0,
+                                    "content": "use a Transformer Decoder with one layer and teacher forcing to generate 6 output sub tokens. We",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                282,
+                                506,
+                                295
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        282,
+                                        465,
+                                        295
+                                    ],
+                                    "score": 1.0,
+                                    "content": "also employ label smoothing of 0.1. As optimizer, we use Adam with a learning rate of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        465,
+                                        282,
+                                        487,
+                                        293
+                                    ],
+                                    "score": 0.9,
+                                    "content": "8 e ^ { - 5 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        487,
+                                        282,
+                                        506,
+                                        295
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                292,
+                                506,
+                                307
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        292,
+                                        174,
+                                        307
+                                    ],
+                                    "score": 1.0,
+                                    "content": "weight decay of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        174,
+                                        293,
+                                        195,
+                                        304
+                                    ],
+                                    "score": 0.9,
+                                    "content": "3 e ^ { - 5 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        195,
+                                        292,
+                                        506,
+                                        307
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Batch size during training is 8 with a simulated batch size of 128 achieved",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                305,
+                                212,
+                                316
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        305,
+                                        212,
+                                        316
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by gradient accumulation.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 11,
+                    "bbox_fs": [
+                        105,
+                        260,
+                        506,
+                        316
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        332,
+                        503,
+                        354
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                331,
+                                505,
+                                345
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        331,
+                                        505,
+                                        345
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Apart from comparing the CODE TRANSFORMER to baselines, we performed the following hyper-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                344,
+                                285,
+                                356
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        344,
+                                        285,
+                                        356
+                                    ],
+                                    "score": 1.0,
+                                    "content": "parameter comparisons and ablation studies:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 14.5,
+                    "bbox_fs": [
+                        106,
+                        331,
+                        505,
+                        356
+                    ]
+                },
+                {
+                    "type": "list",
+                    "bbox": [
+                        133,
+                        365,
+                        505,
+                        531
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                136,
+                                364,
+                                303,
+                                376
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        136,
+                                        364,
+                                        303,
+                                        376
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• CODE TRANSFORMER (structure-only)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16,
+                            "is_list_start_line": true,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                375,
+                                506,
+                                387
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        375,
+                                        506,
+                                        387
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Using only AST information as input, i.e., masking all tokens that do not correspond to a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                387,
+                                505,
+                                398
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        387,
+                                        505,
+                                        398
+                                    ],
+                                    "score": 1.0,
+                                    "content": "leaf of the AST, and removing the token distance as a relation to be used by the model.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                397,
+                                332,
+                                409
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        397,
+                                        332,
+                                        409
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Further, token types are not fed into the model.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                136,
+                                411,
+                                297,
+                                424
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        136,
+                                        411,
+                                        297,
+                                        424
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• CODE TRANSFORMER (context-only)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20,
+                            "is_list_start_line": true,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                423,
+                                505,
+                                434
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        423,
+                                        505,
+                                        434
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Here, we do not include any information on the AST (i.e. node types and distances on the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                433,
+                                505,
+                                447
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        433,
+                                        505,
+                                        447
+                                    ],
+                                    "score": 1.0,
+                                    "content": "AST). This is effectively the XLNet backbone plus encoding of the token type returned by",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                445,
+                                198,
+                                457
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        445,
+                                        198,
+                                        457
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the tokenizer.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                136,
+                                459,
+                                288,
+                                472
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        136,
+                                        459,
+                                        288,
+                                        472
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• CODE TRANSFORMER (Max-Dist.)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24,
+                            "is_list_start_line": true,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                471,
+                                506,
+                                483
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        471,
+                                        506,
+                                        483
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Applying a Max Distance Mask of 5 to the shortest paths distance (i.e., model cannot see",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                140,
+                                481,
+                                505,
+                                495
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        140,
+                                        481,
+                                        505,
+                                        495
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a node that is more than 5 hops away no matter how small the other distances are). Early",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                494,
+                                505,
+                                504
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        494,
+                                        505,
+                                        504
+                                    ],
+                                    "score": 1.0,
+                                    "content": "results showed that, as expected, results deteriorate substantially when limiting our model’s",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                504,
+                                412,
+                                515
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        504,
+                                        412,
+                                        515
+                                    ],
+                                    "score": 1.0,
+                                    "content": "receptive field. Hence, we do not include these results in this work.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                132,
+                                518,
+                                492,
+                                532
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        132,
+                                        518,
+                                        492,
+                                        532
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• Using 16 and 64 bins instead of 32 bins. This had no noticeable effect on performance.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29,
+                            "is_list_start_line": true,
+                            "is_list_end_line": true
+                        }
+                    ],
+                    "index": 22.5,
+                    "bbox_fs": [
+                        132,
+                        364,
+                        506,
+                        532
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        109,
+                        544,
+                        283,
+                        555
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                543,
+                                284,
+                                556
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        543,
+                                        284,
+                                        556
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.7 CODE SUMMARIZATION EXAMPLES",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 30
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        564,
+                        505,
+                        587
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                564,
+                                504,
+                                576
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        564,
+                                        504,
+                                        576
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In the Tables 8, 9, 10, 11, 12, 13, 14 and 15 we present example functions from the Java-small",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                574,
+                                405,
+                                588
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        574,
+                                        405,
+                                        588
+                                    ],
+                                    "score": 1.0,
+                                    "content": "dataset along with the different models’ predictions for the function name.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 31.5,
+                    "bbox_fs": [
+                        105,
+                        564,
+                        504,
+                        588
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        94,
+                        242,
+                        124
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                94,
+                                244,
+                                105
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        94,
+                                        244,
+                                        105
+                                    ],
+                                    "score": 1.0,
+                                    "content": "public Summation next() {",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                105,
+                                225,
+                                114
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        105,
+                                        195,
+                                        114
+                                    ],
+                                    "score": 1.0,
+                                    "content": "return parts",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        195,
+                                        105,
+                                        219,
+                                        114
+                                    ],
+                                    "score": 0.41,
+                                    "content": "[ \\dot { 1 } + + ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        220,
+                                        105,
+                                        225,
+                                        114
+                                    ],
+                                    "score": 1.0,
+                                    "content": ";",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                108,
+                                117,
+                                113,
+                                124
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        108,
+                                        117,
+                                        113,
+                                        124
+                                    ],
+                                    "score": 1.0,
+                                    "content": "}",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        231,
+                        128,
+                        378,
+                        205
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                231,
+                                128,
+                                378,
+                                205
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        231,
+                                        128,
+                                        378,
+                                        205
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                231,
+                                                128,
+                                                378,
+                                                205
+                                            ],
+                                            "score": 0.969,
+                                            "html": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td> get x map</td></tr><tr><td>code2seq</td><td> get parts</td></tr><tr><td>Ours w/o structure</td><td>get</td></tr><tr><td>CODE TRANSFORMER</td><td>get next</td></tr><tr><td>Ground Truth</td><td>next</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "04303ffb667966783611a78b38db4a06a17d54b3303576e3d6f2082eb78c4e3f.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 3.5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        231,
+                                        128,
+                                        378,
+                                        166.5
+                                    ],
+                                    "spans": [],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        231,
+                                        166.5,
+                                        378,
+                                        205.0
+                                    ],
+                                    "spans": [],
+                                    "index": 4
+                                }
+                            ]
+                        },
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                106,
+                                214,
+                                504,
+                                236
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        213,
+                                        505,
+                                        226
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                213,
+                                                505,
+                                                226
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 8: The CODE TRANSFORMER is the only model to correctly identify the notion of getting the",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 5
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        226,
+                                        151,
+                                        237
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                226,
+                                                151,
+                                                237
+                                            ],
+                                            "score": 1.0,
+                                            "content": "next entry.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 6
+                                }
+                            ],
+                            "index": 5.5
+                        }
+                    ],
+                    "index": 4.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        272,
+                        453,
+                        370
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                272,
+                                453,
+                                285
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        272,
+                                        453,
+                                        285
+                                    ],
+                                    "score": 1.0,
+                                    "content": "private Path findCacheFile(Path[] cacheFiles, String fileName) {",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                282,
+                                400,
+                                294
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        282,
+                                        210,
+                                        294
+                                    ],
+                                    "score": 1.0,
+                                    "content": "if (cacheFiles",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        210,
+                                        284,
+                                        222,
+                                        292
+                                    ],
+                                    "score": 0.69,
+                                    "content": "! =",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        223,
+                                        282,
+                                        362,
+                                        294
+                                    ],
+                                    "score": 1.0,
+                                    "content": "null && cacheFiles.length",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        363,
+                                        283,
+                                        383,
+                                        293
+                                    ],
+                                    "score": 0.41,
+                                    "content": "> 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        383,
+                                        282,
+                                        400,
+                                        294
+                                    ],
+                                    "score": 1.0,
+                                    "content": ") {",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                149,
+                                292,
+                                314,
+                                303
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        149,
+                                        292,
+                                        169,
+                                        303
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        172,
+                                        293,
+                                        314,
+                                        303
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(Path file : cacheFiles) {",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                171,
+                                303,
+                                378,
+                                313
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        171,
+                                        303,
+                                        185,
+                                        312
+                                    ],
+                                    "score": 1.0,
+                                    "content": "if",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        187,
+                                        303,
+                                        378,
+                                        313
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(file.getName().equals(fileName)) {",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                192,
+                                312,
+                                259,
+                                324
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        192,
+                                        312,
+                                        259,
+                                        324
+                                    ],
+                                    "score": 1.0,
+                                    "content": "return file;",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                171,
+                                324,
+                                178,
+                                333
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        171,
+                                        324,
+                                        178,
+                                        333
+                                    ],
+                                    "score": 1.0,
+                                    "content": "}",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                352,
+                                192,
+                                363
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        352,
+                                        192,
+                                        363
+                                    ],
+                                    "score": 1.0,
+                                    "content": "return null;",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                108,
+                                365,
+                                113,
+                                371
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        108,
+                                        365,
+                                        113,
+                                        371
+                                    ],
+                                    "score": 1.0,
+                                    "content": "}",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 10.5
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        225,
+                        376,
+                        385,
+                        454
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                225,
+                                376,
+                                385,
+                                454
+                            ],
+                            "group_id": 1,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        225,
+                                        376,
+                                        385,
+                                        454
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                225,
+                                                376,
+                                                385,
+                                                454
+                                            ],
+                                            "score": 0.908,
+                                            "html": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td>get path</td></tr><tr><td>code2seq</td><td>find file</td></tr><tr><td>Ours w/o structure</td><td>get file</td></tr><tr><td>CODE TRANSFORMER</td><td>find cache</td></tr><tr><td>Ground Truth</td><td>find cache file</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "7fce10876c7dbfae8cd1529bce06e79b9baef638e4b20f560a956fd0593414a7.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 18,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        225,
+                                        376,
+                                        385,
+                                        387.14285714285717
+                                    ],
+                                    "spans": [],
+                                    "index": 15
+                                },
+                                {
+                                    "bbox": [
+                                        225,
+                                        387.14285714285717,
+                                        385,
+                                        398.28571428571433
+                                    ],
+                                    "spans": [],
+                                    "index": 16
+                                },
+                                {
+                                    "bbox": [
+                                        225,
+                                        398.28571428571433,
+                                        385,
+                                        409.4285714285715
+                                    ],
+                                    "spans": [],
+                                    "index": 17
+                                },
+                                {
+                                    "bbox": [
+                                        225,
+                                        409.4285714285715,
+                                        385,
+                                        420.57142857142867
+                                    ],
+                                    "spans": [],
+                                    "index": 18
+                                },
+                                {
+                                    "bbox": [
+                                        225,
+                                        420.57142857142867,
+                                        385,
+                                        431.71428571428584
+                                    ],
+                                    "spans": [],
+                                    "index": 19
+                                },
+                                {
+                                    "bbox": [
+                                        225,
+                                        431.71428571428584,
+                                        385,
+                                        442.857142857143
+                                    ],
+                                    "spans": [],
+                                    "index": 20
+                                },
+                                {
+                                    "bbox": [
+                                        225,
+                                        442.857142857143,
+                                        385,
+                                        454.00000000000017
+                                    ],
+                                    "spans": [],
+                                    "index": 21
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        462,
+                        506,
+                        495
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                461,
+                                505,
+                                474
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        461,
+                                        505,
+                                        474
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Table 9: The CODE TRANSFORMER is the only model to both recognize that the task is to find a file",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                473,
+                                505,
+                                486
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        473,
+                                        505,
+                                        486
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as well as the fact that it is about the cache. However, it did not correctly predict the file part of the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                483,
+                                165,
+                                496
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        483,
+                                        165,
+                                        496
+                                    ],
+                                    "score": 1.0,
+                                    "content": "method name.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 23
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        532,
+                        458,
+                        601
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                531,
+                                398,
+                                543
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        531,
+                                        398,
+                                        543
+                                    ],
+                                    "score": 1.0,
+                                    "content": "public int compare(Pair<LoggedJob, JobTraceReader> p1,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                208,
+                                542,
+                                410,
+                                553
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        208,
+                                        542,
+                                        410,
+                                        553
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Pair<LoggedJob, JobTraceReader> p2) {",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                551,
+                                270,
+                                563
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        551,
+                                        182,
+                                        563
+                                    ],
+                                    "score": 1.0,
+                                    "content": "LoggedJob",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        182,
+                                        552,
+                                        221,
+                                        562
+                                    ],
+                                    "score": 0.57,
+                                    "content": "\\ j 1 \\ = \\ \\mathtt { p 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        221,
+                                        551,
+                                        270,
+                                        563
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".first();",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                562,
+                                270,
+                                573
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        562,
+                                        182,
+                                        573
+                                    ],
+                                    "score": 1.0,
+                                    "content": "LoggedJob",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        182,
+                                        563,
+                                        221,
+                                        572
+                                    ],
+                                    "score": 0.51,
+                                    "content": "\\begin{array} { r } { \\dot { \\bf { \\ j } } 2 { \\bf { \\nu } } = { \\bf { \\ p } } 2 } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        221,
+                                        562,
+                                        270,
+                                        573
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".first();",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                129,
+                                572,
+                                415,
+                                583
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        129,
+                                        573,
+                                        163,
+                                        582
+                                    ],
+                                    "score": 1.0,
+                                    "content": "return",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        166,
+                                        572,
+                                        272,
+                                        583
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(j1.getSubmitTime()",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        272,
+                                        573,
+                                        282,
+                                        581
+                                    ],
+                                    "score": 0.54,
+                                    "content": "<",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        282,
+                                        572,
+                                        415,
+                                        583
+                                    ],
+                                    "score": 1.0,
+                                    "content": "j2.getSubmitTime()) ? -1",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                170,
+                                582,
+                                457,
+                                593
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        170,
+                                        582,
+                                        288,
+                                        593
+                                    ],
+                                    "score": 1.0,
+                                    "content": ": (j1.getSubmitTime()",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        288,
+                                        583,
+                                        303,
+                                        592
+                                    ],
+                                    "score": 0.35,
+                                    "content": "= =",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        582,
+                                        457,
+                                        593
+                                    ],
+                                    "score": 1.0,
+                                    "content": "j2.getSubmitTime()) ? 0 : 1;",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                593,
+                                135,
+                                602
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        593,
+                                        135,
+                                        602
+                                    ],
+                                    "score": 1.0,
+                                    "content": "}",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        }
+                    ],
+                    "index": 28
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        221,
+                        606,
+                        388,
+                        684
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                221,
+                                606,
+                                388,
+                                684
+                            ],
+                            "group_id": 2,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        221,
+                                        606,
+                                        388,
+                                        684
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                221,
+                                                606,
+                                                388,
+                                                684
+                                            ],
+                                            "score": 0.96,
+                                            "html": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td>run</td></tr><tr><td>code2seq</td><td> get submit time</td></tr><tr><td>Ours w/o structure</td><td>compare</td></tr><tr><td>CODE TRANSFORMER</td><td>compare</td></tr><tr><td>Ground Truth</td><td>compare</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "fc7647e7d39190fcddd6003a2621a01161522b4db1837436041dcd5808f7523b.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 35,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        221,
+                                        606,
+                                        388,
+                                        617.1428571428571
+                                    ],
+                                    "spans": [],
+                                    "index": 32
+                                },
+                                {
+                                    "bbox": [
+                                        221,
+                                        617.1428571428571,
+                                        388,
+                                        628.2857142857142
+                                    ],
+                                    "spans": [],
+                                    "index": 33
+                                },
+                                {
+                                    "bbox": [
+                                        221,
+                                        628.2857142857142,
+                                        388,
+                                        639.4285714285713
+                                    ],
+                                    "spans": [],
+                                    "index": 34
+                                },
+                                {
+                                    "bbox": [
+                                        221,
+                                        639.4285714285713,
+                                        388,
+                                        650.5714285714284
+                                    ],
+                                    "spans": [],
+                                    "index": 35
+                                },
+                                {
+                                    "bbox": [
+                                        221,
+                                        650.5714285714284,
+                                        388,
+                                        661.7142857142856
+                                    ],
+                                    "spans": [],
+                                    "index": 36
+                                },
+                                {
+                                    "bbox": [
+                                        221,
+                                        661.7142857142856,
+                                        388,
+                                        672.8571428571427
+                                    ],
+                                    "spans": [],
+                                    "index": 37
+                                },
+                                {
+                                    "bbox": [
+                                        221,
+                                        672.8571428571427,
+                                        388,
+                                        683.9999999999998
+                                    ],
+                                    "spans": [],
+                                    "index": 38
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 35
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        691,
+                        504,
+                        714
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                689,
+                                505,
+                                705
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        689,
+                                        505,
+                                        705
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Table 10: The CODE TRANSFORMER and the its context-only variant are the only models correctly",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                702,
+                                333,
+                                716
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        702,
+                                        333,
+                                        716
+                                    ],
+                                    "score": 1.0,
+                                    "content": "recognizing the ‘compare’ template in the method body.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        }
+                    ],
+                    "index": 39.5
+                }
+            ],
+            "page_idx": 18,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        292,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                293,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        293,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        311,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                313,
+                                765
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        313,
+                                        765
+                                    ],
+                                    "score": 1.0,
+                                    "content": "",
+                                    "type": "text",
+                                    "height": 15,
+                                    "width": 14
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        94,
+                        242,
+                        124
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                94,
+                                244,
+                                105
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        94,
+                                        244,
+                                        105
+                                    ],
+                                    "score": 1.0,
+                                    "content": "public Summation next() {",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                105,
+                                225,
+                                114
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        105,
+                                        195,
+                                        114
+                                    ],
+                                    "score": 1.0,
+                                    "content": "return parts",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        195,
+                                        105,
+                                        219,
+                                        114
+                                    ],
+                                    "score": 0.41,
+                                    "content": "[ \\dot { 1 } + + ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        220,
+                                        105,
+                                        225,
+                                        114
+                                    ],
+                                    "score": 1.0,
+                                    "content": ";",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                108,
+                                117,
+                                113,
+                                124
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        108,
+                                        117,
+                                        113,
+                                        124
+                                    ],
+                                    "score": 1.0,
+                                    "content": "}",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1,
+                    "bbox_fs": [
+                        105,
+                        94,
+                        244,
+                        124
+                    ]
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        231,
+                        128,
+                        378,
+                        205
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                231,
+                                128,
+                                378,
+                                205
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        231,
+                                        128,
+                                        378,
+                                        205
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                231,
+                                                128,
+                                                378,
+                                                205
+                                            ],
+                                            "score": 0.969,
+                                            "html": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td> get x map</td></tr><tr><td>code2seq</td><td> get parts</td></tr><tr><td>Ours w/o structure</td><td>get</td></tr><tr><td>CODE TRANSFORMER</td><td>get next</td></tr><tr><td>Ground Truth</td><td>next</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "04303ffb667966783611a78b38db4a06a17d54b3303576e3d6f2082eb78c4e3f.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 3.5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        231,
+                                        128,
+                                        378,
+                                        166.5
+                                    ],
+                                    "spans": [],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        231,
+                                        166.5,
+                                        378,
+                                        205.0
+                                    ],
+                                    "spans": [],
+                                    "index": 4
+                                }
+                            ]
+                        },
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                106,
+                                214,
+                                504,
+                                236
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        213,
+                                        505,
+                                        226
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                213,
+                                                505,
+                                                226
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 8: The CODE TRANSFORMER is the only model to correctly identify the notion of getting the",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 5
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        226,
+                                        151,
+                                        237
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                226,
+                                                151,
+                                                237
+                                            ],
+                                            "score": 1.0,
+                                            "content": "next entry.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 6
+                                }
+                            ],
+                            "index": 5.5
+                        }
+                    ],
+                    "index": 4.5
+                },
+                {
+                    "type": "list",
+                    "bbox": [
+                        106,
+                        272,
+                        453,
+                        370
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                272,
+                                453,
+                                285
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        272,
+                                        453,
+                                        285
+                                    ],
+                                    "score": 1.0,
+                                    "content": "private Path findCacheFile(Path[] cacheFiles, String fileName) {",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                282,
+                                400,
+                                294
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        282,
+                                        210,
+                                        294
+                                    ],
+                                    "score": 1.0,
+                                    "content": "if (cacheFiles",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        210,
+                                        284,
+                                        222,
+                                        292
+                                    ],
+                                    "score": 0.69,
+                                    "content": "! =",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        223,
+                                        282,
+                                        362,
+                                        294
+                                    ],
+                                    "score": 1.0,
+                                    "content": "null && cacheFiles.length",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        363,
+                                        283,
+                                        383,
+                                        293
+                                    ],
+                                    "score": 0.41,
+                                    "content": "> 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        383,
+                                        282,
+                                        400,
+                                        294
+                                    ],
+                                    "score": 1.0,
+                                    "content": ") {",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                149,
+                                292,
+                                314,
+                                303
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        149,
+                                        292,
+                                        169,
+                                        303
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        172,
+                                        293,
+                                        314,
+                                        303
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(Path file : cacheFiles) {",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                171,
+                                303,
+                                378,
+                                313
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        171,
+                                        303,
+                                        185,
+                                        312
+                                    ],
+                                    "score": 1.0,
+                                    "content": "if",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        187,
+                                        303,
+                                        378,
+                                        313
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(file.getName().equals(fileName)) {",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                192,
+                                312,
+                                259,
+                                324
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        192,
+                                        312,
+                                        259,
+                                        324
+                                    ],
+                                    "score": 1.0,
+                                    "content": "return file;",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                171,
+                                324,
+                                178,
+                                333
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        171,
+                                        324,
+                                        178,
+                                        333
+                                    ],
+                                    "score": 1.0,
+                                    "content": "}",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                352,
+                                192,
+                                363
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        352,
+                                        192,
+                                        363
+                                    ],
+                                    "score": 1.0,
+                                    "content": "return null;",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                108,
+                                365,
+                                113,
+                                371
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        108,
+                                        365,
+                                        113,
+                                        371
+                                    ],
+                                    "score": 1.0,
+                                    "content": "}",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14,
+                            "is_list_start_line": true,
+                            "is_list_end_line": true
+                        }
+                    ],
+                    "index": 10.5,
+                    "bbox_fs": [
+                        104,
+                        272,
+                        453,
+                        371
+                    ]
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        225,
+                        376,
+                        385,
+                        454
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                225,
+                                376,
+                                385,
+                                454
+                            ],
+                            "group_id": 1,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        225,
+                                        376,
+                                        385,
+                                        454
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                225,
+                                                376,
+                                                385,
+                                                454
+                                            ],
+                                            "score": 0.908,
+                                            "html": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td>get path</td></tr><tr><td>code2seq</td><td>find file</td></tr><tr><td>Ours w/o structure</td><td>get file</td></tr><tr><td>CODE TRANSFORMER</td><td>find cache</td></tr><tr><td>Ground Truth</td><td>find cache file</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "7fce10876c7dbfae8cd1529bce06e79b9baef638e4b20f560a956fd0593414a7.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 18,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        225,
+                                        376,
+                                        385,
+                                        387.14285714285717
+                                    ],
+                                    "spans": [],
+                                    "index": 15
+                                },
+                                {
+                                    "bbox": [
+                                        225,
+                                        387.14285714285717,
+                                        385,
+                                        398.28571428571433
+                                    ],
+                                    "spans": [],
+                                    "index": 16
+                                },
+                                {
+                                    "bbox": [
+                                        225,
+                                        398.28571428571433,
+                                        385,
+                                        409.4285714285715
+                                    ],
+                                    "spans": [],
+                                    "index": 17
+                                },
+                                {
+                                    "bbox": [
+                                        225,
+                                        409.4285714285715,
+                                        385,
+                                        420.57142857142867
+                                    ],
+                                    "spans": [],
+                                    "index": 18
+                                },
+                                {
+                                    "bbox": [
+                                        225,
+                                        420.57142857142867,
+                                        385,
+                                        431.71428571428584
+                                    ],
+                                    "spans": [],
+                                    "index": 19
+                                },
+                                {
+                                    "bbox": [
+                                        225,
+                                        431.71428571428584,
+                                        385,
+                                        442.857142857143
+                                    ],
+                                    "spans": [],
+                                    "index": 20
+                                },
+                                {
+                                    "bbox": [
+                                        225,
+                                        442.857142857143,
+                                        385,
+                                        454.00000000000017
+                                    ],
+                                    "spans": [],
+                                    "index": 21
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        462,
+                        506,
+                        495
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                461,
+                                505,
+                                474
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        461,
+                                        505,
+                                        474
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Table 9: The CODE TRANSFORMER is the only model to both recognize that the task is to find a file",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                473,
+                                505,
+                                486
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        473,
+                                        505,
+                                        486
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as well as the fact that it is about the cache. However, it did not correctly predict the file part of the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                483,
+                                165,
+                                496
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        483,
+                                        165,
+                                        496
+                                    ],
+                                    "score": 1.0,
+                                    "content": "method name.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 23,
+                    "bbox_fs": [
+                        105,
+                        461,
+                        505,
+                        496
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        532,
+                        458,
+                        601
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                531,
+                                398,
+                                543
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        531,
+                                        398,
+                                        543
+                                    ],
+                                    "score": 1.0,
+                                    "content": "public int compare(Pair<LoggedJob, JobTraceReader> p1,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                208,
+                                542,
+                                410,
+                                553
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        208,
+                                        542,
+                                        410,
+                                        553
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Pair<LoggedJob, JobTraceReader> p2) {",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                551,
+                                270,
+                                563
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        551,
+                                        182,
+                                        563
+                                    ],
+                                    "score": 1.0,
+                                    "content": "LoggedJob",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        182,
+                                        552,
+                                        221,
+                                        562
+                                    ],
+                                    "score": 0.57,
+                                    "content": "\\ j 1 \\ = \\ \\mathtt { p 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        221,
+                                        551,
+                                        270,
+                                        563
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".first();",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                562,
+                                270,
+                                573
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        562,
+                                        182,
+                                        573
+                                    ],
+                                    "score": 1.0,
+                                    "content": "LoggedJob",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        182,
+                                        563,
+                                        221,
+                                        572
+                                    ],
+                                    "score": 0.51,
+                                    "content": "\\begin{array} { r } { \\dot { \\bf { \\ j } } 2 { \\bf { \\nu } } = { \\bf { \\ p } } 2 } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        221,
+                                        562,
+                                        270,
+                                        573
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".first();",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                129,
+                                572,
+                                415,
+                                583
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        129,
+                                        573,
+                                        163,
+                                        582
+                                    ],
+                                    "score": 1.0,
+                                    "content": "return",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        166,
+                                        572,
+                                        272,
+                                        583
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(j1.getSubmitTime()",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        272,
+                                        573,
+                                        282,
+                                        581
+                                    ],
+                                    "score": 0.54,
+                                    "content": "<",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        282,
+                                        572,
+                                        415,
+                                        583
+                                    ],
+                                    "score": 1.0,
+                                    "content": "j2.getSubmitTime()) ? -1",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                170,
+                                582,
+                                457,
+                                593
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        170,
+                                        582,
+                                        288,
+                                        593
+                                    ],
+                                    "score": 1.0,
+                                    "content": ": (j1.getSubmitTime()",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        288,
+                                        583,
+                                        303,
+                                        592
+                                    ],
+                                    "score": 0.35,
+                                    "content": "= =",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        582,
+                                        457,
+                                        593
+                                    ],
+                                    "score": 1.0,
+                                    "content": "j2.getSubmitTime()) ? 0 : 1;",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                593,
+                                135,
+                                602
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        593,
+                                        135,
+                                        602
+                                    ],
+                                    "score": 1.0,
+                                    "content": "}",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        }
+                    ],
+                    "index": 28,
+                    "bbox_fs": [
+                        105,
+                        531,
+                        457,
+                        602
+                    ]
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        221,
+                        606,
+                        388,
+                        684
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                221,
+                                606,
+                                388,
+                                684
+                            ],
+                            "group_id": 2,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        221,
+                                        606,
+                                        388,
+                                        684
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                221,
+                                                606,
+                                                388,
+                                                684
+                                            ],
+                                            "score": 0.96,
+                                            "html": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td>run</td></tr><tr><td>code2seq</td><td> get submit time</td></tr><tr><td>Ours w/o structure</td><td>compare</td></tr><tr><td>CODE TRANSFORMER</td><td>compare</td></tr><tr><td>Ground Truth</td><td>compare</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "fc7647e7d39190fcddd6003a2621a01161522b4db1837436041dcd5808f7523b.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 35,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        221,
+                                        606,
+                                        388,
+                                        617.1428571428571
+                                    ],
+                                    "spans": [],
+                                    "index": 32
+                                },
+                                {
+                                    "bbox": [
+                                        221,
+                                        617.1428571428571,
+                                        388,
+                                        628.2857142857142
+                                    ],
+                                    "spans": [],
+                                    "index": 33
+                                },
+                                {
+                                    "bbox": [
+                                        221,
+                                        628.2857142857142,
+                                        388,
+                                        639.4285714285713
+                                    ],
+                                    "spans": [],
+                                    "index": 34
+                                },
+                                {
+                                    "bbox": [
+                                        221,
+                                        639.4285714285713,
+                                        388,
+                                        650.5714285714284
+                                    ],
+                                    "spans": [],
+                                    "index": 35
+                                },
+                                {
+                                    "bbox": [
+                                        221,
+                                        650.5714285714284,
+                                        388,
+                                        661.7142857142856
+                                    ],
+                                    "spans": [],
+                                    "index": 36
+                                },
+                                {
+                                    "bbox": [
+                                        221,
+                                        661.7142857142856,
+                                        388,
+                                        672.8571428571427
+                                    ],
+                                    "spans": [],
+                                    "index": 37
+                                },
+                                {
+                                    "bbox": [
+                                        221,
+                                        672.8571428571427,
+                                        388,
+                                        683.9999999999998
+                                    ],
+                                    "spans": [],
+                                    "index": 38
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 35
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        691,
+                        504,
+                        714
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                689,
+                                505,
+                                705
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        689,
+                                        505,
+                                        705
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Table 10: The CODE TRANSFORMER and the its context-only variant are the only models correctly",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                702,
+                                333,
+                                716
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        702,
+                                        333,
+                                        716
+                                    ],
+                                    "score": 1.0,
+                                    "content": "recognizing the ‘compare’ template in the method body.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        }
+                    ],
+                    "index": 39.5,
+                    "bbox_fs": [
+                        105,
+                        689,
+                        505,
+                        716
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        92,
+                        367,
+                        153
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                92,
+                                345,
+                                104
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        92,
+                                        345,
+                                        104
+                                    ],
+                                    "score": 1.0,
+                                    "content": "public static MNTPROC fromValue(int value) {",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                101,
+                                367,
+                                114
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        101,
+                                        181,
+                                        114
+                                    ],
+                                    "score": 1.0,
+                                    "content": "if (value",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        181,
+                                        103,
+                                        200,
+                                        113
+                                    ],
+                                    "score": 0.4,
+                                    "content": "< ~ 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        200,
+                                        101,
+                                        250,
+                                        114
+                                    ],
+                                    "score": 1.0,
+                                    "content": "|| value",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        250,
+                                        104,
+                                        266,
+                                        112
+                                    ],
+                                    "score": 0.76,
+                                    "content": "> =",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        266,
+                                        101,
+                                        367,
+                                        114
+                                    ],
+                                    "score": 1.0,
+                                    "content": "values().length) {",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                149,
+                                113,
+                                215,
+                                124
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        149,
+                                        113,
+                                        215,
+                                        124
+                                    ],
+                                    "score": 1.0,
+                                    "content": "return null;",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                130,
+                                126,
+                                134,
+                                131
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        130,
+                                        126,
+                                        134,
+                                        131
+                                    ],
+                                    "score": 1.0,
+                                    "content": "}",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                132,
+                                253,
+                                144
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        132,
+                                        253,
+                                        144
+                                    ],
+                                    "score": 1.0,
+                                    "content": "return values()[value];",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                109,
+                                145,
+                                112,
+                                150
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        109,
+                                        145,
+                                        112,
+                                        150
+                                    ],
+                                    "score": 1.0,
+                                    "content": "}",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        }
+                    ],
+                    "index": 2.5
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        229,
+                        156,
+                        379,
+                        234
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                229,
+                                156,
+                                379,
+                                234
+                            ],
+                            "group_id": 1,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        229,
+                                        156,
+                                        379,
+                                        234
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                229,
+                                                156,
+                                                379,
+                                                234
+                                            ],
+                                            "score": 0.966,
+                                            "html": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td> get value</td></tr><tr><td>code2seq</td><td> get value</td></tr><tr><td>Ours w/o structure</td><td>to</td></tr><tr><td>CODE TRANSFORMER</td><td>from value</td></tr><tr><td>Ground Truth</td><td>from value</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "c731fa631d72aabd1f5e32632f679a09b671309e6980e8efeb5fd4f3681003b9.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 6.5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        229,
+                                        156,
+                                        379,
+                                        195.0
+                                    ],
+                                    "spans": [],
+                                    "index": 6
+                                },
+                                {
+                                    "bbox": [
+                                        229,
+                                        195.0,
+                                        379,
+                                        234.0
+                                    ],
+                                    "spans": [],
+                                    "index": 7
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        242,
+                        505,
+                        265
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                241,
+                                506,
+                                255
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        241,
+                                        506,
+                                        255
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Table 11: The CODE TRANSFORMER is the only model to recognize that the snippet is similar to a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                253,
+                                334,
+                                266
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        253,
+                                        334,
+                                        266
+                                    ],
+                                    "score": 1.0,
+                                    "content": "static factory method which is often preceded with from.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 8.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        298,
+                        429,
+                        308
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                298,
+                                430,
+                                310
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        298,
+                                        430,
+                                        310
+                                    ],
+                                    "score": 1.0,
+                                    "content": "private Iterable<ListBlobItem> listRootBlobs(String aPrefix,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        346,
+                        308,
+                        580,
+                        348
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                347,
+                                307,
+                                495,
+                                319
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        347,
+                                        307,
+                                        495,
+                                        319
+                                    ],
+                                    "score": 1.0,
+                                    "content": "boolean useFlatBlobListing,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                348,
+                                317,
+                                581,
+                                329
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        348,
+                                        317,
+                                        581,
+                                        329
+                                    ],
+                                    "score": 1.0,
+                                    "content": "EnumSet<BlobListingDetails> listingDetails,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                348,
+                                328,
+                                495,
+                                339
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        348,
+                                        328,
+                                        495,
+                                        339
+                                    ],
+                                    "score": 1.0,
+                                    "content": "BlobRequestOptions options,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                348,
+                                338,
+                                494,
+                                349
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        348,
+                                        338,
+                                        494,
+                                        349
+                                    ],
+                                    "score": 1.0,
+                                    "content": "OperationContext opContext)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 12.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        315,
+                        349,
+                        568,
+                        358
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                321,
+                                347,
+                                566,
+                                360
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        321,
+                                        347,
+                                        566,
+                                        360
+                                    ],
+                                    "score": 1.0,
+                                    "content": "throws StorageException, URISyntaxException {",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        114,
+                        359,
+                        579,
+                        389
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                127,
+                                357,
+                                581,
+                                369
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        357,
+                                        320,
+                                        369
+                                    ],
+                                    "score": 1.0,
+                                    "content": "CloudBlobDirectoryWrapper directory",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        320,
+                                        359,
+                                        330,
+                                        367
+                                    ],
+                                    "score": 0.68,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        330,
+                                        357,
+                                        581,
+                                        369
+                                    ],
+                                    "score": 1.0,
+                                    "content": "this.container.getDirectoryReference(aPrefix);",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                366,
+                                410,
+                                380
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        366,
+                                        410,
+                                        380
+                                    ],
+                                    "score": 1.0,
+                                    "content": "return directory.listBlobs(null, useFlatBlobListing,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                272,
+                                377,
+                                468,
+                                389
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        272,
+                                        377,
+                                        468,
+                                        389
+                                    ],
+                                    "score": 1.0,
+                                    "content": "listingDetails, options, opContext);",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        389,
+                        113,
+                        398
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                390,
+                                113,
+                                398
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        390,
+                                        113,
+                                        398
+                                    ],
+                                    "score": 1.0,
+                                    "content": "}",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 19
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        215,
+                        402,
+                        394,
+                        479
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                215,
+                                402,
+                                394,
+                                479
+                            ],
+                            "group_id": 2,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        215,
+                                        402,
+                                        394,
+                                        479
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                215,
+                                                402,
+                                                394,
+                                                479
+                                            ],
+                                            "score": 0.972,
+                                            "html": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td>list blobs</td></tr><tr><td>code2seq</td><td>list blobs</td></tr><tr><td>Ours w/o structure</td><td>list blobs</td></tr><tr><td>CODE TRANSFORMER</td><td>list blobs by prefix</td></tr><tr><td>Ground Truth</td><td>list root blobs</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "4184371f3c5b40e5706dc3536eb808edba7ea9235136630720ca50cbd799e93d.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 22.5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        215,
+                                        402,
+                                        394,
+                                        414.8333333333333
+                                    ],
+                                    "spans": [],
+                                    "index": 20
+                                },
+                                {
+                                    "bbox": [
+                                        215,
+                                        414.8333333333333,
+                                        394,
+                                        427.66666666666663
+                                    ],
+                                    "spans": [],
+                                    "index": 21
+                                },
+                                {
+                                    "bbox": [
+                                        215,
+                                        427.66666666666663,
+                                        394,
+                                        440.49999999999994
+                                    ],
+                                    "spans": [],
+                                    "index": 22
+                                },
+                                {
+                                    "bbox": [
+                                        215,
+                                        440.49999999999994,
+                                        394,
+                                        453.33333333333326
+                                    ],
+                                    "spans": [],
+                                    "index": 23
+                                },
+                                {
+                                    "bbox": [
+                                        215,
+                                        453.33333333333326,
+                                        394,
+                                        466.1666666666666
+                                    ],
+                                    "spans": [],
+                                    "index": 24
+                                },
+                                {
+                                    "bbox": [
+                                        215,
+                                        466.1666666666666,
+                                        394,
+                                        478.9999999999999
+                                    ],
+                                    "spans": [],
+                                    "index": 25
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 22.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        487,
+                        504,
+                        510
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                486,
+                                505,
+                                501
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        486,
+                                        505,
+                                        501
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Table 12: All models could correctly identify the listBlobs() call in the return statement. However,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                497,
+                                499,
+                                511
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        497,
+                                        499,
+                                        511
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the CODE TRANSFORMER additionally comprehended that the specified prefix is quite important.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 26.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        543,
+                        577,
+                        600
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                542,
+                                577,
+                                555
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        542,
+                                        322,
+                                        555
+                                    ],
+                                    "score": 1.0,
+                                    "content": "private static void dumpOpCounts(EnumMap",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        322,
+                                        545,
+                                        328,
+                                        552
+                                    ],
+                                    "score": 0.3,
+                                    "content": "<",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        329,
+                                        542,
+                                        457,
+                                        555
+                                    ],
+                                    "score": 1.0,
+                                    "content": "FSEditLogOpCodes, Holder",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        457,
+                                        545,
+                                        463,
+                                        552
+                                    ],
+                                    "score": 0.33,
+                                    "content": "<",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        463,
+                                        542,
+                                        577,
+                                        555
+                                    ],
+                                    "score": 1.0,
+                                    "content": "<Integer>> opCounts) {",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                552,
+                                341,
+                                565
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        552,
+                                        217,
+                                        565
+                                    ],
+                                    "score": 1.0,
+                                    "content": "StringBuilder sb",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        218,
+                                        555,
+                                        228,
+                                        563
+                                    ],
+                                    "score": 0.73,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        228,
+                                        552,
+                                        341,
+                                        565
+                                    ],
+                                    "score": 1.0,
+                                    "content": "new StringBuilder();",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                561,
+                                459,
+                                576
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        561,
+                                        459,
+                                        576
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sb.append(\"Summary of operations loaded from edit log:\\n \");",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                570,
+                                496,
+                                586
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        570,
+                                        345,
+                                        586
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Joiner.on(\"\\n \").withKeyValueSeparator(\"",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        345,
+                                        574,
+                                        356,
+                                        582
+                                    ],
+                                    "score": 0.3,
+                                    "content": "^ { 1 1 } =",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        356,
+                                        570,
+                                        496,
+                                        586
+                                    ],
+                                    "score": 1.0,
+                                    "content": "\").appendTo(sb, opCounts);",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                581,
+                                309,
+                                596
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        581,
+                                        309,
+                                        596
+                                    ],
+                                    "score": 1.0,
+                                    "content": "FSImage.LOG.debug(sb.toString());",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                108,
+                                594,
+                                114,
+                                601
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        108,
+                                        594,
+                                        114,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": "}",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 30.5
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        220,
+                        606,
+                        388,
+                        685
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                220,
+                                606,
+                                388,
+                                685
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        220,
+                                        606,
+                                        388,
+                                        685
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                220,
+                                                606,
+                                                388,
+                                                685
+                                            ],
+                                            "score": 0.965,
+                                            "html": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td>append</td></tr><tr><td>code2seq</td><td>add</td></tr><tr><td>Ours w/o structure</td><td>log</td></tr><tr><td>CODE TRANSFORMER</td><td>log op counts</td></tr><tr><td>Ground Truth</td><td>dump op counts</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "3539e0325fcec95f6f2a244b7e8480d60028213ed3f48a53d7797b35801c9743.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 36.5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        220,
+                                        606,
+                                        388,
+                                        619.1666666666666
+                                    ],
+                                    "spans": [],
+                                    "index": 34
+                                },
+                                {
+                                    "bbox": [
+                                        220,
+                                        619.1666666666666,
+                                        388,
+                                        632.3333333333333
+                                    ],
+                                    "spans": [],
+                                    "index": 35
+                                },
+                                {
+                                    "bbox": [
+                                        220,
+                                        632.3333333333333,
+                                        388,
+                                        645.4999999999999
+                                    ],
+                                    "spans": [],
+                                    "index": 36
+                                },
+                                {
+                                    "bbox": [
+                                        220,
+                                        645.4999999999999,
+                                        388,
+                                        658.6666666666665
+                                    ],
+                                    "spans": [],
+                                    "index": 37
+                                },
+                                {
+                                    "bbox": [
+                                        220,
+                                        658.6666666666665,
+                                        388,
+                                        671.8333333333331
+                                    ],
+                                    "spans": [],
+                                    "index": 38
+                                },
+                                {
+                                    "bbox": [
+                                        220,
+                                        671.8333333333331,
+                                        388,
+                                        684.9999999999998
+                                    ],
+                                    "spans": [],
+                                    "index": 39
+                                }
+                            ]
+                        },
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                106,
+                                693,
+                                505,
+                                716
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        691,
+                                        505,
+                                        705
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                691,
+                                                505,
+                                                705
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 13: Only the CODE TRANSFORMER could correctly identify that it is the op counts that should",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 40
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        702,
+                                        151,
+                                        718
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                702,
+                                                151,
+                                                718
+                                            ],
+                                            "score": 1.0,
+                                            "content": "be logged.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 41
+                                }
+                            ],
+                            "index": 40.5
+                        }
+                    ],
+                    "index": 38.5
+                }
+            ],
+            "page_idx": 19,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        292,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                293,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        293,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        311,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                298,
+                                749,
+                                313,
+                                764
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        298,
+                                        749,
+                                        313,
+                                        764
+                                    ],
+                                    "score": 1.0,
+                                    "content": "",
+                                    "type": "text",
+                                    "height": 15,
+                                    "width": 15
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "list",
+                    "bbox": [
+                        106,
+                        92,
+                        367,
+                        153
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                92,
+                                345,
+                                104
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        92,
+                                        345,
+                                        104
+                                    ],
+                                    "score": 1.0,
+                                    "content": "public static MNTPROC fromValue(int value) {",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0,
+                            "is_list_start_line": true,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                101,
+                                367,
+                                114
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        101,
+                                        181,
+                                        114
+                                    ],
+                                    "score": 1.0,
+                                    "content": "if (value",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        181,
+                                        103,
+                                        200,
+                                        113
+                                    ],
+                                    "score": 0.4,
+                                    "content": "< ~ 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        200,
+                                        101,
+                                        250,
+                                        114
+                                    ],
+                                    "score": 1.0,
+                                    "content": "|| value",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        250,
+                                        104,
+                                        266,
+                                        112
+                                    ],
+                                    "score": 0.76,
+                                    "content": "> =",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        266,
+                                        101,
+                                        367,
+                                        114
+                                    ],
+                                    "score": 1.0,
+                                    "content": "values().length) {",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                149,
+                                113,
+                                215,
+                                124
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        149,
+                                        113,
+                                        215,
+                                        124
+                                    ],
+                                    "score": 1.0,
+                                    "content": "return null;",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                130,
+                                126,
+                                134,
+                                131
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        130,
+                                        126,
+                                        134,
+                                        131
+                                    ],
+                                    "score": 1.0,
+                                    "content": "}",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                132,
+                                253,
+                                144
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        132,
+                                        253,
+                                        144
+                                    ],
+                                    "score": 1.0,
+                                    "content": "return values()[value];",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                109,
+                                145,
+                                112,
+                                150
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        109,
+                                        145,
+                                        112,
+                                        150
+                                    ],
+                                    "score": 1.0,
+                                    "content": "}",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5,
+                            "is_list_start_line": true,
+                            "is_list_end_line": true
+                        }
+                    ],
+                    "index": 2.5,
+                    "bbox_fs": [
+                        105,
+                        92,
+                        367,
+                        150
+                    ]
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        229,
+                        156,
+                        379,
+                        234
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                229,
+                                156,
+                                379,
+                                234
+                            ],
+                            "group_id": 1,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        229,
+                                        156,
+                                        379,
+                                        234
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                229,
+                                                156,
+                                                379,
+                                                234
+                                            ],
+                                            "score": 0.966,
+                                            "html": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td> get value</td></tr><tr><td>code2seq</td><td> get value</td></tr><tr><td>Ours w/o structure</td><td>to</td></tr><tr><td>CODE TRANSFORMER</td><td>from value</td></tr><tr><td>Ground Truth</td><td>from value</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "c731fa631d72aabd1f5e32632f679a09b671309e6980e8efeb5fd4f3681003b9.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 6.5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        229,
+                                        156,
+                                        379,
+                                        195.0
+                                    ],
+                                    "spans": [],
+                                    "index": 6
+                                },
+                                {
+                                    "bbox": [
+                                        229,
+                                        195.0,
+                                        379,
+                                        234.0
+                                    ],
+                                    "spans": [],
+                                    "index": 7
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        242,
+                        505,
+                        265
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                241,
+                                506,
+                                255
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        241,
+                                        506,
+                                        255
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Table 11: The CODE TRANSFORMER is the only model to recognize that the snippet is similar to a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                253,
+                                334,
+                                266
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        253,
+                                        334,
+                                        266
+                                    ],
+                                    "score": 1.0,
+                                    "content": "static factory method which is often preceded with from.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 8.5,
+                    "bbox_fs": [
+                        105,
+                        241,
+                        506,
+                        266
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        298,
+                        429,
+                        308
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                298,
+                                430,
+                                310
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        298,
+                                        430,
+                                        310
+                                    ],
+                                    "score": 1.0,
+                                    "content": "private Iterable<ListBlobItem> listRootBlobs(String aPrefix,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 10,
+                    "bbox_fs": [
+                        105,
+                        298,
+                        430,
+                        310
+                    ]
+                },
+                {
+                    "type": "list",
+                    "bbox": [
+                        346,
+                        308,
+                        580,
+                        348
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                347,
+                                307,
+                                495,
+                                319
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        347,
+                                        307,
+                                        495,
+                                        319
+                                    ],
+                                    "score": 1.0,
+                                    "content": "boolean useFlatBlobListing,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                348,
+                                317,
+                                581,
+                                329
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        348,
+                                        317,
+                                        581,
+                                        329
+                                    ],
+                                    "score": 1.0,
+                                    "content": "EnumSet<BlobListingDetails> listingDetails,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                348,
+                                328,
+                                495,
+                                339
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        348,
+                                        328,
+                                        495,
+                                        339
+                                    ],
+                                    "score": 1.0,
+                                    "content": "BlobRequestOptions options,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                348,
+                                338,
+                                494,
+                                349
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        348,
+                                        338,
+                                        494,
+                                        349
+                                    ],
+                                    "score": 1.0,
+                                    "content": "OperationContext opContext)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14,
+                            "is_list_start_line": true
+                        }
+                    ],
+                    "index": 12.5,
+                    "bbox_fs": [
+                        347,
+                        307,
+                        581,
+                        349
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        315,
+                        349,
+                        568,
+                        358
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                321,
+                                347,
+                                566,
+                                360
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        321,
+                                        347,
+                                        566,
+                                        360
+                                    ],
+                                    "score": 1.0,
+                                    "content": "throws StorageException, URISyntaxException {",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 15,
+                    "bbox_fs": [
+                        321,
+                        347,
+                        566,
+                        360
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        114,
+                        359,
+                        579,
+                        389
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                127,
+                                357,
+                                581,
+                                369
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        357,
+                                        320,
+                                        369
+                                    ],
+                                    "score": 1.0,
+                                    "content": "CloudBlobDirectoryWrapper directory",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        320,
+                                        359,
+                                        330,
+                                        367
+                                    ],
+                                    "score": 0.68,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        330,
+                                        357,
+                                        581,
+                                        369
+                                    ],
+                                    "score": 1.0,
+                                    "content": "this.container.getDirectoryReference(aPrefix);",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                366,
+                                410,
+                                380
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        366,
+                                        410,
+                                        380
+                                    ],
+                                    "score": 1.0,
+                                    "content": "return directory.listBlobs(null, useFlatBlobListing,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                272,
+                                377,
+                                468,
+                                389
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        272,
+                                        377,
+                                        468,
+                                        389
+                                    ],
+                                    "score": 1.0,
+                                    "content": "listingDetails, options, opContext);",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 17,
+                    "bbox_fs": [
+                        126,
+                        357,
+                        581,
+                        389
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        389,
+                        113,
+                        398
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                390,
+                                113,
+                                398
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        390,
+                                        113,
+                                        398
+                                    ],
+                                    "score": 1.0,
+                                    "content": "}",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 19,
+                    "bbox_fs": [
+                        107,
+                        390,
+                        113,
+                        398
+                    ]
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        215,
+                        402,
+                        394,
+                        479
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                215,
+                                402,
+                                394,
+                                479
+                            ],
+                            "group_id": 2,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        215,
+                                        402,
+                                        394,
+                                        479
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                215,
+                                                402,
+                                                394,
+                                                479
+                                            ],
+                                            "score": 0.972,
+                                            "html": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td>list blobs</td></tr><tr><td>code2seq</td><td>list blobs</td></tr><tr><td>Ours w/o structure</td><td>list blobs</td></tr><tr><td>CODE TRANSFORMER</td><td>list blobs by prefix</td></tr><tr><td>Ground Truth</td><td>list root blobs</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "4184371f3c5b40e5706dc3536eb808edba7ea9235136630720ca50cbd799e93d.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 22.5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        215,
+                                        402,
+                                        394,
+                                        414.8333333333333
+                                    ],
+                                    "spans": [],
+                                    "index": 20
+                                },
+                                {
+                                    "bbox": [
+                                        215,
+                                        414.8333333333333,
+                                        394,
+                                        427.66666666666663
+                                    ],
+                                    "spans": [],
+                                    "index": 21
+                                },
+                                {
+                                    "bbox": [
+                                        215,
+                                        427.66666666666663,
+                                        394,
+                                        440.49999999999994
+                                    ],
+                                    "spans": [],
+                                    "index": 22
+                                },
+                                {
+                                    "bbox": [
+                                        215,
+                                        440.49999999999994,
+                                        394,
+                                        453.33333333333326
+                                    ],
+                                    "spans": [],
+                                    "index": 23
+                                },
+                                {
+                                    "bbox": [
+                                        215,
+                                        453.33333333333326,
+                                        394,
+                                        466.1666666666666
+                                    ],
+                                    "spans": [],
+                                    "index": 24
+                                },
+                                {
+                                    "bbox": [
+                                        215,
+                                        466.1666666666666,
+                                        394,
+                                        478.9999999999999
+                                    ],
+                                    "spans": [],
+                                    "index": 25
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 22.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        487,
+                        504,
+                        510
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                486,
+                                505,
+                                501
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        486,
+                                        505,
+                                        501
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Table 12: All models could correctly identify the listBlobs() call in the return statement. However,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                497,
+                                499,
+                                511
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        497,
+                                        499,
+                                        511
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the CODE TRANSFORMER additionally comprehended that the specified prefix is quite important.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 26.5,
+                    "bbox_fs": [
+                        105,
+                        486,
+                        505,
+                        511
+                    ]
+                },
+                {
+                    "type": "list",
+                    "bbox": [
+                        104,
+                        543,
+                        577,
+                        600
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                542,
+                                577,
+                                555
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        542,
+                                        322,
+                                        555
+                                    ],
+                                    "score": 1.0,
+                                    "content": "private static void dumpOpCounts(EnumMap",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        322,
+                                        545,
+                                        328,
+                                        552
+                                    ],
+                                    "score": 0.3,
+                                    "content": "<",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        329,
+                                        542,
+                                        457,
+                                        555
+                                    ],
+                                    "score": 1.0,
+                                    "content": "FSEditLogOpCodes, Holder",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        457,
+                                        545,
+                                        463,
+                                        552
+                                    ],
+                                    "score": 0.33,
+                                    "content": "<",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        463,
+                                        542,
+                                        577,
+                                        555
+                                    ],
+                                    "score": 1.0,
+                                    "content": "<Integer>> opCounts) {",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                552,
+                                341,
+                                565
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        552,
+                                        217,
+                                        565
+                                    ],
+                                    "score": 1.0,
+                                    "content": "StringBuilder sb",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        218,
+                                        555,
+                                        228,
+                                        563
+                                    ],
+                                    "score": 0.73,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        228,
+                                        552,
+                                        341,
+                                        565
+                                    ],
+                                    "score": 1.0,
+                                    "content": "new StringBuilder();",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                561,
+                                459,
+                                576
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        561,
+                                        459,
+                                        576
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sb.append(\"Summary of operations loaded from edit log:\\n \");",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                570,
+                                496,
+                                586
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        570,
+                                        345,
+                                        586
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Joiner.on(\"\\n \").withKeyValueSeparator(\"",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        345,
+                                        574,
+                                        356,
+                                        582
+                                    ],
+                                    "score": 0.3,
+                                    "content": "^ { 1 1 } =",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        356,
+                                        570,
+                                        496,
+                                        586
+                                    ],
+                                    "score": 1.0,
+                                    "content": "\").appendTo(sb, opCounts);",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                581,
+                                309,
+                                596
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        581,
+                                        309,
+                                        596
+                                    ],
+                                    "score": 1.0,
+                                    "content": "FSImage.LOG.debug(sb.toString());",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                108,
+                                594,
+                                114,
+                                601
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        108,
+                                        594,
+                                        114,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": "}",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33,
+                            "is_list_start_line": true,
+                            "is_list_end_line": true
+                        }
+                    ],
+                    "index": 30.5,
+                    "bbox_fs": [
+                        105,
+                        542,
+                        577,
+                        601
+                    ]
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        220,
+                        606,
+                        388,
+                        685
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                220,
+                                606,
+                                388,
+                                685
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        220,
+                                        606,
+                                        388,
+                                        685
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                220,
+                                                606,
+                                                388,
+                                                685
+                                            ],
+                                            "score": 0.965,
+                                            "html": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td>append</td></tr><tr><td>code2seq</td><td>add</td></tr><tr><td>Ours w/o structure</td><td>log</td></tr><tr><td>CODE TRANSFORMER</td><td>log op counts</td></tr><tr><td>Ground Truth</td><td>dump op counts</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "3539e0325fcec95f6f2a244b7e8480d60028213ed3f48a53d7797b35801c9743.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 36.5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        220,
+                                        606,
+                                        388,
+                                        619.1666666666666
+                                    ],
+                                    "spans": [],
+                                    "index": 34
+                                },
+                                {
+                                    "bbox": [
+                                        220,
+                                        619.1666666666666,
+                                        388,
+                                        632.3333333333333
+                                    ],
+                                    "spans": [],
+                                    "index": 35
+                                },
+                                {
+                                    "bbox": [
+                                        220,
+                                        632.3333333333333,
+                                        388,
+                                        645.4999999999999
+                                    ],
+                                    "spans": [],
+                                    "index": 36
+                                },
+                                {
+                                    "bbox": [
+                                        220,
+                                        645.4999999999999,
+                                        388,
+                                        658.6666666666665
+                                    ],
+                                    "spans": [],
+                                    "index": 37
+                                },
+                                {
+                                    "bbox": [
+                                        220,
+                                        658.6666666666665,
+                                        388,
+                                        671.8333333333331
+                                    ],
+                                    "spans": [],
+                                    "index": 38
+                                },
+                                {
+                                    "bbox": [
+                                        220,
+                                        671.8333333333331,
+                                        388,
+                                        684.9999999999998
+                                    ],
+                                    "spans": [],
+                                    "index": 39
+                                }
+                            ]
+                        },
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                106,
+                                693,
+                                505,
+                                716
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        691,
+                                        505,
+                                        705
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                691,
+                                                505,
+                                                705
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 13: Only the CODE TRANSFORMER could correctly identify that it is the op counts that should",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 40
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        702,
+                                        151,
+                                        718
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                702,
+                                                151,
+                                                718
+                                            ],
+                                            "score": 1.0,
+                                            "content": "be logged.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 41
+                                }
+                            ],
+                            "index": 40.5
+                        }
+                    ],
+                    "index": 38.5
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        151,
+                        479,
+                        213
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                151,
+                                479,
+                                163
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        151,
+                                        479,
+                                        163
+                                    ],
+                                    "score": 1.0,
+                                    "content": "static String execCommand(File f, String... cmd) throws IOException {",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                162,
+                                362,
+                                172
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        162,
+                                        201,
+                                        172
+                                    ],
+                                    "score": 1.0,
+                                    "content": "String[] args",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        202,
+                                        163,
+                                        212,
+                                        171
+                                    ],
+                                    "score": 0.75,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        212,
+                                        162,
+                                        331,
+                                        172
+                                    ],
+                                    "score": 1.0,
+                                    "content": "new String[cmd.length",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        332,
+                                        163,
+                                        340,
+                                        171
+                                    ],
+                                    "score": 0.34,
+                                    "content": "^ +",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        340,
+                                        162,
+                                        362,
+                                        172
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1];",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                171,
+                                376,
+                                183
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        171,
+                                        376,
+                                        183
+                                    ],
+                                    "score": 1.0,
+                                    "content": "System.arraycopy(cmd, 0, args, 0, cmd.length);",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                181,
+                                345,
+                                193
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        181,
+                                        218,
+                                        193
+                                    ],
+                                    "score": 1.0,
+                                    "content": "args[cmd.length]",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        218,
+                                        183,
+                                        228,
+                                        191
+                                    ],
+                                    "score": 0.77,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        228,
+                                        181,
+                                        345,
+                                        193
+                                    ],
+                                    "score": 1.0,
+                                    "content": "f.getCanonicalPath();",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                191,
+                                343,
+                                202
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        191,
+                                        201,
+                                        202
+                                    ],
+                                    "score": 1.0,
+                                    "content": "String output",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        201,
+                                        193,
+                                        212,
+                                        200
+                                    ],
+                                    "score": 0.8,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        212,
+                                        191,
+                                        343,
+                                        202
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Shell.execCommand(args);",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                201,
+                                205,
+                                213
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        201,
+                                        205,
+                                        213
+                                    ],
+                                    "score": 1.0,
+                                    "content": "return output;",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        }
+                    ],
+                    "index": 2.5
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        216,
+                        225,
+                        393,
+                        303
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                216,
+                                225,
+                                393,
+                                303
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        216,
+                                        225,
+                                        393,
+                                        303
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                216,
+                                                225,
+                                                393,
+                                                303
+                                            ],
+                                            "score": 0.97,
+                                            "html": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td>get canonical path</td></tr><tr><td>code2seq</td><td>exec</td></tr><tr><td>Ours w/o structure</td><td> get output</td></tr><tr><td>CODE TRANSFORMER</td><td>exec command</td></tr><tr><td>Ground Truth</td><td>exec command</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "3c5bfe70032cf08db67ee0f3135ec46e80e42b50a65cc9210b7b528695c79ab7.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 8.5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        216,
+                                        225,
+                                        393,
+                                        238.0
+                                    ],
+                                    "spans": [],
+                                    "index": 6
+                                },
+                                {
+                                    "bbox": [
+                                        216,
+                                        238.0,
+                                        393,
+                                        251.0
+                                    ],
+                                    "spans": [],
+                                    "index": 7
+                                },
+                                {
+                                    "bbox": [
+                                        216,
+                                        251.0,
+                                        393,
+                                        264.0
+                                    ],
+                                    "spans": [],
+                                    "index": 8
+                                },
+                                {
+                                    "bbox": [
+                                        216,
+                                        264.0,
+                                        393,
+                                        277.0
+                                    ],
+                                    "spans": [],
+                                    "index": 9
+                                },
+                                {
+                                    "bbox": [
+                                        216,
+                                        277.0,
+                                        393,
+                                        290.0
+                                    ],
+                                    "spans": [],
+                                    "index": 10
+                                },
+                                {
+                                    "bbox": [
+                                        216,
+                                        290.0,
+                                        393,
+                                        303.0
+                                    ],
+                                    "spans": [],
+                                    "index": 11
+                                }
+                            ]
+                        },
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                104,
+                                311,
+                                505,
+                                334
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        311,
+                                        505,
+                                        324
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                311,
+                                                505,
+                                                324
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 14: Only the CODE TRANSFORMER and code2seq could identify that the relevant part of the",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 12
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        320,
+                                        429,
+                                        336
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                320,
+                                                429,
+                                                336
+                                            ],
+                                            "score": 1.0,
+                                            "content": "method is concerned with executing a command instead of returning something.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 13
+                                }
+                            ],
+                            "index": 12.5
+                        }
+                    ],
+                    "index": 10.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        106,
+                        485,
+                        398,
+                        495
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                484,
+                                400,
+                                497
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        484,
+                                        400,
+                                        497
+                                    ],
+                                    "score": 1.0,
+                                    "content": "protected void subView(Class<? extends SubView> cls) {",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        109,
+                        492,
+                        511,
+                        537
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                127,
+                                493,
+                                232,
+                                506
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        493,
+                                        232,
+                                        506
+                                    ],
+                                    "score": 1.0,
+                                    "content": "indent(of(ENDTAG));",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                504,
+                                217,
+                                516
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        504,
+                                        217,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sb.setLength(0);",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                514,
+                                512,
+                                526
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        514,
+                                        512,
+                                        526
+                                    ],
+                                    "score": 1.0,
+                                    "content": "out.print(sb.append('[').append(cls.getName()).append(']').toString());",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                524,
+                                205,
+                                536
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        524,
+                                        205,
+                                        536
+                                    ],
+                                    "score": 1.0,
+                                    "content": "out.println();",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 16.5
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        223,
+                        548,
+                        385,
+                        626
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                223,
+                                548,
+                                385,
+                                626
+                            ],
+                            "group_id": 1,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        223,
+                                        548,
+                                        385,
+                                        626
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                223,
+                                                548,
+                                                385,
+                                                626
+                                            ],
+                                            "score": 0.962,
+                                            "html": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td>print</td></tr><tr><td>code2seq</td><td>print</td></tr><tr><td>Ours w/o structure</td><td>print</td></tr><tr><td>CODE TRANSFORMER</td><td>print sub view</td></tr><tr><td>Ground Truth</td><td>sub view</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "0c4c2219f8a76155c82fd9cf1ddec51733b172b4b12ee945147b97301cb67ad3.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 21.5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        223,
+                                        548,
+                                        385,
+                                        561.0
+                                    ],
+                                    "spans": [],
+                                    "index": 19
+                                },
+                                {
+                                    "bbox": [
+                                        223,
+                                        561.0,
+                                        385,
+                                        574.0
+                                    ],
+                                    "spans": [],
+                                    "index": 20
+                                },
+                                {
+                                    "bbox": [
+                                        223,
+                                        574.0,
+                                        385,
+                                        587.0
+                                    ],
+                                    "spans": [],
+                                    "index": 21
+                                },
+                                {
+                                    "bbox": [
+                                        223,
+                                        587.0,
+                                        385,
+                                        600.0
+                                    ],
+                                    "spans": [],
+                                    "index": 22
+                                },
+                                {
+                                    "bbox": [
+                                        223,
+                                        600.0,
+                                        385,
+                                        613.0
+                                    ],
+                                    "spans": [],
+                                    "index": 23
+                                },
+                                {
+                                    "bbox": [
+                                        223,
+                                        613.0,
+                                        385,
+                                        626.0
+                                    ],
+                                    "spans": [],
+                                    "index": 24
+                                }
+                            ]
+                        },
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                106,
+                                634,
+                                505,
+                                657
+                            ],
+                            "group_id": 1,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        634,
+                                        506,
+                                        647
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                634,
+                                                506,
+                                                647
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 15: Only the CODE TRANSFORMER was able to link the print functionality to the object that",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 25
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        644,
+                                        488,
+                                        657
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                644,
+                                                488,
+                                                657
+                                            ],
+                                            "score": 1.0,
+                                            "content": "should be printed, which can only be inferred from the object’s class in the method parameters.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 26
+                                }
+                            ],
+                            "index": 25.5
+                        }
+                    ],
+                    "index": 23.5
+                }
+            ],
+            "page_idx": 20,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        292,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                293,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        293,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        310,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                298,
+                                750,
+                                312,
+                                764
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        298,
+                                        750,
+                                        312,
+                                        764
+                                    ],
+                                    "score": 1.0,
+                                    "content": "",
+                                    "type": "text",
+                                    "height": 14,
+                                    "width": 14
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        151,
+                        479,
+                        213
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                151,
+                                479,
+                                163
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        151,
+                                        479,
+                                        163
+                                    ],
+                                    "score": 1.0,
+                                    "content": "static String execCommand(File f, String... cmd) throws IOException {",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                162,
+                                362,
+                                172
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        162,
+                                        201,
+                                        172
+                                    ],
+                                    "score": 1.0,
+                                    "content": "String[] args",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        202,
+                                        163,
+                                        212,
+                                        171
+                                    ],
+                                    "score": 0.75,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        212,
+                                        162,
+                                        331,
+                                        172
+                                    ],
+                                    "score": 1.0,
+                                    "content": "new String[cmd.length",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        332,
+                                        163,
+                                        340,
+                                        171
+                                    ],
+                                    "score": 0.34,
+                                    "content": "^ +",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        340,
+                                        162,
+                                        362,
+                                        172
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1];",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                171,
+                                376,
+                                183
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        171,
+                                        376,
+                                        183
+                                    ],
+                                    "score": 1.0,
+                                    "content": "System.arraycopy(cmd, 0, args, 0, cmd.length);",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                181,
+                                345,
+                                193
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        181,
+                                        218,
+                                        193
+                                    ],
+                                    "score": 1.0,
+                                    "content": "args[cmd.length]",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        218,
+                                        183,
+                                        228,
+                                        191
+                                    ],
+                                    "score": 0.77,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        228,
+                                        181,
+                                        345,
+                                        193
+                                    ],
+                                    "score": 1.0,
+                                    "content": "f.getCanonicalPath();",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                191,
+                                343,
+                                202
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        191,
+                                        201,
+                                        202
+                                    ],
+                                    "score": 1.0,
+                                    "content": "String output",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        201,
+                                        193,
+                                        212,
+                                        200
+                                    ],
+                                    "score": 0.8,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        212,
+                                        191,
+                                        343,
+                                        202
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Shell.execCommand(args);",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                201,
+                                205,
+                                213
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        201,
+                                        205,
+                                        213
+                                    ],
+                                    "score": 1.0,
+                                    "content": "return output;",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        }
+                    ],
+                    "index": 2.5,
+                    "bbox_fs": [
+                        106,
+                        151,
+                        479,
+                        213
+                    ]
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        216,
+                        225,
+                        393,
+                        303
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                216,
+                                225,
+                                393,
+                                303
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        216,
+                                        225,
+                                        393,
+                                        303
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                216,
+                                                225,
+                                                393,
+                                                303
+                                            ],
+                                            "score": 0.97,
+                                            "html": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td>get canonical path</td></tr><tr><td>code2seq</td><td>exec</td></tr><tr><td>Ours w/o structure</td><td> get output</td></tr><tr><td>CODE TRANSFORMER</td><td>exec command</td></tr><tr><td>Ground Truth</td><td>exec command</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "3c5bfe70032cf08db67ee0f3135ec46e80e42b50a65cc9210b7b528695c79ab7.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 8.5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        216,
+                                        225,
+                                        393,
+                                        238.0
+                                    ],
+                                    "spans": [],
+                                    "index": 6
+                                },
+                                {
+                                    "bbox": [
+                                        216,
+                                        238.0,
+                                        393,
+                                        251.0
+                                    ],
+                                    "spans": [],
+                                    "index": 7
+                                },
+                                {
+                                    "bbox": [
+                                        216,
+                                        251.0,
+                                        393,
+                                        264.0
+                                    ],
+                                    "spans": [],
+                                    "index": 8
+                                },
+                                {
+                                    "bbox": [
+                                        216,
+                                        264.0,
+                                        393,
+                                        277.0
+                                    ],
+                                    "spans": [],
+                                    "index": 9
+                                },
+                                {
+                                    "bbox": [
+                                        216,
+                                        277.0,
+                                        393,
+                                        290.0
+                                    ],
+                                    "spans": [],
+                                    "index": 10
+                                },
+                                {
+                                    "bbox": [
+                                        216,
+                                        290.0,
+                                        393,
+                                        303.0
+                                    ],
+                                    "spans": [],
+                                    "index": 11
+                                }
+                            ]
+                        },
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                104,
+                                311,
+                                505,
+                                334
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        311,
+                                        505,
+                                        324
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                311,
+                                                505,
+                                                324
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 14: Only the CODE TRANSFORMER and code2seq could identify that the relevant part of the",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 12
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        320,
+                                        429,
+                                        336
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                320,
+                                                429,
+                                                336
+                                            ],
+                                            "score": 1.0,
+                                            "content": "method is concerned with executing a command instead of returning something.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 13
+                                }
+                            ],
+                            "index": 12.5
+                        }
+                    ],
+                    "index": 10.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        106,
+                        485,
+                        398,
+                        495
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                484,
+                                400,
+                                497
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        484,
+                                        400,
+                                        497
+                                    ],
+                                    "score": 1.0,
+                                    "content": "protected void subView(Class<? extends SubView> cls) {",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "type": "list",
+                    "bbox": [
+                        109,
+                        492,
+                        511,
+                        537
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                127,
+                                493,
+                                232,
+                                506
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        493,
+                                        232,
+                                        506
+                                    ],
+                                    "score": 1.0,
+                                    "content": "indent(of(ENDTAG));",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                504,
+                                217,
+                                516
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        504,
+                                        217,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sb.setLength(0);",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16,
+                            "is_list_start_line": true,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                514,
+                                512,
+                                526
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        514,
+                                        512,
+                                        526
+                                    ],
+                                    "score": 1.0,
+                                    "content": "out.print(sb.append('[').append(cls.getName()).append(']').toString());",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17,
+                            "is_list_start_line": true,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                524,
+                                205,
+                                536
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        524,
+                                        205,
+                                        536
+                                    ],
+                                    "score": 1.0,
+                                    "content": "out.println();",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18,
+                            "is_list_start_line": true,
+                            "is_list_end_line": true
+                        }
+                    ],
+                    "index": 16.5,
+                    "bbox_fs": [
+                        127,
+                        493,
+                        512,
+                        536
+                    ]
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        223,
+                        548,
+                        385,
+                        626
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                223,
+                                548,
+                                385,
+                                626
+                            ],
+                            "group_id": 1,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        223,
+                                        548,
+                                        385,
+                                        626
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                223,
+                                                548,
+                                                385,
+                                                626
+                                            ],
+                                            "score": 0.962,
+                                            "html": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td>print</td></tr><tr><td>code2seq</td><td>print</td></tr><tr><td>Ours w/o structure</td><td>print</td></tr><tr><td>CODE TRANSFORMER</td><td>print sub view</td></tr><tr><td>Ground Truth</td><td>sub view</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "0c4c2219f8a76155c82fd9cf1ddec51733b172b4b12ee945147b97301cb67ad3.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 21.5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        223,
+                                        548,
+                                        385,
+                                        561.0
+                                    ],
+                                    "spans": [],
+                                    "index": 19
+                                },
+                                {
+                                    "bbox": [
+                                        223,
+                                        561.0,
+                                        385,
+                                        574.0
+                                    ],
+                                    "spans": [],
+                                    "index": 20
+                                },
+                                {
+                                    "bbox": [
+                                        223,
+                                        574.0,
+                                        385,
+                                        587.0
+                                    ],
+                                    "spans": [],
+                                    "index": 21
+                                },
+                                {
+                                    "bbox": [
+                                        223,
+                                        587.0,
+                                        385,
+                                        600.0
+                                    ],
+                                    "spans": [],
+                                    "index": 22
+                                },
+                                {
+                                    "bbox": [
+                                        223,
+                                        600.0,
+                                        385,
+                                        613.0
+                                    ],
+                                    "spans": [],
+                                    "index": 23
+                                },
+                                {
+                                    "bbox": [
+                                        223,
+                                        613.0,
+                                        385,
+                                        626.0
+                                    ],
+                                    "spans": [],
+                                    "index": 24
+                                }
+                            ]
+                        },
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                106,
+                                634,
+                                505,
+                                657
+                            ],
+                            "group_id": 1,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        634,
+                                        506,
+                                        647
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                634,
+                                                506,
+                                                647
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 15: Only the CODE TRANSFORMER was able to link the print functionality to the object that",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 25
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        644,
+                                        488,
+                                        657
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                644,
+                                                488,
+                                                657
+                                            ],
+                                            "score": 1.0,
+                                            "content": "should be printed, which can only be inferred from the object’s class in the method parameters.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 26
+                                }
+                            ],
+                            "index": 25.5
+                        }
+                    ],
+                    "index": 23.5
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "image",
+                    "bbox": [
+                        169,
+                        84,
+                        442,
+                        250
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                169,
+                                84,
+                                442,
+                                250
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        169,
+                                        84,
+                                        442,
+                                        250
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                169,
+                                                84,
+                                                442,
+                                                250
+                                            ],
+                                            "score": 0.968,
+                                            "type": "image",
+                                            "image_path": "1225dc2212652b0900da96594dc1baedeb731793c2a7f99b2f39f0a306a759b8.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        169,
+                                        84,
+                                        442,
+                                        139.33333333333334
+                                    ],
+                                    "spans": [],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        169,
+                                        139.33333333333334,
+                                        442,
+                                        194.66666666666669
+                                    ],
+                                    "spans": [],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        169,
+                                        194.66666666666669,
+                                        442,
+                                        250.00000000000003
+                                    ],
+                                    "spans": [],
+                                    "index": 2
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                147,
+                                263,
+                                462,
+                                276
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        147,
+                                        263,
+                                        464,
+                                        277
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                147,
+                                                263,
+                                                464,
+                                                277
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 7: Share of tokens in the labels also occurring in the bodies of methods.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 2.0
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        108,
+                        286,
+                        504,
+                        415
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                108,
+                                286,
+                                504,
+                                415
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        108,
+                                        286,
+                                        504,
+                                        415
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                108,
+                                                286,
+                                                504,
+                                                415
+                                            ],
+                                            "score": 0.973,
+                                            "html": "<table><tr><td rowspan=\"2\">Model</td><td colspan=\"2\">Python</td><td colspan=\"3\">Javascript</td><td colspan=\"2\"></td><td colspan=\"2\">Ruby</td><td colspan=\"3\">Go</td></tr><tr><td>Prec.</td><td>Rec.</td><td>F1</td><td>Prec.</td><td>Rec.</td><td>F1</td><td>Prec.</td><td>Rec.</td><td>F1</td><td>Prec.</td><td>Rec.</td><td>F1</td></tr><tr><td>code2seq</td><td>1</td><td>1</td><td>1</td><td>-</td><td>1</td><td>1</td><td>=</td><td>1</td><td>1</td><td>1</td><td>1</td><td>-</td></tr><tr><td>GREAT</td><td>34.93</td><td>31.12</td><td>31.61</td><td>29.69</td><td>24.24</td><td>25.55</td><td>25.69</td><td>21.49</td><td>22.18</td><td>48.38</td><td>45.97</td><td>45.71</td></tr><tr><td>Ours w/o structure</td><td>36.87</td><td>32.17</td><td>32.97</td><td>31.30</td><td>25.03</td><td>26.64</td><td>31.43</td><td>25.34</td><td>26.63</td><td>49.78</td><td>46.73</td><td>46.69</td></tr><tr><td>Ours w/o pointer net</td><td>38.77</td><td>31.72</td><td>33.27</td><td>32.70</td><td>25.50</td><td>27.33</td><td>32.12</td><td>30.17</td><td>29.36</td><td>53.09</td><td>48.70</td><td>49.26</td></tr><tr><td>Ours</td><td>36.68</td><td>33.86</td><td>33.84</td><td>33.36</td><td>27.55</td><td>29.02</td><td>31.53</td><td>24.72</td><td>26.43</td><td>52.00</td><td>47.35</td><td>47.93</td></tr><tr><td>code2seq (Multilanguage)</td><td>-</td><td>=</td><td>=</td><td></td><td>=</td><td>=</td><td></td><td></td><td></td><td></td><td></td><td>-</td></tr><tr><td>GREAT (Multilanguage)</td><td>35.73</td><td>30.81</td><td>31.74</td><td>31.49</td><td>26.17</td><td>27.41</td><td>29.72</td><td>24.20</td><td>25.43</td><td>50.32</td><td>47.94</td><td>47.66</td></tr><tr><td>Ours w/o structure (Mult.)</td><td>36.78</td><td>29.92</td><td>31.58</td><td>32.60</td><td>26.02</td><td>27.74</td><td>31.71</td><td>26.07</td><td>27.24</td><td>51.91</td><td>47.58</td><td>48.15</td></tr><tr><td>Ours w/o pointer (Mult.)</td><td>37.18</td><td>30.52</td><td>32.04</td><td>33.95</td><td>25.92</td><td>28.11</td><td>32.76</td><td>25.04</td><td>27.01</td><td>53.50</td><td>48.54</td><td>49.35</td></tr><tr><td>Ours (Multilanguage)</td><td>38.10</td><td>33.32</td><td>34.18</td><td>34.29</td><td>28.69</td><td>30.08</td><td>33.30</td><td>28.33</td><td>29.29</td><td>53.86</td><td>50.46</td><td>50.61</td></tr><tr><td>Ours (Mult. + Finetune)</td><td>38.29</td><td>32.41</td><td>33.65</td><td>34.43</td><td>28.28</td><td>29.91</td><td>32.89</td><td>27.15</td><td>28.49</td><td>53.85</td><td>50.85</td><td></td></tr><tr><td>Ours (Mult.+ LMPretrain)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>50.81</td></tr><tr><td></td><td>38.97</td><td>34.77</td><td>35.34</td><td>35.23</td><td>30.26</td><td>31.38</td><td>33.73</td><td>29.15</td><td>29.94</td><td>55.31</td><td>52.03</td><td>52.13</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "f9846de1ac74fbb68c2e86b16559380e7f8fc1f6b4b397c66475b197f4726324.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        108,
+                                        286,
+                                        504,
+                                        329.0
+                                    ],
+                                    "spans": [],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        108,
+                                        329.0,
+                                        504,
+                                        372.0
+                                    ],
+                                    "spans": [],
+                                    "index": 5
+                                },
+                                {
+                                    "bbox": [
+                                        108,
+                                        372.0,
+                                        504,
+                                        415.0
+                                    ],
+                                    "spans": [],
+                                    "index": 6
+                                }
+                            ]
+                        },
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                163,
+                                423,
+                                448,
+                                435
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        161,
+                                        421,
+                                        448,
+                                        437
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                161,
+                                                421,
+                                                448,
+                                                437
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 16: Code summarization results on the CSN dataset (sample-F1).",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 7
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 6.0
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        456,
+                        341,
+                        468
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                455,
+                                342,
+                                469
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        455,
+                                        342,
+                                        469
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.8 ESTIMATION OF POINTER NETWORK POTENTIAL",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        477,
+                        505,
+                        598
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                477,
+                                505,
+                                489
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        477,
+                                        505,
+                                        489
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In Table 2 we observe that the pointer network improves the F1 score for all languages except Go,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                488,
+                                506,
+                                501
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        488,
+                                        506,
+                                        501
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where counterintuitively it leads to reduced performance as measured by F1 score on the test set",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                499,
+                                505,
+                                511
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        499,
+                                        505,
+                                        511
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(while it improves by about 3 points on validation). To investigate this, in Figure 7 we plot the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                509,
+                                506,
+                                524
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        509,
+                                        506,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": "share of tokens in the labels also occurring in the bodies of methods in the different languages.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                521,
+                                505,
+                                533
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        521,
+                                        505,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Intuitively, this gives an indication on how much gain we can expect from using a pointer network.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                532,
+                                505,
+                                545
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        532,
+                                        505,
+                                        545
+                                    ],
+                                    "score": 1.0,
+                                    "content": "If the share were zero, then no token in the labels ever occur in the bodies of the methods, so the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                543,
+                                506,
+                                556
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        543,
+                                        506,
+                                        556
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pointer network cannot improve the prediction by pointing at the input. We see that for Go, there is",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                554,
+                                506,
+                                566
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        554,
+                                        506,
+                                        566
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a strong mismatch between the test partition and the train/validation partitions, which much fewer",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                565,
+                                505,
+                                577
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        565,
+                                        505,
+                                        577
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tokens from the labels occurring in the bodies of methods on test compared to train/validation. Thus,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                576,
+                                506,
+                                588
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        576,
+                                        506,
+                                        588
+                                    ],
+                                    "score": 1.0,
+                                    "content": "we attribute the drop in performance observed by adding a pointer network on Go to this apparent",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                587,
+                                240,
+                                599
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        587,
+                                        240,
+                                        599
+                                    ],
+                                    "score": 1.0,
+                                    "content": "violation of the i.i.d. assumption.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        611,
+                        435,
+                        623
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                610,
+                                436,
+                                625
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        610,
+                                        436,
+                                        625
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.9 CODE SUMMARIZATION RESULTS ON THE CSN DATASET (SAMPLE-F1)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 20
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        632,
+                        472,
+                        644
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                630,
+                                475,
+                                646
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        630,
+                                        475,
+                                        646
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In Table 16, we present our results on the CSN dataset as measured by the sample-F1 score.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 21
+                }
+            ],
+            "page_idx": 21,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        292,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                293,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        293,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        311,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                312,
+                                764
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        312,
+                                        764
+                                    ],
+                                    "score": 1.0,
+                                    "content": "22",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "image",
+                    "bbox": [
+                        169,
+                        84,
+                        442,
+                        250
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                169,
+                                84,
+                                442,
+                                250
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        169,
+                                        84,
+                                        442,
+                                        250
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                169,
+                                                84,
+                                                442,
+                                                250
+                                            ],
+                                            "score": 0.968,
+                                            "type": "image",
+                                            "image_path": "1225dc2212652b0900da96594dc1baedeb731793c2a7f99b2f39f0a306a759b8.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        169,
+                                        84,
+                                        442,
+                                        139.33333333333334
+                                    ],
+                                    "spans": [],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        169,
+                                        139.33333333333334,
+                                        442,
+                                        194.66666666666669
+                                    ],
+                                    "spans": [],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        169,
+                                        194.66666666666669,
+                                        442,
+                                        250.00000000000003
+                                    ],
+                                    "spans": [],
+                                    "index": 2
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                147,
+                                263,
+                                462,
+                                276
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        147,
+                                        263,
+                                        464,
+                                        277
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                147,
+                                                263,
+                                                464,
+                                                277
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 7: Share of tokens in the labels also occurring in the bodies of methods.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 2.0
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        108,
+                        286,
+                        504,
+                        415
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                108,
+                                286,
+                                504,
+                                415
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        108,
+                                        286,
+                                        504,
+                                        415
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                108,
+                                                286,
+                                                504,
+                                                415
+                                            ],
+                                            "score": 0.973,
+                                            "html": "<table><tr><td rowspan=\"2\">Model</td><td colspan=\"2\">Python</td><td colspan=\"3\">Javascript</td><td colspan=\"2\"></td><td colspan=\"2\">Ruby</td><td colspan=\"3\">Go</td></tr><tr><td>Prec.</td><td>Rec.</td><td>F1</td><td>Prec.</td><td>Rec.</td><td>F1</td><td>Prec.</td><td>Rec.</td><td>F1</td><td>Prec.</td><td>Rec.</td><td>F1</td></tr><tr><td>code2seq</td><td>1</td><td>1</td><td>1</td><td>-</td><td>1</td><td>1</td><td>=</td><td>1</td><td>1</td><td>1</td><td>1</td><td>-</td></tr><tr><td>GREAT</td><td>34.93</td><td>31.12</td><td>31.61</td><td>29.69</td><td>24.24</td><td>25.55</td><td>25.69</td><td>21.49</td><td>22.18</td><td>48.38</td><td>45.97</td><td>45.71</td></tr><tr><td>Ours w/o structure</td><td>36.87</td><td>32.17</td><td>32.97</td><td>31.30</td><td>25.03</td><td>26.64</td><td>31.43</td><td>25.34</td><td>26.63</td><td>49.78</td><td>46.73</td><td>46.69</td></tr><tr><td>Ours w/o pointer net</td><td>38.77</td><td>31.72</td><td>33.27</td><td>32.70</td><td>25.50</td><td>27.33</td><td>32.12</td><td>30.17</td><td>29.36</td><td>53.09</td><td>48.70</td><td>49.26</td></tr><tr><td>Ours</td><td>36.68</td><td>33.86</td><td>33.84</td><td>33.36</td><td>27.55</td><td>29.02</td><td>31.53</td><td>24.72</td><td>26.43</td><td>52.00</td><td>47.35</td><td>47.93</td></tr><tr><td>code2seq (Multilanguage)</td><td>-</td><td>=</td><td>=</td><td></td><td>=</td><td>=</td><td></td><td></td><td></td><td></td><td></td><td>-</td></tr><tr><td>GREAT (Multilanguage)</td><td>35.73</td><td>30.81</td><td>31.74</td><td>31.49</td><td>26.17</td><td>27.41</td><td>29.72</td><td>24.20</td><td>25.43</td><td>50.32</td><td>47.94</td><td>47.66</td></tr><tr><td>Ours w/o structure (Mult.)</td><td>36.78</td><td>29.92</td><td>31.58</td><td>32.60</td><td>26.02</td><td>27.74</td><td>31.71</td><td>26.07</td><td>27.24</td><td>51.91</td><td>47.58</td><td>48.15</td></tr><tr><td>Ours w/o pointer (Mult.)</td><td>37.18</td><td>30.52</td><td>32.04</td><td>33.95</td><td>25.92</td><td>28.11</td><td>32.76</td><td>25.04</td><td>27.01</td><td>53.50</td><td>48.54</td><td>49.35</td></tr><tr><td>Ours (Multilanguage)</td><td>38.10</td><td>33.32</td><td>34.18</td><td>34.29</td><td>28.69</td><td>30.08</td><td>33.30</td><td>28.33</td><td>29.29</td><td>53.86</td><td>50.46</td><td>50.61</td></tr><tr><td>Ours (Mult. + Finetune)</td><td>38.29</td><td>32.41</td><td>33.65</td><td>34.43</td><td>28.28</td><td>29.91</td><td>32.89</td><td>27.15</td><td>28.49</td><td>53.85</td><td>50.85</td><td></td></tr><tr><td>Ours (Mult.+ LMPretrain)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>50.81</td></tr><tr><td></td><td>38.97</td><td>34.77</td><td>35.34</td><td>35.23</td><td>30.26</td><td>31.38</td><td>33.73</td><td>29.15</td><td>29.94</td><td>55.31</td><td>52.03</td><td>52.13</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "f9846de1ac74fbb68c2e86b16559380e7f8fc1f6b4b397c66475b197f4726324.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        108,
+                                        286,
+                                        504,
+                                        329.0
+                                    ],
+                                    "spans": [],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        108,
+                                        329.0,
+                                        504,
+                                        372.0
+                                    ],
+                                    "spans": [],
+                                    "index": 5
+                                },
+                                {
+                                    "bbox": [
+                                        108,
+                                        372.0,
+                                        504,
+                                        415.0
+                                    ],
+                                    "spans": [],
+                                    "index": 6
+                                }
+                            ]
+                        },
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                163,
+                                423,
+                                448,
+                                435
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        161,
+                                        421,
+                                        448,
+                                        437
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                161,
+                                                421,
+                                                448,
+                                                437
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 16: Code summarization results on the CSN dataset (sample-F1).",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 7
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 6.0
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        456,
+                        341,
+                        468
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                455,
+                                342,
+                                469
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        455,
+                                        342,
+                                        469
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.8 ESTIMATION OF POINTER NETWORK POTENTIAL",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        477,
+                        505,
+                        598
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                477,
+                                505,
+                                489
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        477,
+                                        505,
+                                        489
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In Table 2 we observe that the pointer network improves the F1 score for all languages except Go,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                488,
+                                506,
+                                501
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        488,
+                                        506,
+                                        501
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where counterintuitively it leads to reduced performance as measured by F1 score on the test set",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                499,
+                                505,
+                                511
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        499,
+                                        505,
+                                        511
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(while it improves by about 3 points on validation). To investigate this, in Figure 7 we plot the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                509,
+                                506,
+                                524
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        509,
+                                        506,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": "share of tokens in the labels also occurring in the bodies of methods in the different languages.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                521,
+                                505,
+                                533
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        521,
+                                        505,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Intuitively, this gives an indication on how much gain we can expect from using a pointer network.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                532,
+                                505,
+                                545
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        532,
+                                        505,
+                                        545
+                                    ],
+                                    "score": 1.0,
+                                    "content": "If the share were zero, then no token in the labels ever occur in the bodies of the methods, so the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                543,
+                                506,
+                                556
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        543,
+                                        506,
+                                        556
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pointer network cannot improve the prediction by pointing at the input. We see that for Go, there is",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                554,
+                                506,
+                                566
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        554,
+                                        506,
+                                        566
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a strong mismatch between the test partition and the train/validation partitions, which much fewer",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                565,
+                                505,
+                                577
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        565,
+                                        505,
+                                        577
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tokens from the labels occurring in the bodies of methods on test compared to train/validation. Thus,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                576,
+                                506,
+                                588
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        576,
+                                        506,
+                                        588
+                                    ],
+                                    "score": 1.0,
+                                    "content": "we attribute the drop in performance observed by adding a pointer network on Go to this apparent",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                587,
+                                240,
+                                599
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        587,
+                                        240,
+                                        599
+                                    ],
+                                    "score": 1.0,
+                                    "content": "violation of the i.i.d. assumption.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 14,
+                    "bbox_fs": [
+                        104,
+                        477,
+                        506,
+                        599
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        611,
+                        435,
+                        623
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                610,
+                                436,
+                                625
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        610,
+                                        436,
+                                        625
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.9 CODE SUMMARIZATION RESULTS ON THE CSN DATASET (SAMPLE-F1)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 20
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        632,
+                        472,
+                        644
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                630,
+                                475,
+                                646
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        630,
+                                        475,
+                                        646
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In Table 16, we present our results on the CSN dataset as measured by the sample-F1 score.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 21,
+                    "bbox_fs": [
+                        104,
+                        630,
+                        475,
+                        646
+                    ]
+                }
+            ]
+        }
+    ],
+    "_backend": "pipeline",
+    "_version_name": "2.2.2"
+}
\ No newline at end of file
diff --git a/parse/train/Xh5eMZVONGF/Xh5eMZVONGF_model.json b/parse/train/Xh5eMZVONGF/Xh5eMZVONGF_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..bdcddfb61f6c257233b1b8fb98bbae56835eb0e9
--- /dev/null
+++ b/parse/train/Xh5eMZVONGF/Xh5eMZVONGF_model.json
@@ -0,0 +1,24418 @@
+[
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    398,
+                    753,
+                    1302,
+                    753,
+                    1302,
+                    1180,
+                    398,
+                    1180
+                ],
+                "score": 0.984
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1298,
+                    1403,
+                    1298,
+                    1403,
+                    1545,
+                    298,
+                    1545
+                ],
+                "score": 0.98
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1560,
+                    1403,
+                    1560,
+                    1403,
+                    1835,
+                    298,
+                    1835
+                ],
+                "score": 0.98
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1850,
+                    1403,
+                    1850,
+                    1403,
+                    2034,
+                    298,
+                    2034
+                ],
+                "score": 0.979
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    299,
+                    220,
+                    1400,
+                    220,
+                    1400,
+                    324,
+                    299,
+                    324
+                ],
+                "score": 0.964
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    314,
+                    517,
+                    650,
+                    517,
+                    650,
+                    608,
+                    314,
+                    608
+                ],
+                "score": 0.95
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    1015,
+                    377,
+                    1385,
+                    377,
+                    1385,
+                    469,
+                    1015,
+                    469
+                ],
+                "score": 0.948
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    1014,
+                    517,
+                    1373,
+                    517,
+                    1373,
+                    608,
+                    1014,
+                    608
+                ],
+                "score": 0.939
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    314,
+                    376,
+                    794,
+                    376,
+                    794,
+                    470,
+                    314,
+                    470
+                ],
+                "score": 0.927
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    302,
+                    1233,
+                    573,
+                    1233,
+                    573,
+                    1268,
+                    302,
+                    1268
+                ],
+                "score": 0.898
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    773,
+                    689,
+                    927,
+                    689,
+                    927,
+                    722,
+                    773,
+                    722
+                ],
+                "score": 0.875
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    299,
+                    75,
+                    813,
+                    75,
+                    813,
+                    104,
+                    299,
+                    104
+                ],
+                "score": 0.875
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    842,
+                    2088,
+                    857,
+                    2088,
+                    857,
+                    2112,
+                    842,
+                    2112
+                ],
+                "score": 0.609
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    216.0,
+                    1405.0,
+                    216.0,
+                    1405.0,
+                    273.0,
+                    292.0,
+                    273.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    273.0,
+                    1377.0,
+                    273.0,
+                    1377.0,
+                    328.0,
+                    293.0,
+                    328.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1226.0,
+                    580.0,
+                    1226.0,
+                    580.0,
+                    1277.0,
+                    293.0,
+                    1277.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    768.0,
+                    685.0,
+                    934.0,
+                    685.0,
+                    934.0,
+                    728.0,
+                    768.0,
+                    728.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    72.0,
+                    815.0,
+                    72.0,
+                    815.0,
+                    108.0,
+                    295.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    841.0,
+                    2088.0,
+                    858.0,
+                    2088.0,
+                    858.0,
+                    2116.0,
+                    841.0,
+                    2116.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    395.0,
+                    753.0,
+                    1306.0,
+                    753.0,
+                    1306.0,
+                    788.0,
+                    395.0,
+                    788.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    783.0,
+                    1304.0,
+                    783.0,
+                    1304.0,
+                    818.0,
+                    393.0,
+                    818.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    814.0,
+                    1305.0,
+                    814.0,
+                    1305.0,
+                    849.0,
+                    394.0,
+                    849.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    844.0,
+                    1305.0,
+                    844.0,
+                    1305.0,
+                    878.0,
+                    393.0,
+                    878.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    876.0,
+                    1306.0,
+                    876.0,
+                    1306.0,
+                    911.0,
+                    394.0,
+                    911.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    905.0,
+                    1307.0,
+                    905.0,
+                    1307.0,
+                    943.0,
+                    393.0,
+                    943.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    937.0,
+                    1307.0,
+                    937.0,
+                    1307.0,
+                    972.0,
+                    393.0,
+                    972.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    967.0,
+                    1306.0,
+                    967.0,
+                    1306.0,
+                    1000.0,
+                    392.0,
+                    1000.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    998.0,
+                    1304.0,
+                    998.0,
+                    1304.0,
+                    1033.0,
+                    394.0,
+                    1033.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1028.0,
+                    1305.0,
+                    1028.0,
+                    1305.0,
+                    1062.0,
+                    394.0,
+                    1062.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1057.0,
+                    1306.0,
+                    1057.0,
+                    1306.0,
+                    1092.0,
+                    394.0,
+                    1092.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1089.0,
+                    1307.0,
+                    1089.0,
+                    1307.0,
+                    1124.0,
+                    394.0,
+                    1124.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1119.0,
+                    1306.0,
+                    1119.0,
+                    1306.0,
+                    1154.0,
+                    394.0,
+                    1154.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1150.0,
+                    893.0,
+                    1150.0,
+                    893.0,
+                    1185.0,
+                    394.0,
+                    1185.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1300.0,
+                    1404.0,
+                    1300.0,
+                    1404.0,
+                    1334.0,
+                    294.0,
+                    1334.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1331.0,
+                    1405.0,
+                    1331.0,
+                    1405.0,
+                    1365.0,
+                    294.0,
+                    1365.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1361.0,
+                    1405.0,
+                    1361.0,
+                    1405.0,
+                    1395.0,
+                    294.0,
+                    1395.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1390.0,
+                    1407.0,
+                    1390.0,
+                    1407.0,
+                    1428.0,
+                    293.0,
+                    1428.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1423.0,
+                    1403.0,
+                    1423.0,
+                    1403.0,
+                    1456.0,
+                    296.0,
+                    1456.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1453.0,
+                    1405.0,
+                    1453.0,
+                    1405.0,
+                    1487.0,
+                    294.0,
+                    1487.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1482.0,
+                    1405.0,
+                    1482.0,
+                    1405.0,
+                    1518.0,
+                    293.0,
+                    1518.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1513.0,
+                    980.0,
+                    1513.0,
+                    980.0,
+                    1549.0,
+                    293.0,
+                    1549.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1559.0,
+                    1404.0,
+                    1559.0,
+                    1404.0,
+                    1595.0,
+                    296.0,
+                    1595.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1589.0,
+                    1407.0,
+                    1589.0,
+                    1407.0,
+                    1626.0,
+                    294.0,
+                    1626.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1619.0,
+                    1405.0,
+                    1619.0,
+                    1405.0,
+                    1656.0,
+                    294.0,
+                    1656.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1651.0,
+                    1407.0,
+                    1651.0,
+                    1407.0,
+                    1687.0,
+                    293.0,
+                    1687.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1679.0,
+                    1408.0,
+                    1679.0,
+                    1408.0,
+                    1718.0,
+                    291.0,
+                    1718.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1712.0,
+                    1405.0,
+                    1712.0,
+                    1405.0,
+                    1748.0,
+                    296.0,
+                    1748.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1743.0,
+                    1404.0,
+                    1743.0,
+                    1404.0,
+                    1776.0,
+                    294.0,
+                    1776.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1774.0,
+                    1405.0,
+                    1774.0,
+                    1405.0,
+                    1808.0,
+                    294.0,
+                    1808.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1804.0,
+                    695.0,
+                    1804.0,
+                    695.0,
+                    1841.0,
+                    294.0,
+                    1841.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1848.0,
+                    1405.0,
+                    1848.0,
+                    1405.0,
+                    1886.0,
+                    293.0,
+                    1886.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1880.0,
+                    1407.0,
+                    1880.0,
+                    1407.0,
+                    1917.0,
+                    293.0,
+                    1917.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1910.0,
+                    1405.0,
+                    1910.0,
+                    1405.0,
+                    1946.0,
+                    296.0,
+                    1946.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1942.0,
+                    1407.0,
+                    1942.0,
+                    1407.0,
+                    1977.0,
+                    294.0,
+                    1977.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1972.0,
+                    1407.0,
+                    1972.0,
+                    1407.0,
+                    2008.0,
+                    294.0,
+                    2008.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    2002.0,
+                    1276.0,
+                    2002.0,
+                    1276.0,
+                    2036.0,
+                    294.0,
+                    2036.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    311.0,
+                    515.0,
+                    489.0,
+                    515.0,
+                    489.0,
+                    549.0,
+                    311.0,
+                    549.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    311.0,
+                    542.0,
+                    539.0,
+                    542.0,
+                    539.0,
+                    582.0,
+                    311.0,
+                    582.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    316.0,
+                    579.0,
+                    652.0,
+                    579.0,
+                    652.0,
+                    611.0,
+                    316.0,
+                    611.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1013.0,
+                    375.0,
+                    1214.0,
+                    375.0,
+                    1214.0,
+                    409.0,
+                    1013.0,
+                    409.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1013.0,
+                    404.0,
+                    1239.0,
+                    404.0,
+                    1239.0,
+                    441.0,
+                    1013.0,
+                    441.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1012.0,
+                    440.0,
+                    1386.0,
+                    440.0,
+                    1386.0,
+                    469.0,
+                    1012.0,
+                    469.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1014.0,
+                    517.0,
+                    1273.0,
+                    517.0,
+                    1273.0,
+                    549.0,
+                    1014.0,
+                    549.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1013.0,
+                    548.0,
+                    1373.0,
+                    548.0,
+                    1373.0,
+                    578.0,
+                    1013.0,
+                    578.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1013.0,
+                    580.0,
+                    1352.0,
+                    580.0,
+                    1352.0,
+                    609.0,
+                    1013.0,
+                    609.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    313.0,
+                    378.0,
+                    720.0,
+                    378.0,
+                    720.0,
+                    410.0,
+                    313.0,
+                    410.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    312.0,
+                    408.0,
+                    674.0,
+                    408.0,
+                    674.0,
+                    439.0,
+                    312.0,
+                    439.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    314.0,
+                    437.0,
+                    796.0,
+                    437.0,
+                    796.0,
+                    473.0,
+                    314.0,
+                    473.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 0,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1418,
+                    1404,
+                    1418,
+                    1404,
+                    1756,
+                    297,
+                    1756
+                ],
+                "score": 0.982
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1020,
+                    1404,
+                    1020,
+                    1404,
+                    1296,
+                    298,
+                    1296
+                ],
+                "score": 0.981
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    789,
+                    1403,
+                    789,
+                    1403,
+                    1005,
+                    298,
+                    1005
+                ],
+                "score": 0.979
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1771,
+                    1403,
+                    1771,
+                    1403,
+                    1894,
+                    298,
+                    1894
+                ],
+                "score": 0.971
+            },
+            {
+                "category_id": 4,
+                "poly": [
+                    295,
+                    544,
+                    1406,
+                    544,
+                    1406,
+                    728,
+                    295,
+                    728
+                ],
+                "score": 0.961
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    296,
+                    1919,
+                    1403,
+                    1919,
+                    1403,
+                    2034,
+                    296,
+                    2034
+                ],
+                "score": 0.96
+            },
+            {
+                "category_id": 3,
+                "poly": [
+                    462,
+                    224,
+                    1239,
+                    224,
+                    1239,
+                    517,
+                    462,
+                    517
+                ],
+                "score": 0.923
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    301,
+                    1341,
+                    580,
+                    1341,
+                    580,
+                    1376,
+                    301,
+                    1376
+                ],
+                "score": 0.896
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    299,
+                    76,
+                    812,
+                    76,
+                    812,
+                    104,
+                    299,
+                    104
+                ],
+                "score": 0.881
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2089,
+                    858,
+                    2089,
+                    858,
+                    2112,
+                    841,
+                    2112
+                ],
+                "score": 0.736
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    546.0,
+                    1404.0,
+                    546.0,
+                    1404.0,
+                    578.0,
+                    295.0,
+                    578.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    575.0,
+                    1404.0,
+                    575.0,
+                    1404.0,
+                    612.0,
+                    293.0,
+                    612.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    606.0,
+                    1404.0,
+                    606.0,
+                    1404.0,
+                    641.0,
+                    293.0,
+                    641.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    637.0,
+                    1404.0,
+                    637.0,
+                    1404.0,
+                    673.0,
+                    295.0,
+                    673.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    669.0,
+                    1404.0,
+                    669.0,
+                    1404.0,
+                    701.0,
+                    295.0,
+                    701.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    699.0,
+                    1009.0,
+                    699.0,
+                    1009.0,
+                    731.0,
+                    297.0,
+                    731.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    332.0,
+                    1915.0,
+                    1357.0,
+                    1915.0,
+                    1357.0,
+                    1954.0,
+                    332.0,
+                    1954.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    327.0,
+                    1940.0,
+                    1407.0,
+                    1940.0,
+                    1407.0,
+                    1989.0,
+                    327.0,
+                    1989.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1975.0,
+                    1405.0,
+                    1975.0,
+                    1405.0,
+                    2011.0,
+                    293.0,
+                    2011.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    2002.0,
+                    889.0,
+                    2002.0,
+                    889.0,
+                    2040.0,
+                    294.0,
+                    2040.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    459.0,
+                    228.0,
+                    799.0,
+                    228.0,
+                    799.0,
+                    256.0,
+                    459.0,
+                    256.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    897.0,
+                    228.0,
+                    1242.0,
+                    228.0,
+                    1242.0,
+                    256.0,
+                    897.0,
+                    256.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    686.0,
+                    291.0,
+                    713.0,
+                    291.0,
+                    713.0,
+                    315.0,
+                    686.0,
+                    315.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    515.0,
+                    316.0,
+                    714.0,
+                    316.0,
+                    714.0,
+                    345.0,
+                    515.0,
+                    345.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    725.0,
+                    311.0,
+                    776.0,
+                    311.0,
+                    776.0,
+                    334.0,
+                    725.0,
+                    334.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    536.0,
+                    338.0,
+                    709.0,
+                    338.0,
+                    709.0,
+                    368.0,
+                    536.0,
+                    368.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    745.0,
+                    338.0,
+                    784.0,
+                    338.0,
+                    784.0,
+                    375.0,
+                    745.0,
+                    375.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    972.0,
+                    341.0,
+                    1004.0,
+                    341.0,
+                    1004.0,
+                    370.0,
+                    972.0,
+                    370.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    540.0,
+                    363.0,
+                    649.0,
+                    363.0,
+                    649.0,
+                    389.0,
+                    540.0,
+                    389.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    910.0,
+                    362.0,
+                    957.0,
+                    362.0,
+                    957.0,
+                    380.0,
+                    910.0,
+                    380.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    470.0,
+                    381.0,
+                    508.0,
+                    381.0,
+                    508.0,
+                    419.0,
+                    470.0,
+                    419.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    608.0,
+                    383.0,
+                    746.0,
+                    383.0,
+                    746.0,
+                    409.0,
+                    608.0,
+                    409.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    539.0,
+                    404.0,
+                    604.0,
+                    404.0,
+                    604.0,
+                    431.0,
+                    539.0,
+                    431.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    710.0,
+                    411.0,
+                    726.0,
+                    411.0,
+                    726.0,
+                    429.0,
+                    710.0,
+                    429.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1055.0,
+                    409.0,
+                    1083.0,
+                    409.0,
+                    1083.0,
+                    439.0,
+                    1055.0,
+                    439.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1178.0,
+                    413.0,
+                    1200.0,
+                    413.0,
+                    1200.0,
+                    434.0,
+                    1178.0,
+                    434.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    561.0,
+                    430.0,
+                    724.0,
+                    430.0,
+                    724.0,
+                    450.0,
+                    561.0,
+                    450.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    749.0,
+                    422.0,
+                    784.0,
+                    422.0,
+                    784.0,
+                    455.0,
+                    749.0,
+                    455.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    993.0,
+                    433.0,
+                    1045.0,
+                    433.0,
+                    1045.0,
+                    456.0,
+                    993.0,
+                    456.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    591.0,
+                    491.0,
+                    672.0,
+                    491.0,
+                    672.0,
+                    518.0,
+                    591.0,
+                    518.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1024.0,
+                    488.0,
+                    1120.0,
+                    488.0,
+                    1120.0,
+                    520.0,
+                    1024.0,
+                    520.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    559.0,
+                    300.5,
+                    615.0,
+                    300.5,
+                    615.0,
+                    325.0,
+                    559.0,
+                    325.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    746.25,
+                    393.0,
+                    804.25,
+                    393.0,
+                    804.25,
+                    416.5,
+                    746.25,
+                    416.5
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1337.0,
+                    587.0,
+                    1337.0,
+                    587.0,
+                    1383.0,
+                    291.0,
+                    1383.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    73.0,
+                    815.0,
+                    73.0,
+                    815.0,
+                    108.0,
+                    295.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    839.0,
+                    2086.0,
+                    862.0,
+                    2086.0,
+                    862.0,
+                    2121.0,
+                    839.0,
+                    2121.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1416.0,
+                    1404.0,
+                    1416.0,
+                    1404.0,
+                    1455.0,
+                    294.0,
+                    1455.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1448.0,
+                    1402.0,
+                    1448.0,
+                    1402.0,
+                    1487.0,
+                    292.0,
+                    1487.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1480.0,
+                    1404.0,
+                    1480.0,
+                    1404.0,
+                    1515.0,
+                    294.0,
+                    1515.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1514.0,
+                    1404.0,
+                    1514.0,
+                    1404.0,
+                    1545.0,
+                    295.0,
+                    1545.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1541.0,
+                    1404.0,
+                    1541.0,
+                    1404.0,
+                    1575.0,
+                    292.0,
+                    1575.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1575.0,
+                    1405.0,
+                    1575.0,
+                    1405.0,
+                    1606.0,
+                    295.0,
+                    1606.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1601.0,
+                    1405.0,
+                    1601.0,
+                    1405.0,
+                    1637.0,
+                    292.0,
+                    1637.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1633.0,
+                    1405.0,
+                    1633.0,
+                    1405.0,
+                    1668.0,
+                    294.0,
+                    1668.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1663.0,
+                    1405.0,
+                    1663.0,
+                    1405.0,
+                    1698.0,
+                    294.0,
+                    1698.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1694.0,
+                    1406.0,
+                    1694.0,
+                    1406.0,
+                    1729.0,
+                    294.0,
+                    1729.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1725.0,
+                    1082.0,
+                    1725.0,
+                    1082.0,
+                    1760.0,
+                    295.0,
+                    1760.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1018.0,
+                    1404.0,
+                    1018.0,
+                    1404.0,
+                    1058.0,
+                    295.0,
+                    1058.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1052.0,
+                    1406.0,
+                    1052.0,
+                    1406.0,
+                    1085.0,
+                    294.0,
+                    1085.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1082.0,
+                    1404.0,
+                    1082.0,
+                    1404.0,
+                    1115.0,
+                    294.0,
+                    1115.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1111.0,
+                    1406.0,
+                    1111.0,
+                    1406.0,
+                    1148.0,
+                    294.0,
+                    1148.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1141.0,
+                    1402.0,
+                    1141.0,
+                    1402.0,
+                    1178.0,
+                    294.0,
+                    1178.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1171.0,
+                    1404.0,
+                    1171.0,
+                    1404.0,
+                    1210.0,
+                    292.0,
+                    1210.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1204.0,
+                    1401.0,
+                    1204.0,
+                    1401.0,
+                    1236.0,
+                    294.0,
+                    1236.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1231.0,
+                    1404.0,
+                    1231.0,
+                    1404.0,
+                    1270.0,
+                    293.0,
+                    1270.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1264.0,
+                    838.0,
+                    1264.0,
+                    838.0,
+                    1300.0,
+                    294.0,
+                    1300.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    787.0,
+                    1407.0,
+                    787.0,
+                    1407.0,
+                    827.0,
+                    293.0,
+                    827.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    819.0,
+                    1405.0,
+                    819.0,
+                    1405.0,
+                    855.0,
+                    293.0,
+                    855.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    851.0,
+                    1405.0,
+                    851.0,
+                    1405.0,
+                    886.0,
+                    294.0,
+                    886.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    882.0,
+                    1405.0,
+                    882.0,
+                    1405.0,
+                    917.0,
+                    294.0,
+                    917.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    912.0,
+                    1404.0,
+                    912.0,
+                    1404.0,
+                    946.0,
+                    294.0,
+                    946.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    944.0,
+                    1404.0,
+                    944.0,
+                    1404.0,
+                    978.0,
+                    294.0,
+                    978.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    974.0,
+                    1159.0,
+                    974.0,
+                    1159.0,
+                    1007.0,
+                    293.0,
+                    1007.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1772.0,
+                    1402.0,
+                    1772.0,
+                    1402.0,
+                    1805.0,
+                    296.0,
+                    1805.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1802.0,
+                    1405.0,
+                    1802.0,
+                    1405.0,
+                    1835.0,
+                    294.0,
+                    1835.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1831.0,
+                    1403.0,
+                    1831.0,
+                    1403.0,
+                    1867.0,
+                    293.0,
+                    1867.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1864.0,
+                    1403.0,
+                    1864.0,
+                    1403.0,
+                    1896.0,
+                    296.0,
+                    1896.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 1,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    315,
+                    1404,
+                    315,
+                    1404,
+                    682,
+                    297,
+                    682
+                ],
+                "score": 0.983
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    703,
+                    1404,
+                    703,
+                    1404,
+                    983,
+                    297,
+                    983
+                ],
+                "score": 0.983
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1471,
+                    1403,
+                    1471,
+                    1403,
+                    1627,
+                    298,
+                    1627
+                ],
+                "score": 0.978
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1640,
+                    1403,
+                    1640,
+                    1403,
+                    1764,
+                    297,
+                    1764
+                ],
+                "score": 0.975
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1251,
+                    1404,
+                    1251,
+                    1404,
+                    1345,
+                    299,
+                    1345
+                ],
+                "score": 0.971
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    294,
+                    229,
+                    1399,
+                    229,
+                    1399,
+                    293,
+                    294,
+                    293
+                ],
+                "score": 0.953
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    300,
+                    1964,
+                    1404,
+                    1964,
+                    1404,
+                    2039,
+                    300,
+                    2039
+                ],
+                "score": 0.95
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1395,
+                    1400,
+                    1395,
+                    1400,
+                    1458,
+                    299,
+                    1458
+                ],
+                "score": 0.95
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    584,
+                    1166,
+                    1114,
+                    1166,
+                    1114,
+                    1243,
+                    584,
+                    1243
+                ],
+                "score": 0.938
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1091,
+                    1400,
+                    1091,
+                    1400,
+                    1156,
+                    298,
+                    1156
+                ],
+                "score": 0.938
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    327,
+                    1860,
+                    1335,
+                    1860,
+                    1335,
+                    1956,
+                    327,
+                    1956
+                ],
+                "score": 0.928
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1824,
+                    536,
+                    1824,
+                    536,
+                    1854,
+                    297,
+                    1854
+                ],
+                "score": 0.927
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    661,
+                    1345,
+                    1039,
+                    1345,
+                    1039,
+                    1388,
+                    661,
+                    1388
+                ],
+                "score": 0.906
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    300,
+                    75,
+                    813,
+                    75,
+                    813,
+                    105,
+                    300,
+                    105
+                ],
+                "score": 0.904
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    291,
+                    1023,
+                    1370,
+                    1023,
+                    1370,
+                    1062,
+                    291,
+                    1062
+                ],
+                "score": 0.871
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1366,
+                    1189,
+                    1400,
+                    1189,
+                    1400,
+                    1219,
+                    1366,
+                    1219
+                ],
+                "score": 0.869
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1366,
+                    1352,
+                    1400,
+                    1352,
+                    1400,
+                    1381,
+                    1366,
+                    1381
+                ],
+                "score": 0.865
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1366,
+                    1781,
+                    1400,
+                    1781,
+                    1400,
+                    1810,
+                    1366,
+                    1810
+                ],
+                "score": 0.865
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1366,
+                    1870,
+                    1400,
+                    1870,
+                    1400,
+                    1899,
+                    1366,
+                    1899
+                ],
+                "score": 0.842
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    590,
+                    1774,
+                    1110,
+                    1774,
+                    1110,
+                    1817,
+                    590,
+                    1817
+                ],
+                "score": 0.655
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2088,
+                    859,
+                    2088,
+                    859,
+                    2112,
+                    841,
+                    2112
+                ],
+                "score": 0.649
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2088,
+                    859,
+                    2088,
+                    859,
+                    2112,
+                    841,
+                    2112
+                ],
+                "score": 0.542
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    589,
+                    1774,
+                    1112,
+                    1774,
+                    1112,
+                    1817,
+                    589,
+                    1817
+                ],
+                "score": 0.274
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    660,
+                    1345,
+                    1038,
+                    1345,
+                    1038,
+                    1387,
+                    660,
+                    1387
+                ],
+                "score": 0.109
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    582,
+                    1164,
+                    1113,
+                    1164,
+                    1113,
+                    1243,
+                    582,
+                    1243
+                ],
+                "score": 0.94,
+                "latex": "{ \\mathrm { A t t e n t i o n } } ( Q , K , V ) = { \\mathrm { s o f t m a x } } \\left( { \\frac { Q K ^ { T } } { \\sqrt { d _ { k } } } } \\right) V ,"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    328,
+                    1859,
+                    1339,
+                    1859,
+                    1339,
+                    1958,
+                    328,
+                    1958
+                ],
+                "score": 0.94,
+                "latex": "A _ { i j } = \\underbrace { { E } _ { i } ^ { T } W _ { q } ^ { T } W _ { k } } _ { ( \\mathrm { u } ) { A } _ { i j } ^ { \\mathrm { c e } } } { + \\underbrace { { E } _ { i } ^ { T } W _ { q } ^ { T } W _ { k } { \\phi } ( p _ { j } ) } _ { ( \\mathrm { b } ) { A } _ { i j } ^ { \\mathrm { c p } } } } + \\underbrace { { \\phi } ( p _ { i } ) ^ { T } W _ { q } ^ { T } W _ { k } { E } _ { j } } _ { ( \\mathrm { c } ) { A } _ { i j } ^ { \\mathrm { c e } } } { + \\underbrace { { { \\phi } ( p _ { i } ) } ^ { T } W _ { q } ^ { T } W _ { k } { \\phi } ( p _ { j } ) } _ { ( \\mathrm { d } ) { A } _ { i j } ^ { \\mathrm { p } } } } ."
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    658,
+                    1343,
+                    1040,
+                    1343,
+                    1040,
+                    1389,
+                    658,
+                    1389
+                ],
+                "score": 0.93,
+                "latex": "\\pmb { A } _ { i j } = \\pmb { Q } _ { i } ^ { T } \\pmb { K } _ { j } = \\pmb { E } _ { i } ^ { T } \\pmb { W } _ { q } ^ { T } \\pmb { W } _ { k } \\pmb { E } _ { j } ,"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    373,
+                    1393,
+                    519,
+                    1393,
+                    519,
+                    1429,
+                    373,
+                    1429
+                ],
+                "score": 0.93,
+                "latex": "E _ { i } , E _ { j } \\in \\mathbb { R } ^ { d }"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    588,
+                    1772,
+                    1108,
+                    1772,
+                    1108,
+                    1818,
+                    588,
+                    1818
+                ],
+                "score": 0.92,
+                "latex": "A _ { i j } = ( E _ { i } + \\phi ( p _ { i } ) ) ^ { T } W _ { q } ^ { T } W _ { k } ( E _ { j } + \\phi ( p _ { j } ) ) , ,"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    824,
+                    1285,
+                    923,
+                    1285,
+                    923,
+                    1316,
+                    824,
+                    1316
+                ],
+                "score": 0.92,
+                "latex": "d _ { k } = d _ { v }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    1701,
+                    436,
+                    1701,
+                    436,
+                    1734,
+                    298,
+                    1734
+                ],
+                "score": 0.92,
+                "latex": "\\phi : \\mathbb { R } \\to \\mathbb { R } ^ { d }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    374,
+                    1252,
+                    559,
+                    1252,
+                    559,
+                    1286,
+                    374,
+                    1286
+                ],
+                "score": 0.91,
+                "latex": "Q , K \\in \\mathbb { R } ^ { N \\times d _ { k } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    848,
+                    1967,
+                    894,
+                    1967,
+                    894,
+                    2003,
+                    848,
+                    2003
+                ],
+                "score": 0.91,
+                "latex": "{ \\cal { A } } _ { i j } ^ { \\mathrm { c c } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    796,
+                    2002,
+                    842,
+                    2002,
+                    842,
+                    2041,
+                    796,
+                    2041
+                ],
+                "score": 0.9,
+                "latex": "A _ { i j } ^ { \\mathrm { c p } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    612,
+                    1251,
+                    757,
+                    1251,
+                    757,
+                    1283,
+                    612,
+                    1283
+                ],
+                "score": 0.9,
+                "latex": "V \\in \\mathbb { R } ^ { N \\times d _ { v } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1150,
+                    1255,
+                    1181,
+                    1255,
+                    1181,
+                    1285,
+                    1150,
+                    1285
+                ],
+                "score": 0.89,
+                "latex": "d _ { k }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    1316,
+                    338,
+                    1316,
+                    338,
+                    1350,
+                    298,
+                    1350
+                ],
+                "score": 0.89,
+                "latex": "K _ { j }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1270,
+                    1286,
+                    1306,
+                    1286,
+                    1306,
+                    1317,
+                    1270,
+                    1317
+                ],
+                "score": 0.89,
+                "latex": "Q _ { i }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    345,
+                    1286,
+                    375,
+                    1286,
+                    375,
+                    1315,
+                    345,
+                    1315
+                ],
+                "score": 0.88,
+                "latex": "d _ { v }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    706,
+                    1706,
+                    732,
+                    1706,
+                    732,
+                    1734,
+                    706,
+                    1734
+                ],
+                "score": 0.84,
+                "latex": "p _ { i }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    603,
+                    1397,
+                    621,
+                    1397,
+                    621,
+                    1423,
+                    603,
+                    1423
+                ],
+                "score": 0.82,
+                "latex": "d"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1016,
+                    1398,
+                    1029,
+                    1398,
+                    1029,
+                    1423,
+                    1016,
+                    1423
+                ],
+                "score": 0.79,
+                "latex": "i"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    670,
+                    2005,
+                    683,
+                    2005,
+                    683,
+                    2030,
+                    670,
+                    2030
+                ],
+                "score": 0.79,
+                "latex": "i"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1078,
+                    1397,
+                    1094,
+                    1397,
+                    1094,
+                    1428,
+                    1078,
+                    1428
+                ],
+                "score": 0.78,
+                "latex": "j"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    731,
+                    2005,
+                    747,
+                    2005,
+                    747,
+                    2035,
+                    731,
+                    2035
+                ],
+                "score": 0.77,
+                "latex": "j"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    774,
+                    1254,
+                    803,
+                    1254,
+                    803,
+                    1282,
+                    774,
+                    1282
+                ],
+                "score": 0.76,
+                "latex": "N"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1152,
+                    1395,
+                    1196,
+                    1395,
+                    1196,
+                    1430,
+                    1152,
+                    1430
+                ],
+                "score": 0.63,
+                "latex": "W _ { q }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1204,
+                    1392,
+                    1360,
+                    1392,
+                    1360,
+                    1429,
+                    1204,
+                    1429
+                ],
+                "score": 0.61,
+                "latex": "W _ { k } \\in \\mathbb { R } ^ { d _ { k } \\times d }"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    73.0,
+                    815.0,
+                    73.0,
+                    815.0,
+                    108.0,
+                    295.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1022.0,
+                    1377.0,
+                    1022.0,
+                    1377.0,
+                    1064.0,
+                    291.0,
+                    1064.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    838.0,
+                    2085.0,
+                    862.0,
+                    2085.0,
+                    862.0,
+                    2118.0,
+                    838.0,
+                    2118.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    838.0,
+                    2085.0,
+                    862.0,
+                    2085.0,
+                    862.0,
+                    2118.0,
+                    838.0,
+                    2118.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    315.0,
+                    1405.0,
+                    315.0,
+                    1405.0,
+                    353.0,
+                    294.0,
+                    353.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    345.0,
+                    1406.0,
+                    345.0,
+                    1406.0,
+                    383.0,
+                    294.0,
+                    383.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    376.0,
+                    1404.0,
+                    376.0,
+                    1404.0,
+                    412.0,
+                    294.0,
+                    412.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    404.0,
+                    1405.0,
+                    404.0,
+                    1405.0,
+                    446.0,
+                    292.0,
+                    446.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    439.0,
+                    1405.0,
+                    439.0,
+                    1405.0,
+                    473.0,
+                    295.0,
+                    473.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    469.0,
+                    1405.0,
+                    469.0,
+                    1405.0,
+                    503.0,
+                    295.0,
+                    503.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    500.0,
+                    1405.0,
+                    500.0,
+                    1405.0,
+                    534.0,
+                    294.0,
+                    534.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    529.0,
+                    1407.0,
+                    529.0,
+                    1407.0,
+                    567.0,
+                    294.0,
+                    567.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    557.0,
+                    1406.0,
+                    557.0,
+                    1406.0,
+                    597.0,
+                    291.0,
+                    597.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    588.0,
+                    1405.0,
+                    588.0,
+                    1405.0,
+                    626.0,
+                    292.0,
+                    626.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    620.0,
+                    1407.0,
+                    620.0,
+                    1407.0,
+                    658.0,
+                    292.0,
+                    658.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    648.0,
+                    403.0,
+                    648.0,
+                    403.0,
+                    685.0,
+                    295.0,
+                    685.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    706.0,
+                    1405.0,
+                    706.0,
+                    1405.0,
+                    739.0,
+                    296.0,
+                    739.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    737.0,
+                    1405.0,
+                    737.0,
+                    1405.0,
+                    770.0,
+                    295.0,
+                    770.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    765.0,
+                    1405.0,
+                    765.0,
+                    1405.0,
+                    802.0,
+                    292.0,
+                    802.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    795.0,
+                    1406.0,
+                    795.0,
+                    1406.0,
+                    832.0,
+                    294.0,
+                    832.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    827.0,
+                    1406.0,
+                    827.0,
+                    1406.0,
+                    864.0,
+                    292.0,
+                    864.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    855.0,
+                    1406.0,
+                    855.0,
+                    1406.0,
+                    893.0,
+                    292.0,
+                    893.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    889.0,
+                    1405.0,
+                    889.0,
+                    1405.0,
+                    922.0,
+                    295.0,
+                    922.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    914.0,
+                    1406.0,
+                    914.0,
+                    1406.0,
+                    958.0,
+                    292.0,
+                    958.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    949.0,
+                    1346.0,
+                    949.0,
+                    1346.0,
+                    984.0,
+                    292.0,
+                    984.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    1473.0,
+                    1404.0,
+                    1473.0,
+                    1404.0,
+                    1506.0,
+                    297.0,
+                    1506.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1498.0,
+                    1405.0,
+                    1498.0,
+                    1405.0,
+                    1541.0,
+                    292.0,
+                    1541.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1534.0,
+                    1404.0,
+                    1534.0,
+                    1404.0,
+                    1568.0,
+                    296.0,
+                    1568.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1562.0,
+                    1407.0,
+                    1562.0,
+                    1407.0,
+                    1600.0,
+                    294.0,
+                    1600.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1596.0,
+                    1031.0,
+                    1596.0,
+                    1031.0,
+                    1628.0,
+                    294.0,
+                    1628.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1638.0,
+                    1404.0,
+                    1638.0,
+                    1404.0,
+                    1678.0,
+                    292.0,
+                    1678.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1670.0,
+                    1404.0,
+                    1670.0,
+                    1404.0,
+                    1706.0,
+                    292.0,
+                    1706.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1702.0,
+                    297.0,
+                    1702.0,
+                    297.0,
+                    1738.0,
+                    293.0,
+                    1738.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    437.0,
+                    1702.0,
+                    705.0,
+                    1702.0,
+                    705.0,
+                    1738.0,
+                    437.0,
+                    1738.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    733.0,
+                    1702.0,
+                    1405.0,
+                    1702.0,
+                    1405.0,
+                    1738.0,
+                    733.0,
+                    1738.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1732.0,
+                    971.0,
+                    1732.0,
+                    971.0,
+                    1768.0,
+                    293.0,
+                    1768.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1247.0,
+                    373.0,
+                    1247.0,
+                    373.0,
+                    1291.0,
+                    293.0,
+                    1291.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    560.0,
+                    1247.0,
+                    611.0,
+                    1247.0,
+                    611.0,
+                    1291.0,
+                    560.0,
+                    1291.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    758.0,
+                    1247.0,
+                    773.0,
+                    1247.0,
+                    773.0,
+                    1291.0,
+                    758.0,
+                    1291.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    804.0,
+                    1247.0,
+                    1149.0,
+                    1247.0,
+                    1149.0,
+                    1291.0,
+                    804.0,
+                    1291.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1182.0,
+                    1247.0,
+                    1405.0,
+                    1247.0,
+                    1405.0,
+                    1291.0,
+                    1182.0,
+                    1291.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1281.0,
+                    344.0,
+                    1281.0,
+                    344.0,
+                    1321.0,
+                    293.0,
+                    1321.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    376.0,
+                    1281.0,
+                    823.0,
+                    1281.0,
+                    823.0,
+                    1321.0,
+                    376.0,
+                    1321.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    924.0,
+                    1281.0,
+                    1269.0,
+                    1281.0,
+                    1269.0,
+                    1321.0,
+                    924.0,
+                    1321.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1307.0,
+                    1281.0,
+                    1403.0,
+                    1281.0,
+                    1403.0,
+                    1321.0,
+                    1307.0,
+                    1321.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    339.0,
+                    1315.0,
+                    544.0,
+                    1315.0,
+                    544.0,
+                    1349.0,
+                    339.0,
+                    1349.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    229.0,
+                    1401.0,
+                    229.0,
+                    1401.0,
+                    265.0,
+                    295.0,
+                    265.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    261.0,
+                    1385.0,
+                    261.0,
+                    1385.0,
+                    297.0,
+                    295.0,
+                    297.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    298.0,
+                    1965.0,
+                    847.0,
+                    1965.0,
+                    847.0,
+                    2003.0,
+                    298.0,
+                    2003.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    895.0,
+                    1965.0,
+                    1405.0,
+                    1965.0,
+                    1405.0,
+                    2003.0,
+                    895.0,
+                    2003.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1999.0,
+                    669.0,
+                    1999.0,
+                    669.0,
+                    2041.0,
+                    295.0,
+                    2041.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    684.0,
+                    1999.0,
+                    730.0,
+                    1999.0,
+                    730.0,
+                    2041.0,
+                    684.0,
+                    2041.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    748.0,
+                    1999.0,
+                    795.0,
+                    1999.0,
+                    795.0,
+                    2041.0,
+                    748.0,
+                    2041.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    843.0,
+                    1999.0,
+                    1405.0,
+                    1999.0,
+                    1405.0,
+                    2041.0,
+                    843.0,
+                    2041.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1386.0,
+                    372.0,
+                    1386.0,
+                    372.0,
+                    1434.0,
+                    293.0,
+                    1434.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    520.0,
+                    1386.0,
+                    602.0,
+                    1386.0,
+                    602.0,
+                    1434.0,
+                    520.0,
+                    1434.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    622.0,
+                    1386.0,
+                    1015.0,
+                    1386.0,
+                    1015.0,
+                    1434.0,
+                    622.0,
+                    1434.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1030.0,
+                    1386.0,
+                    1077.0,
+                    1386.0,
+                    1077.0,
+                    1434.0,
+                    1030.0,
+                    1434.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1095.0,
+                    1386.0,
+                    1151.0,
+                    1386.0,
+                    1151.0,
+                    1434.0,
+                    1095.0,
+                    1434.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1197.0,
+                    1386.0,
+                    1203.0,
+                    1386.0,
+                    1203.0,
+                    1434.0,
+                    1197.0,
+                    1434.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1361.0,
+                    1386.0,
+                    1409.0,
+                    1386.0,
+                    1409.0,
+                    1434.0,
+                    1361.0,
+                    1434.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1425.0,
+                    872.0,
+                    1425.0,
+                    872.0,
+                    1461.0,
+                    295.0,
+                    1461.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1090.0,
+                    1404.0,
+                    1090.0,
+                    1404.0,
+                    1129.0,
+                    294.0,
+                    1129.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1125.0,
+                    1364.0,
+                    1125.0,
+                    1364.0,
+                    1157.0,
+                    296.0,
+                    1157.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    298.0,
+                    1823.0,
+                    535.0,
+                    1823.0,
+                    535.0,
+                    1855.0,
+                    298.0,
+                    1855.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 2,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    445,
+                    1404,
+                    445,
+                    1404,
+                    662,
+                    297,
+                    662
+                ],
+                "score": 0.978
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    753,
+                    1405,
+                    753,
+                    1405,
+                    976,
+                    297,
+                    976
+                ],
+                "score": 0.978
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1000,
+                    744,
+                    1000,
+                    744,
+                    1243,
+                    297,
+                    1243
+                ],
+                "score": 0.976
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1764,
+                    1404,
+                    1764,
+                    1404,
+                    1919,
+                    297,
+                    1919
+                ],
+                "score": 0.976
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1587,
+                    1404,
+                    1587,
+                    1404,
+                    1744,
+                    297,
+                    1744
+                ],
+                "score": 0.976
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1382,
+                    1404,
+                    1382,
+                    1404,
+                    1565,
+                    298,
+                    1565
+                ],
+                "score": 0.971
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1941,
+                    1402,
+                    1941,
+                    1402,
+                    2035,
+                    298,
+                    2035
+                ],
+                "score": 0.97
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1260,
+                    744,
+                    1260,
+                    744,
+                    1382,
+                    298,
+                    1382
+                ],
+                "score": 0.967
+            },
+            {
+                "category_id": 3,
+                "poly": [
+                    773,
+                    1034,
+                    1395,
+                    1034,
+                    1395,
+                    1305,
+                    773,
+                    1305
+                ],
+                "score": 0.962
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    289,
+                    227,
+                    1402,
+                    227,
+                    1402,
+                    299,
+                    289,
+                    299
+                ],
+                "score": 0.952
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    291,
+                    312,
+                    1403,
+                    312,
+                    1403,
+                    377,
+                    291,
+                    377
+                ],
+                "score": 0.948
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    403,
+                    388,
+                    1296,
+                    388,
+                    1296,
+                    432,
+                    403,
+                    432
+                ],
+                "score": 0.925
+            },
+            {
+                "category_id": 4,
+                "poly": [
+                    814,
+                    1328,
+                    1353,
+                    1328,
+                    1353,
+                    1360,
+                    814,
+                    1360
+                ],
+                "score": 0.916
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    299,
+                    75,
+                    813,
+                    75,
+                    813,
+                    105,
+                    299,
+                    105
+                ],
+                "score": 0.909
+            },
+            {
+                "category_id": 9,
+                "poly": [
+                    1366,
+                    396,
+                    1400,
+                    396,
+                    1400,
+                    426,
+                    1366,
+                    426
+                ],
+                "score": 0.878
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2089,
+                    858,
+                    2089,
+                    858,
+                    2111,
+                    841,
+                    2111
+                ],
+                "score": 0.767
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    302,
+                    695,
+                    1253,
+                    695,
+                    1253,
+                    729,
+                    302,
+                    729
+                ],
+                "score": 0.75
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    302,
+                    695,
+                    1253,
+                    695,
+                    1253,
+                    729,
+                    302,
+                    729
+                ],
+                "score": 0.171
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1229,
+                    345,
+                    1323,
+                    345,
+                    1323,
+                    379,
+                    1229,
+                    379
+                ],
+                "score": 0.92,
+                "latex": "\\phi ( r _ { i \\to j } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    799,
+                    345,
+                    862,
+                    345,
+                    862,
+                    378,
+                    799,
+                    378
+                ],
+                "score": 0.92,
+                "latex": "\\phi ( p _ { i } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    823,
+                    1712,
+                    953,
+                    1712,
+                    953,
+                    1745,
+                    823,
+                    1745
+                ],
+                "score": 0.92,
+                "latex": "r _ { j  i } = - 2"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    357,
+                    1712,
+                    466,
+                    1712,
+                    466,
+                    1745,
+                    357,
+                    1745
+                ],
+                "score": 0.92,
+                "latex": "r _ { i \\to j } = 2"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1123,
+                    443,
+                    1251,
+                    443,
+                    1251,
+                    477,
+                    1123,
+                    477
+                ],
+                "score": 0.92,
+                "latex": "\\boldsymbol { u } , \\boldsymbol { v } \\in \\mathbb { R } ^ { d _ { k } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    620,
+                    229,
+                    666,
+                    229,
+                    666,
+                    269,
+                    620,
+                    269
+                ],
+                "score": 0.92,
+                "latex": "A _ { i j } ^ { \\mathrm { p c } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1202,
+                    1860,
+                    1350,
+                    1860,
+                    1350,
+                    1890,
+                    1202,
+                    1890
+                ],
+                "score": 0.91,
+                "latex": "r _ { v _ { 1 }  v _ { 3 } } ~ = ~ 2"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1317,
+                    1826,
+                    1370,
+                    1826,
+                    1370,
+                    1860,
+                    1317,
+                    1860
+                ],
+                "score": 0.91,
+                "latex": "\\{ v _ { i } \\}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    379,
+                    815,
+                    445,
+                    815,
+                    445,
+                    853,
+                    379,
+                    853
+                ],
+                "score": 0.91,
+                "latex": "W _ { r } ^ { ( s ) }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1174,
+                    2003,
+                    1231,
+                    2003,
+                    1231,
+                    2036,
+                    1174,
+                    2036
+                ],
+                "score": 0.91,
+                "latex": "( i , j )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    361,
+                    264,
+                    409,
+                    264,
+                    409,
+                    306,
+                    361,
+                    306
+                ],
+                "score": 0.9,
+                "latex": "A _ { i j } ^ { \\mathrm { p p } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    297,
+                    1888,
+                    453,
+                    1888,
+                    453,
+                    1922,
+                    297,
+                    1922
+                ],
+                "score": 0.9,
+                "latex": "r _ { v _ { 3 }  v _ { 1 } } = - 2"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    489,
+                    477,
+                    534,
+                    477,
+                    534,
+                    508,
+                    489,
+                    508
+                ],
+                "score": 0.9,
+                "latex": "W _ { r }"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    405,
+                    387,
+                    1294,
+                    387,
+                    1294,
+                    433,
+                    405,
+                    433
+                ],
+                "score": 0.9,
+                "latex": "\\begin{array} { r } { A _ { i j } ^ { \\mathrm { r e l } } = \\ E _ { i } ^ { T } W _ { q } ^ { T } W _ { k } E _ { j } + E _ { i } ^ { T } W _ { q } ^ { T } W _ { r } \\phi ( r _ { i  j } ) + u ^ { T } W _ { k } E _ { j } + v ^ { T } W _ { r } \\phi ( r _ { i  j } ) , } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    371,
+                    453,
+                    428,
+                    453,
+                    428,
+                    480,
+                    371,
+                    480
+                ],
+                "score": 0.9,
+                "latex": "r _ { i \\to j }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    921,
+                    449,
+                    937,
+                    449,
+                    937,
+                    479,
+                    921,
+                    479
+                ],
+                "score": 0.84,
+                "latex": "j"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    703,
+                    1713,
+                    720,
+                    1713,
+                    720,
+                    1743,
+                    703,
+                    1743
+                ],
+                "score": 0.81,
+                "latex": "j"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    810,
+                    450,
+                    823,
+                    450,
+                    823,
+                    474,
+                    810,
+                    474
+                ],
+                "score": 0.78,
+                "latex": "i"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    1062,
+                    315,
+                    1062,
+                    315,
+                    1093,
+                    298,
+                    1093
+                ],
+                "score": 0.78,
+                "latex": "j"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    753,
+                    1713,
+                    766,
+                    1713,
+                    766,
+                    1738,
+                    753,
+                    1738
+                ],
+                "score": 0.76,
+                "latex": "i"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1341,
+                    2005,
+                    1355,
+                    2005,
+                    1355,
+                    2030,
+                    1341,
+                    2030
+                ],
+                "score": 0.75,
+                "latex": "i"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    557,
+                    233,
+                    571,
+                    233,
+                    571,
+                    259,
+                    557,
+                    259
+                ],
+                "score": 0.72,
+                "latex": "i"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    545,
+                    1063,
+                    560,
+                    1063,
+                    560,
+                    1088,
+                    545,
+                    1088
+                ],
+                "score": 0.7,
+                "latex": "i"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    297,
+                    270,
+                    310,
+                    270,
+                    310,
+                    296,
+                    297,
+                    296
+                ],
+                "score": 0.67,
+                "latex": "i"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    594,
+                    829,
+                    610,
+                    829,
+                    610,
+                    850,
+                    594,
+                    850
+                ],
+                "score": 0.58,
+                "latex": "s"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1200.0,
+                    1069.0,
+                    1276.0,
+                    1069.0,
+                    1276.0,
+                    1091.0,
+                    1200.0,
+                    1091.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    941.0,
+                    1084.0,
+                    965.0,
+                    1084.0,
+                    965.0,
+                    1139.0,
+                    941.0,
+                    1139.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1212.0,
+                    1091.0,
+                    1261.0,
+                    1091.0,
+                    1261.0,
+                    1114.0,
+                    1212.0,
+                    1114.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1206.0,
+                    1112.0,
+                    1269.0,
+                    1112.0,
+                    1269.0,
+                    1141.0,
+                    1206.0,
+                    1141.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    773.0,
+                    1151.0,
+                    842.0,
+                    1151.0,
+                    842.0,
+                    1181.0,
+                    773.0,
+                    1181.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    917.0,
+                    1168.0,
+                    941.0,
+                    1168.0,
+                    941.0,
+                    1193.0,
+                    917.0,
+                    1193.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1198.0,
+                    1176.0,
+                    1278.0,
+                    1176.0,
+                    1278.0,
+                    1198.0,
+                    1198.0,
+                    1198.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1196.0,
+                    1195.0,
+                    1278.0,
+                    1195.0,
+                    1278.0,
+                    1223.0,
+                    1196.0,
+                    1223.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1331.0,
+                    1223.0,
+                    1382.0,
+                    1223.0,
+                    1382.0,
+                    1253.0,
+                    1331.0,
+                    1253.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1202.0,
+                    1249.0,
+                    1269.0,
+                    1249.0,
+                    1269.0,
+                    1283.0,
+                    1202.0,
+                    1283.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1316.0,
+                    1250.0,
+                    1395.0,
+                    1250.0,
+                    1395.0,
+                    1275.0,
+                    1316.0,
+                    1275.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1198.0,
+                    1276.0,
+                    1278.0,
+                    1276.0,
+                    1278.0,
+                    1301.0,
+                    1198.0,
+                    1301.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1320.0,
+                    1272.0,
+                    1391.0,
+                    1272.0,
+                    1391.0,
+                    1298.0,
+                    1320.0,
+                    1298.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    810.0,
+                    1323.0,
+                    1358.0,
+                    1323.0,
+                    1358.0,
+                    1366.0,
+                    810.0,
+                    1366.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    73.0,
+                    815.0,
+                    73.0,
+                    815.0,
+                    108.0,
+                    295.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    838.0,
+                    2086.0,
+                    862.0,
+                    2086.0,
+                    862.0,
+                    2118.0,
+                    838.0,
+                    2118.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    694.0,
+                    1260.0,
+                    694.0,
+                    1260.0,
+                    732.0,
+                    294.0,
+                    732.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    445.0,
+                    370.0,
+                    445.0,
+                    370.0,
+                    482.0,
+                    293.0,
+                    482.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    429.0,
+                    445.0,
+                    809.0,
+                    445.0,
+                    809.0,
+                    482.0,
+                    429.0,
+                    482.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    824.0,
+                    445.0,
+                    920.0,
+                    445.0,
+                    920.0,
+                    482.0,
+                    824.0,
+                    482.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    938.0,
+                    445.0,
+                    1122.0,
+                    445.0,
+                    1122.0,
+                    482.0,
+                    938.0,
+                    482.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1252.0,
+                    445.0,
+                    1405.0,
+                    445.0,
+                    1405.0,
+                    482.0,
+                    1252.0,
+                    482.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    475.0,
+                    488.0,
+                    475.0,
+                    488.0,
+                    514.0,
+                    294.0,
+                    514.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    535.0,
+                    475.0,
+                    1405.0,
+                    475.0,
+                    1405.0,
+                    514.0,
+                    535.0,
+                    514.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    506.0,
+                    1406.0,
+                    506.0,
+                    1406.0,
+                    545.0,
+                    294.0,
+                    545.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    540.0,
+                    1404.0,
+                    540.0,
+                    1404.0,
+                    571.0,
+                    296.0,
+                    571.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    567.0,
+                    1405.0,
+                    567.0,
+                    1405.0,
+                    603.0,
+                    294.0,
+                    603.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    598.0,
+                    1407.0,
+                    598.0,
+                    1407.0,
+                    634.0,
+                    292.0,
+                    634.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    632.0,
+                    510.0,
+                    632.0,
+                    510.0,
+                    664.0,
+                    296.0,
+                    664.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    752.0,
+                    1403.0,
+                    752.0,
+                    1403.0,
+                    789.0,
+                    294.0,
+                    789.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    785.0,
+                    1405.0,
+                    785.0,
+                    1405.0,
+                    820.0,
+                    295.0,
+                    820.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    446.0,
+                    822.0,
+                    593.0,
+                    822.0,
+                    593.0,
+                    857.0,
+                    446.0,
+                    857.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    611.0,
+                    822.0,
+                    1405.0,
+                    822.0,
+                    1405.0,
+                    857.0,
+                    611.0,
+                    857.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    854.0,
+                    1403.0,
+                    854.0,
+                    1403.0,
+                    886.0,
+                    296.0,
+                    886.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    885.0,
+                    1403.0,
+                    885.0,
+                    1403.0,
+                    916.0,
+                    296.0,
+                    916.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    912.0,
+                    1406.0,
+                    912.0,
+                    1406.0,
+                    949.0,
+                    292.0,
+                    949.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    942.0,
+                    496.0,
+                    942.0,
+                    496.0,
+                    978.0,
+                    294.0,
+                    978.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    286.0,
+                    812.5,
+                    456.0,
+                    812.5,
+                    456.0,
+                    865.5,
+                    286.0,
+                    865.5
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    999.0,
+                    747.0,
+                    999.0,
+                    747.0,
+                    1032.0,
+                    296.0,
+                    1032.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1030.0,
+                    747.0,
+                    1030.0,
+                    747.0,
+                    1063.0,
+                    295.0,
+                    1063.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1062.0,
+                    297.0,
+                    1062.0,
+                    297.0,
+                    1091.0,
+                    294.0,
+                    1091.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    316.0,
+                    1062.0,
+                    544.0,
+                    1062.0,
+                    544.0,
+                    1091.0,
+                    316.0,
+                    1091.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    561.0,
+                    1062.0,
+                    747.0,
+                    1062.0,
+                    747.0,
+                    1091.0,
+                    561.0,
+                    1091.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1089.0,
+                    746.0,
+                    1089.0,
+                    746.0,
+                    1120.0,
+                    295.0,
+                    1120.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1122.0,
+                    747.0,
+                    1122.0,
+                    747.0,
+                    1152.0,
+                    294.0,
+                    1152.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1151.0,
+                    747.0,
+                    1151.0,
+                    747.0,
+                    1184.0,
+                    294.0,
+                    1184.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1181.0,
+                    747.0,
+                    1181.0,
+                    747.0,
+                    1214.0,
+                    294.0,
+                    1214.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1210.0,
+                    422.0,
+                    1210.0,
+                    422.0,
+                    1245.0,
+                    295.0,
+                    1245.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1766.0,
+                    1405.0,
+                    1766.0,
+                    1405.0,
+                    1799.0,
+                    296.0,
+                    1799.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1795.0,
+                    1404.0,
+                    1795.0,
+                    1404.0,
+                    1828.0,
+                    296.0,
+                    1828.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1824.0,
+                    1316.0,
+                    1824.0,
+                    1316.0,
+                    1861.0,
+                    295.0,
+                    1861.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1371.0,
+                    1824.0,
+                    1406.0,
+                    1824.0,
+                    1406.0,
+                    1861.0,
+                    1371.0,
+                    1861.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    287.0,
+                    1851.0,
+                    1201.0,
+                    1851.0,
+                    1201.0,
+                    1899.0,
+                    287.0,
+                    1899.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1351.0,
+                    1851.0,
+                    1410.0,
+                    1851.0,
+                    1410.0,
+                    1899.0,
+                    1351.0,
+                    1899.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    290.0,
+                    1887.0,
+                    465.0,
+                    1887.0,
+                    465.0,
+                    1926.0,
+                    290.0,
+                    1926.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1587.0,
+                    1402.0,
+                    1587.0,
+                    1402.0,
+                    1621.0,
+                    296.0,
+                    1621.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1617.0,
+                    1405.0,
+                    1617.0,
+                    1405.0,
+                    1653.0,
+                    295.0,
+                    1653.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1644.0,
+                    1405.0,
+                    1644.0,
+                    1405.0,
+                    1688.0,
+                    291.0,
+                    1688.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1678.0,
+                    1407.0,
+                    1678.0,
+                    1407.0,
+                    1716.0,
+                    295.0,
+                    1716.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1706.0,
+                    356.0,
+                    1706.0,
+                    356.0,
+                    1747.0,
+                    294.0,
+                    1747.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    467.0,
+                    1706.0,
+                    702.0,
+                    1706.0,
+                    702.0,
+                    1747.0,
+                    467.0,
+                    1747.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    721.0,
+                    1706.0,
+                    752.0,
+                    1706.0,
+                    752.0,
+                    1747.0,
+                    721.0,
+                    1747.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    767.0,
+                    1706.0,
+                    822.0,
+                    1706.0,
+                    822.0,
+                    1747.0,
+                    767.0,
+                    1747.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    954.0,
+                    1706.0,
+                    1201.0,
+                    1706.0,
+                    1201.0,
+                    1747.0,
+                    954.0,
+                    1747.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1383.0,
+                    1404.0,
+                    1383.0,
+                    1404.0,
+                    1414.0,
+                    296.0,
+                    1414.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1412.0,
+                    1404.0,
+                    1412.0,
+                    1404.0,
+                    1447.0,
+                    294.0,
+                    1447.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1441.0,
+                    1407.0,
+                    1441.0,
+                    1407.0,
+                    1479.0,
+                    292.0,
+                    1479.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1474.0,
+                    1404.0,
+                    1474.0,
+                    1404.0,
+                    1506.0,
+                    293.0,
+                    1506.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1503.0,
+                    1407.0,
+                    1503.0,
+                    1407.0,
+                    1539.0,
+                    292.0,
+                    1539.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1535.0,
+                    671.0,
+                    1535.0,
+                    671.0,
+                    1567.0,
+                    296.0,
+                    1567.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1941.0,
+                    1406.0,
+                    1941.0,
+                    1406.0,
+                    1978.0,
+                    293.0,
+                    1978.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1972.0,
+                    1403.0,
+                    1972.0,
+                    1403.0,
+                    2006.0,
+                    294.0,
+                    2006.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    2001.0,
+                    1173.0,
+                    2001.0,
+                    1173.0,
+                    2039.0,
+                    293.0,
+                    2039.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1232.0,
+                    2001.0,
+                    1340.0,
+                    2001.0,
+                    1340.0,
+                    2039.0,
+                    1232.0,
+                    2039.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1356.0,
+                    2001.0,
+                    1406.0,
+                    2001.0,
+                    1406.0,
+                    2039.0,
+                    1356.0,
+                    2039.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1258.0,
+                    747.0,
+                    1258.0,
+                    747.0,
+                    1291.0,
+                    296.0,
+                    1291.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1291.0,
+                    746.0,
+                    1291.0,
+                    746.0,
+                    1322.0,
+                    296.0,
+                    1322.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1320.0,
+                    748.0,
+                    1320.0,
+                    748.0,
+                    1352.0,
+                    293.0,
+                    1352.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1351.0,
+                    746.0,
+                    1351.0,
+                    746.0,
+                    1384.0,
+                    295.0,
+                    1384.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    224.0,
+                    556.0,
+                    224.0,
+                    556.0,
+                    268.0,
+                    292.0,
+                    268.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    572.0,
+                    224.0,
+                    619.0,
+                    224.0,
+                    619.0,
+                    268.0,
+                    572.0,
+                    268.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    667.0,
+                    224.0,
+                    1407.0,
+                    224.0,
+                    1407.0,
+                    268.0,
+                    667.0,
+                    268.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    263.0,
+                    296.0,
+                    263.0,
+                    296.0,
+                    305.0,
+                    293.0,
+                    305.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    311.0,
+                    263.0,
+                    360.0,
+                    263.0,
+                    360.0,
+                    305.0,
+                    311.0,
+                    305.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    410.0,
+                    263.0,
+                    1126.0,
+                    263.0,
+                    1126.0,
+                    305.0,
+                    410.0,
+                    305.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    310.0,
+                    1405.0,
+                    310.0,
+                    1405.0,
+                    352.0,
+                    292.0,
+                    352.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    342.0,
+                    798.0,
+                    342.0,
+                    798.0,
+                    383.0,
+                    292.0,
+                    383.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    863.0,
+                    342.0,
+                    1228.0,
+                    342.0,
+                    1228.0,
+                    383.0,
+                    863.0,
+                    383.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1324.0,
+                    342.0,
+                    1336.0,
+                    342.0,
+                    1336.0,
+                    383.0,
+                    1324.0,
+                    383.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    694.0,
+                    1260.0,
+                    694.0,
+                    1260.0,
+                    732.0,
+                    294.0,
+                    732.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 3,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1384,
+                    1404,
+                    1384,
+                    1404,
+                    1661,
+                    298,
+                    1661
+                ],
+                "score": 0.982
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1064,
+                    1404,
+                    1064,
+                    1404,
+                    1278,
+                    298,
+                    1278
+                ],
+                "score": 0.981
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1788,
+                    1403,
+                    1788,
+                    1403,
+                    2034,
+                    298,
+                    2034
+                ],
+                "score": 0.979
+            },
+            {
+                "category_id": 3,
+                "poly": [
+                    322,
+                    224,
+                    1386,
+                    224,
+                    1386,
+                    694,
+                    322,
+                    694
+                ],
+                "score": 0.974
+            },
+            {
+                "category_id": 4,
+                "poly": [
+                    297,
+                    725,
+                    1404,
+                    725,
+                    1404,
+                    910,
+                    297,
+                    910
+                ],
+                "score": 0.97
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    977,
+                    1400,
+                    977,
+                    1400,
+                    1040,
+                    298,
+                    1040
+                ],
+                "score": 0.952
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    300,
+                    1714,
+                    674,
+                    1714,
+                    674,
+                    1749,
+                    300,
+                    1749
+                ],
+                "score": 0.892
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    300,
+                    76,
+                    812,
+                    76,
+                    812,
+                    104,
+                    300,
+                    104
+                ],
+                "score": 0.883
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    299,
+                    1326,
+                    941,
+                    1326,
+                    941,
+                    1356,
+                    299,
+                    1356
+                ],
+                "score": 0.831
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2088,
+                    858,
+                    2088,
+                    858,
+                    2112,
+                    841,
+                    2112
+                ],
+                "score": 0.704
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    603,
+                    1416,
+                    697,
+                    1416,
+                    697,
+                    1450,
+                    603,
+                    1450
+                ],
+                "score": 0.92,
+                "latex": "\\phi ( r _ { i \\to j } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1038,
+                    1537,
+                    1137,
+                    1537,
+                    1137,
+                    1567,
+                    1038,
+                    1567
+                ],
+                "score": 0.91,
+                "latex": "k \\ll N ^ { 2 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1047,
+                    1386,
+                    1182,
+                    1386,
+                    1182,
+                    1415,
+                    1047,
+                    1415
+                ],
+                "score": 0.91,
+                "latex": "N \\times N \\times d"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    946,
+                    1630,
+                    1030,
+                    1630,
+                    1030,
+                    1658,
+                    946,
+                    1658
+                ],
+                "score": 0.9,
+                "latex": "k = 3 2"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    697,
+                    981,
+                    714,
+                    981,
+                    714,
+                    1011,
+                    697,
+                    1011
+                ],
+                "score": 0.84,
+                "latex": "j"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    905,
+                    1417,
+                    934,
+                    1417,
+                    934,
+                    1444,
+                    905,
+                    1444
+                ],
+                "score": 0.81,
+                "latex": "N"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    229.0,
+                    679.0,
+                    229.0,
+                    679.0,
+                    260.0,
+                    322.0,
+                    260.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    886.0,
+                    231.0,
+                    1064.0,
+                    231.0,
+                    1064.0,
+                    257.0,
+                    886.0,
+                    257.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1274.0,
+                    226.0,
+                    1337.0,
+                    226.0,
+                    1337.0,
+                    255.0,
+                    1274.0,
+                    255.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    555.0,
+                    254.0,
+                    596.0,
+                    254.0,
+                    596.0,
+                    292.0,
+                    555.0,
+                    292.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1228.0,
+                    245.0,
+                    1382.0,
+                    245.0,
+                    1382.0,
+                    300.0,
+                    1228.0,
+                    300.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    380.0,
+                    287.0,
+                    593.0,
+                    287.0,
+                    593.0,
+                    338.0,
+                    380.0,
+                    338.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    805.0,
+                    305.0,
+                    908.0,
+                    305.0,
+                    908.0,
+                    334.0,
+                    805.0,
+                    334.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    922.0,
+                    288.0,
+                    1059.0,
+                    288.0,
+                    1059.0,
+                    337.0,
+                    922.0,
+                    337.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1078.0,
+                    294.0,
+                    1167.0,
+                    294.0,
+                    1167.0,
+                    326.0,
+                    1078.0,
+                    326.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1230.0,
+                    309.0,
+                    1281.0,
+                    309.0,
+                    1281.0,
+                    334.0,
+                    1230.0,
+                    334.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1283.0,
+                    308.0,
+                    1375.0,
+                    308.0,
+                    1375.0,
+                    335.0,
+                    1283.0,
+                    335.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    405.0,
+                    335.0,
+                    522.0,
+                    335.0,
+                    522.0,
+                    361.0,
+                    405.0,
+                    361.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1080.0,
+                    325.0,
+                    1162.0,
+                    325.0,
+                    1162.0,
+                    354.0,
+                    1080.0,
+                    354.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1263.0,
+                    343.0,
+                    1300.0,
+                    343.0,
+                    1300.0,
+                    358.0,
+                    1263.0,
+                    358.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    334.0,
+                    353.0,
+                    374.0,
+                    353.0,
+                    374.0,
+                    392.0,
+                    334.0,
+                    392.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    447.0,
+                    353.0,
+                    619.0,
+                    353.0,
+                    619.0,
+                    387.0,
+                    447.0,
+                    387.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1076.0,
+                    352.0,
+                    1166.0,
+                    352.0,
+                    1166.0,
+                    384.0,
+                    1076.0,
+                    384.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1298.0,
+                    358.0,
+                    1312.0,
+                    358.0,
+                    1312.0,
+                    377.0,
+                    1298.0,
+                    377.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    379.0,
+                    690.0,
+                    379.0,
+                    690.0,
+                    466.0,
+                    324.0,
+                    466.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    778.0,
+                    394.0,
+                    1043.0,
+                    394.0,
+                    1043.0,
+                    466.0,
+                    778.0,
+                    466.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1073.0,
+                    379.0,
+                    1170.0,
+                    379.0,
+                    1170.0,
+                    458.0,
+                    1073.0,
+                    458.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1264.0,
+                    392.0,
+                    1345.0,
+                    392.0,
+                    1345.0,
+                    455.0,
+                    1264.0,
+                    455.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1284.0,
+                    454.0,
+                    1326.0,
+                    454.0,
+                    1326.0,
+                    474.0,
+                    1284.0,
+                    474.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    865.0,
+                    474.0,
+                    879.0,
+                    474.0,
+                    879.0,
+                    490.0,
+                    865.0,
+                    490.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    918.0,
+                    478.0,
+                    936.0,
+                    478.0,
+                    936.0,
+                    491.0,
+                    918.0,
+                    491.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    964.0,
+                    480.0,
+                    978.0,
+                    480.0,
+                    978.0,
+                    490.0,
+                    964.0,
+                    490.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1295.0,
+                    473.0,
+                    1315.0,
+                    473.0,
+                    1315.0,
+                    493.0,
+                    1295.0,
+                    493.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    365.0,
+                    499.0,
+                    397.0,
+                    499.0,
+                    397.0,
+                    529.0,
+                    365.0,
+                    529.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    837.0,
+                    509.0,
+                    989.0,
+                    509.0,
+                    989.0,
+                    546.0,
+                    837.0,
+                    546.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1036.0,
+                    509.0,
+                    1077.0,
+                    509.0,
+                    1077.0,
+                    547.0,
+                    1036.0,
+                    547.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1144.0,
+                    497.0,
+                    1174.0,
+                    497.0,
+                    1174.0,
+                    518.0,
+                    1144.0,
+                    518.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1264.0,
+                    508.0,
+                    1345.0,
+                    508.0,
+                    1345.0,
+                    531.0,
+                    1264.0,
+                    531.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1110.0,
+                    537.0,
+                    1143.0,
+                    537.0,
+                    1143.0,
+                    559.0,
+                    1110.0,
+                    559.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    402.0,
+                    553.0,
+                    439.0,
+                    553.0,
+                    439.0,
+                    588.0,
+                    402.0,
+                    588.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1021.0,
+                    550.0,
+                    1099.0,
+                    550.0,
+                    1099.0,
+                    578.0,
+                    1021.0,
+                    578.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    852.0,
+                    588.0,
+                    862.0,
+                    588.0,
+                    862.0,
+                    600.0,
+                    852.0,
+                    600.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    967.0,
+                    588.0,
+                    976.0,
+                    588.0,
+                    976.0,
+                    599.0,
+                    967.0,
+                    599.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1027.0,
+                    574.0,
+                    1090.0,
+                    574.0,
+                    1090.0,
+                    598.0,
+                    1027.0,
+                    598.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1212.0,
+                    574.0,
+                    1391.0,
+                    574.0,
+                    1391.0,
+                    599.0,
+                    1212.0,
+                    599.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1212.0,
+                    593.0,
+                    1314.0,
+                    593.0,
+                    1314.0,
+                    618.0,
+                    1212.0,
+                    618.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    424.0,
+                    647.0,
+                    482.0,
+                    647.0,
+                    482.0,
+                    674.0,
+                    424.0,
+                    674.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    489.0,
+                    625.0,
+                    525.0,
+                    625.0,
+                    525.0,
+                    660.0,
+                    489.0,
+                    660.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    621.0,
+                    630.0,
+                    644.0,
+                    630.0,
+                    644.0,
+                    650.0,
+                    621.0,
+                    650.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    810.0,
+                    617.0,
+                    945.0,
+                    617.0,
+                    945.0,
+                    639.0,
+                    810.0,
+                    639.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1046.0,
+                    641.0,
+                    1175.0,
+                    641.0,
+                    1175.0,
+                    689.0,
+                    1046.0,
+                    689.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1210.0,
+                    612.0,
+                    1392.0,
+                    612.0,
+                    1392.0,
+                    679.0,
+                    1210.0,
+                    679.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    634.25,
+                    307.5,
+                    650.25,
+                    307.5,
+                    650.25,
+                    345.5,
+                    634.25,
+                    345.5
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    617.0,
+                    364.5,
+                    686.0,
+                    364.5,
+                    686.0,
+                    392.0,
+                    617.0,
+                    392.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1285.0,
+                    540.0,
+                    1324.0,
+                    540.0,
+                    1324.0,
+                    577.0,
+                    1285.0,
+                    577.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    725.0,
+                    1404.0,
+                    725.0,
+                    1404.0,
+                    762.0,
+                    294.0,
+                    762.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    755.0,
+                    1404.0,
+                    755.0,
+                    1404.0,
+                    793.0,
+                    294.0,
+                    793.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    787.0,
+                    1404.0,
+                    787.0,
+                    1404.0,
+                    823.0,
+                    295.0,
+                    823.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    816.0,
+                    1405.0,
+                    816.0,
+                    1405.0,
+                    851.0,
+                    294.0,
+                    851.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    847.0,
+                    1406.0,
+                    847.0,
+                    1406.0,
+                    885.0,
+                    291.0,
+                    885.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    880.0,
+                    1004.0,
+                    880.0,
+                    1004.0,
+                    912.0,
+                    296.0,
+                    912.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1713.0,
+                    678.0,
+                    1713.0,
+                    678.0,
+                    1754.0,
+                    294.0,
+                    1754.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    73.0,
+                    815.0,
+                    73.0,
+                    815.0,
+                    108.0,
+                    295.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1324.0,
+                    948.0,
+                    1324.0,
+                    948.0,
+                    1360.0,
+                    292.0,
+                    1360.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    839.0,
+                    2085.0,
+                    861.0,
+                    2085.0,
+                    861.0,
+                    2120.0,
+                    839.0,
+                    2120.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1382.0,
+                    1046.0,
+                    1382.0,
+                    1046.0,
+                    1419.0,
+                    294.0,
+                    1419.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1183.0,
+                    1382.0,
+                    1405.0,
+                    1382.0,
+                    1405.0,
+                    1419.0,
+                    1183.0,
+                    1419.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1416.0,
+                    602.0,
+                    1416.0,
+                    602.0,
+                    1453.0,
+                    293.0,
+                    1453.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    698.0,
+                    1416.0,
+                    904.0,
+                    1416.0,
+                    904.0,
+                    1453.0,
+                    698.0,
+                    1453.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    935.0,
+                    1416.0,
+                    1405.0,
+                    1416.0,
+                    1405.0,
+                    1453.0,
+                    935.0,
+                    1453.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1444.0,
+                    1404.0,
+                    1444.0,
+                    1404.0,
+                    1483.0,
+                    293.0,
+                    1483.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1475.0,
+                    1404.0,
+                    1475.0,
+                    1404.0,
+                    1515.0,
+                    292.0,
+                    1515.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1508.0,
+                    1404.0,
+                    1508.0,
+                    1404.0,
+                    1545.0,
+                    293.0,
+                    1545.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1536.0,
+                    1037.0,
+                    1536.0,
+                    1037.0,
+                    1576.0,
+                    293.0,
+                    1576.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1138.0,
+                    1536.0,
+                    1404.0,
+                    1536.0,
+                    1404.0,
+                    1576.0,
+                    1138.0,
+                    1576.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1568.0,
+                    1404.0,
+                    1568.0,
+                    1404.0,
+                    1605.0,
+                    293.0,
+                    1605.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1598.0,
+                    1407.0,
+                    1598.0,
+                    1407.0,
+                    1636.0,
+                    292.0,
+                    1636.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1631.0,
+                    945.0,
+                    1631.0,
+                    945.0,
+                    1664.0,
+                    296.0,
+                    1664.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1031.0,
+                    1631.0,
+                    1252.0,
+                    1631.0,
+                    1252.0,
+                    1664.0,
+                    1031.0,
+                    1664.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1061.0,
+                    1405.0,
+                    1061.0,
+                    1405.0,
+                    1101.0,
+                    293.0,
+                    1101.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1095.0,
+                    1404.0,
+                    1095.0,
+                    1404.0,
+                    1129.0,
+                    294.0,
+                    1129.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1126.0,
+                    1402.0,
+                    1126.0,
+                    1402.0,
+                    1160.0,
+                    294.0,
+                    1160.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1156.0,
+                    1404.0,
+                    1156.0,
+                    1404.0,
+                    1191.0,
+                    294.0,
+                    1191.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1187.0,
+                    1404.0,
+                    1187.0,
+                    1404.0,
+                    1221.0,
+                    294.0,
+                    1221.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1216.0,
+                    1404.0,
+                    1216.0,
+                    1404.0,
+                    1251.0,
+                    294.0,
+                    1251.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1245.0,
+                    1379.0,
+                    1245.0,
+                    1379.0,
+                    1281.0,
+                    293.0,
+                    1281.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1787.0,
+                    1403.0,
+                    1787.0,
+                    1403.0,
+                    1823.0,
+                    293.0,
+                    1823.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1818.0,
+                    1405.0,
+                    1818.0,
+                    1405.0,
+                    1855.0,
+                    293.0,
+                    1855.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1849.0,
+                    1405.0,
+                    1849.0,
+                    1405.0,
+                    1885.0,
+                    293.0,
+                    1885.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1882.0,
+                    1405.0,
+                    1882.0,
+                    1405.0,
+                    1916.0,
+                    294.0,
+                    1916.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1911.0,
+                    1405.0,
+                    1911.0,
+                    1405.0,
+                    1946.0,
+                    292.0,
+                    1946.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1942.0,
+                    1405.0,
+                    1942.0,
+                    1405.0,
+                    1976.0,
+                    294.0,
+                    1976.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1973.0,
+                    1405.0,
+                    1973.0,
+                    1405.0,
+                    2007.0,
+                    294.0,
+                    2007.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    2002.0,
+                    1405.0,
+                    2002.0,
+                    1405.0,
+                    2036.0,
+                    293.0,
+                    2036.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    978.0,
+                    696.0,
+                    978.0,
+                    696.0,
+                    1014.0,
+                    296.0,
+                    1014.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    715.0,
+                    978.0,
+                    1404.0,
+                    978.0,
+                    1404.0,
+                    1014.0,
+                    715.0,
+                    1014.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1009.0,
+                    992.0,
+                    1009.0,
+                    992.0,
+                    1044.0,
+                    294.0,
+                    1044.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 4,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1318,
+                    1404,
+                    1318,
+                    1404,
+                    1715,
+                    298,
+                    1715
+                ],
+                "score": 0.983
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    874,
+                    1404,
+                    874,
+                    1404,
+                    1089,
+                    298,
+                    1089
+                ],
+                "score": 0.979
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1111,
+                    1402,
+                    1111,
+                    1402,
+                    1296,
+                    298,
+                    1296
+                ],
+                "score": 0.978
+            },
+            {
+                "category_id": 5,
+                "poly": [
+                    929,
+                    521,
+                    1403,
+                    521,
+                    1403,
+                    748,
+                    929,
+                    748
+                ],
+                "score": 0.977,
+                "html": "<table><tr><td></td><td colspan=\"3\">Samples per partition</td></tr><tr><td>Dataset</td><td>Train</td><td>Val.</td><td>Test</td></tr><tr><td>CSN-Python</td><td>412,178</td><td>23,107</td><td>22,176</td></tr><tr><td>CSN-Javascript</td><td>123,889</td><td>8,253</td><td>6,483</td></tr><tr><td>CSN-Ruby</td><td>48,791</td><td>2,209</td><td>2,279</td></tr><tr><td>CSN-Go</td><td>317,832</td><td>14,242</td><td>14,291</td></tr><tr><td>Java-small</td><td>691,974</td><td>23,844</td><td>57,088</td></tr></table>"
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    315,
+                    1402,
+                    315,
+                    1402,
+                    469,
+                    298,
+                    469
+                ],
+                "score": 0.975
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    300,
+                    1888,
+                    1402,
+                    1888,
+                    1402,
+                    1982,
+                    300,
+                    1982
+                ],
+                "score": 0.969
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    485,
+                    901,
+                    485,
+                    901,
+                    831,
+                    299,
+                    831
+                ],
+                "score": 0.969
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    294,
+                    229,
+                    1400,
+                    229,
+                    1400,
+                    292,
+                    294,
+                    292
+                ],
+                "score": 0.953
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    328,
+                    2006,
+                    856,
+                    2006,
+                    856,
+                    2034,
+                    328,
+                    2034
+                ],
+                "score": 0.914
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    299,
+                    1761,
+                    480,
+                    1761,
+                    480,
+                    1797,
+                    299,
+                    1797
+                ],
+                "score": 0.892
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    303,
+                    1833,
+                    834,
+                    1833,
+                    834,
+                    1861,
+                    303,
+                    1861
+                ],
+                "score": 0.889
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    300,
+                    76,
+                    812,
+                    76,
+                    812,
+                    104,
+                    300,
+                    104
+                ],
+                "score": 0.887
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    820,
+                    1221,
+                    820,
+                    1221,
+                    851,
+                    299,
+                    851
+                ],
+                "score": 0.821
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    840,
+                    2089,
+                    858,
+                    2089,
+                    858,
+                    2112,
+                    840,
+                    2112
+                ],
+                "score": 0.777
+            },
+            {
+                "category_id": 7,
+                "poly": [
+                    1017,
+                    770,
+                    1309,
+                    770,
+                    1309,
+                    800,
+                    1017,
+                    800
+                ],
+                "score": 0.308
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1203,
+                    1351,
+                    1230,
+                    1351,
+                    1230,
+                    1377,
+                    1203,
+                    1377
+                ],
+                "score": 0.75,
+                "latex": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    331.0,
+                    2001.0,
+                    856.0,
+                    2001.0,
+                    856.0,
+                    2038.0,
+                    331.0,
+                    2038.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1757.0,
+                    485.0,
+                    1757.0,
+                    485.0,
+                    1804.0,
+                    291.0,
+                    1804.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1832.0,
+                    839.0,
+                    1832.0,
+                    839.0,
+                    1866.0,
+                    296.0,
+                    1866.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    73.0,
+                    815.0,
+                    73.0,
+                    815.0,
+                    108.0,
+                    295.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    840.0,
+                    2087.0,
+                    861.0,
+                    2087.0,
+                    861.0,
+                    2118.0,
+                    840.0,
+                    2118.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1014.0,
+                    767.0,
+                    1312.0,
+                    767.0,
+                    1312.0,
+                    802.0,
+                    1014.0,
+                    802.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1318.0,
+                    1404.0,
+                    1318.0,
+                    1404.0,
+                    1355.0,
+                    294.0,
+                    1355.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1347.0,
+                    1202.0,
+                    1347.0,
+                    1202.0,
+                    1384.0,
+                    293.0,
+                    1384.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1231.0,
+                    1347.0,
+                    1406.0,
+                    1347.0,
+                    1406.0,
+                    1384.0,
+                    1231.0,
+                    1384.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1379.0,
+                    1406.0,
+                    1379.0,
+                    1406.0,
+                    1416.0,
+                    294.0,
+                    1416.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1409.0,
+                    1405.0,
+                    1409.0,
+                    1405.0,
+                    1444.0,
+                    292.0,
+                    1444.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1440.0,
+                    1402.0,
+                    1440.0,
+                    1402.0,
+                    1476.0,
+                    294.0,
+                    1476.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1471.0,
+                    1404.0,
+                    1471.0,
+                    1404.0,
+                    1507.0,
+                    294.0,
+                    1507.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1500.0,
+                    1406.0,
+                    1500.0,
+                    1406.0,
+                    1539.0,
+                    296.0,
+                    1539.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1529.0,
+                    1406.0,
+                    1529.0,
+                    1406.0,
+                    1571.0,
+                    292.0,
+                    1571.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1563.0,
+                    1405.0,
+                    1563.0,
+                    1405.0,
+                    1599.0,
+                    293.0,
+                    1599.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1592.0,
+                    1405.0,
+                    1592.0,
+                    1405.0,
+                    1632.0,
+                    293.0,
+                    1632.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1623.0,
+                    1407.0,
+                    1623.0,
+                    1407.0,
+                    1659.0,
+                    292.0,
+                    1659.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1652.0,
+                    1407.0,
+                    1652.0,
+                    1407.0,
+                    1691.0,
+                    293.0,
+                    1691.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1685.0,
+                    1379.0,
+                    1685.0,
+                    1379.0,
+                    1721.0,
+                    293.0,
+                    1721.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    871.0,
+                    1405.0,
+                    871.0,
+                    1405.0,
+                    913.0,
+                    293.0,
+                    913.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    900.0,
+                    1405.0,
+                    900.0,
+                    1405.0,
+                    943.0,
+                    292.0,
+                    943.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    937.0,
+                    1402.0,
+                    937.0,
+                    1402.0,
+                    968.0,
+                    296.0,
+                    968.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    966.0,
+                    1405.0,
+                    966.0,
+                    1405.0,
+                    1000.0,
+                    293.0,
+                    1000.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    995.0,
+                    1405.0,
+                    995.0,
+                    1405.0,
+                    1029.0,
+                    293.0,
+                    1029.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1023.0,
+                    1406.0,
+                    1023.0,
+                    1406.0,
+                    1064.0,
+                    292.0,
+                    1064.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1055.0,
+                    1345.0,
+                    1055.0,
+                    1345.0,
+                    1096.0,
+                    292.0,
+                    1096.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1113.0,
+                    1403.0,
+                    1113.0,
+                    1403.0,
+                    1145.0,
+                    294.0,
+                    1145.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1144.0,
+                    1404.0,
+                    1144.0,
+                    1404.0,
+                    1176.0,
+                    296.0,
+                    1176.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1174.0,
+                    1404.0,
+                    1174.0,
+                    1404.0,
+                    1206.0,
+                    296.0,
+                    1206.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1202.0,
+                    1407.0,
+                    1202.0,
+                    1407.0,
+                    1239.0,
+                    293.0,
+                    1239.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1235.0,
+                    1404.0,
+                    1235.0,
+                    1404.0,
+                    1267.0,
+                    296.0,
+                    1267.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1265.0,
+                    891.0,
+                    1265.0,
+                    891.0,
+                    1300.0,
+                    296.0,
+                    1300.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    317.0,
+                    1404.0,
+                    317.0,
+                    1404.0,
+                    350.0,
+                    296.0,
+                    350.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    346.0,
+                    1402.0,
+                    346.0,
+                    1402.0,
+                    383.0,
+                    294.0,
+                    383.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    373.0,
+                    1406.0,
+                    373.0,
+                    1406.0,
+                    414.0,
+                    292.0,
+                    414.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    407.0,
+                    1404.0,
+                    407.0,
+                    1404.0,
+                    444.0,
+                    294.0,
+                    444.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    437.0,
+                    1375.0,
+                    437.0,
+                    1375.0,
+                    474.0,
+                    294.0,
+                    474.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1886.0,
+                    1406.0,
+                    1886.0,
+                    1406.0,
+                    1924.0,
+                    295.0,
+                    1924.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1917.0,
+                    1404.0,
+                    1917.0,
+                    1404.0,
+                    1954.0,
+                    294.0,
+                    1954.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1951.0,
+                    1404.0,
+                    1951.0,
+                    1404.0,
+                    1982.0,
+                    295.0,
+                    1982.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    484.0,
+                    902.0,
+                    484.0,
+                    902.0,
+                    517.0,
+                    296.0,
+                    517.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    514.0,
+                    904.0,
+                    514.0,
+                    904.0,
+                    550.0,
+                    295.0,
+                    550.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    546.0,
+                    904.0,
+                    546.0,
+                    904.0,
+                    579.0,
+                    295.0,
+                    579.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    577.0,
+                    903.0,
+                    577.0,
+                    903.0,
+                    608.0,
+                    295.0,
+                    608.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    607.0,
+                    904.0,
+                    607.0,
+                    904.0,
+                    639.0,
+                    294.0,
+                    639.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    636.0,
+                    903.0,
+                    636.0,
+                    903.0,
+                    669.0,
+                    294.0,
+                    669.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    668.0,
+                    904.0,
+                    668.0,
+                    904.0,
+                    702.0,
+                    296.0,
+                    702.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    698.0,
+                    905.0,
+                    698.0,
+                    905.0,
+                    731.0,
+                    293.0,
+                    731.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    728.0,
+                    905.0,
+                    728.0,
+                    905.0,
+                    764.0,
+                    294.0,
+                    764.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    758.0,
+                    904.0,
+                    758.0,
+                    904.0,
+                    794.0,
+                    292.0,
+                    794.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    790.0,
+                    903.0,
+                    790.0,
+                    903.0,
+                    821.0,
+                    296.0,
+                    821.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    529.0,
+                    822.0,
+                    545.0,
+                    822.0,
+                    545.0,
+                    833.0,
+                    529.0,
+                    833.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    574.0,
+                    821.0,
+                    622.0,
+                    821.0,
+                    622.0,
+                    834.0,
+                    574.0,
+                    834.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    666.0,
+                    824.0,
+                    675.0,
+                    824.0,
+                    675.0,
+                    831.0,
+                    666.0,
+                    831.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    845.0,
+                    819.0,
+                    880.0,
+                    819.0,
+                    880.0,
+                    836.0,
+                    845.0,
+                    836.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    230.0,
+                    1405.0,
+                    230.0,
+                    1405.0,
+                    266.0,
+                    296.0,
+                    266.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    261.0,
+                    1087.0,
+                    261.0,
+                    1087.0,
+                    296.0,
+                    296.0,
+                    296.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    817.0,
+                    1226.0,
+                    817.0,
+                    1226.0,
+                    855.0,
+                    292.0,
+                    855.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 5,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    649,
+                    1404,
+                    649,
+                    1404,
+                    925,
+                    297,
+                    925
+                ],
+                "score": 0.983
+            },
+            {
+                "category_id": 5,
+                "poly": [
+                    300,
+                    177,
+                    1399,
+                    177,
+                    1399,
+                    534,
+                    300,
+                    534
+                ],
+                "score": 0.982,
+                "html": "<table><tr><td rowspan=\"2\">Model</td><td colspan=\"3\">Python</td><td colspan=\"3\">Javascript</td><td colspan=\"3\">Ruby</td><td colspan=\"3\">Go</td></tr><tr><td>Prec.</td><td>Rec.</td><td>F1</td><td>Prec.</td><td>Rec.</td><td>F1</td><td>Prec.</td><td>Rec.</td><td>F1</td><td>Prec.</td><td>Rec.</td><td>F1</td></tr><tr><td>code2seq</td><td>35.79</td><td>24.85</td><td>29.34</td><td>30.18</td><td>19.88</td><td>23.97</td><td>23.23</td><td>10.31</td><td>14.28</td><td>52.30</td><td>43.43</td><td>47.45</td></tr><tr><td>GREAT</td><td>35.07</td><td>31.59</td><td>33.24</td><td>31.20</td><td>26.84</td><td>28.86</td><td>24.64</td><td>22.23</td><td>23.38</td><td>50.01</td><td>46.51</td><td>48.20</td></tr><tr><td>Ours w/o structure</td><td>37.38</td><td>31.98</td><td>34.47</td><td>33.17</td><td>26.70</td><td>29.59</td><td>29.85</td><td>25.87</td><td>27.72</td><td>51.78</td><td>47.57</td><td>49.59</td></tr><tr><td>Ours w/o pointer net</td><td>37.74</td><td>31.85</td><td>34.55</td><td>33.12</td><td>28.70</td><td>30.75</td><td>23.32</td><td>25.21</td><td>24.23</td><td>54.31</td><td>50.12</td><td>52.13</td></tr><tr><td>Ours</td><td>36.40</td><td>33.66</td><td>34.97</td><td>35.06</td><td>29.61</td><td>32.11</td><td>31.42</td><td>24.46</td><td>27.50</td><td>55.10</td><td>48.05</td><td>51.34</td></tr><tr><td>code2seq (Multilanguage)</td><td>34.49</td><td>25.49</td><td>29.32</td><td>31.62</td><td>22.16</td><td>26.06</td><td>23.97</td><td>17.06</td><td>19.93</td><td>52.70</td><td>44.36</td><td>48.17</td></tr><tr><td>GREAT (Multilanguage)</td><td>36.75</td><td>31.54</td><td>33.94</td><td>33.58</td><td>27.78</td><td>30.41</td><td>30.05</td><td>24.33</td><td>26.89</td><td>52.65</td><td>48.30</td><td>50.38</td></tr><tr><td>Ours w/o structure (Mult.)</td><td>38.48</td><td>30.14</td><td>33.80</td><td>35.38</td><td>27.41</td><td>30.89</td><td>32.61</td><td>26.76</td><td>29.40</td><td>55.03</td><td>47.34</td><td>50.90</td></tr><tr><td>Ours w/o pointer (Mult.)</td><td>38.91</td><td>33.12</td><td>35.78</td><td>37.21</td><td>29.75</td><td>33.07</td><td>34.52</td><td>27.31</td><td>30.50</td><td>56.07</td><td>50.76</td><td>53.28</td></tr><tr><td>Ours (Multilanguage)</td><td>38.89</td><td>33.82</td><td>36.18</td><td>36.95</td><td>29.98</td><td>33.10</td><td>33.93</td><td>28.94</td><td>31.24</td><td>56.00</td><td>50.44</td><td>53.07</td></tr><tr><td>Ours (Mult.+ Finetune)</td><td>39.85</td><td>32.79</td><td>35.98</td><td>37.00</td><td>29.79</td><td>33.00</td><td>35.85</td><td>27.75</td><td>31.28</td><td>55.63</td><td>51.12</td><td>53.28</td></tr><tr><td>Ours (Mult. + LM Pretrain)</td><td>39.67</td><td>35.29</td><td>37.35</td><td>37.06</td><td>31.94</td><td>34.31</td><td>35.19</td><td>29.36</td><td>32.01</td><td>57.73</td><td>51.89</td><td>54.65</td></tr></table>"
+            },
+            {
+                "category_id": 5,
+                "poly": [
+                    877,
+                    1285,
+                    1378,
+                    1285,
+                    1378,
+                    1677,
+                    877,
+                    1677
+                ],
+                "score": 0.98,
+                "html": "<table><tr><td>Model</td><td>Prec.</td><td>Rec.</td><td>F1</td></tr><tr><td>Without pointer net code2seq Ours w/o structure Ours w/o context</td><td>51.23 50.70 51.81</td><td>37.31 45.49 46.04</td><td>43.18 47.96</td></tr><tr><td>Ours With pointer net</td><td>50.33</td><td>46.80</td><td>48.75 48.50</td></tr><tr><td>Fernandes et al. (2019)</td><td>=</td><td>1</td><td>51.4</td></tr><tr><td>GREAT Ours w/o structure</td><td>53.60</td><td>46.41</td><td>49.75</td></tr><tr><td>Ours w/o context</td><td>55.48</td><td>46.07</td><td>50.34</td></tr><tr><td></td><td>54.45</td><td>45.29</td><td>49.45</td></tr><tr><td>Ours</td><td>54.85</td><td>49.84</td><td>52.22</td></tr><tr><td>Ours + Pretrain</td><td>57.02</td><td>50.87</td><td>53.77</td></tr></table>"
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    959,
+                    1403,
+                    959,
+                    1403,
+                    1174,
+                    298,
+                    1174
+                ],
+                "score": 0.98
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1287,
+                    822,
+                    1287,
+                    822,
+                    1741,
+                    299,
+                    1741
+                ],
+                "score": 0.976
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1881,
+                    1402,
+                    1881,
+                    1402,
+                    2034,
+                    299,
+                    2034
+                ],
+                "score": 0.973
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1743,
+                    1403,
+                    1743,
+                    1403,
+                    1865,
+                    299,
+                    1865
+                ],
+                "score": 0.965
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1208,
+                    1402,
+                    1208,
+                    1402,
+                    1270,
+                    299,
+                    1270
+                ],
+                "score": 0.939
+            },
+            {
+                "category_id": 6,
+                "poly": [
+                    464,
+                    557,
+                    1230,
+                    557,
+                    1230,
+                    589,
+                    464,
+                    589
+                ],
+                "score": 0.883
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    300,
+                    76,
+                    812,
+                    76,
+                    812,
+                    105,
+                    300,
+                    105
+                ],
+                "score": 0.88
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    842,
+                    2088,
+                    858,
+                    2088,
+                    858,
+                    2111,
+                    842,
+                    2111
+                ],
+                "score": 0.655
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    842,
+                    2088,
+                    859,
+                    2088,
+                    859,
+                    2111,
+                    842,
+                    2111
+                ],
+                "score": 0.234
+            },
+            {
+                "category_id": 7,
+                "poly": [
+                    846,
+                    1700,
+                    1400,
+                    1700,
+                    1400,
+                    1730,
+                    846,
+                    1730
+                ],
+                "score": 0.174
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    416,
+                    486,
+                    433,
+                    486,
+                    433,
+                    504,
+                    416,
+                    504
+                ],
+                "score": 0.65,
+                "latex": "^ +"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    416,
+                    508,
+                    433,
+                    508,
+                    433,
+                    527,
+                    416,
+                    527
+                ],
+                "score": 0.41,
+                "latex": "^ +"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    464.0,
+                    552.0,
+                    1233.0,
+                    552.0,
+                    1233.0,
+                    594.0,
+                    464.0,
+                    594.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    71.0,
+                    815.0,
+                    71.0,
+                    815.0,
+                    108.0,
+                    294.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    840.0,
+                    2086.0,
+                    860.0,
+                    2086.0,
+                    860.0,
+                    2119.0,
+                    840.0,
+                    2119.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    840.0,
+                    2087.0,
+                    861.0,
+                    2087.0,
+                    861.0,
+                    2119.0,
+                    840.0,
+                    2119.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    843.0,
+                    1696.0,
+                    1403.0,
+                    1696.0,
+                    1403.0,
+                    1734.0,
+                    843.0,
+                    1734.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    651.0,
+                    1401.0,
+                    651.0,
+                    1401.0,
+                    684.0,
+                    295.0,
+                    684.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    679.0,
+                    1405.0,
+                    679.0,
+                    1405.0,
+                    717.0,
+                    294.0,
+                    717.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    710.0,
+                    1406.0,
+                    710.0,
+                    1406.0,
+                    748.0,
+                    294.0,
+                    748.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    740.0,
+                    1405.0,
+                    740.0,
+                    1405.0,
+                    777.0,
+                    294.0,
+                    777.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    773.0,
+                    1404.0,
+                    773.0,
+                    1404.0,
+                    805.0,
+                    295.0,
+                    805.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    801.0,
+                    1405.0,
+                    801.0,
+                    1405.0,
+                    838.0,
+                    294.0,
+                    838.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    833.0,
+                    1406.0,
+                    833.0,
+                    1406.0,
+                    869.0,
+                    295.0,
+                    869.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    863.0,
+                    1406.0,
+                    863.0,
+                    1406.0,
+                    899.0,
+                    294.0,
+                    899.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    890.0,
+                    1248.0,
+                    890.0,
+                    1248.0,
+                    932.0,
+                    294.0,
+                    932.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    958.0,
+                    1403.0,
+                    958.0,
+                    1403.0,
+                    993.0,
+                    294.0,
+                    993.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    990.0,
+                    1404.0,
+                    990.0,
+                    1404.0,
+                    1026.0,
+                    293.0,
+                    1026.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1021.0,
+                    1404.0,
+                    1021.0,
+                    1404.0,
+                    1055.0,
+                    294.0,
+                    1055.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1049.0,
+                    1407.0,
+                    1049.0,
+                    1407.0,
+                    1090.0,
+                    292.0,
+                    1090.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1080.0,
+                    1405.0,
+                    1080.0,
+                    1405.0,
+                    1118.0,
+                    293.0,
+                    1118.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1111.0,
+                    1404.0,
+                    1111.0,
+                    1404.0,
+                    1148.0,
+                    292.0,
+                    1148.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1143.0,
+                    1375.0,
+                    1143.0,
+                    1375.0,
+                    1181.0,
+                    294.0,
+                    1181.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    1286.0,
+                    824.0,
+                    1286.0,
+                    824.0,
+                    1317.0,
+                    297.0,
+                    1317.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1315.0,
+                    825.0,
+                    1315.0,
+                    825.0,
+                    1349.0,
+                    295.0,
+                    1349.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1345.0,
+                    826.0,
+                    1345.0,
+                    826.0,
+                    1383.0,
+                    293.0,
+                    1383.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1377.0,
+                    826.0,
+                    1377.0,
+                    826.0,
+                    1410.0,
+                    293.0,
+                    1410.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1407.0,
+                    826.0,
+                    1407.0,
+                    826.0,
+                    1441.0,
+                    294.0,
+                    1441.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1439.0,
+                    827.0,
+                    1439.0,
+                    827.0,
+                    1470.0,
+                    294.0,
+                    1470.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1469.0,
+                    826.0,
+                    1469.0,
+                    826.0,
+                    1499.0,
+                    295.0,
+                    1499.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1497.0,
+                    827.0,
+                    1497.0,
+                    827.0,
+                    1534.0,
+                    293.0,
+                    1534.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1530.0,
+                    826.0,
+                    1530.0,
+                    826.0,
+                    1562.0,
+                    295.0,
+                    1562.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1561.0,
+                    826.0,
+                    1561.0,
+                    826.0,
+                    1592.0,
+                    295.0,
+                    1592.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1590.0,
+                    825.0,
+                    1590.0,
+                    825.0,
+                    1625.0,
+                    293.0,
+                    1625.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1622.0,
+                    826.0,
+                    1622.0,
+                    826.0,
+                    1652.0,
+                    294.0,
+                    1652.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1653.0,
+                    826.0,
+                    1653.0,
+                    826.0,
+                    1684.0,
+                    293.0,
+                    1684.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1681.0,
+                    825.0,
+                    1681.0,
+                    825.0,
+                    1715.0,
+                    294.0,
+                    1715.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1710.0,
+                    826.0,
+                    1710.0,
+                    826.0,
+                    1746.0,
+                    294.0,
+                    1746.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    1884.0,
+                    1403.0,
+                    1884.0,
+                    1403.0,
+                    1913.0,
+                    297.0,
+                    1913.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1909.0,
+                    1404.0,
+                    1909.0,
+                    1404.0,
+                    1947.0,
+                    294.0,
+                    1947.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    1943.0,
+                    1403.0,
+                    1943.0,
+                    1403.0,
+                    1976.0,
+                    297.0,
+                    1976.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1973.0,
+                    1403.0,
+                    1973.0,
+                    1403.0,
+                    2006.0,
+                    295.0,
+                    2006.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    2004.0,
+                    1404.0,
+                    2004.0,
+                    1404.0,
+                    2034.0,
+                    294.0,
+                    2034.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1742.0,
+                    1405.0,
+                    1742.0,
+                    1405.0,
+                    1777.0,
+                    295.0,
+                    1777.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    298.0,
+                    1776.0,
+                    1402.0,
+                    1776.0,
+                    1402.0,
+                    1805.0,
+                    298.0,
+                    1805.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1805.0,
+                    1404.0,
+                    1805.0,
+                    1404.0,
+                    1838.0,
+                    295.0,
+                    1838.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1835.0,
+                    1361.0,
+                    1835.0,
+                    1361.0,
+                    1866.0,
+                    294.0,
+                    1866.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    1207.0,
+                    1404.0,
+                    1207.0,
+                    1404.0,
+                    1243.0,
+                    297.0,
+                    1243.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1239.0,
+                    731.0,
+                    1239.0,
+                    731.0,
+                    1272.0,
+                    294.0,
+                    1272.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 6,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1246,
+                    1403,
+                    1246,
+                    1403,
+                    1429,
+                    298,
+                    1429
+                ],
+                "score": 0.978
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1015,
+                    1403,
+                    1015,
+                    1403,
+                    1230,
+                    299,
+                    1230
+                ],
+                "score": 0.978
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    755,
+                    1404,
+                    755,
+                    1404,
+                    1000,
+                    297,
+                    1000
+                ],
+                "score": 0.976
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1570,
+                    1404,
+                    1570,
+                    1404,
+                    1845,
+                    298,
+                    1845
+                ],
+                "score": 0.975
+            },
+            {
+                "category_id": 5,
+                "poly": [
+                    985,
+                    406,
+                    1379,
+                    406,
+                    1379,
+                    591,
+                    985,
+                    591
+                ],
+                "score": 0.971,
+                "html": "<table><tr><td>AST distance</td><td>F1 score</td></tr><tr><td>Sibling shortest paths</td><td>46.17</td></tr><tr><td>Ancestor shortest paths</td><td>47.89</td></tr><tr><td>Shortest paths</td><td>47.76</td></tr><tr><td>Personalized PageRank</td><td>48.47</td></tr><tr><td>All the above (c.f. Table 3)</td><td>48.75</td></tr></table>"
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    300,
+                    1444,
+                    1402,
+                    1444,
+                    1402,
+                    1537,
+                    300,
+                    1537
+                ],
+                "score": 0.969
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    416,
+                    940,
+                    416,
+                    940,
+                    661,
+                    299,
+                    661
+                ],
+                "score": 0.969
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    300,
+                    1861,
+                    1401,
+                    1861,
+                    1401,
+                    1985,
+                    300,
+                    1985
+                ],
+                "score": 0.968
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    301,
+                    229,
+                    1402,
+                    229,
+                    1402,
+                    323,
+                    301,
+                    323
+                ],
+                "score": 0.959
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    662,
+                    1403,
+                    662,
+                    1403,
+                    722,
+                    299,
+                    722
+                ],
+                "score": 0.942
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    327,
+                    2006,
+                    1110,
+                    2006,
+                    1110,
+                    2034,
+                    327,
+                    2034
+                ],
+                "score": 0.905
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    300,
+                    76,
+                    812,
+                    76,
+                    812,
+                    104,
+                    300,
+                    104
+                ],
+                "score": 0.893
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    301,
+                    360,
+                    836,
+                    360,
+                    836,
+                    389,
+                    301,
+                    389
+                ],
+                "score": 0.857
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2089,
+                    858,
+                    2089,
+                    858,
+                    2111,
+                    841,
+                    2111
+                ],
+                "score": 0.794
+            },
+            {
+                "category_id": 6,
+                "poly": [
+                    976,
+                    614,
+                    1393,
+                    614,
+                    1393,
+                    645,
+                    976,
+                    645
+                ],
+                "score": 0.727
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1320,
+                    1506,
+                    1387,
+                    1506,
+                    1387,
+                    1535,
+                    1320,
+                    1535
+                ],
+                "score": 0.9,
+                "latex": "122 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    471,
+                    1506,
+                    537,
+                    1506,
+                    537,
+                    1535,
+                    471,
+                    1535
+                ],
+                "score": 0.86,
+                "latex": "112 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1174,
+                    1474,
+                    1204,
+                    1474,
+                    1204,
+                    1504,
+                    1174,
+                    1504
+                ],
+                "score": 0.67,
+                "latex": "2 ^ { 4 }"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    329.0,
+                    1999.0,
+                    1113.0,
+                    1999.0,
+                    1113.0,
+                    2040.0,
+                    329.0,
+                    2040.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    73.0,
+                    815.0,
+                    73.0,
+                    815.0,
+                    108.0,
+                    295.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    358.0,
+                    840.0,
+                    358.0,
+                    840.0,
+                    394.0,
+                    295.0,
+                    394.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    839.0,
+                    2086.0,
+                    860.0,
+                    2086.0,
+                    860.0,
+                    2116.0,
+                    839.0,
+                    2116.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    970.0,
+                    607.0,
+                    1394.0,
+                    607.0,
+                    1394.0,
+                    651.0,
+                    970.0,
+                    651.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1247.0,
+                    1404.0,
+                    1247.0,
+                    1404.0,
+                    1278.0,
+                    296.0,
+                    1278.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1276.0,
+                    1404.0,
+                    1276.0,
+                    1404.0,
+                    1307.0,
+                    296.0,
+                    1307.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1303.0,
+                    1405.0,
+                    1303.0,
+                    1405.0,
+                    1343.0,
+                    293.0,
+                    1343.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1336.0,
+                    1403.0,
+                    1336.0,
+                    1403.0,
+                    1372.0,
+                    293.0,
+                    1372.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1365.0,
+                    1407.0,
+                    1365.0,
+                    1407.0,
+                    1404.0,
+                    293.0,
+                    1404.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1396.0,
+                    1375.0,
+                    1396.0,
+                    1375.0,
+                    1435.0,
+                    293.0,
+                    1435.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1013.0,
+                    1403.0,
+                    1013.0,
+                    1403.0,
+                    1050.0,
+                    293.0,
+                    1050.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1049.0,
+                    1404.0,
+                    1049.0,
+                    1404.0,
+                    1079.0,
+                    295.0,
+                    1079.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1077.0,
+                    1405.0,
+                    1077.0,
+                    1405.0,
+                    1111.0,
+                    295.0,
+                    1111.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1108.0,
+                    1405.0,
+                    1108.0,
+                    1405.0,
+                    1142.0,
+                    295.0,
+                    1142.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1134.0,
+                    1407.0,
+                    1134.0,
+                    1407.0,
+                    1174.0,
+                    293.0,
+                    1174.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1168.0,
+                    1405.0,
+                    1168.0,
+                    1405.0,
+                    1202.0,
+                    295.0,
+                    1202.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1199.0,
+                    994.0,
+                    1199.0,
+                    994.0,
+                    1233.0,
+                    295.0,
+                    1233.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    754.0,
+                    1404.0,
+                    754.0,
+                    1404.0,
+                    789.0,
+                    294.0,
+                    789.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    788.0,
+                    1404.0,
+                    788.0,
+                    1404.0,
+                    821.0,
+                    294.0,
+                    821.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    815.0,
+                    1406.0,
+                    815.0,
+                    1406.0,
+                    852.0,
+                    294.0,
+                    852.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    845.0,
+                    1406.0,
+                    845.0,
+                    1406.0,
+                    884.0,
+                    292.0,
+                    884.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    875.0,
+                    1406.0,
+                    875.0,
+                    1406.0,
+                    913.0,
+                    292.0,
+                    913.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    904.0,
+                    1406.0,
+                    904.0,
+                    1406.0,
+                    946.0,
+                    292.0,
+                    946.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    937.0,
+                    1406.0,
+                    937.0,
+                    1406.0,
+                    975.0,
+                    294.0,
+                    975.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    967.0,
+                    1404.0,
+                    967.0,
+                    1404.0,
+                    1006.0,
+                    292.0,
+                    1006.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1569.0,
+                    1405.0,
+                    1569.0,
+                    1405.0,
+                    1606.0,
+                    296.0,
+                    1606.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1602.0,
+                    1404.0,
+                    1602.0,
+                    1404.0,
+                    1635.0,
+                    296.0,
+                    1635.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1629.0,
+                    1406.0,
+                    1629.0,
+                    1406.0,
+                    1668.0,
+                    293.0,
+                    1668.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1657.0,
+                    1406.0,
+                    1657.0,
+                    1406.0,
+                    1700.0,
+                    292.0,
+                    1700.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1692.0,
+                    1406.0,
+                    1692.0,
+                    1406.0,
+                    1728.0,
+                    293.0,
+                    1728.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1721.0,
+                    1406.0,
+                    1721.0,
+                    1406.0,
+                    1758.0,
+                    293.0,
+                    1758.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1752.0,
+                    1406.0,
+                    1752.0,
+                    1406.0,
+                    1790.0,
+                    292.0,
+                    1790.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1778.0,
+                    1405.0,
+                    1778.0,
+                    1405.0,
+                    1822.0,
+                    291.0,
+                    1822.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1812.0,
+                    1404.0,
+                    1812.0,
+                    1404.0,
+                    1851.0,
+                    293.0,
+                    1851.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1445.0,
+                    1404.0,
+                    1445.0,
+                    1404.0,
+                    1478.0,
+                    295.0,
+                    1478.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1474.0,
+                    1173.0,
+                    1474.0,
+                    1173.0,
+                    1510.0,
+                    293.0,
+                    1510.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1205.0,
+                    1474.0,
+                    1406.0,
+                    1474.0,
+                    1406.0,
+                    1510.0,
+                    1205.0,
+                    1510.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1506.0,
+                    470.0,
+                    1506.0,
+                    470.0,
+                    1540.0,
+                    295.0,
+                    1540.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    538.0,
+                    1506.0,
+                    1319.0,
+                    1506.0,
+                    1319.0,
+                    1540.0,
+                    538.0,
+                    1540.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1388.0,
+                    1506.0,
+                    1398.0,
+                    1506.0,
+                    1398.0,
+                    1540.0,
+                    1388.0,
+                    1540.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    416.0,
+                    943.0,
+                    416.0,
+                    943.0,
+                    449.0,
+                    295.0,
+                    449.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    446.0,
+                    943.0,
+                    446.0,
+                    943.0,
+                    481.0,
+                    294.0,
+                    481.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    476.0,
+                    944.0,
+                    476.0,
+                    944.0,
+                    511.0,
+                    293.0,
+                    511.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    507.0,
+                    944.0,
+                    507.0,
+                    944.0,
+                    540.0,
+                    294.0,
+                    540.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    539.0,
+                    944.0,
+                    539.0,
+                    944.0,
+                    570.0,
+                    294.0,
+                    570.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    570.0,
+                    945.0,
+                    570.0,
+                    945.0,
+                    601.0,
+                    292.0,
+                    601.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    599.0,
+                    944.0,
+                    599.0,
+                    944.0,
+                    631.0,
+                    294.0,
+                    631.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    631.0,
+                    945.0,
+                    631.0,
+                    945.0,
+                    664.0,
+                    296.0,
+                    664.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1860.0,
+                    1406.0,
+                    1860.0,
+                    1406.0,
+                    1896.0,
+                    295.0,
+                    1896.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1891.0,
+                    1406.0,
+                    1891.0,
+                    1406.0,
+                    1928.0,
+                    295.0,
+                    1928.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1923.0,
+                    1403.0,
+                    1923.0,
+                    1403.0,
+                    1956.0,
+                    296.0,
+                    1956.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1955.0,
+                    1403.0,
+                    1955.0,
+                    1403.0,
+                    1987.0,
+                    296.0,
+                    1987.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    230.0,
+                    1407.0,
+                    230.0,
+                    1407.0,
+                    264.0,
+                    293.0,
+                    264.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    261.0,
+                    1404.0,
+                    261.0,
+                    1404.0,
+                    297.0,
+                    295.0,
+                    297.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    289.0,
+                    1028.0,
+                    289.0,
+                    1028.0,
+                    326.0,
+                    295.0,
+                    326.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    658.0,
+                    1403.0,
+                    658.0,
+                    1403.0,
+                    696.0,
+                    294.0,
+                    696.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    686.0,
+                    1221.0,
+                    686.0,
+                    1221.0,
+                    728.0,
+                    293.0,
+                    728.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 7,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1703,
+                    1403,
+                    1703,
+                    1403,
+                    2010,
+                    298,
+                    2010
+                ],
+                "score": 0.983
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1175,
+                    1403,
+                    1175,
+                    1403,
+                    1482,
+                    298,
+                    1482
+                ],
+                "score": 0.981
+            },
+            {
+                "category_id": 3,
+                "poly": [
+                    383,
+                    178,
+                    1319,
+                    178,
+                    1319,
+                    671,
+                    383,
+                    671
+                ],
+                "score": 0.972
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    301,
+                    1497,
+                    1400,
+                    1497,
+                    1400,
+                    1590,
+                    301,
+                    1590
+                ],
+                "score": 0.965
+            },
+            {
+                "category_id": 4,
+                "poly": [
+                    296,
+                    993,
+                    1405,
+                    993,
+                    1405,
+                    1115,
+                    296,
+                    1115
+                ],
+                "score": 0.948
+            },
+            {
+                "category_id": 4,
+                "poly": [
+                    297,
+                    688,
+                    1396,
+                    688,
+                    1396,
+                    721,
+                    297,
+                    721
+                ],
+                "score": 0.916
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    299,
+                    1636,
+                    543,
+                    1636,
+                    543,
+                    1670,
+                    299,
+                    1670
+                ],
+                "score": 0.886
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    76,
+                    812,
+                    76,
+                    812,
+                    104,
+                    298,
+                    104
+                ],
+                "score": 0.88
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    840,
+                    2088,
+                    858,
+                    2088,
+                    858,
+                    2111,
+                    840,
+                    2111
+                ],
+                "score": 0.787
+            },
+            {
+                "category_id": 3,
+                "poly": [
+                    348,
+                    751,
+                    1320,
+                    751,
+                    1320,
+                    967,
+                    348,
+                    967
+                ],
+                "score": 0.771
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    349,
+                    750,
+                    759,
+                    750,
+                    759,
+                    970,
+                    349,
+                    970
+                ],
+                "score": 0.374
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    929,
+                    830,
+                    999,
+                    830,
+                    999,
+                    848,
+                    929,
+                    848
+                ],
+                "score": 0.64,
+                "latex": "\\scriptstyle { \\begin{array} { r l } { S } & { { } = = = } \\\\ { \\sqrt { \\phantom { } } } \\end{array} }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    923,
+                    807,
+                    985,
+                    807,
+                    985,
+                    826,
+                    923,
+                    826
+                ],
+                "score": 0.62,
+                "latex": "\\scriptstyle { \\begin{array} { r l } { \\mathbf { S } } & { { } = = = } \\\\ { \\mathbf { S } } & { { } = = = } \\end{array} }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1114,
+                    806,
+                    1216,
+                    806,
+                    1216,
+                    826,
+                    1114,
+                    826
+                ],
+                "score": 0.53,
+                "latex": "s \\ \\mathrm { ~ \\ = = = ~ \\ ~ } \\cdot \\mathrm { ~ f ~ }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    930,
+                    852,
+                    997,
+                    852,
+                    997,
+                    871,
+                    930,
+                    871
+                ],
+                "score": 0.5,
+                "latex": "\\scriptstyle { \\begin{array} { r l } { S } & { { } = = = } \\\\ { \\sqrt { \\phantom { } } } \\end{array} }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1083,
+                    850,
+                    1217,
+                    850,
+                    1217,
+                    872,
+                    1083,
+                    872
+                ],
+                "score": 0.48,
+                "latex": "| \\mathrm { ~  ~ { ~ \\cal ~ s ~ } ~ } = = { } | \\mathrm { ~  ~ { ~ \\cal ~ O ~ } ~ } ^ { \\prime } |"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    895,
+                    786,
+                    915,
+                    786,
+                    915,
+                    804,
+                    895,
+                    804
+                ],
+                "score": 0.26,
+                "latex": "="
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    628.0,
+                    182.0,
+                    706.0,
+                    182.0,
+                    706.0,
+                    212.0,
+                    628.0,
+                    212.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    750.0,
+                    194.0,
+                    760.0,
+                    194.0,
+                    760.0,
+                    204.0,
+                    750.0,
+                    204.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    780.0,
+                    184.0,
+                    882.0,
+                    184.0,
+                    882.0,
+                    212.0,
+                    780.0,
+                    212.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    920.0,
+                    190.0,
+                    943.0,
+                    190.0,
+                    943.0,
+                    208.0,
+                    920.0,
+                    208.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    957.0,
+                    186.0,
+                    998.0,
+                    186.0,
+                    998.0,
+                    213.0,
+                    957.0,
+                    213.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1065.0,
+                    181.0,
+                    1122.0,
+                    181.0,
+                    1122.0,
+                    215.0,
+                    1065.0,
+                    215.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1052.0,
+                    240.0,
+                    1312.0,
+                    240.0,
+                    1312.0,
+                    271.0,
+                    1052.0,
+                    271.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1050.0,
+                    271.0,
+                    1301.0,
+                    271.0,
+                    1301.0,
+                    301.0,
+                    1050.0,
+                    301.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    993.0,
+                    1406.0,
+                    993.0,
+                    1406.0,
+                    1029.0,
+                    294.0,
+                    1029.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1022.0,
+                    1407.0,
+                    1022.0,
+                    1407.0,
+                    1059.0,
+                    291.0,
+                    1059.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1055.0,
+                    1406.0,
+                    1055.0,
+                    1406.0,
+                    1091.0,
+                    294.0,
+                    1091.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1084.0,
+                    1257.0,
+                    1084.0,
+                    1257.0,
+                    1120.0,
+                    293.0,
+                    1120.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    684.0,
+                    1401.0,
+                    684.0,
+                    1401.0,
+                    727.0,
+                    297.0,
+                    727.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1629.0,
+                    549.0,
+                    1629.0,
+                    549.0,
+                    1679.0,
+                    292.0,
+                    1679.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    73.0,
+                    816.0,
+                    73.0,
+                    816.0,
+                    108.0,
+                    295.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    839.0,
+                    2087.0,
+                    860.0,
+                    2087.0,
+                    860.0,
+                    2117.0,
+                    839.0,
+                    2117.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    347.0,
+                    747.0,
+                    552.0,
+                    747.0,
+                    552.0,
+                    775.0,
+                    347.0,
+                    775.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    370.0,
+                    769.0,
+                    527.0,
+                    769.0,
+                    527.0,
+                    797.0,
+                    370.0,
+                    797.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    852.0,
+                    761.0,
+                    1322.0,
+                    761.0,
+                    1322.0,
+                    785.0,
+                    852.0,
+                    785.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    370.0,
+                    792.0,
+                    555.0,
+                    792.0,
+                    555.0,
+                    819.0,
+                    370.0,
+                    819.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    568.0,
+                    792.0,
+                    612.0,
+                    792.0,
+                    612.0,
+                    819.0,
+                    568.0,
+                    819.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    626.0,
+                    793.0,
+                    690.0,
+                    793.0,
+                    690.0,
+                    818.0,
+                    626.0,
+                    818.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    871.0,
+                    783.0,
+                    894.0,
+                    783.0,
+                    894.0,
+                    807.0,
+                    871.0,
+                    807.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    916.0,
+                    783.0,
+                    1111.0,
+                    783.0,
+                    1111.0,
+                    807.0,
+                    916.0,
+                    807.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    369.0,
+                    815.0,
+                    566.0,
+                    815.0,
+                    566.0,
+                    863.0,
+                    369.0,
+                    863.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    581.0,
+                    837.0,
+                    624.0,
+                    837.0,
+                    624.0,
+                    862.0,
+                    581.0,
+                    862.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    637.0,
+                    837.0,
+                    702.0,
+                    837.0,
+                    702.0,
+                    862.0,
+                    637.0,
+                    862.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    871.0,
+                    803.0,
+                    922.0,
+                    803.0,
+                    922.0,
+                    851.0,
+                    871.0,
+                    851.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1000.0,
+                    803.0,
+                    1076.0,
+                    803.0,
+                    1076.0,
+                    851.0,
+                    1000.0,
+                    851.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1086.0,
+                    810.0,
+                    1156.0,
+                    810.0,
+                    1156.0,
+                    850.0,
+                    1086.0,
+                    850.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1217.0,
+                    804.0,
+                    1228.0,
+                    804.0,
+                    1228.0,
+                    851.0,
+                    1217.0,
+                    851.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    896.0,
+                    849.0,
+                    929.0,
+                    849.0,
+                    929.0,
+                    872.0,
+                    896.0,
+                    872.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    998.0,
+                    849.0,
+                    1065.0,
+                    849.0,
+                    1065.0,
+                    872.0,
+                    998.0,
+                    872.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1071.0,
+                    848.0,
+                    1082.0,
+                    848.0,
+                    1082.0,
+                    873.0,
+                    1071.0,
+                    873.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1218.0,
+                    848.0,
+                    1252.0,
+                    848.0,
+                    1252.0,
+                    873.0,
+                    1218.0,
+                    873.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    860.0,
+                    543.0,
+                    860.0,
+                    543.0,
+                    884.0,
+                    393.0,
+                    884.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    371.0,
+                    882.0,
+                    564.0,
+                    882.0,
+                    564.0,
+                    906.0,
+                    371.0,
+                    906.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    896.0,
+                    870.0,
+                    1052.0,
+                    870.0,
+                    1052.0,
+                    898.0,
+                    896.0,
+                    898.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    900.0,
+                    766.0,
+                    900.0,
+                    766.0,
+                    955.0,
+                    392.0,
+                    955.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    854.0,
+                    943.0,
+                    863.0,
+                    943.0,
+                    863.0,
+                    958.0,
+                    854.0,
+                    958.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    872.0,
+                    914.0,
+                    1017.0,
+                    914.0,
+                    1017.0,
+                    941.0,
+                    872.0,
+                    941.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    372.0,
+                    953.0,
+                    386.0,
+                    953.0,
+                    386.0,
+                    969.0,
+                    372.0,
+                    969.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1703.0,
+                    1404.0,
+                    1703.0,
+                    1404.0,
+                    1740.0,
+                    294.0,
+                    1740.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1736.0,
+                    1405.0,
+                    1736.0,
+                    1405.0,
+                    1771.0,
+                    296.0,
+                    1771.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1765.0,
+                    1405.0,
+                    1765.0,
+                    1405.0,
+                    1801.0,
+                    293.0,
+                    1801.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1797.0,
+                    1405.0,
+                    1797.0,
+                    1405.0,
+                    1832.0,
+                    294.0,
+                    1832.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1826.0,
+                    1405.0,
+                    1826.0,
+                    1405.0,
+                    1862.0,
+                    293.0,
+                    1862.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1857.0,
+                    1405.0,
+                    1857.0,
+                    1405.0,
+                    1891.0,
+                    292.0,
+                    1891.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1885.0,
+                    1408.0,
+                    1885.0,
+                    1408.0,
+                    1925.0,
+                    291.0,
+                    1925.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1918.0,
+                    1405.0,
+                    1918.0,
+                    1405.0,
+                    1953.0,
+                    294.0,
+                    1953.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1948.0,
+                    1405.0,
+                    1948.0,
+                    1405.0,
+                    1984.0,
+                    294.0,
+                    1984.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1979.0,
+                    1157.0,
+                    1979.0,
+                    1157.0,
+                    2014.0,
+                    294.0,
+                    2014.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1173.0,
+                    1404.0,
+                    1173.0,
+                    1404.0,
+                    1214.0,
+                    292.0,
+                    1214.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1206.0,
+                    1407.0,
+                    1206.0,
+                    1407.0,
+                    1243.0,
+                    291.0,
+                    1243.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1237.0,
+                    1405.0,
+                    1237.0,
+                    1405.0,
+                    1273.0,
+                    293.0,
+                    1273.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1270.0,
+                    1404.0,
+                    1270.0,
+                    1404.0,
+                    1302.0,
+                    296.0,
+                    1302.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1298.0,
+                    1405.0,
+                    1298.0,
+                    1405.0,
+                    1334.0,
+                    294.0,
+                    1334.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1330.0,
+                    1407.0,
+                    1330.0,
+                    1407.0,
+                    1365.0,
+                    294.0,
+                    1365.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1359.0,
+                    1405.0,
+                    1359.0,
+                    1405.0,
+                    1395.0,
+                    294.0,
+                    1395.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1390.0,
+                    1405.0,
+                    1390.0,
+                    1405.0,
+                    1425.0,
+                    294.0,
+                    1425.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1419.0,
+                    1407.0,
+                    1419.0,
+                    1407.0,
+                    1458.0,
+                    293.0,
+                    1458.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1451.0,
+                    1156.0,
+                    1451.0,
+                    1156.0,
+                    1486.0,
+                    293.0,
+                    1486.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1494.0,
+                    1405.0,
+                    1494.0,
+                    1405.0,
+                    1534.0,
+                    295.0,
+                    1534.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1528.0,
+                    1404.0,
+                    1528.0,
+                    1404.0,
+                    1564.0,
+                    295.0,
+                    1564.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1558.0,
+                    1394.0,
+                    1558.0,
+                    1394.0,
+                    1595.0,
+                    295.0,
+                    1595.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    348.0,
+                    750.0,
+                    552.0,
+                    750.0,
+                    552.0,
+                    775.0,
+                    348.0,
+                    775.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    369.0,
+                    772.0,
+                    527.0,
+                    772.0,
+                    527.0,
+                    797.0,
+                    369.0,
+                    797.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    371.0,
+                    793.0,
+                    561.0,
+                    793.0,
+                    561.0,
+                    818.0,
+                    371.0,
+                    818.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    569.0,
+                    794.0,
+                    612.0,
+                    794.0,
+                    612.0,
+                    815.0,
+                    569.0,
+                    815.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    624.0,
+                    792.0,
+                    689.0,
+                    792.0,
+                    689.0,
+                    817.0,
+                    624.0,
+                    817.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    815.0,
+                    529.0,
+                    815.0,
+                    529.0,
+                    840.0,
+                    393.0,
+                    840.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    371.0,
+                    837.0,
+                    575.0,
+                    837.0,
+                    575.0,
+                    862.0,
+                    371.0,
+                    862.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    578.0,
+                    834.0,
+                    701.0,
+                    834.0,
+                    701.0,
+                    863.0,
+                    578.0,
+                    863.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    860.0,
+                    543.0,
+                    860.0,
+                    543.0,
+                    885.0,
+                    393.0,
+                    885.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    371.0,
+                    882.0,
+                    564.0,
+                    882.0,
+                    564.0,
+                    907.0,
+                    371.0,
+                    907.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    395.0,
+                    903.0,
+                    694.0,
+                    903.0,
+                    694.0,
+                    931.0,
+                    395.0,
+                    931.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    697.0,
+                    905.0,
+                    760.0,
+                    905.0,
+                    760.0,
+                    929.0,
+                    697.0,
+                    929.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    922.0,
+                    686.0,
+                    922.0,
+                    686.0,
+                    954.0,
+                    393.0,
+                    954.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    375.0,
+                    957.0,
+                    384.0,
+                    957.0,
+                    384.0,
+                    966.0,
+                    375.0,
+                    966.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 8,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1231,
+                    1403,
+                    1231,
+                    1403,
+                    1326,
+                    298,
+                    1326
+                ],
+                "score": 0.906
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1426,
+                    1405,
+                    1426,
+                    1405,
+                    1551,
+                    297,
+                    1551
+                ],
+                "score": 0.903
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1057,
+                    1404,
+                    1057,
+                    1404,
+                    1213,
+                    298,
+                    1213
+                ],
+                "score": 0.898
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    300,
+                    76,
+                    813,
+                    76,
+                    813,
+                    105,
+                    300,
+                    105
+                ],
+                "score": 0.887
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    279,
+                    1404,
+                    279,
+                    1404,
+                    463,
+                    297,
+                    463
+                ],
+                "score": 0.886
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1343,
+                    1401,
+                    1343,
+                    1401,
+                    1409,
+                    296,
+                    1409
+                ],
+                "score": 0.884
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1653,
+                    1404,
+                    1653,
+                    1404,
+                    1808,
+                    297,
+                    1808
+                ],
+                "score": 0.865
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    831,
+                    1399,
+                    831,
+                    1399,
+                    924,
+                    297,
+                    924
+                ],
+                "score": 0.861
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    300,
+                    228,
+                    488,
+                    228,
+                    488,
+                    261,
+                    300,
+                    261
+                ],
+                "score": 0.856
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    944,
+                    1400,
+                    944,
+                    1400,
+                    1039,
+                    296,
+                    1039
+                ],
+                "score": 0.855
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    657,
+                    1405,
+                    657,
+                    1405,
+                    811,
+                    296,
+                    811
+                ],
+                "score": 0.853
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    300,
+                    1910,
+                    1403,
+                    1910,
+                    1403,
+                    2035,
+                    300,
+                    2035
+                ],
+                "score": 0.841
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    289,
+                    1827,
+                    1401,
+                    1827,
+                    1401,
+                    1893,
+                    289,
+                    1893
+                ],
+                "score": 0.829
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    836,
+                    2088,
+                    865,
+                    2088,
+                    865,
+                    2112,
+                    836,
+                    2112
+                ],
+                "score": 0.822
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    483,
+                    1404,
+                    483,
+                    1404,
+                    637,
+                    297,
+                    637
+                ],
+                "score": 0.815
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    1570,
+                    1403,
+                    1570,
+                    1403,
+                    1635,
+                    295,
+                    1635
+                ],
+                "score": 0.813
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    742,
+                    1011,
+                    760,
+                    1011,
+                    760,
+                    1032,
+                    742,
+                    1032
+                ],
+                "score": 0.52,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    904,
+                    1297,
+                    922,
+                    1297,
+                    922,
+                    1319,
+                    904,
+                    1319
+                ],
+                "score": 0.47,
+                "latex": "="
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    71.0,
+                    815.0,
+                    71.0,
+                    815.0,
+                    108.0,
+                    294.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    227.0,
+                    491.0,
+                    227.0,
+                    491.0,
+                    265.0,
+                    295.0,
+                    265.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    832.0,
+                    2084.0,
+                    871.0,
+                    2084.0,
+                    871.0,
+                    2123.0,
+                    832.0,
+                    2123.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1229.0,
+                    1403.0,
+                    1229.0,
+                    1403.0,
+                    1270.0,
+                    295.0,
+                    1270.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    1263.0,
+                    1404.0,
+                    1263.0,
+                    1404.0,
+                    1297.0,
+                    323.0,
+                    1297.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1291.0,
+                    903.0,
+                    1291.0,
+                    903.0,
+                    1331.0,
+                    322.0,
+                    1331.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    923.0,
+                    1291.0,
+                    1100.0,
+                    1291.0,
+                    1100.0,
+                    1331.0,
+                    923.0,
+                    1331.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1428.0,
+                    1403.0,
+                    1428.0,
+                    1403.0,
+                    1460.0,
+                    294.0,
+                    1460.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    1458.0,
+                    1405.0,
+                    1458.0,
+                    1405.0,
+                    1491.0,
+                    323.0,
+                    1491.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    319.0,
+                    1487.0,
+                    1406.0,
+                    1487.0,
+                    1406.0,
+                    1526.0,
+                    319.0,
+                    1526.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    1515.0,
+                    399.0,
+                    1515.0,
+                    399.0,
+                    1555.0,
+                    320.0,
+                    1555.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    1059.0,
+                    1402.0,
+                    1059.0,
+                    1402.0,
+                    1092.0,
+                    297.0,
+                    1092.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1088.0,
+                    1404.0,
+                    1088.0,
+                    1404.0,
+                    1126.0,
+                    322.0,
+                    1126.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1120.0,
+                    1405.0,
+                    1120.0,
+                    1405.0,
+                    1155.0,
+                    321.0,
+                    1155.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    1148.0,
+                    1405.0,
+                    1148.0,
+                    1405.0,
+                    1186.0,
+                    323.0,
+                    1186.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1178.0,
+                    1365.0,
+                    1178.0,
+                    1365.0,
+                    1216.0,
+                    322.0,
+                    1216.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    277.0,
+                    1405.0,
+                    277.0,
+                    1405.0,
+                    314.0,
+                    292.0,
+                    314.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    325.0,
+                    310.0,
+                    1401.0,
+                    310.0,
+                    1401.0,
+                    342.0,
+                    325.0,
+                    342.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    341.0,
+                    1404.0,
+                    341.0,
+                    1404.0,
+                    376.0,
+                    322.0,
+                    376.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    368.0,
+                    1405.0,
+                    368.0,
+                    1405.0,
+                    406.0,
+                    320.0,
+                    406.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    400.0,
+                    1406.0,
+                    400.0,
+                    1406.0,
+                    434.0,
+                    322.0,
+                    434.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    433.0,
+                    986.0,
+                    433.0,
+                    986.0,
+                    465.0,
+                    324.0,
+                    465.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1344.0,
+                    1405.0,
+                    1344.0,
+                    1405.0,
+                    1380.0,
+                    296.0,
+                    1380.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    1373.0,
+                    1405.0,
+                    1373.0,
+                    1405.0,
+                    1412.0,
+                    320.0,
+                    1412.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1653.0,
+                    1405.0,
+                    1653.0,
+                    1405.0,
+                    1691.0,
+                    295.0,
+                    1691.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1684.0,
+                    1406.0,
+                    1684.0,
+                    1406.0,
+                    1723.0,
+                    321.0,
+                    1723.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    1716.0,
+                    1406.0,
+                    1716.0,
+                    1406.0,
+                    1753.0,
+                    324.0,
+                    1753.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1742.0,
+                    1404.0,
+                    1742.0,
+                    1404.0,
+                    1786.0,
+                    322.0,
+                    1786.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    325.0,
+                    1777.0,
+                    886.0,
+                    1777.0,
+                    886.0,
+                    1810.0,
+                    325.0,
+                    1810.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    829.0,
+                    1404.0,
+                    829.0,
+                    1404.0,
+                    867.0,
+                    293.0,
+                    867.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    863.0,
+                    1404.0,
+                    863.0,
+                    1404.0,
+                    897.0,
+                    322.0,
+                    897.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    888.0,
+                    398.0,
+                    888.0,
+                    398.0,
+                    927.0,
+                    320.0,
+                    927.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    940.0,
+                    1405.0,
+                    940.0,
+                    1405.0,
+                    983.0,
+                    294.0,
+                    983.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    976.0,
+                    1401.0,
+                    976.0,
+                    1401.0,
+                    1010.0,
+                    324.0,
+                    1010.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    326.0,
+                    1006.0,
+                    741.0,
+                    1006.0,
+                    741.0,
+                    1041.0,
+                    326.0,
+                    1041.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    761.0,
+                    1006.0,
+                    923.0,
+                    1006.0,
+                    923.0,
+                    1041.0,
+                    761.0,
+                    1041.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    657.0,
+                    1405.0,
+                    657.0,
+                    1405.0,
+                    694.0,
+                    294.0,
+                    694.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    688.0,
+                    1405.0,
+                    688.0,
+                    1405.0,
+                    725.0,
+                    323.0,
+                    725.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    713.0,
+                    1406.0,
+                    713.0,
+                    1406.0,
+                    760.0,
+                    320.0,
+                    760.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    747.0,
+                    1402.0,
+                    747.0,
+                    1402.0,
+                    786.0,
+                    320.0,
+                    786.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    779.0,
+                    789.0,
+                    779.0,
+                    789.0,
+                    815.0,
+                    322.0,
+                    815.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1910.0,
+                    1407.0,
+                    1910.0,
+                    1407.0,
+                    1947.0,
+                    295.0,
+                    1947.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1942.0,
+                    1405.0,
+                    1942.0,
+                    1405.0,
+                    1978.0,
+                    321.0,
+                    1978.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    1974.0,
+                    1405.0,
+                    1974.0,
+                    1405.0,
+                    2008.0,
+                    320.0,
+                    2008.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    2002.0,
+                    1404.0,
+                    2002.0,
+                    1404.0,
+                    2037.0,
+                    321.0,
+                    2037.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1825.0,
+                    1403.0,
+                    1825.0,
+                    1403.0,
+                    1864.0,
+                    293.0,
+                    1864.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1859.0,
+                    1032.0,
+                    1859.0,
+                    1032.0,
+                    1894.0,
+                    321.0,
+                    1894.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    478.0,
+                    1406.0,
+                    478.0,
+                    1406.0,
+                    524.0,
+                    292.0,
+                    524.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    514.0,
+                    1404.0,
+                    514.0,
+                    1404.0,
+                    551.0,
+                    322.0,
+                    551.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    544.0,
+                    1404.0,
+                    544.0,
+                    1404.0,
+                    578.0,
+                    320.0,
+                    578.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    575.0,
+                    1406.0,
+                    575.0,
+                    1406.0,
+                    609.0,
+                    321.0,
+                    609.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    605.0,
+                    988.0,
+                    605.0,
+                    988.0,
+                    641.0,
+                    320.0,
+                    641.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    1572.0,
+                    1404.0,
+                    1572.0,
+                    1404.0,
+                    1608.0,
+                    297.0,
+                    1608.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1603.0,
+                    1245.0,
+                    1603.0,
+                    1245.0,
+                    1636.0,
+                    322.0,
+                    1636.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 9,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1942,
+                    1402,
+                    1942,
+                    1402,
+                    2034,
+                    299,
+                    2034
+                ],
+                "score": 0.901
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    300,
+                    75,
+                    813,
+                    75,
+                    813,
+                    105,
+                    300,
+                    105
+                ],
+                "score": 0.88
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    312,
+                    228,
+                    1398,
+                    228,
+                    1398,
+                    294,
+                    312,
+                    294
+                ],
+                "score": 0.858
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    836,
+                    2088,
+                    863,
+                    2088,
+                    863,
+                    2113,
+                    836,
+                    2113
+                ],
+                "score": 0.819
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    314,
+                    1400,
+                    314,
+                    1400,
+                    377,
+                    295,
+                    377
+                ],
+                "score": 0.805
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    294,
+                    1651,
+                    1399,
+                    1651,
+                    1399,
+                    1715,
+                    294,
+                    1715
+                ],
+                "score": 0.782
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1734,
+                    1404,
+                    1734,
+                    1404,
+                    1920,
+                    298,
+                    1920
+                ],
+                "score": 0.756
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    1339,
+                    1398,
+                    1339,
+                    1398,
+                    1404,
+                    295,
+                    1404
+                ],
+                "score": 0.749
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    397,
+                    1404,
+                    397,
+                    1404,
+                    552,
+                    297,
+                    552
+                ],
+                "score": 0.739
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    293,
+                    882,
+                    1401,
+                    882,
+                    1401,
+                    977,
+                    293,
+                    977
+                ],
+                "score": 0.737
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1225,
+                    1400,
+                    1225,
+                    1400,
+                    1319,
+                    299,
+                    1319
+                ],
+                "score": 0.731
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1537,
+                    1404,
+                    1537,
+                    1404,
+                    1631,
+                    298,
+                    1631
+                ],
+                "score": 0.73
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    302,
+                    1110,
+                    1396,
+                    1110,
+                    1396,
+                    1206,
+                    302,
+                    1206
+                ],
+                "score": 0.717
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    571,
+                    1398,
+                    571,
+                    1398,
+                    637,
+                    296,
+                    637
+                ],
+                "score": 0.71
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    302,
+                    996,
+                    1399,
+                    996,
+                    1399,
+                    1093,
+                    302,
+                    1093
+                ],
+                "score": 0.688
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1422,
+                    1404,
+                    1422,
+                    1404,
+                    1517,
+                    298,
+                    1517
+                ],
+                "score": 0.677
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    654,
+                    1400,
+                    654,
+                    1400,
+                    749,
+                    295,
+                    749
+                ],
+                "score": 0.619
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    768,
+                    1405,
+                    768,
+                    1405,
+                    863,
+                    295,
+                    863
+                ],
+                "score": 0.251
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    742,
+                    1178,
+                    760,
+                    1178,
+                    760,
+                    1199,
+                    742,
+                    1199
+                ],
+                "score": 0.51,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    904,
+                    1490,
+                    921,
+                    1490,
+                    921,
+                    1512,
+                    904,
+                    1512
+                ],
+                "score": 0.44,
+                "latex": "="
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    73.0,
+                    815.0,
+                    73.0,
+                    815.0,
+                    108.0,
+                    295.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    832.0,
+                    2085.0,
+                    868.0,
+                    2085.0,
+                    868.0,
+                    2125.0,
+                    832.0,
+                    2125.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1941.0,
+                    1402.0,
+                    1941.0,
+                    1402.0,
+                    1975.0,
+                    295.0,
+                    1975.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    1971.0,
+                    1403.0,
+                    1971.0,
+                    1403.0,
+                    2005.0,
+                    324.0,
+                    2005.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    2001.0,
+                    612.0,
+                    2001.0,
+                    612.0,
+                    2035.0,
+                    322.0,
+                    2035.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    229.0,
+                    1403.0,
+                    229.0,
+                    1403.0,
+                    264.0,
+                    323.0,
+                    264.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    325.0,
+                    262.0,
+                    1048.0,
+                    262.0,
+                    1048.0,
+                    295.0,
+                    325.0,
+                    295.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    312.0,
+                    1405.0,
+                    312.0,
+                    1405.0,
+                    348.0,
+                    295.0,
+                    348.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    346.0,
+                    1003.0,
+                    346.0,
+                    1003.0,
+                    377.0,
+                    323.0,
+                    377.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1650.0,
+                    1404.0,
+                    1650.0,
+                    1404.0,
+                    1689.0,
+                    294.0,
+                    1689.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    1682.0,
+                    533.0,
+                    1682.0,
+                    533.0,
+                    1715.0,
+                    324.0,
+                    1715.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1735.0,
+                    1406.0,
+                    1735.0,
+                    1406.0,
+                    1771.0,
+                    296.0,
+                    1771.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    1766.0,
+                    1404.0,
+                    1766.0,
+                    1404.0,
+                    1801.0,
+                    323.0,
+                    1801.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1795.0,
+                    1405.0,
+                    1795.0,
+                    1405.0,
+                    1832.0,
+                    321.0,
+                    1832.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1828.0,
+                    1402.0,
+                    1828.0,
+                    1402.0,
+                    1860.0,
+                    322.0,
+                    1860.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1856.0,
+                    1403.0,
+                    1856.0,
+                    1403.0,
+                    1893.0,
+                    321.0,
+                    1893.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    1886.0,
+                    1038.0,
+                    1886.0,
+                    1038.0,
+                    1923.0,
+                    323.0,
+                    1923.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1335.0,
+                    1403.0,
+                    1335.0,
+                    1403.0,
+                    1379.0,
+                    293.0,
+                    1379.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1372.0,
+                    589.0,
+                    1372.0,
+                    589.0,
+                    1403.0,
+                    321.0,
+                    1403.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    396.0,
+                    833.0,
+                    396.0,
+                    833.0,
+                    429.0,
+                    297.0,
+                    429.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    901.0,
+                    395.0,
+                    1404.0,
+                    395.0,
+                    1404.0,
+                    432.0,
+                    901.0,
+                    432.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    429.0,
+                    380.0,
+                    429.0,
+                    380.0,
+                    463.0,
+                    321.0,
+                    463.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    409.0,
+                    424.0,
+                    1405.0,
+                    424.0,
+                    1405.0,
+                    463.0,
+                    409.0,
+                    463.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    456.0,
+                    1406.0,
+                    456.0,
+                    1406.0,
+                    493.0,
+                    320.0,
+                    493.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    486.0,
+                    810.0,
+                    486.0,
+                    810.0,
+                    524.0,
+                    321.0,
+                    524.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    847.0,
+                    486.0,
+                    1404.0,
+                    486.0,
+                    1404.0,
+                    525.0,
+                    847.0,
+                    525.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    518.0,
+                    1161.0,
+                    518.0,
+                    1161.0,
+                    556.0,
+                    322.0,
+                    556.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    882.0,
+                    1404.0,
+                    882.0,
+                    1404.0,
+                    919.0,
+                    293.0,
+                    919.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    914.0,
+                    1406.0,
+                    914.0,
+                    1406.0,
+                    954.0,
+                    321.0,
+                    954.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    944.0,
+                    575.0,
+                    944.0,
+                    575.0,
+                    978.0,
+                    321.0,
+                    978.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1223.0,
+                    1402.0,
+                    1223.0,
+                    1402.0,
+                    1261.0,
+                    294.0,
+                    1261.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    1257.0,
+                    1404.0,
+                    1257.0,
+                    1404.0,
+                    1291.0,
+                    323.0,
+                    1291.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    319.0,
+                    1287.0,
+                    622.0,
+                    1287.0,
+                    622.0,
+                    1319.0,
+                    319.0,
+                    1319.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1538.0,
+                    1402.0,
+                    1538.0,
+                    1402.0,
+                    1572.0,
+                    296.0,
+                    1572.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1567.0,
+                    1405.0,
+                    1567.0,
+                    1405.0,
+                    1607.0,
+                    321.0,
+                    1607.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    325.0,
+                    1600.0,
+                    1071.0,
+                    1600.0,
+                    1071.0,
+                    1634.0,
+                    325.0,
+                    1634.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1110.0,
+                    1401.0,
+                    1110.0,
+                    1401.0,
+                    1146.0,
+                    294.0,
+                    1146.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    1142.0,
+                    1400.0,
+                    1142.0,
+                    1400.0,
+                    1178.0,
+                    323.0,
+                    1178.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    325.0,
+                    1174.0,
+                    741.0,
+                    1174.0,
+                    741.0,
+                    1208.0,
+                    325.0,
+                    1208.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    761.0,
+                    1174.0,
+                    936.0,
+                    1174.0,
+                    936.0,
+                    1208.0,
+                    761.0,
+                    1208.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    573.0,
+                    1402.0,
+                    573.0,
+                    1402.0,
+                    605.0,
+                    296.0,
+                    605.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    600.0,
+                    1254.0,
+                    600.0,
+                    1254.0,
+                    639.0,
+                    320.0,
+                    639.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    996.0,
+                    1403.0,
+                    996.0,
+                    1403.0,
+                    1035.0,
+                    296.0,
+                    1035.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    1030.0,
+                    1404.0,
+                    1030.0,
+                    1404.0,
+                    1064.0,
+                    324.0,
+                    1064.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1058.0,
+                    1331.0,
+                    1058.0,
+                    1331.0,
+                    1095.0,
+                    322.0,
+                    1095.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    1423.0,
+                    1405.0,
+                    1423.0,
+                    1405.0,
+                    1457.0,
+                    297.0,
+                    1457.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1454.0,
+                    1403.0,
+                    1454.0,
+                    1403.0,
+                    1489.0,
+                    322.0,
+                    1489.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1482.0,
+                    903.0,
+                    1482.0,
+                    903.0,
+                    1523.0,
+                    322.0,
+                    1523.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    922.0,
+                    1482.0,
+                    1101.0,
+                    1482.0,
+                    1101.0,
+                    1523.0,
+                    922.0,
+                    1523.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    655.0,
+                    1402.0,
+                    655.0,
+                    1402.0,
+                    689.0,
+                    295.0,
+                    689.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    687.0,
+                    1405.0,
+                    687.0,
+                    1405.0,
+                    721.0,
+                    322.0,
+                    721.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    716.0,
+                    611.0,
+                    716.0,
+                    611.0,
+                    748.0,
+                    321.0,
+                    748.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    768.0,
+                    1405.0,
+                    768.0,
+                    1405.0,
+                    806.0,
+                    294.0,
+                    806.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    800.0,
+                    1403.0,
+                    800.0,
+                    1403.0,
+                    836.0,
+                    323.0,
+                    836.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    326.0,
+                    831.0,
+                    545.0,
+                    831.0,
+                    545.0,
+                    867.0,
+                    326.0,
+                    867.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 10,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 2,
+                "poly": [
+                    300,
+                    75,
+                    813,
+                    75,
+                    813,
+                    105,
+                    300,
+                    105
+                ],
+                "score": 0.889
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    229,
+                    1399,
+                    229,
+                    1399,
+                    323,
+                    298,
+                    323
+                ],
+                "score": 0.858
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    294,
+                    783,
+                    1402,
+                    783,
+                    1402,
+                    848,
+                    294,
+                    848
+                ],
+                "score": 0.853
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1880,
+                    1404,
+                    1880,
+                    1404,
+                    2034,
+                    298,
+                    2034
+                ],
+                "score": 0.85
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1450,
+                    1404,
+                    1450,
+                    1404,
+                    1606,
+                    297,
+                    1606
+                ],
+                "score": 0.836
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    424,
+                    1400,
+                    424,
+                    1400,
+                    518,
+                    299,
+                    518
+                ],
+                "score": 0.834
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    836,
+                    2088,
+                    865,
+                    2088,
+                    865,
+                    2113,
+                    836,
+                    2113
+                ],
+                "score": 0.829
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    293,
+                    948,
+                    1399,
+                    948,
+                    1399,
+                    1013,
+                    293,
+                    1013
+                ],
+                "score": 0.826
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    292,
+                    701,
+                    1402,
+                    701,
+                    1402,
+                    766,
+                    292,
+                    766
+                ],
+                "score": 0.814
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1286,
+                    1401,
+                    1286,
+                    1401,
+                    1350,
+                    299,
+                    1350
+                ],
+                "score": 0.811
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1367,
+                    1400,
+                    1367,
+                    1400,
+                    1432,
+                    296,
+                    1432
+                ],
+                "score": 0.806
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1624,
+                    1398,
+                    1624,
+                    1398,
+                    1688,
+                    296,
+                    1688
+                ],
+                "score": 0.804
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    290,
+                    536,
+                    1400,
+                    536,
+                    1400,
+                    601,
+                    290,
+                    601
+                ],
+                "score": 0.799
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1030,
+                    1400,
+                    1030,
+                    1400,
+                    1125,
+                    299,
+                    1125
+                ],
+                "score": 0.795
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1706,
+                    1404,
+                    1706,
+                    1404,
+                    1860,
+                    297,
+                    1860
+                ],
+                "score": 0.793
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    291,
+                    342,
+                    1399,
+                    342,
+                    1399,
+                    406,
+                    291,
+                    406
+                ],
+                "score": 0.786
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1143,
+                    1404,
+                    1143,
+                    1404,
+                    1268,
+                    297,
+                    1268
+                ],
+                "score": 0.781
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    618,
+                    1400,
+                    618,
+                    1400,
+                    683,
+                    296,
+                    683
+                ],
+                "score": 0.77
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    293,
+                    866,
+                    1402,
+                    866,
+                    1402,
+                    930,
+                    293,
+                    930
+                ],
+                "score": 0.704
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    73.0,
+                    815.0,
+                    73.0,
+                    815.0,
+                    108.0,
+                    295.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    832.0,
+                    2085.0,
+                    870.0,
+                    2085.0,
+                    870.0,
+                    2124.0,
+                    832.0,
+                    2124.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    226.0,
+                    1404.0,
+                    226.0,
+                    1404.0,
+                    268.0,
+                    293.0,
+                    268.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    261.0,
+                    1405.0,
+                    261.0,
+                    1405.0,
+                    295.0,
+                    323.0,
+                    295.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    291.0,
+                    612.0,
+                    291.0,
+                    612.0,
+                    326.0,
+                    323.0,
+                    326.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    783.0,
+                    1404.0,
+                    783.0,
+                    1404.0,
+                    819.0,
+                    297.0,
+                    819.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    816.0,
+                    894.0,
+                    816.0,
+                    894.0,
+                    848.0,
+                    321.0,
+                    848.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1880.0,
+                    1403.0,
+                    1880.0,
+                    1403.0,
+                    1916.0,
+                    293.0,
+                    1916.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1909.0,
+                    1405.0,
+                    1909.0,
+                    1405.0,
+                    1948.0,
+                    321.0,
+                    1948.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    317.0,
+                    1938.0,
+                    1405.0,
+                    1938.0,
+                    1405.0,
+                    1982.0,
+                    317.0,
+                    1982.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    1969.0,
+                    1405.0,
+                    1969.0,
+                    1405.0,
+                    2009.0,
+                    320.0,
+                    2009.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1999.0,
+                    1361.0,
+                    1999.0,
+                    1361.0,
+                    2039.0,
+                    322.0,
+                    2039.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    1452.0,
+                    1402.0,
+                    1452.0,
+                    1402.0,
+                    1485.0,
+                    297.0,
+                    1485.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1481.0,
+                    1405.0,
+                    1481.0,
+                    1405.0,
+                    1517.0,
+                    322.0,
+                    1517.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    1507.0,
+                    1405.0,
+                    1507.0,
+                    1405.0,
+                    1553.0,
+                    320.0,
+                    1553.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1540.0,
+                    1402.0,
+                    1540.0,
+                    1402.0,
+                    1580.0,
+                    321.0,
+                    1580.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1573.0,
+                    789.0,
+                    1573.0,
+                    789.0,
+                    1608.0,
+                    322.0,
+                    1608.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    421.0,
+                    1405.0,
+                    421.0,
+                    1405.0,
+                    461.0,
+                    293.0,
+                    461.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    453.0,
+                    1405.0,
+                    453.0,
+                    1405.0,
+                    493.0,
+                    322.0,
+                    493.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    487.0,
+                    682.0,
+                    487.0,
+                    682.0,
+                    521.0,
+                    324.0,
+                    521.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    948.0,
+                    1404.0,
+                    948.0,
+                    1404.0,
+                    984.0,
+                    296.0,
+                    984.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    979.0,
+                    1033.0,
+                    979.0,
+                    1033.0,
+                    1013.0,
+                    321.0,
+                    1013.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    701.0,
+                    1405.0,
+                    701.0,
+                    1405.0,
+                    737.0,
+                    295.0,
+                    737.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    734.0,
+                    980.0,
+                    734.0,
+                    980.0,
+                    766.0,
+                    321.0,
+                    766.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1282.0,
+                    1405.0,
+                    1282.0,
+                    1405.0,
+                    1326.0,
+                    293.0,
+                    1326.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    1317.0,
+                    1095.0,
+                    1317.0,
+                    1095.0,
+                    1353.0,
+                    324.0,
+                    1353.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1363.0,
+                    1405.0,
+                    1363.0,
+                    1405.0,
+                    1409.0,
+                    294.0,
+                    1409.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1398.0,
+                    1131.0,
+                    1398.0,
+                    1131.0,
+                    1434.0,
+                    322.0,
+                    1434.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1624.0,
+                    1403.0,
+                    1624.0,
+                    1403.0,
+                    1660.0,
+                    296.0,
+                    1660.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    326.0,
+                    1655.0,
+                    1377.0,
+                    1655.0,
+                    1377.0,
+                    1691.0,
+                    326.0,
+                    1691.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    538.0,
+                    1402.0,
+                    538.0,
+                    1402.0,
+                    574.0,
+                    294.0,
+                    574.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    569.0,
+                    1231.0,
+                    569.0,
+                    1231.0,
+                    602.0,
+                    321.0,
+                    602.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1030.0,
+                    1402.0,
+                    1030.0,
+                    1402.0,
+                    1067.0,
+                    294.0,
+                    1067.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1062.0,
+                    1405.0,
+                    1062.0,
+                    1405.0,
+                    1099.0,
+                    322.0,
+                    1099.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    1092.0,
+                    1092.0,
+                    1092.0,
+                    1092.0,
+                    1126.0,
+                    320.0,
+                    1126.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1704.0,
+                    1405.0,
+                    1704.0,
+                    1405.0,
+                    1743.0,
+                    295.0,
+                    1743.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1735.0,
+                    1406.0,
+                    1735.0,
+                    1406.0,
+                    1774.0,
+                    322.0,
+                    1774.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1767.0,
+                    1405.0,
+                    1767.0,
+                    1405.0,
+                    1804.0,
+                    322.0,
+                    1804.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    319.0,
+                    1794.0,
+                    1405.0,
+                    1794.0,
+                    1405.0,
+                    1836.0,
+                    319.0,
+                    1836.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1828.0,
+                    718.0,
+                    1828.0,
+                    718.0,
+                    1865.0,
+                    321.0,
+                    1865.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    342.0,
+                    1402.0,
+                    342.0,
+                    1402.0,
+                    378.0,
+                    296.0,
+                    378.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    373.0,
+                    1216.0,
+                    373.0,
+                    1216.0,
+                    407.0,
+                    323.0,
+                    407.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1140.0,
+                    1406.0,
+                    1140.0,
+                    1406.0,
+                    1183.0,
+                    294.0,
+                    1183.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1175.0,
+                    1406.0,
+                    1175.0,
+                    1406.0,
+                    1211.0,
+                    322.0,
+                    1211.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1207.0,
+                    1404.0,
+                    1207.0,
+                    1404.0,
+                    1238.0,
+                    322.0,
+                    1238.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    325.0,
+                    1236.0,
+                    1272.0,
+                    1236.0,
+                    1272.0,
+                    1269.0,
+                    325.0,
+                    1269.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    620.0,
+                    1404.0,
+                    620.0,
+                    1404.0,
+                    656.0,
+                    295.0,
+                    656.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    649.0,
+                    1272.0,
+                    649.0,
+                    1272.0,
+                    684.0,
+                    322.0,
+                    684.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    866.0,
+                    1404.0,
+                    866.0,
+                    1404.0,
+                    902.0,
+                    295.0,
+                    902.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    897.0,
+                    830.0,
+                    897.0,
+                    830.0,
+                    931.0,
+                    324.0,
+                    931.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 11,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 2,
+                "poly": [
+                    300,
+                    75,
+                    813,
+                    75,
+                    813,
+                    105,
+                    300,
+                    105
+                ],
+                "score": 0.881
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    836,
+                    2088,
+                    865,
+                    2088,
+                    865,
+                    2113,
+                    836,
+                    2113
+                ],
+                "score": 0.837
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    303,
+                    229,
+                    1400,
+                    229,
+                    1400,
+                    324,
+                    303,
+                    324
+                ],
+                "score": 0.818
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    301,
+                    1653,
+                    1402,
+                    1653,
+                    1402,
+                    1716,
+                    301,
+                    1716
+                ],
+                "score": 0.806
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    879,
+                    1401,
+                    879,
+                    1401,
+                    944,
+                    296,
+                    944
+                ],
+                "score": 0.773
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    765,
+                    1405,
+                    765,
+                    1405,
+                    861,
+                    297,
+                    861
+                ],
+                "score": 0.762
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    294,
+                    343,
+                    1402,
+                    343,
+                    1402,
+                    407,
+                    294,
+                    407
+                ],
+                "score": 0.754
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    961,
+                    1404,
+                    961,
+                    1404,
+                    1118,
+                    297,
+                    1118
+                ],
+                "score": 0.73
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    651,
+                    1405,
+                    651,
+                    1405,
+                    746,
+                    298,
+                    746
+                ],
+                "score": 0.719
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    300,
+                    1250,
+                    1401,
+                    1250,
+                    1401,
+                    1345,
+                    300,
+                    1345
+                ],
+                "score": 0.703
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1477,
+                    1404,
+                    1477,
+                    1404,
+                    1632,
+                    296,
+                    1632
+                ],
+                "score": 0.694
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    569,
+                    1398,
+                    569,
+                    1398,
+                    634,
+                    295,
+                    634
+                ],
+                "score": 0.693
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    426,
+                    1404,
+                    426,
+                    1404,
+                    550,
+                    297,
+                    550
+                ],
+                "score": 0.691
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1364,
+                    1403,
+                    1364,
+                    1403,
+                    1459,
+                    297,
+                    1459
+                ],
+                "score": 0.669
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1137,
+                    1401,
+                    1137,
+                    1401,
+                    1232,
+                    299,
+                    1232
+                ],
+                "score": 0.669
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    742,
+                    1204,
+                    760,
+                    1204,
+                    760,
+                    1226,
+                    742,
+                    1226
+                ],
+                "score": 0.66,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    976,
+                    833,
+                    994,
+                    833,
+                    994,
+                    855,
+                    976,
+                    855
+                ],
+                "score": 0.44,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1101,
+                    295,
+                    1119,
+                    295,
+                    1119,
+                    318,
+                    1101,
+                    318
+                ],
+                "score": 0.4,
+                "latex": "{ . } ="
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    73.0,
+                    815.0,
+                    73.0,
+                    815.0,
+                    108.0,
+                    295.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    832.0,
+                    2085.0,
+                    870.0,
+                    2085.0,
+                    870.0,
+                    2123.0,
+                    832.0,
+                    2123.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    224.0,
+                    1405.0,
+                    224.0,
+                    1405.0,
+                    270.0,
+                    294.0,
+                    270.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    261.0,
+                    1404.0,
+                    261.0,
+                    1404.0,
+                    297.0,
+                    322.0,
+                    297.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    291.0,
+                    1100.0,
+                    291.0,
+                    1100.0,
+                    329.0,
+                    323.0,
+                    329.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1120.0,
+                    291.0,
+                    1299.0,
+                    291.0,
+                    1299.0,
+                    329.0,
+                    1120.0,
+                    329.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1653.0,
+                    1406.0,
+                    1653.0,
+                    1406.0,
+                    1688.0,
+                    295.0,
+                    1688.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1682.0,
+                    1027.0,
+                    1682.0,
+                    1027.0,
+                    1718.0,
+                    321.0,
+                    1718.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    877.0,
+                    1406.0,
+                    877.0,
+                    1406.0,
+                    915.0,
+                    296.0,
+                    915.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    910.0,
+                    936.0,
+                    910.0,
+                    936.0,
+                    945.0,
+                    321.0,
+                    945.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    766.0,
+                    1403.0,
+                    766.0,
+                    1403.0,
+                    801.0,
+                    295.0,
+                    801.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    796.0,
+                    1405.0,
+                    796.0,
+                    1405.0,
+                    834.0,
+                    321.0,
+                    834.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    825.0,
+                    975.0,
+                    825.0,
+                    975.0,
+                    866.0,
+                    321.0,
+                    866.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    995.0,
+                    825.0,
+                    1156.0,
+                    825.0,
+                    1156.0,
+                    866.0,
+                    995.0,
+                    866.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    343.0,
+                    1404.0,
+                    343.0,
+                    1404.0,
+                    379.0,
+                    297.0,
+                    379.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    374.0,
+                    1195.0,
+                    374.0,
+                    1195.0,
+                    410.0,
+                    321.0,
+                    410.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    965.0,
+                    1402.0,
+                    965.0,
+                    1402.0,
+                    998.0,
+                    296.0,
+                    998.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    319.0,
+                    993.0,
+                    1407.0,
+                    993.0,
+                    1407.0,
+                    1034.0,
+                    319.0,
+                    1034.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    1023.0,
+                    1406.0,
+                    1023.0,
+                    1406.0,
+                    1060.0,
+                    320.0,
+                    1060.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1054.0,
+                    1406.0,
+                    1054.0,
+                    1406.0,
+                    1089.0,
+                    321.0,
+                    1089.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    1085.0,
+                    988.0,
+                    1085.0,
+                    988.0,
+                    1121.0,
+                    320.0,
+                    1121.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    649.0,
+                    1405.0,
+                    649.0,
+                    1405.0,
+                    690.0,
+                    293.0,
+                    690.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    683.0,
+                    1403.0,
+                    683.0,
+                    1403.0,
+                    718.0,
+                    321.0,
+                    718.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    716.0,
+                    798.0,
+                    716.0,
+                    798.0,
+                    747.0,
+                    320.0,
+                    747.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1248.0,
+                    1405.0,
+                    1248.0,
+                    1405.0,
+                    1288.0,
+                    293.0,
+                    1288.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    1282.0,
+                    1406.0,
+                    1282.0,
+                    1406.0,
+                    1319.0,
+                    323.0,
+                    1319.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    1312.0,
+                    936.0,
+                    1312.0,
+                    936.0,
+                    1346.0,
+                    324.0,
+                    1346.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1479.0,
+                    1405.0,
+                    1479.0,
+                    1405.0,
+                    1512.0,
+                    295.0,
+                    1512.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    1507.0,
+                    1406.0,
+                    1507.0,
+                    1406.0,
+                    1545.0,
+                    323.0,
+                    1545.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1539.0,
+                    1402.0,
+                    1539.0,
+                    1402.0,
+                    1576.0,
+                    322.0,
+                    1576.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    1566.0,
+                    1402.0,
+                    1566.0,
+                    1402.0,
+                    1606.0,
+                    320.0,
+                    1606.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    1600.0,
+                    407.0,
+                    1600.0,
+                    407.0,
+                    1634.0,
+                    320.0,
+                    1634.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    568.0,
+                    1404.0,
+                    568.0,
+                    1404.0,
+                    605.0,
+                    294.0,
+                    605.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    600.0,
+                    1402.0,
+                    600.0,
+                    1402.0,
+                    635.0,
+                    323.0,
+                    635.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    424.0,
+                    1405.0,
+                    424.0,
+                    1405.0,
+                    464.0,
+                    294.0,
+                    464.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    456.0,
+                    1405.0,
+                    456.0,
+                    1405.0,
+                    492.0,
+                    322.0,
+                    492.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    487.0,
+                    1404.0,
+                    487.0,
+                    1404.0,
+                    523.0,
+                    322.0,
+                    523.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    521.0,
+                    669.0,
+                    521.0,
+                    669.0,
+                    550.0,
+                    322.0,
+                    550.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1363.0,
+                    1403.0,
+                    1363.0,
+                    1403.0,
+                    1401.0,
+                    295.0,
+                    1401.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    1394.0,
+                    1403.0,
+                    1394.0,
+                    1403.0,
+                    1432.0,
+                    324.0,
+                    1432.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    1426.0,
+                    881.0,
+                    1426.0,
+                    881.0,
+                    1460.0,
+                    324.0,
+                    1460.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    1138.0,
+                    1403.0,
+                    1138.0,
+                    1403.0,
+                    1172.0,
+                    297.0,
+                    1172.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    319.0,
+                    1165.0,
+                    1403.0,
+                    1165.0,
+                    1403.0,
+                    1205.0,
+                    319.0,
+                    1205.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    325.0,
+                    1200.0,
+                    741.0,
+                    1200.0,
+                    741.0,
+                    1234.0,
+                    325.0,
+                    1234.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    761.0,
+                    1200.0,
+                    938.0,
+                    1200.0,
+                    938.0,
+                    1234.0,
+                    761.0,
+                    1234.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 12,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 5,
+                "poly": [
+                    559,
+                    224,
+                    1139,
+                    224,
+                    1139,
+                    413,
+                    559,
+                    413
+                ],
+                "score": 0.975,
+                "html": "<table><tr><td></td><td>Python</td><td>Javascript</td><td>Go</td><td>Ruby</td></tr><tr><td>Python</td><td>1.00</td><td>0.43</td><td>0.42</td><td>0.79</td></tr><tr><td>Javascript</td><td>0.43</td><td>1.00</td><td>0.84</td><td>0.39</td></tr><tr><td>Go</td><td>0.43</td><td>0.84</td><td>1.00</td><td>0.38</td></tr><tr><td>Ruby</td><td>0.79</td><td>0.39</td><td>0.38</td><td>1.00</td></tr></table>"
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1150,
+                    1405,
+                    1150,
+                    1405,
+                    1243,
+                    299,
+                    1243
+                ],
+                "score": 0.975
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    624,
+                    1404,
+                    624,
+                    1404,
+                    746,
+                    298,
+                    746
+                ],
+                "score": 0.975
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    762,
+                    1405,
+                    762,
+                    1405,
+                    979,
+                    297,
+                    979
+                ],
+                "score": 0.975
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1522,
+                    1405,
+                    1522,
+                    1405,
+                    1649,
+                    297,
+                    1649
+                ],
+                "score": 0.974
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1334,
+                    1404,
+                    1334,
+                    1404,
+                    1429,
+                    298,
+                    1429
+                ],
+                "score": 0.972
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    366,
+                    1911,
+                    1403,
+                    1911,
+                    1403,
+                    2034,
+                    366,
+                    2034
+                ],
+                "score": 0.953
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1663,
+                    1400,
+                    1663,
+                    1400,
+                    1726,
+                    296,
+                    1726
+                ],
+                "score": 0.951
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    438,
+                    1258,
+                    1257,
+                    1258,
+                    1257,
+                    1321,
+                    438,
+                    1321
+                ],
+                "score": 0.941
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    301,
+                    1094,
+                    757,
+                    1094,
+                    757,
+                    1125,
+                    301,
+                    1125
+                ],
+                "score": 0.904
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    299,
+                    75,
+                    813,
+                    75,
+                    813,
+                    105,
+                    299,
+                    105
+                ],
+                "score": 0.903
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    301,
+                    1024,
+                    509,
+                    1024,
+                    509,
+                    1058,
+                    301,
+                    1058
+                ],
+                "score": 0.902
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    301,
+                    1763,
+                    640,
+                    1763,
+                    640,
+                    1796,
+                    301,
+                    1796
+                ],
+                "score": 0.898
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    302,
+                    556,
+                    626,
+                    556,
+                    626,
+                    589,
+                    302,
+                    589
+                ],
+                "score": 0.893
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    302,
+                    1467,
+                    897,
+                    1467,
+                    897,
+                    1498,
+                    302,
+                    1498
+                ],
+                "score": 0.891
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    361,
+                    1867,
+                    1150,
+                    1867,
+                    1150,
+                    1902,
+                    361,
+                    1902
+                ],
+                "score": 0.877
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    300,
+                    1821,
+                    890,
+                    1821,
+                    890,
+                    1853,
+                    300,
+                    1853
+                ],
+                "score": 0.854
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    836,
+                    2088,
+                    864,
+                    2088,
+                    864,
+                    2112,
+                    836,
+                    2112
+                ],
+                "score": 0.834
+            },
+            {
+                "category_id": 6,
+                "poly": [
+                    298,
+                    434,
+                    1399,
+                    434,
+                    1399,
+                    497,
+                    298,
+                    497
+                ],
+                "score": 0.496
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    443,
+                    1258,
+                    755,
+                    1258,
+                    755,
+                    1320,
+                    443,
+                    1320
+                ],
+                "score": 0.472
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    897,
+                    1259,
+                    1255,
+                    1259,
+                    1255,
+                    1320,
+                    897,
+                    1320
+                ],
+                "score": 0.45
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    434,
+                    1399,
+                    434,
+                    1399,
+                    497,
+                    298,
+                    497
+                ],
+                "score": 0.419
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    441,
+                    1257,
+                    1256,
+                    1257,
+                    1256,
+                    1319,
+                    441,
+                    1319
+                ],
+                "score": 0.93,
+                "latex": "\\phi ( r _ { i  j } ) _ { 2 k } = \\sin ( \\frac { r _ { i  j } } { M ^ { 2 k / d } } ) \\qquad \\phi ( r _ { i  j } ) _ { 2 k + 1 } = \\cos ( \\frac { r _ { i  j } } { M ^ { 2 k / d } } ) ,"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    375,
+                    1334,
+                    549,
+                    1334,
+                    549,
+                    1368,
+                    375,
+                    1368
+                ],
+                "score": 0.92,
+                "latex": "1 \\leq k < d / 2"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1161,
+                    1149,
+                    1298,
+                    1149,
+                    1298,
+                    1183,
+                    1161,
+                    1183
+                ],
+                "score": 0.92,
+                "latex": "\\phi : \\mathbb { R } \\to \\mathbb { R } ^ { d }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    1367,
+                    454,
+                    1367,
+                    454,
+                    1398,
+                    298,
+                    1398
+                ],
+                "score": 0.86,
+                "latex": "M = 1 0 , 0 0 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1044,
+                    1336,
+                    1078,
+                    1336,
+                    1078,
+                    1363,
+                    1044,
+                    1363
+                ],
+                "score": 0.84,
+                "latex": "M"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1383,
+                    1153,
+                    1402,
+                    1153,
+                    1402,
+                    1179,
+                    1383,
+                    1179
+                ],
+                "score": 0.78,
+                "latex": "d"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1094.0,
+                    762.0,
+                    1094.0,
+                    762.0,
+                    1129.0,
+                    296.0,
+                    1129.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    73.0,
+                    815.0,
+                    73.0,
+                    815.0,
+                    108.0,
+                    295.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1019.0,
+                    513.0,
+                    1019.0,
+                    513.0,
+                    1065.0,
+                    295.0,
+                    1065.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    1764.0,
+                    640.0,
+                    1764.0,
+                    640.0,
+                    1797.0,
+                    297.0,
+                    1797.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    299.0,
+                    557.0,
+                    628.0,
+                    557.0,
+                    628.0,
+                    593.0,
+                    299.0,
+                    593.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1467.0,
+                    904.0,
+                    1467.0,
+                    904.0,
+                    1502.0,
+                    296.0,
+                    1502.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1821.0,
+                    890.0,
+                    1821.0,
+                    890.0,
+                    1856.0,
+                    296.0,
+                    1856.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    832.0,
+                    2085.0,
+                    870.0,
+                    2085.0,
+                    870.0,
+                    2123.0,
+                    832.0,
+                    2123.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    432.0,
+                    1403.0,
+                    432.0,
+                    1403.0,
+                    468.0,
+                    296.0,
+                    468.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    468.0,
+                    411.0,
+                    468.0,
+                    411.0,
+                    496.0,
+                    294.0,
+                    496.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1148.0,
+                    1160.0,
+                    1148.0,
+                    1160.0,
+                    1186.0,
+                    293.0,
+                    1186.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1299.0,
+                    1148.0,
+                    1382.0,
+                    1148.0,
+                    1382.0,
+                    1186.0,
+                    1299.0,
+                    1186.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1403.0,
+                    1148.0,
+                    1406.0,
+                    1148.0,
+                    1406.0,
+                    1186.0,
+                    1403.0,
+                    1186.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1182.0,
+                    1405.0,
+                    1182.0,
+                    1405.0,
+                    1216.0,
+                    293.0,
+                    1216.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1212.0,
+                    576.0,
+                    1212.0,
+                    576.0,
+                    1247.0,
+                    295.0,
+                    1247.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    625.0,
+                    1405.0,
+                    625.0,
+                    1405.0,
+                    661.0,
+                    294.0,
+                    661.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    656.0,
+                    1405.0,
+                    656.0,
+                    1405.0,
+                    688.0,
+                    294.0,
+                    688.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    685.0,
+                    1405.0,
+                    685.0,
+                    1405.0,
+                    721.0,
+                    292.0,
+                    721.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    716.0,
+                    522.0,
+                    716.0,
+                    522.0,
+                    749.0,
+                    295.0,
+                    749.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    760.0,
+                    1405.0,
+                    760.0,
+                    1405.0,
+                    802.0,
+                    292.0,
+                    802.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    791.0,
+                    1403.0,
+                    791.0,
+                    1403.0,
+                    830.0,
+                    295.0,
+                    830.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    825.0,
+                    1403.0,
+                    825.0,
+                    1403.0,
+                    859.0,
+                    295.0,
+                    859.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    851.0,
+                    1405.0,
+                    851.0,
+                    1405.0,
+                    893.0,
+                    294.0,
+                    893.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    884.0,
+                    1403.0,
+                    884.0,
+                    1403.0,
+                    921.0,
+                    294.0,
+                    921.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    916.0,
+                    1403.0,
+                    916.0,
+                    1403.0,
+                    951.0,
+                    295.0,
+                    951.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    945.0,
+                    1129.0,
+                    945.0,
+                    1129.0,
+                    987.0,
+                    294.0,
+                    987.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1524.0,
+                    1403.0,
+                    1524.0,
+                    1403.0,
+                    1557.0,
+                    294.0,
+                    1557.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1554.0,
+                    1405.0,
+                    1554.0,
+                    1405.0,
+                    1589.0,
+                    294.0,
+                    1589.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1583.0,
+                    1406.0,
+                    1583.0,
+                    1406.0,
+                    1621.0,
+                    291.0,
+                    1621.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1613.0,
+                    425.0,
+                    1613.0,
+                    425.0,
+                    1657.0,
+                    291.0,
+                    1657.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1333.0,
+                    374.0,
+                    1333.0,
+                    374.0,
+                    1372.0,
+                    293.0,
+                    1372.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    550.0,
+                    1333.0,
+                    1043.0,
+                    1333.0,
+                    1043.0,
+                    1372.0,
+                    550.0,
+                    1372.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1079.0,
+                    1333.0,
+                    1405.0,
+                    1333.0,
+                    1405.0,
+                    1372.0,
+                    1079.0,
+                    1372.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    455.0,
+                    1364.0,
+                    1405.0,
+                    1364.0,
+                    1405.0,
+                    1401.0,
+                    455.0,
+                    1401.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1397.0,
+                    573.0,
+                    1397.0,
+                    573.0,
+                    1431.0,
+                    294.0,
+                    1431.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    357.0,
+                    1909.0,
+                    915.0,
+                    1909.0,
+                    915.0,
+                    1946.0,
+                    357.0,
+                    1946.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    946.0,
+                    1910.0,
+                    1404.0,
+                    1910.0,
+                    1404.0,
+                    1945.0,
+                    946.0,
+                    1945.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    1941.0,
+                    451.0,
+                    1941.0,
+                    451.0,
+                    1974.0,
+                    393.0,
+                    1974.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    484.0,
+                    1946.0,
+                    605.0,
+                    1946.0,
+                    605.0,
+                    1973.0,
+                    484.0,
+                    1973.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    630.0,
+                    1942.0,
+                    822.0,
+                    1942.0,
+                    822.0,
+                    1977.0,
+                    630.0,
+                    1977.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    940.0,
+                    1945.0,
+                    1404.0,
+                    1945.0,
+                    1404.0,
+                    1974.0,
+                    940.0,
+                    1974.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    1973.0,
+                    1406.0,
+                    1973.0,
+                    1406.0,
+                    2007.0,
+                    392.0,
+                    2007.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    2003.0,
+                    703.0,
+                    2003.0,
+                    703.0,
+                    2035.0,
+                    394.0,
+                    2035.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1661.0,
+                    1404.0,
+                    1661.0,
+                    1404.0,
+                    1697.0,
+                    295.0,
+                    1697.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1695.0,
+                    901.0,
+                    1695.0,
+                    901.0,
+                    1726.0,
+                    296.0,
+                    1726.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    362.0,
+                    1864.0,
+                    1151.0,
+                    1864.0,
+                    1151.0,
+                    1907.0,
+                    362.0,
+                    1907.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    432.0,
+                    1403.0,
+                    432.0,
+                    1403.0,
+                    468.0,
+                    296.0,
+                    468.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    468.0,
+                    411.0,
+                    468.0,
+                    411.0,
+                    496.0,
+                    294.0,
+                    496.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 13,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 2,
+                "poly": [
+                    300,
+                    76,
+                    813,
+                    76,
+                    813,
+                    104,
+                    300,
+                    104
+                ],
+                "score": 0.875
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    836,
+                    2088,
+                    865,
+                    2088,
+                    865,
+                    2113,
+                    836,
+                    2113
+                ],
+                "score": 0.85
+            },
+            {
+                "category_id": 5,
+                "poly": [
+                    296,
+                    34,
+                    1473,
+                    34,
+                    1473,
+                    1905,
+                    296,
+                    1905
+                ],
+                "score": 0.422,
+                "html": "<table><tr><td colspan=\"2\">Published as a conference paper at ICLR 2021</td></tr><tr><td></td><td></td></tr><tr><td>function isEqualArray(a，b){ if (a return true;</td><td></td></tr><tr><td>if ((a === undefined) undefined)）{ return false;</td><td>func areSameFloat32Array(a，b []float32） bool if len(a) != len(b){ return false</td></tr><tr><td>var =a.length; if (i !== b.length){ return false;</td><td>for i := O;i &lt; len(a);i++{ if a[i]!=b[i]{ return false J</td></tr><tr><td>while (i--）{ if(a[i] !== b[i]）{ return false; }</td><td>return true</td></tr><tr><td>return true;</td><td></td></tr><tr><td>function main() var rawData $(&#x27; .HeaderTexture[data-login- user-email]&#x27;) .data() ;</td><td>func TaskSayHello(t *tasking.T){</td></tr><tr><td>if (rawData) 1 me={</td><td>username := t.Flags.String(&quot;name&quot;) if username user, := user.Current ()</td></tr><tr><td>name:rawData.loginUserName, mail: rawData.loginUserEmail }；</td><td>username = user.Name</td></tr><tr><td>getCartId(function (cart）{ me.cart = cart;</td><td>} ift.Flags.Bool(&quot;verbose&quot;)</td></tr><tr><td>injectMenu(); refreshUsers(actions.updateUsers); listenOnChanges(onChange);</td><td>t.Logf(&quot;Hello %s, the time now is %s\\n&quot;, username，time.Now())</td></tr><tr><td>listenonorderConfirm(onConfirm); ）；</td><td>}else{ t.Logf(&quot;Hello %s\\n&quot;,username)</td></tr><tr><td>} else{ caliback(&#x27;no user&#x27;);</td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>func Backup(filename string)error{</td></tr><tr><td></td><td></td></tr><tr><td></td><td>info，err := os.Stat(filename) if err != nil</td></tr><tr><td></td><td>if os.IsNotExist(err）{</td></tr><tr><td></td><td>return nil</td></tr><tr><td></td><td>return err</td></tr><tr><td></td><td></td></tr><tr><td>def _load_rule_file(self, filename):</td><td>if info.Size() == 0{ return nil</td></tr><tr><td>if not (os.path.exists(filename)):</td><td>}</td></tr><tr><td>sys.stderr.write(</td><td>files，err ：= filepath.Glob(</td></tr><tr><td>&quot;rflint: %s: No such file or &quot;directory\\n&quot; % filename</td><td>filename + _BACKUP_SUFFIX</td></tr><tr><td>return</td><td>） if err nil 1</td></tr><tr><td>try:</td><td>return err</td></tr><tr><td>basename = os.path.basename(filename)</td><td>}</td></tr><tr><td>(name，ext）= os.path.splitext(basename) imp.load_source(name,filename)</td><td> numBackup := byte(1)</td></tr><tr><td>except Exception as e: sys.stderr.write(</td><td>if len(files) !=0{</td></tr><tr><td>&quot;rflint: %s: exception while</td><td>lastFile := files[len(files)-1]</td></tr><tr><td>&quot;loading:%s\\n&quot; % (filename, str(e))</td><td>numBackup = lastFile[len(lastFile)-2] + 1</td></tr><tr><td></td><td>if numBackup &gt;</td></tr><tr><td></td><td>numBackup = &#x27;1&#x27;</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>else{</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>&#x27;1&#x27;</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>numBackup =</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>return Copy (filename,</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>fmt.Sprintf(&quot;%s+%s~&quot;,</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>string(numBackup)))</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr></table>"
+            },
+            {
+                "category_id": 7,
+                "poly": [
+                    299,
+                    1903,
+                    1403,
+                    1903,
+                    1403,
+                    1968,
+                    299,
+                    1968
+                ],
+                "score": 0.397
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1037,
+                    851,
+                    1059,
+                    851,
+                    1059,
+                    867,
+                    1037,
+                    867
+                ],
+                "score": 0.73,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1037,
+                    830,
+                    1060,
+                    830,
+                    1060,
+                    845,
+                    1037,
+                    845
+                ],
+                "score": 0.71,
+                "latex": ": ="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1048,
+                    1625,
+                    1071,
+                    1625,
+                    1071,
+                    1641,
+                    1048,
+                    1641
+                ],
+                "score": 0.69,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    543,
+                    1509,
+                    564,
+                    1509,
+                    564,
+                    1525,
+                    543,
+                    1525
+                ],
+                "score": 0.68,
+                "latex": "^ { - }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    530,
+                    903,
+                    553,
+                    903,
+                    553,
+                    920,
+                    530,
+                    920
+                ],
+                "score": 0.67,
+                "latex": "^ { - }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1050,
+                    807,
+                    1082,
+                    807,
+                    1082,
+                    824,
+                    1050,
+                    824
+                ],
+                "score": 0.65,
+                "latex": "= -"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1051,
+                    1604,
+                    1071,
+                    1604,
+                    1071,
+                    1620,
+                    1051,
+                    1620
+                ],
+                "score": 0.57,
+                "latex": "^ { - }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1050,
+                    1394,
+                    1071,
+                    1394,
+                    1071,
+                    1410,
+                    1050,
+                    1410
+                ],
+                "score": 0.56,
+                "latex": "{ } = { }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    962,
+                    461,
+                    1032,
+                    461,
+                    1032,
+                    481,
+                    962,
+                    481
+                ],
+                "score": 0.54,
+                "latex": " { \\mathrm { ~  ~ \\dot { ~ } { ~ 1 ~ } ~ } } : = 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1072,
+                    1666,
+                    1092,
+                    1666,
+                    1092,
+                    1683,
+                    1072,
+                    1683
+                ],
+                "score": 0.52,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1075,
+                    1581,
+                    1122,
+                    1581,
+                    1122,
+                    1601,
+                    1075,
+                    1601
+                ],
+                "score": 0.47,
+                "latex": "! = 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1033,
+                    483,
+                    1058,
+                    483,
+                    1058,
+                    501,
+                    1033,
+                    501
+                ],
+                "score": 0.47,
+                "latex": "! ="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1083,
+                    1645,
+                    1100,
+                    1645,
+                    1100,
+                    1662,
+                    1083,
+                    1662
+                ],
+                "score": 0.46,
+                "latex": ">"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1026,
+                    787,
+                    1047,
+                    787,
+                    1047,
+                    804,
+                    1026,
+                    804
+                ],
+                "score": 0.44,
+                "latex": ": ="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1032,
+                    398,
+                    1059,
+                    398,
+                    1059,
+                    417,
+                    1032,
+                    417
+                ],
+                "score": 0.42,
+                "latex": "! ="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    447,
+                    462,
+                    487,
+                    462,
+                    487,
+                    480,
+                    447,
+                    480
+                ],
+                "score": 0.41,
+                "latex": "\\begin{array} { r l } { \\dot { \\perp } } & { { } = } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    575,
+                    1530,
+                    597,
+                    1530,
+                    597,
+                    1546,
+                    575,
+                    1546
+                ],
+                "score": 0.4,
+                "latex": "^ { - }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1054,
+                    461,
+                    1092,
+                    461,
+                    1092,
+                    481,
+                    1054,
+                    481
+                ],
+                "score": 0.4,
+                "latex": "\\dot { \\perp } <"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1032,
+                    1540,
+                    1059,
+                    1540,
+                    1059,
+                    1559,
+                    1032,
+                    1559
+                ],
+                "score": 0.35,
+                "latex": ": ="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1184,
+                    460,
+                    1222,
+                    460,
+                    1222,
+                    481,
+                    1184,
+                    481
+                ],
+                "score": 0.34,
+                "latex": "\\dot { \\perp } + +"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    454,
+                    378,
+                    521,
+                    378,
+                    521,
+                    396,
+                    454,
+                    396
+                ],
+                "score": 0.34,
+                "latex": "( \\mathsf { a } \\quad = ="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1039,
+                    1416,
+                    1057,
+                    1416,
+                    1057,
+                    1432,
+                    1039,
+                    1432
+                ],
+                "score": 0.32,
+                "latex": "^ +"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    488,
+                    734,
+                    533,
+                    734,
+                    533,
+                    753,
+                    488,
+                    753
+                ],
+                "score": 0.29,
+                "latex": "= ~ \\textsf { S } \\iota"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1048,
+                    1728,
+                    1101,
+                    1728,
+                    1101,
+                    1747,
+                    1048,
+                    1747
+                ],
+                "score": 0.28,
+                "latex": "\\qquad = \\quad 1 1"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1040,
+                    1163,
+                    1059,
+                    1163,
+                    1059,
+                    1178,
+                    1040,
+                    1178
+                ],
+                "score": 0.27,
+                "latex": "^ { - }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    456,
+                    399,
+                    520,
+                    399,
+                    520,
+                    418,
+                    456,
+                    418
+                ],
+                "score": 0.26,
+                "latex": ": { \\mathrm { b } } \\ = = ="
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    72.0,
+                    816.0,
+                    72.0,
+                    816.0,
+                    110.0,
+                    294.0,
+                    110.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    832.0,
+                    2085.0,
+                    870.0,
+                    2085.0,
+                    870.0,
+                    2123.0,
+                    832.0,
+                    2123.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1899.0,
+                    1405.0,
+                    1899.0,
+                    1405.0,
+                    1938.0,
+                    294.0,
+                    1938.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1930.0,
+                    623.0,
+                    1930.0,
+                    623.0,
+                    1970.0,
+                    294.0,
+                    1970.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 14,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 3,
+                "poly": [
+                    513,
+                    222,
+                    1169,
+                    222,
+                    1169,
+                    734,
+                    513,
+                    734
+                ],
+                "score": 0.967
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    364,
+                    1421,
+                    1402,
+                    1421,
+                    1402,
+                    1513,
+                    364,
+                    1513
+                ],
+                "score": 0.952
+            },
+            {
+                "category_id": 4,
+                "poly": [
+                    365,
+                    755,
+                    1335,
+                    755,
+                    1335,
+                    789,
+                    365,
+                    789
+                ],
+                "score": 0.924
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    395,
+                    1674,
+                    1403,
+                    1674,
+                    1403,
+                    2008,
+                    395,
+                    2008
+                ],
+                "score": 0.916
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    361,
+                    1582,
+                    1402,
+                    1582,
+                    1402,
+                    1671,
+                    361,
+                    1671
+                ],
+                "score": 0.908
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    361,
+                    906,
+                    1403,
+                    906,
+                    1403,
+                    968,
+                    361,
+                    968
+                ],
+                "score": 0.895
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    299,
+                    76,
+                    812,
+                    76,
+                    812,
+                    104,
+                    299,
+                    104
+                ],
+                "score": 0.889
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    362,
+                    1531,
+                    1033,
+                    1531,
+                    1033,
+                    1563,
+                    362,
+                    1563
+                ],
+                "score": 0.868
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    836,
+                    2088,
+                    865,
+                    2088,
+                    865,
+                    2112,
+                    836,
+                    2112
+                ],
+                "score": 0.848
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    355,
+                    1288,
+                    1367,
+                    1288,
+                    1367,
+                    1321,
+                    355,
+                    1321
+                ],
+                "score": 0.847
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    360,
+                    1207,
+                    1398,
+                    1207,
+                    1398,
+                    1271,
+                    360,
+                    1271
+                ],
+                "score": 0.84
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    364,
+                    856,
+                    690,
+                    856,
+                    690,
+                    888,
+                    364,
+                    888
+                ],
+                "score": 0.788
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    362,
+                    1097,
+                    1403,
+                    1097,
+                    1403,
+                    1190,
+                    362,
+                    1190
+                ],
+                "score": 0.785
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    363,
+                    986,
+                    1405,
+                    986,
+                    1405,
+                    1078,
+                    363,
+                    1078
+                ],
+                "score": 0.781
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    299,
+                    1362,
+                    1001,
+                    1362,
+                    1001,
+                    1395,
+                    299,
+                    1395
+                ],
+                "score": 0.658
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1362,
+                    1001,
+                    1362,
+                    1001,
+                    1395,
+                    299,
+                    1395
+                ],
+                "score": 0.258
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    898,
+                    1238,
+                    944,
+                    1238,
+                    944,
+                    1272,
+                    898,
+                    1272
+                ],
+                "score": 0.85,
+                "latex": "^ { \\bullet } \\backslash \\boldsymbol { \\mathrm { n } } ^ { \\prime }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1169,
+                    1100,
+                    1206,
+                    1100,
+                    1206,
+                    1127,
+                    1169,
+                    1127
+                ],
+                "score": 0.6,
+                "latex": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    535.0,
+                    226.0,
+                    694.0,
+                    226.0,
+                    694.0,
+                    259.0,
+                    535.0,
+                    259.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    529.0,
+                    263.0,
+                    798.0,
+                    263.0,
+                    798.0,
+                    292.0,
+                    529.0,
+                    292.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    863.0,
+                    253.0,
+                    973.0,
+                    253.0,
+                    973.0,
+                    285.0,
+                    863.0,
+                    285.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    527.0,
+                    283.0,
+                    561.0,
+                    283.0,
+                    561.0,
+                    314.0,
+                    527.0,
+                    314.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    599.0,
+                    288.0,
+                    653.0,
+                    288.0,
+                    653.0,
+                    315.0,
+                    599.0,
+                    315.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1002.0,
+                    302.0,
+                    1165.0,
+                    302.0,
+                    1165.0,
+                    327.0,
+                    1002.0,
+                    327.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    741.0,
+                    363.0,
+                    809.0,
+                    363.0,
+                    809.0,
+                    393.0,
+                    741.0,
+                    393.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    839.0,
+                    325.0,
+                    984.0,
+                    325.0,
+                    984.0,
+                    386.0,
+                    839.0,
+                    386.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    999.0,
+                    323.0,
+                    1174.0,
+                    323.0,
+                    1174.0,
+                    393.0,
+                    999.0,
+                    393.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    741.0,
+                    383.0,
+                    832.0,
+                    383.0,
+                    832.0,
+                    417.0,
+                    741.0,
+                    417.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    999.0,
+                    383.0,
+                    1110.0,
+                    383.0,
+                    1110.0,
+                    416.0,
+                    999.0,
+                    416.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    776.0,
+                    425.0,
+                    868.0,
+                    425.0,
+                    868.0,
+                    459.0,
+                    776.0,
+                    459.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    974.0,
+                    424.0,
+                    1069.0,
+                    424.0,
+                    1069.0,
+                    460.0,
+                    974.0,
+                    460.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1042.0,
+                    472.0,
+                    1134.0,
+                    472.0,
+                    1134.0,
+                    498.0,
+                    1042.0,
+                    498.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    676.0,
+                    511.0,
+                    770.0,
+                    511.0,
+                    770.0,
+                    544.0,
+                    676.0,
+                    544.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    868.0,
+                    512.0,
+                    979.0,
+                    512.0,
+                    979.0,
+                    544.0,
+                    868.0,
+                    544.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    915.0,
+                    572.0,
+                    932.0,
+                    572.0,
+                    932.0,
+                    587.0,
+                    915.0,
+                    587.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    889.0,
+                    594.0,
+                    957.0,
+                    594.0,
+                    957.0,
+                    637.0,
+                    889.0,
+                    637.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    912.0,
+                    654.0,
+                    934.0,
+                    654.0,
+                    934.0,
+                    674.0,
+                    912.0,
+                    674.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    887.0,
+                    682.0,
+                    961.0,
+                    682.0,
+                    961.0,
+                    723.0,
+                    887.0,
+                    723.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    361.0,
+                    753.0,
+                    1338.0,
+                    753.0,
+                    1338.0,
+                    793.0,
+                    361.0,
+                    793.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    73.0,
+                    815.0,
+                    73.0,
+                    815.0,
+                    108.0,
+                    295.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    832.0,
+                    2084.0,
+                    871.0,
+                    2084.0,
+                    871.0,
+                    2123.0,
+                    832.0,
+                    2123.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1358.0,
+                    1005.0,
+                    1358.0,
+                    1005.0,
+                    1402.0,
+                    293.0,
+                    1402.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    361.0,
+                    1419.0,
+                    1405.0,
+                    1419.0,
+                    1405.0,
+                    1456.0,
+                    361.0,
+                    1456.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    1448.0,
+                    1405.0,
+                    1448.0,
+                    1405.0,
+                    1487.0,
+                    393.0,
+                    1487.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    395.0,
+                    1480.0,
+                    1023.0,
+                    1480.0,
+                    1023.0,
+                    1516.0,
+                    395.0,
+                    1516.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1670.0,
+                    1406.0,
+                    1670.0,
+                    1406.0,
+                    1707.0,
+                    394.0,
+                    1707.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    395.0,
+                    1704.0,
+                    1406.0,
+                    1704.0,
+                    1406.0,
+                    1736.0,
+                    395.0,
+                    1736.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    1735.0,
+                    1407.0,
+                    1735.0,
+                    1407.0,
+                    1768.0,
+                    392.0,
+                    1768.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    1763.0,
+                    1404.0,
+                    1763.0,
+                    1404.0,
+                    1797.0,
+                    393.0,
+                    1797.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    1792.0,
+                    1407.0,
+                    1792.0,
+                    1407.0,
+                    1830.0,
+                    392.0,
+                    1830.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    1823.0,
+                    1407.0,
+                    1823.0,
+                    1407.0,
+                    1860.0,
+                    392.0,
+                    1860.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    395.0,
+                    1856.0,
+                    1406.0,
+                    1856.0,
+                    1406.0,
+                    1891.0,
+                    395.0,
+                    1891.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    395.0,
+                    1886.0,
+                    1405.0,
+                    1886.0,
+                    1405.0,
+                    1918.0,
+                    395.0,
+                    1918.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    1913.0,
+                    1407.0,
+                    1913.0,
+                    1407.0,
+                    1951.0,
+                    392.0,
+                    1951.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1946.0,
+                    1405.0,
+                    1946.0,
+                    1405.0,
+                    1980.0,
+                    394.0,
+                    1980.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    1979.0,
+                    646.0,
+                    1979.0,
+                    646.0,
+                    2010.0,
+                    392.0,
+                    2010.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    360.0,
+                    1582.0,
+                    1403.0,
+                    1582.0,
+                    1403.0,
+                    1615.0,
+                    360.0,
+                    1615.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    1610.0,
+                    1403.0,
+                    1610.0,
+                    1403.0,
+                    1647.0,
+                    393.0,
+                    1647.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    1638.0,
+                    544.0,
+                    1638.0,
+                    544.0,
+                    1675.0,
+                    393.0,
+                    1675.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    359.0,
+                    905.0,
+                    1404.0,
+                    905.0,
+                    1404.0,
+                    941.0,
+                    359.0,
+                    941.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    401.0,
+                    937.0,
+                    687.0,
+                    937.0,
+                    687.0,
+                    969.0,
+                    401.0,
+                    969.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    359.0,
+                    1528.0,
+                    1036.0,
+                    1528.0,
+                    1036.0,
+                    1568.0,
+                    359.0,
+                    1568.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    357.0,
+                    1287.0,
+                    1369.0,
+                    1287.0,
+                    1369.0,
+                    1324.0,
+                    357.0,
+                    1324.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    360.0,
+                    1204.0,
+                    1405.0,
+                    1204.0,
+                    1405.0,
+                    1244.0,
+                    360.0,
+                    1244.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1238.0,
+                    897.0,
+                    1238.0,
+                    897.0,
+                    1274.0,
+                    394.0,
+                    1274.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    945.0,
+                    1238.0,
+                    957.0,
+                    1238.0,
+                    957.0,
+                    1274.0,
+                    945.0,
+                    1274.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    359.0,
+                    853.0,
+                    695.0,
+                    853.0,
+                    695.0,
+                    893.0,
+                    359.0,
+                    893.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    360.0,
+                    1095.0,
+                    1168.0,
+                    1095.0,
+                    1168.0,
+                    1133.0,
+                    360.0,
+                    1133.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1207.0,
+                    1095.0,
+                    1404.0,
+                    1095.0,
+                    1404.0,
+                    1133.0,
+                    1207.0,
+                    1133.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    399.0,
+                    1128.0,
+                    1404.0,
+                    1128.0,
+                    1404.0,
+                    1162.0,
+                    399.0,
+                    1162.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    1154.0,
+                    1347.0,
+                    1154.0,
+                    1347.0,
+                    1195.0,
+                    393.0,
+                    1195.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    358.0,
+                    983.0,
+                    1404.0,
+                    983.0,
+                    1404.0,
+                    1024.0,
+                    358.0,
+                    1024.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1015.0,
+                    1405.0,
+                    1015.0,
+                    1405.0,
+                    1052.0,
+                    394.0,
+                    1052.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    391.0,
+                    1041.0,
+                    504.0,
+                    1041.0,
+                    504.0,
+                    1088.0,
+                    391.0,
+                    1088.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1358.0,
+                    1005.0,
+                    1358.0,
+                    1005.0,
+                    1402.0,
+                    293.0,
+                    1402.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 15,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1850,
+                    1404,
+                    1850,
+                    1404,
+                    2033,
+                    298,
+                    2033
+                ],
+                "score": 0.971
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1569,
+                    1404,
+                    1569,
+                    1404,
+                    1752,
+                    298,
+                    1752
+                ],
+                "score": 0.968
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    428,
+                    394,
+                    1404,
+                    394,
+                    1404,
+                    781,
+                    428,
+                    781
+                ],
+                "score": 0.959
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    361,
+                    277,
+                    1403,
+                    277,
+                    1403,
+                    340,
+                    361,
+                    340
+                ],
+                "score": 0.922
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    300,
+                    76,
+                    813,
+                    76,
+                    813,
+                    104,
+                    300,
+                    104
+                ],
+                "score": 0.885
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    302,
+                    1791,
+                    766,
+                    1791,
+                    766,
+                    1823,
+                    302,
+                    1823
+                ],
+                "score": 0.881
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    300,
+                    1512,
+                    797,
+                    1512,
+                    797,
+                    1542,
+                    300,
+                    1542
+                ],
+                "score": 0.874
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    836,
+                    2088,
+                    864,
+                    2088,
+                    864,
+                    2112,
+                    836,
+                    2112
+                ],
+                "score": 0.841
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    396,
+                    793,
+                    1402,
+                    793,
+                    1402,
+                    1037,
+                    396,
+                    1037
+                ],
+                "score": 0.819
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    363,
+                    351,
+                    1173,
+                    351,
+                    1173,
+                    383,
+                    363,
+                    383
+                ],
+                "score": 0.796
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    363,
+                    1048,
+                    1403,
+                    1048,
+                    1403,
+                    1262,
+                    363,
+                    1262
+                ],
+                "score": 0.594
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    230,
+                    1193,
+                    230,
+                    1193,
+                    262,
+                    298,
+                    262
+                ],
+                "score": 0.506
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    368,
+                    1379,
+                    1401,
+                    1379,
+                    1401,
+                    1470,
+                    368,
+                    1470
+                ],
+                "score": 0.429
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    364,
+                    1275,
+                    1400,
+                    1275,
+                    1400,
+                    1367,
+                    364,
+                    1367
+                ],
+                "score": 0.4
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    230,
+                    1193,
+                    230,
+                    1193,
+                    262,
+                    298,
+                    262
+                ],
+                "score": 0.164
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1006,
+                    1202,
+                    1168,
+                    1202,
+                    1168,
+                    1232,
+                    1006,
+                    1232
+                ],
+                "score": 0.9,
+                "latex": "- 4 , - 3 , \\dots , 4"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    800,
+                    455,
+                    844,
+                    455,
+                    844,
+                    484,
+                    800,
+                    484
+                ],
+                "score": 0.89,
+                "latex": "e ^ { - 5 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    483,
+                    456,
+                    590,
+                    456,
+                    590,
+                    485,
+                    483,
+                    485
+                ],
+                "score": 0.89,
+                "latex": "\\alpha = 0 . 1 5"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1062,
+                    456,
+                    1249,
+                    456,
+                    1249,
+                    487,
+                    1062,
+                    487
+                ],
+                "score": 0.89,
+                "latex": "- \\log P P R > 5"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1180,
+                    1441,
+                    1289,
+                    1441,
+                    1289,
+                    1469,
+                    1180,
+                    1469
+                ],
+                "score": 0.76,
+                "latex": "= ~ 1 0 0 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    395,
+                    1441,
+                    482,
+                    1441,
+                    482,
+                    1470,
+                    395,
+                    1470
+                ],
+                "score": 0.76,
+                "latex": "= ~ 5 1 2"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1192,
+                    1086,
+                    1210,
+                    1086,
+                    1210,
+                    1112,
+                    1192,
+                    1112
+                ],
+                "score": 0.62,
+                "latex": "y"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1032,
+                    1085,
+                    1050,
+                    1085,
+                    1050,
+                    1108,
+                    1032,
+                    1108
+                ],
+                "score": 0.48,
+                "latex": "x"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    644,
+                    313,
+                    664,
+                    313,
+                    664,
+                    337,
+                    644,
+                    337
+                ],
+                "score": 0.45,
+                "latex": ">"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    568,
+                    713,
+                    639,
+                    713,
+                    639,
+                    744,
+                    568,
+                    744
+                ],
+                "score": 0.25,
+                "latex": "1 , 0 0 0"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    72.0,
+                    816.0,
+                    72.0,
+                    816.0,
+                    110.0,
+                    294.0,
+                    110.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    1791.0,
+                    771.0,
+                    1791.0,
+                    771.0,
+                    1827.0,
+                    297.0,
+                    1827.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1511.0,
+                    801.0,
+                    1511.0,
+                    801.0,
+                    1545.0,
+                    296.0,
+                    1545.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    832.0,
+                    2085.0,
+                    869.0,
+                    2085.0,
+                    869.0,
+                    2124.0,
+                    832.0,
+                    2124.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    226.0,
+                    1196.0,
+                    226.0,
+                    1196.0,
+                    267.0,
+                    295.0,
+                    267.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1848.0,
+                    1405.0,
+                    1848.0,
+                    1405.0,
+                    1885.0,
+                    295.0,
+                    1885.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1880.0,
+                    1404.0,
+                    1880.0,
+                    1404.0,
+                    1915.0,
+                    294.0,
+                    1915.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1910.0,
+                    1404.0,
+                    1910.0,
+                    1404.0,
+                    1947.0,
+                    293.0,
+                    1947.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1940.0,
+                    1404.0,
+                    1940.0,
+                    1404.0,
+                    1978.0,
+                    293.0,
+                    1978.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1971.0,
+                    1405.0,
+                    1971.0,
+                    1405.0,
+                    2007.0,
+                    293.0,
+                    2007.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    2002.0,
+                    585.0,
+                    2002.0,
+                    585.0,
+                    2038.0,
+                    294.0,
+                    2038.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1567.0,
+                    1406.0,
+                    1567.0,
+                    1406.0,
+                    1606.0,
+                    293.0,
+                    1606.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1596.0,
+                    1405.0,
+                    1596.0,
+                    1405.0,
+                    1638.0,
+                    292.0,
+                    1638.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1630.0,
+                    1405.0,
+                    1630.0,
+                    1405.0,
+                    1666.0,
+                    294.0,
+                    1666.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1658.0,
+                    1404.0,
+                    1658.0,
+                    1404.0,
+                    1695.0,
+                    293.0,
+                    1695.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1690.0,
+                    1407.0,
+                    1690.0,
+                    1407.0,
+                    1726.0,
+                    292.0,
+                    1726.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1721.0,
+                    556.0,
+                    1721.0,
+                    556.0,
+                    1757.0,
+                    294.0,
+                    1757.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    427.0,
+                    394.0,
+                    801.0,
+                    394.0,
+                    801.0,
+                    428.0,
+                    427.0,
+                    428.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    449.0,
+                    424.0,
+                    1402.0,
+                    424.0,
+                    1402.0,
+                    459.0,
+                    449.0,
+                    459.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    449.0,
+                    453.0,
+                    482.0,
+                    453.0,
+                    482.0,
+                    491.0,
+                    449.0,
+                    491.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    591.0,
+                    453.0,
+                    799.0,
+                    453.0,
+                    799.0,
+                    491.0,
+                    591.0,
+                    491.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    845.0,
+                    453.0,
+                    1061.0,
+                    453.0,
+                    1061.0,
+                    491.0,
+                    845.0,
+                    491.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1250.0,
+                    453.0,
+                    1405.0,
+                    453.0,
+                    1405.0,
+                    491.0,
+                    1250.0,
+                    491.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    451.0,
+                    490.0,
+                    592.0,
+                    490.0,
+                    592.0,
+                    515.0,
+                    451.0,
+                    515.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    431.0,
+                    523.0,
+                    898.0,
+                    523.0,
+                    898.0,
+                    554.0,
+                    431.0,
+                    554.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    430.0,
+                    559.0,
+                    1405.0,
+                    559.0,
+                    1405.0,
+                    592.0,
+                    430.0,
+                    592.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    449.0,
+                    591.0,
+                    1406.0,
+                    591.0,
+                    1406.0,
+                    622.0,
+                    449.0,
+                    622.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    448.0,
+                    620.0,
+                    1405.0,
+                    620.0,
+                    1405.0,
+                    655.0,
+                    448.0,
+                    655.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    450.0,
+                    652.0,
+                    1406.0,
+                    652.0,
+                    1406.0,
+                    685.0,
+                    450.0,
+                    685.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    447.0,
+                    682.0,
+                    1405.0,
+                    682.0,
+                    1405.0,
+                    714.0,
+                    447.0,
+                    714.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    448.0,
+                    714.0,
+                    567.0,
+                    714.0,
+                    567.0,
+                    745.0,
+                    448.0,
+                    745.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    640.0,
+                    714.0,
+                    918.0,
+                    714.0,
+                    918.0,
+                    745.0,
+                    640.0,
+                    745.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    428.0,
+                    747.0,
+                    1371.0,
+                    747.0,
+                    1371.0,
+                    782.0,
+                    428.0,
+                    782.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    361.0,
+                    274.0,
+                    1404.0,
+                    274.0,
+                    1404.0,
+                    312.0,
+                    361.0,
+                    312.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    309.0,
+                    643.0,
+                    309.0,
+                    643.0,
+                    344.0,
+                    394.0,
+                    344.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    665.0,
+                    309.0,
+                    742.0,
+                    309.0,
+                    742.0,
+                    344.0,
+                    665.0,
+                    344.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    791.0,
+                    1405.0,
+                    791.0,
+                    1405.0,
+                    827.0,
+                    393.0,
+                    827.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    822.0,
+                    1406.0,
+                    822.0,
+                    1406.0,
+                    859.0,
+                    393.0,
+                    859.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    854.0,
+                    1405.0,
+                    854.0,
+                    1405.0,
+                    888.0,
+                    394.0,
+                    888.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    884.0,
+                    1406.0,
+                    884.0,
+                    1406.0,
+                    917.0,
+                    394.0,
+                    917.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    915.0,
+                    1405.0,
+                    915.0,
+                    1405.0,
+                    948.0,
+                    394.0,
+                    948.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    945.0,
+                    1405.0,
+                    945.0,
+                    1405.0,
+                    978.0,
+                    394.0,
+                    978.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    974.0,
+                    1406.0,
+                    974.0,
+                    1406.0,
+                    1011.0,
+                    393.0,
+                    1011.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    1005.0,
+                    1172.0,
+                    1005.0,
+                    1172.0,
+                    1043.0,
+                    392.0,
+                    1043.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    359.0,
+                    348.0,
+                    1173.0,
+                    348.0,
+                    1173.0,
+                    387.0,
+                    359.0,
+                    387.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    358.0,
+                    1046.0,
+                    1406.0,
+                    1046.0,
+                    1406.0,
+                    1083.0,
+                    358.0,
+                    1083.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1078.0,
+                    1031.0,
+                    1078.0,
+                    1031.0,
+                    1116.0,
+                    394.0,
+                    1116.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1051.0,
+                    1078.0,
+                    1191.0,
+                    1078.0,
+                    1191.0,
+                    1116.0,
+                    1051.0,
+                    1116.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1211.0,
+                    1078.0,
+                    1405.0,
+                    1078.0,
+                    1405.0,
+                    1116.0,
+                    1211.0,
+                    1116.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    395.0,
+                    1110.0,
+                    1404.0,
+                    1110.0,
+                    1404.0,
+                    1144.0,
+                    395.0,
+                    1144.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1139.0,
+                    1404.0,
+                    1139.0,
+                    1404.0,
+                    1175.0,
+                    394.0,
+                    1175.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    1170.0,
+                    1405.0,
+                    1170.0,
+                    1405.0,
+                    1205.0,
+                    393.0,
+                    1205.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    395.0,
+                    1200.0,
+                    1005.0,
+                    1200.0,
+                    1005.0,
+                    1235.0,
+                    395.0,
+                    1235.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1169.0,
+                    1200.0,
+                    1405.0,
+                    1200.0,
+                    1405.0,
+                    1235.0,
+                    1169.0,
+                    1235.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1227.0,
+                    1132.0,
+                    1227.0,
+                    1132.0,
+                    1270.0,
+                    394.0,
+                    1270.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    226.0,
+                    1196.0,
+                    226.0,
+                    1196.0,
+                    267.0,
+                    295.0,
+                    267.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    360.0,
+                    1377.0,
+                    1405.0,
+                    1377.0,
+                    1405.0,
+                    1414.0,
+                    360.0,
+                    1414.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    395.0,
+                    1409.0,
+                    1404.0,
+                    1409.0,
+                    1404.0,
+                    1444.0,
+                    395.0,
+                    1444.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    483.0,
+                    1441.0,
+                    1179.0,
+                    1441.0,
+                    1179.0,
+                    1472.0,
+                    483.0,
+                    1472.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1290.0,
+                    1441.0,
+                    1300.0,
+                    1441.0,
+                    1300.0,
+                    1472.0,
+                    1290.0,
+                    1472.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    358.0,
+                    1272.0,
+                    1405.0,
+                    1272.0,
+                    1405.0,
+                    1311.0,
+                    358.0,
+                    1311.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1305.0,
+                    1405.0,
+                    1305.0,
+                    1405.0,
+                    1343.0,
+                    394.0,
+                    1343.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    395.0,
+                    1335.0,
+                    774.0,
+                    1335.0,
+                    774.0,
+                    1371.0,
+                    395.0,
+                    1371.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 16,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    371,
+                    1014,
+                    1404,
+                    1014,
+                    1404,
+                    1475,
+                    371,
+                    1475
+                ],
+                "score": 0.972
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    724,
+                    1404,
+                    724,
+                    1404,
+                    879,
+                    297,
+                    879
+                ],
+                "score": 0.972
+            },
+            {
+                "category_id": 5,
+                "poly": [
+                    885,
+                    300,
+                    1218,
+                    300,
+                    1218,
+                    546,
+                    885,
+                    546
+                ],
+                "score": 0.969,
+                "html": "<table><tr><td>Hyperparameter</td><td>Value</td></tr><tr><td>Activation</td><td>GELU</td></tr><tr><td>Num. layers</td><td>3</td></tr><tr><td>d</td><td>1024</td></tr><tr><td>dFF</td><td>2048</td></tr><tr><td>Pdropout</td><td>0.2</td></tr><tr><td>Num.heads</td><td>8</td></tr></table>"
+            },
+            {
+                "category_id": 5,
+                "poly": [
+                    466,
+                    272,
+                    823,
+                    272,
+                    823,
+                    552,
+                    466,
+                    552
+                ],
+                "score": 0.968,
+                "html": "<table><tr><td>Hyperparameter</td><td>Value</td></tr><tr><td>Activation</td><td>GELU</td></tr><tr><td>Input Nonlinearity</td><td>tanh</td></tr><tr><td>Num. layers</td><td>3</td></tr><tr><td>d</td><td>1024</td></tr><tr><td>dFF</td><td>2048</td></tr><tr><td>Pdropout</td><td>0.2</td></tr><tr><td>Num.heads</td><td>8</td></tr></table>"
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1568,
+                    1404,
+                    1568,
+                    1404,
+                    1631,
+                    297,
+                    1631
+                ],
+                "score": 0.945
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    923,
+                    1399,
+                    923,
+                    1399,
+                    986,
+                    299,
+                    986
+                ],
+                "score": 0.945
+            },
+            {
+                "category_id": 6,
+                "poly": [
+                    586,
+                    576,
+                    1115,
+                    576,
+                    1115,
+                    609,
+                    586,
+                    609
+                ],
+                "score": 0.904
+            },
+            {
+                "category_id": 6,
+                "poly": [
+                    870,
+                    240,
+                    1236,
+                    240,
+                    1236,
+                    295,
+                    870,
+                    295
+                ],
+                "score": 0.901
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    303,
+                    1512,
+                    787,
+                    1512,
+                    787,
+                    1542,
+                    303,
+                    1542
+                ],
+                "score": 0.892
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    301,
+                    668,
+                    644,
+                    668,
+                    644,
+                    699,
+                    301,
+                    699
+                ],
+                "score": 0.89
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    299,
+                    76,
+                    813,
+                    76,
+                    813,
+                    104,
+                    299,
+                    104
+                ],
+                "score": 0.889
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    836,
+                    2088,
+                    865,
+                    2088,
+                    865,
+                    2112,
+                    836,
+                    2112
+                ],
+                "score": 0.844
+            },
+            {
+                "category_id": 6,
+                "poly": [
+                    508,
+                    241,
+                    780,
+                    241,
+                    780,
+                    268,
+                    508,
+                    268
+                ],
+                "score": 0.784
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    485,
+                    815,
+                    543,
+                    815,
+                    543,
+                    845,
+                    485,
+                    845
+                ],
+                "score": 0.9,
+                "latex": "3 e ^ { - 5 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1293,
+                    785,
+                    1353,
+                    785,
+                    1353,
+                    815,
+                    1293,
+                    815
+                ],
+                "score": 0.9,
+                "latex": "8 e ^ { - 5 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    485,
+                    450,
+                    539,
+                    450,
+                    539,
+                    481,
+                    485,
+                    481
+                ],
+                "score": 0.33,
+                "latex": "d _ { F F }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    485,
+                    419,
+                    504,
+                    419,
+                    504,
+                    446,
+                    485,
+                    446
+                ],
+                "score": 0.3,
+                "latex": "d"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    582.0,
+                    567.0,
+                    1116.0,
+                    567.0,
+                    1116.0,
+                    618.0,
+                    582.0,
+                    618.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    867.0,
+                    237.0,
+                    1241.0,
+                    237.0,
+                    1241.0,
+                    273.0,
+                    867.0,
+                    273.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    866.0,
+                    265.0,
+                    939.0,
+                    265.0,
+                    939.0,
+                    301.0,
+                    866.0,
+                    301.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    1511.0,
+                    791.0,
+                    1511.0,
+                    791.0,
+                    1545.0,
+                    297.0,
+                    1545.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    668.0,
+                    645.0,
+                    668.0,
+                    645.0,
+                    701.0,
+                    296.0,
+                    701.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    73.0,
+                    815.0,
+                    73.0,
+                    815.0,
+                    108.0,
+                    295.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    832.0,
+                    2085.0,
+                    870.0,
+                    2085.0,
+                    870.0,
+                    2122.0,
+                    832.0,
+                    2122.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    506.0,
+                    239.0,
+                    783.0,
+                    239.0,
+                    783.0,
+                    270.0,
+                    506.0,
+                    270.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    380.0,
+                    1012.0,
+                    843.0,
+                    1012.0,
+                    843.0,
+                    1047.0,
+                    380.0,
+                    1047.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    1042.0,
+                    1407.0,
+                    1042.0,
+                    1407.0,
+                    1077.0,
+                    393.0,
+                    1077.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1075.0,
+                    1404.0,
+                    1075.0,
+                    1404.0,
+                    1108.0,
+                    394.0,
+                    1108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1105.0,
+                    923.0,
+                    1105.0,
+                    923.0,
+                    1138.0,
+                    394.0,
+                    1138.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    380.0,
+                    1144.0,
+                    826.0,
+                    1144.0,
+                    826.0,
+                    1180.0,
+                    380.0,
+                    1180.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1176.0,
+                    1403.0,
+                    1176.0,
+                    1403.0,
+                    1208.0,
+                    394.0,
+                    1208.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    1205.0,
+                    1403.0,
+                    1205.0,
+                    1403.0,
+                    1243.0,
+                    393.0,
+                    1243.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    395.0,
+                    1237.0,
+                    552.0,
+                    1237.0,
+                    552.0,
+                    1270.0,
+                    395.0,
+                    1270.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    379.0,
+                    1277.0,
+                    801.0,
+                    1277.0,
+                    801.0,
+                    1312.0,
+                    379.0,
+                    1312.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    1309.0,
+                    1407.0,
+                    1309.0,
+                    1407.0,
+                    1344.0,
+                    393.0,
+                    1344.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    391.0,
+                    1338.0,
+                    1403.0,
+                    1338.0,
+                    1403.0,
+                    1375.0,
+                    391.0,
+                    1375.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    395.0,
+                    1373.0,
+                    1403.0,
+                    1373.0,
+                    1403.0,
+                    1402.0,
+                    395.0,
+                    1402.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    1402.0,
+                    1145.0,
+                    1402.0,
+                    1145.0,
+                    1433.0,
+                    393.0,
+                    1433.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    369.0,
+                    1440.0,
+                    1367.0,
+                    1440.0,
+                    1367.0,
+                    1478.0,
+                    369.0,
+                    1478.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    724.0,
+                    1405.0,
+                    724.0,
+                    1405.0,
+                    759.0,
+                    296.0,
+                    759.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    754.0,
+                    1405.0,
+                    754.0,
+                    1405.0,
+                    790.0,
+                    295.0,
+                    790.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    784.0,
+                    1292.0,
+                    784.0,
+                    1292.0,
+                    820.0,
+                    294.0,
+                    820.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1354.0,
+                    784.0,
+                    1406.0,
+                    784.0,
+                    1406.0,
+                    820.0,
+                    1354.0,
+                    820.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    812.0,
+                    484.0,
+                    812.0,
+                    484.0,
+                    853.0,
+                    294.0,
+                    853.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    544.0,
+                    812.0,
+                    1406.0,
+                    812.0,
+                    1406.0,
+                    853.0,
+                    544.0,
+                    853.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    848.0,
+                    591.0,
+                    848.0,
+                    591.0,
+                    880.0,
+                    293.0,
+                    880.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1569.0,
+                    1402.0,
+                    1569.0,
+                    1402.0,
+                    1601.0,
+                    296.0,
+                    1601.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1597.0,
+                    1127.0,
+                    1597.0,
+                    1127.0,
+                    1634.0,
+                    294.0,
+                    1634.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    920.0,
+                    1403.0,
+                    920.0,
+                    1403.0,
+                    960.0,
+                    295.0,
+                    960.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    957.0,
+                    794.0,
+                    957.0,
+                    794.0,
+                    989.0,
+                    295.0,
+                    989.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 17,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 5,
+                "poly": [
+                    642,
+                    356,
+                    1051,
+                    356,
+                    1051,
+                    572,
+                    642,
+                    572
+                ],
+                "score": 0.969,
+                "html": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td> get x map</td></tr><tr><td>code2seq</td><td> get parts</td></tr><tr><td>Ours w/o structure</td><td>get</td></tr><tr><td>CODE TRANSFORMER</td><td>get next</td></tr><tr><td>Ground Truth</td><td>next</td></tr></table>"
+            },
+            {
+                "category_id": 5,
+                "poly": [
+                    615,
+                    1684,
+                    1079,
+                    1684,
+                    1079,
+                    1900,
+                    615,
+                    1900
+                ],
+                "score": 0.96,
+                "html": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td>run</td></tr><tr><td>code2seq</td><td> get submit time</td></tr><tr><td>Ours w/o structure</td><td>compare</td></tr><tr><td>CODE TRANSFORMER</td><td>compare</td></tr><tr><td>Ground Truth</td><td>compare</td></tr></table>"
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    1479,
+                    1274,
+                    1479,
+                    1274,
+                    1672,
+                    295,
+                    1672
+                ],
+                "score": 0.928
+            },
+            {
+                "category_id": 5,
+                "poly": [
+                    627,
+                    1046,
+                    1070,
+                    1046,
+                    1070,
+                    1262,
+                    627,
+                    1262
+                ],
+                "score": 0.908,
+                "html": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td>get path</td></tr><tr><td>code2seq</td><td>find file</td></tr><tr><td>Ours w/o structure</td><td>get file</td></tr><tr><td>CODE TRANSFORMER</td><td>find cache</td></tr><tr><td>Ground Truth</td><td>find cache file</td></tr></table>"
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    263,
+                    674,
+                    263,
+                    674,
+                    346,
+                    295,
+                    346
+                ],
+                "score": 0.901
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    299,
+                    75,
+                    813,
+                    75,
+                    813,
+                    105,
+                    299,
+                    105
+                ],
+                "score": 0.885
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    836,
+                    2088,
+                    865,
+                    2088,
+                    865,
+                    2113,
+                    836,
+                    2113
+                ],
+                "score": 0.859
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    758,
+                    1259,
+                    758,
+                    1259,
+                    1030,
+                    296,
+                    1030
+                ],
+                "score": 0.851
+            },
+            {
+                "category_id": 6,
+                "poly": [
+                    295,
+                    595,
+                    1402,
+                    595,
+                    1402,
+                    658,
+                    295,
+                    658
+                ],
+                "score": 0.742
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1921,
+                    1402,
+                    1921,
+                    1402,
+                    1986,
+                    298,
+                    1986
+                ],
+                "score": 0.737
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1284,
+                    1406,
+                    1284,
+                    1406,
+                    1377,
+                    297,
+                    1377
+                ],
+                "score": 0.647
+            },
+            {
+                "category_id": 6,
+                "poly": [
+                    297,
+                    1284,
+                    1406,
+                    1284,
+                    1406,
+                    1377,
+                    297,
+                    1377
+                ],
+                "score": 0.158
+            },
+            {
+                "category_id": 6,
+                "poly": [
+                    298,
+                    1921,
+                    1402,
+                    1921,
+                    1402,
+                    1986,
+                    298,
+                    1986
+                ],
+                "score": 0.145
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    585,
+                    789,
+                    619,
+                    789,
+                    619,
+                    812,
+                    585,
+                    812
+                ],
+                "score": 0.69,
+                "latex": "! ="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    507,
+                    1536,
+                    614,
+                    1536,
+                    614,
+                    1563,
+                    507,
+                    1563
+                ],
+                "score": 0.57,
+                "latex": "\\ j 1 \\ = \\ \\mathtt { p 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    758,
+                    1592,
+                    784,
+                    1592,
+                    784,
+                    1616,
+                    758,
+                    1616
+                ],
+                "score": 0.54,
+                "latex": "<"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    508,
+                    1564,
+                    615,
+                    1564,
+                    615,
+                    1591,
+                    508,
+                    1591
+                ],
+                "score": 0.51,
+                "latex": "\\begin{array} { r } { \\dot { \\bf { \\ j } } 2 { \\bf { \\nu } } = { \\bf { \\ p } } 2 } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    543,
+                    293,
+                    611,
+                    293,
+                    611,
+                    319,
+                    543,
+                    319
+                ],
+                "score": 0.41,
+                "latex": "[ \\dot { 1 } + + ]"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1009,
+                    788,
+                    1064,
+                    788,
+                    1064,
+                    814,
+                    1009,
+                    814
+                ],
+                "score": 0.41,
+                "latex": "> 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    802,
+                    1621,
+                    844,
+                    1621,
+                    844,
+                    1645,
+                    802,
+                    1645
+                ],
+                "score": 0.35,
+                "latex": "= ="
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    73.0,
+                    815.0,
+                    73.0,
+                    815.0,
+                    108.0,
+                    295.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    832.0,
+                    2086.0,
+                    870.0,
+                    2086.0,
+                    870.0,
+                    2125.0,
+                    832.0,
+                    2125.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    592.0,
+                    1404.0,
+                    592.0,
+                    1404.0,
+                    630.0,
+                    294.0,
+                    630.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    628.0,
+                    420.0,
+                    628.0,
+                    420.0,
+                    661.0,
+                    294.0,
+                    661.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1283.0,
+                    1404.0,
+                    1283.0,
+                    1404.0,
+                    1317.0,
+                    295.0,
+                    1317.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1314.0,
+                    1404.0,
+                    1314.0,
+                    1404.0,
+                    1350.0,
+                    292.0,
+                    1350.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1344.0,
+                    461.0,
+                    1344.0,
+                    461.0,
+                    1378.0,
+                    294.0,
+                    1378.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1915.0,
+                    1403.0,
+                    1915.0,
+                    1403.0,
+                    1959.0,
+                    293.0,
+                    1959.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1951.0,
+                    925.0,
+                    1951.0,
+                    925.0,
+                    1990.0,
+                    293.0,
+                    1990.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1477.0,
+                    1108.0,
+                    1477.0,
+                    1108.0,
+                    1511.0,
+                    293.0,
+                    1511.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    578.0,
+                    1508.0,
+                    1139.0,
+                    1508.0,
+                    1139.0,
+                    1537.0,
+                    578.0,
+                    1537.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    354.0,
+                    1532.0,
+                    506.0,
+                    1532.0,
+                    506.0,
+                    1566.0,
+                    354.0,
+                    1566.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    615.0,
+                    1532.0,
+                    751.0,
+                    1532.0,
+                    751.0,
+                    1566.0,
+                    615.0,
+                    1566.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    1562.0,
+                    507.0,
+                    1562.0,
+                    507.0,
+                    1594.0,
+                    355.0,
+                    1594.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    616.0,
+                    1562.0,
+                    750.0,
+                    1562.0,
+                    750.0,
+                    1594.0,
+                    616.0,
+                    1594.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    360.0,
+                    1594.0,
+                    454.0,
+                    1594.0,
+                    454.0,
+                    1617.0,
+                    360.0,
+                    1617.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    462.0,
+                    1589.0,
+                    757.0,
+                    1589.0,
+                    757.0,
+                    1621.0,
+                    462.0,
+                    1621.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    785.0,
+                    1589.0,
+                    1155.0,
+                    1589.0,
+                    1155.0,
+                    1621.0,
+                    785.0,
+                    1621.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    474.0,
+                    1617.0,
+                    801.0,
+                    1617.0,
+                    801.0,
+                    1649.0,
+                    474.0,
+                    1649.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    845.0,
+                    1617.0,
+                    1271.0,
+                    1617.0,
+                    1271.0,
+                    1649.0,
+                    845.0,
+                    1649.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    357.0,
+                    1649.0,
+                    375.0,
+                    1649.0,
+                    375.0,
+                    1673.0,
+                    357.0,
+                    1673.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    263.0,
+                    678.0,
+                    263.0,
+                    678.0,
+                    292.0,
+                    294.0,
+                    292.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    356.0,
+                    292.0,
+                    542.0,
+                    292.0,
+                    542.0,
+                    319.0,
+                    356.0,
+                    319.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    612.0,
+                    292.0,
+                    627.0,
+                    292.0,
+                    627.0,
+                    319.0,
+                    612.0,
+                    319.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    300.0,
+                    325.0,
+                    316.0,
+                    325.0,
+                    316.0,
+                    345.0,
+                    300.0,
+                    345.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    756.0,
+                    1260.0,
+                    756.0,
+                    1260.0,
+                    792.0,
+                    291.0,
+                    792.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    785.0,
+                    584.0,
+                    785.0,
+                    584.0,
+                    818.0,
+                    355.0,
+                    818.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    620.0,
+                    785.0,
+                    1008.0,
+                    785.0,
+                    1008.0,
+                    818.0,
+                    620.0,
+                    818.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1065.0,
+                    785.0,
+                    1113.0,
+                    785.0,
+                    1113.0,
+                    818.0,
+                    1065.0,
+                    818.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    414.0,
+                    813.0,
+                    471.0,
+                    813.0,
+                    471.0,
+                    844.0,
+                    414.0,
+                    844.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    480.0,
+                    815.0,
+                    874.0,
+                    815.0,
+                    874.0,
+                    844.0,
+                    480.0,
+                    844.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    476.0,
+                    843.0,
+                    515.0,
+                    843.0,
+                    515.0,
+                    868.0,
+                    476.0,
+                    868.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    520.0,
+                    843.0,
+                    1050.0,
+                    843.0,
+                    1050.0,
+                    872.0,
+                    520.0,
+                    872.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    534.0,
+                    867.0,
+                    720.0,
+                    867.0,
+                    720.0,
+                    901.0,
+                    534.0,
+                    901.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    477.0,
+                    902.0,
+                    495.0,
+                    902.0,
+                    495.0,
+                    925.0,
+                    477.0,
+                    925.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    357.0,
+                    980.0,
+                    536.0,
+                    980.0,
+                    536.0,
+                    1010.0,
+                    357.0,
+                    1010.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    301.0,
+                    1014.0,
+                    315.0,
+                    1014.0,
+                    315.0,
+                    1031.0,
+                    301.0,
+                    1031.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1915.0,
+                    1403.0,
+                    1915.0,
+                    1403.0,
+                    1959.0,
+                    293.0,
+                    1959.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1951.0,
+                    925.0,
+                    1951.0,
+                    925.0,
+                    1990.0,
+                    293.0,
+                    1990.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1283.0,
+                    1404.0,
+                    1283.0,
+                    1404.0,
+                    1317.0,
+                    295.0,
+                    1317.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1314.0,
+                    1404.0,
+                    1314.0,
+                    1404.0,
+                    1350.0,
+                    292.0,
+                    1350.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1344.0,
+                    461.0,
+                    1344.0,
+                    461.0,
+                    1378.0,
+                    294.0,
+                    1378.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 18,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 5,
+                "poly": [
+                    599,
+                    1117,
+                    1095,
+                    1117,
+                    1095,
+                    1333,
+                    599,
+                    1333
+                ],
+                "score": 0.972,
+                "html": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td>list blobs</td></tr><tr><td>code2seq</td><td>list blobs</td></tr><tr><td>Ours w/o structure</td><td>list blobs</td></tr><tr><td>CODE TRANSFORMER</td><td>list blobs by prefix</td></tr><tr><td>Ground Truth</td><td>list root blobs</td></tr></table>"
+            },
+            {
+                "category_id": 5,
+                "poly": [
+                    638,
+                    436,
+                    1053,
+                    436,
+                    1053,
+                    651,
+                    638,
+                    651
+                ],
+                "score": 0.966,
+                "html": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td> get value</td></tr><tr><td>code2seq</td><td> get value</td></tr><tr><td>Ours w/o structure</td><td>to</td></tr><tr><td>CODE TRANSFORMER</td><td>from value</td></tr><tr><td>Ground Truth</td><td>from value</td></tr></table>"
+            },
+            {
+                "category_id": 5,
+                "poly": [
+                    612,
+                    1686,
+                    1080,
+                    1686,
+                    1080,
+                    1903,
+                    612,
+                    1903
+                ],
+                "score": 0.965,
+                "html": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td>append</td></tr><tr><td>code2seq</td><td>add</td></tr><tr><td>Ours w/o structure</td><td>log</td></tr><tr><td>CODE TRANSFORMER</td><td>log op counts</td></tr><tr><td>Ground Truth</td><td>dump op counts</td></tr></table>"
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    299,
+                    75,
+                    813,
+                    75,
+                    813,
+                    105,
+                    299,
+                    105
+                ],
+                "score": 0.879
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    290,
+                    1510,
+                    1604,
+                    1510,
+                    1604,
+                    1667,
+                    290,
+                    1667
+                ],
+                "score": 0.874
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    834,
+                    2087,
+                    866,
+                    2087,
+                    866,
+                    2113,
+                    834,
+                    2113
+                ],
+                "score": 0.866
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    293,
+                    674,
+                    1403,
+                    674,
+                    1403,
+                    737,
+                    293,
+                    737
+                ],
+                "score": 0.823
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    318,
+                    998,
+                    1611,
+                    998,
+                    1611,
+                    1081,
+                    318,
+                    1081
+                ],
+                "score": 0.797
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    258,
+                    1022,
+                    258,
+                    1022,
+                    425,
+                    296,
+                    425
+                ],
+                "score": 0.629
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    293,
+                    1355,
+                    1401,
+                    1355,
+                    1401,
+                    1419,
+                    293,
+                    1419
+                ],
+                "score": 0.605
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    830,
+                    1194,
+                    830,
+                    1194,
+                    858,
+                    299,
+                    858
+                ],
+                "score": 0.523
+            },
+            {
+                "category_id": 6,
+                "poly": [
+                    295,
+                    1925,
+                    1403,
+                    1925,
+                    1403,
+                    1990,
+                    295,
+                    1990
+                ],
+                "score": 0.366
+            },
+            {
+                "category_id": 6,
+                "poly": [
+                    293,
+                    1355,
+                    1401,
+                    1355,
+                    1401,
+                    1419,
+                    293,
+                    1419
+                ],
+                "score": 0.335
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    962,
+                    858,
+                    1613,
+                    858,
+                    1613,
+                    968,
+                    962,
+                    968
+                ],
+                "score": 0.184
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1081,
+                    314,
+                    1081,
+                    314,
+                    1108,
+                    298,
+                    1108
+                ],
+                "score": 0.16
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    297,
+                    260,
+                    962,
+                    260,
+                    962,
+                    286,
+                    297,
+                    286
+                ],
+                "score": 0.138
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    877,
+                    971,
+                    1580,
+                    971,
+                    1580,
+                    996,
+                    877,
+                    996
+                ],
+                "score": 0.101
+            },
+            {
+                "category_id": 6,
+                "poly": [
+                    293,
+                    674,
+                    1403,
+                    674,
+                    1403,
+                    737,
+                    293,
+                    737
+                ],
+                "score": 0.097
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    697,
+                    290,
+                    740,
+                    290,
+                    740,
+                    313,
+                    697,
+                    313
+                ],
+                "score": 0.76,
+                "latex": "> ="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    606,
+                    1542,
+                    635,
+                    1542,
+                    635,
+                    1564,
+                    606,
+                    1564
+                ],
+                "score": 0.73,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    891,
+                    999,
+                    918,
+                    999,
+                    918,
+                    1021,
+                    891,
+                    1021
+                ],
+                "score": 0.68,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    504,
+                    288,
+                    556,
+                    288,
+                    556,
+                    314,
+                    504,
+                    314
+                ],
+                "score": 0.4,
+                "latex": "< ~ 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1271,
+                    1515,
+                    1287,
+                    1515,
+                    1287,
+                    1535,
+                    1271,
+                    1535
+                ],
+                "score": 0.33,
+                "latex": "<"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    897,
+                    1515,
+                    913,
+                    1515,
+                    913,
+                    1535,
+                    897,
+                    1535
+                ],
+                "score": 0.3,
+                "latex": "<"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    960,
+                    1597,
+                    989,
+                    1597,
+                    989,
+                    1618,
+                    960,
+                    1618
+                ],
+                "score": 0.3,
+                "latex": "^ { 1 1 } ="
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    73.0,
+                    815.0,
+                    73.0,
+                    815.0,
+                    108.0,
+                    295.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    828.0,
+                    2083.0,
+                    872.0,
+                    2083.0,
+                    872.0,
+                    2124.0,
+                    828.0,
+                    2124.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1920.0,
+                    1405.0,
+                    1920.0,
+                    1405.0,
+                    1961.0,
+                    294.0,
+                    1961.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1952.0,
+                    422.0,
+                    1952.0,
+                    422.0,
+                    1995.0,
+                    292.0,
+                    1995.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1351.0,
+                    1403.0,
+                    1351.0,
+                    1403.0,
+                    1392.0,
+                    295.0,
+                    1392.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1383.0,
+                    1388.0,
+                    1383.0,
+                    1388.0,
+                    1422.0,
+                    293.0,
+                    1422.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    257.0,
+                    961.0,
+                    257.0,
+                    961.0,
+                    291.0,
+                    293.0,
+                    291.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    671.0,
+                    1406.0,
+                    671.0,
+                    1406.0,
+                    711.0,
+                    293.0,
+                    711.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    704.0,
+                    929.0,
+                    704.0,
+                    929.0,
+                    740.0,
+                    295.0,
+                    740.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1508.0,
+                    896.0,
+                    1508.0,
+                    896.0,
+                    1542.0,
+                    292.0,
+                    1542.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    914.0,
+                    1508.0,
+                    1270.0,
+                    1508.0,
+                    1270.0,
+                    1542.0,
+                    914.0,
+                    1542.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1288.0,
+                    1508.0,
+                    1604.0,
+                    1508.0,
+                    1604.0,
+                    1542.0,
+                    1288.0,
+                    1542.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    1535.0,
+                    605.0,
+                    1535.0,
+                    605.0,
+                    1571.0,
+                    353.0,
+                    1571.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    636.0,
+                    1535.0,
+                    948.0,
+                    1535.0,
+                    948.0,
+                    1571.0,
+                    636.0,
+                    1571.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    352.0,
+                    1559.0,
+                    1276.0,
+                    1559.0,
+                    1276.0,
+                    1601.0,
+                    352.0,
+                    1601.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    351.0,
+                    1585.0,
+                    959.0,
+                    1585.0,
+                    959.0,
+                    1629.0,
+                    351.0,
+                    1629.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    990.0,
+                    1585.0,
+                    1379.0,
+                    1585.0,
+                    1379.0,
+                    1629.0,
+                    990.0,
+                    1629.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    351.0,
+                    1616.0,
+                    859.0,
+                    1616.0,
+                    859.0,
+                    1658.0,
+                    351.0,
+                    1658.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    300.0,
+                    1650.0,
+                    317.0,
+                    1650.0,
+                    317.0,
+                    1670.0,
+                    300.0,
+                    1670.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    671.0,
+                    1406.0,
+                    671.0,
+                    1406.0,
+                    711.0,
+                    293.0,
+                    711.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    704.0,
+                    929.0,
+                    704.0,
+                    929.0,
+                    740.0,
+                    295.0,
+                    740.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    994.0,
+                    890.0,
+                    994.0,
+                    890.0,
+                    1025.0,
+                    355.0,
+                    1025.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    919.0,
+                    994.0,
+                    1616.0,
+                    994.0,
+                    1616.0,
+                    1025.0,
+                    919.0,
+                    1025.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    352.0,
+                    1017.0,
+                    1140.0,
+                    1017.0,
+                    1140.0,
+                    1057.0,
+                    352.0,
+                    1057.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    757.0,
+                    1048.0,
+                    1301.0,
+                    1048.0,
+                    1301.0,
+                    1082.0,
+                    757.0,
+                    1082.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    256.0,
+                    967.0,
+                    256.0,
+                    967.0,
+                    289.0,
+                    294.0,
+                    289.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    352.0,
+                    283.0,
+                    503.0,
+                    283.0,
+                    503.0,
+                    319.0,
+                    352.0,
+                    319.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    557.0,
+                    283.0,
+                    696.0,
+                    283.0,
+                    696.0,
+                    319.0,
+                    557.0,
+                    319.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    741.0,
+                    283.0,
+                    1022.0,
+                    283.0,
+                    1022.0,
+                    319.0,
+                    741.0,
+                    319.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    414.0,
+                    315.0,
+                    598.0,
+                    315.0,
+                    598.0,
+                    346.0,
+                    414.0,
+                    346.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    362.0,
+                    350.0,
+                    373.0,
+                    350.0,
+                    373.0,
+                    365.0,
+                    362.0,
+                    365.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    354.0,
+                    369.0,
+                    703.0,
+                    369.0,
+                    703.0,
+                    401.0,
+                    354.0,
+                    401.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    304.0,
+                    405.0,
+                    312.0,
+                    405.0,
+                    312.0,
+                    419.0,
+                    304.0,
+                    419.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1351.0,
+                    1403.0,
+                    1351.0,
+                    1403.0,
+                    1392.0,
+                    295.0,
+                    1392.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1383.0,
+                    1388.0,
+                    1383.0,
+                    1388.0,
+                    1422.0,
+                    293.0,
+                    1422.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    829.0,
+                    1196.0,
+                    829.0,
+                    1196.0,
+                    863.0,
+                    293.0,
+                    863.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    965.0,
+                    854.0,
+                    1376.0,
+                    854.0,
+                    1376.0,
+                    888.0,
+                    965.0,
+                    888.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    967.0,
+                    883.0,
+                    1614.0,
+                    883.0,
+                    1614.0,
+                    916.0,
+                    967.0,
+                    916.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    968.0,
+                    913.0,
+                    1375.0,
+                    913.0,
+                    1375.0,
+                    943.0,
+                    968.0,
+                    943.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    969.0,
+                    941.0,
+                    1374.0,
+                    941.0,
+                    1374.0,
+                    970.0,
+                    969.0,
+                    970.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    298.0,
+                    1084.0,
+                    315.0,
+                    1084.0,
+                    315.0,
+                    1107.0,
+                    298.0,
+                    1107.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    893.0,
+                    965.0,
+                    1574.0,
+                    965.0,
+                    1574.0,
+                    1001.0,
+                    893.0,
+                    1001.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 19,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 5,
+                "poly": [
+                    601,
+                    626,
+                    1092,
+                    626,
+                    1092,
+                    844,
+                    601,
+                    844
+                ],
+                "score": 0.97,
+                "html": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td>get canonical path</td></tr><tr><td>code2seq</td><td>exec</td></tr><tr><td>Ours w/o structure</td><td> get output</td></tr><tr><td>CODE TRANSFORMER</td><td>exec command</td></tr><tr><td>Ground Truth</td><td>exec command</td></tr></table>"
+            },
+            {
+                "category_id": 5,
+                "poly": [
+                    621,
+                    1523,
+                    1071,
+                    1523,
+                    1071,
+                    1740,
+                    621,
+                    1740
+                ],
+                "score": 0.962,
+                "html": "<table><tr><td>Model</td><td>Prediction</td></tr><tr><td>GREAT</td><td>print</td></tr><tr><td>code2seq</td><td>print</td></tr><tr><td>Ours w/o structure</td><td>print</td></tr><tr><td>CODE TRANSFORMER</td><td>print sub view</td></tr><tr><td>Ground Truth</td><td>sub view</td></tr></table>"
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    422,
+                    1332,
+                    422,
+                    1332,
+                    592,
+                    297,
+                    592
+                ],
+                "score": 0.96
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    299,
+                    75,
+                    813,
+                    75,
+                    813,
+                    105,
+                    299,
+                    105
+                ],
+                "score": 0.884
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    305,
+                    1369,
+                    1420,
+                    1369,
+                    1420,
+                    1494,
+                    305,
+                    1494
+                ],
+                "score": 0.744
+            },
+            {
+                "category_id": 6,
+                "poly": [
+                    296,
+                    1762,
+                    1404,
+                    1762,
+                    1404,
+                    1826,
+                    296,
+                    1826
+                ],
+                "score": 0.625
+            },
+            {
+                "category_id": 6,
+                "poly": [
+                    289,
+                    865,
+                    1404,
+                    865,
+                    1404,
+                    929,
+                    289,
+                    929
+                ],
+                "score": 0.613
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    834,
+                    2088,
+                    863,
+                    2088,
+                    863,
+                    2113,
+                    834,
+                    2113
+                ],
+                "score": 0.608
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    295,
+                    1348,
+                    1106,
+                    1348,
+                    1106,
+                    1376,
+                    295,
+                    1376
+                ],
+                "score": 0.391
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    1348,
+                    1106,
+                    1348,
+                    1106,
+                    1376,
+                    295,
+                    1376
+                ],
+                "score": 0.288
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    834,
+                    2088,
+                    863,
+                    2088,
+                    863,
+                    2113,
+                    834,
+                    2113
+                ],
+                "score": 0.243
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1762,
+                    1404,
+                    1762,
+                    1404,
+                    1826,
+                    296,
+                    1826
+                ],
+                "score": 0.228
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    289,
+                    865,
+                    1404,
+                    865,
+                    1404,
+                    929,
+                    289,
+                    929
+                ],
+                "score": 0.19
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    561,
+                    537,
+                    590,
+                    537,
+                    590,
+                    558,
+                    561,
+                    558
+                ],
+                "score": 0.8,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    607,
+                    509,
+                    635,
+                    509,
+                    635,
+                    532,
+                    607,
+                    532
+                ],
+                "score": 0.77,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    562,
+                    454,
+                    590,
+                    454,
+                    590,
+                    475,
+                    562,
+                    475
+                ],
+                "score": 0.75,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    923,
+                    454,
+                    946,
+                    454,
+                    946,
+                    475,
+                    923,
+                    475
+                ],
+                "score": 0.34,
+                "latex": "^ +"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    73.0,
+                    815.0,
+                    73.0,
+                    815.0,
+                    108.0,
+                    295.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1762.0,
+                    1406.0,
+                    1762.0,
+                    1406.0,
+                    1798.0,
+                    296.0,
+                    1798.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1791.0,
+                    1356.0,
+                    1791.0,
+                    1356.0,
+                    1827.0,
+                    295.0,
+                    1827.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    865.0,
+                    1403.0,
+                    865.0,
+                    1403.0,
+                    901.0,
+                    296.0,
+                    901.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    891.0,
+                    1192.0,
+                    891.0,
+                    1192.0,
+                    934.0,
+                    292.0,
+                    934.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    830.0,
+                    2085.0,
+                    868.0,
+                    2085.0,
+                    868.0,
+                    2124.0,
+                    830.0,
+                    2124.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1345.0,
+                    1113.0,
+                    1345.0,
+                    1113.0,
+                    1381.0,
+                    292.0,
+                    1381.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    830.0,
+                    2085.0,
+                    868.0,
+                    2085.0,
+                    868.0,
+                    2124.0,
+                    830.0,
+                    2124.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    420.0,
+                    1332.0,
+                    420.0,
+                    1332.0,
+                    453.0,
+                    295.0,
+                    453.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    356.0,
+                    450.0,
+                    561.0,
+                    450.0,
+                    561.0,
+                    480.0,
+                    356.0,
+                    480.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    591.0,
+                    450.0,
+                    922.0,
+                    450.0,
+                    922.0,
+                    480.0,
+                    591.0,
+                    480.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    947.0,
+                    450.0,
+                    1006.0,
+                    450.0,
+                    1006.0,
+                    480.0,
+                    947.0,
+                    480.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    477.0,
+                    1046.0,
+                    477.0,
+                    1046.0,
+                    511.0,
+                    355.0,
+                    511.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    503.0,
+                    606.0,
+                    503.0,
+                    606.0,
+                    538.0,
+                    353.0,
+                    538.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    636.0,
+                    503.0,
+                    960.0,
+                    503.0,
+                    960.0,
+                    538.0,
+                    636.0,
+                    538.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    356.0,
+                    532.0,
+                    560.0,
+                    532.0,
+                    560.0,
+                    562.0,
+                    356.0,
+                    562.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    591.0,
+                    532.0,
+                    955.0,
+                    532.0,
+                    955.0,
+                    562.0,
+                    591.0,
+                    562.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    355.0,
+                    559.0,
+                    570.0,
+                    559.0,
+                    570.0,
+                    593.0,
+                    355.0,
+                    593.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    354.0,
+                    1372.0,
+                    646.0,
+                    1372.0,
+                    646.0,
+                    1406.0,
+                    354.0,
+                    1406.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    354.0,
+                    1402.0,
+                    603.0,
+                    1402.0,
+                    603.0,
+                    1435.0,
+                    354.0,
+                    1435.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    354.0,
+                    1430.0,
+                    1423.0,
+                    1430.0,
+                    1423.0,
+                    1463.0,
+                    354.0,
+                    1463.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    354.0,
+                    1456.0,
+                    570.0,
+                    1456.0,
+                    570.0,
+                    1489.0,
+                    354.0,
+                    1489.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1345.0,
+                    1113.0,
+                    1345.0,
+                    1113.0,
+                    1381.0,
+                    292.0,
+                    1381.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1762.0,
+                    1406.0,
+                    1762.0,
+                    1406.0,
+                    1798.0,
+                    296.0,
+                    1798.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1791.0,
+                    1356.0,
+                    1791.0,
+                    1356.0,
+                    1827.0,
+                    295.0,
+                    1827.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    865.0,
+                    1403.0,
+                    865.0,
+                    1403.0,
+                    901.0,
+                    296.0,
+                    901.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    891.0,
+                    1192.0,
+                    891.0,
+                    1192.0,
+                    934.0,
+                    292.0,
+                    934.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 20,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1326,
+                    1405,
+                    1326,
+                    1405,
+                    1662,
+                    297,
+                    1662
+                ],
+                "score": 0.982
+            },
+            {
+                "category_id": 5,
+                "poly": [
+                    302,
+                    796,
+                    1400,
+                    796,
+                    1400,
+                    1155,
+                    302,
+                    1155
+                ],
+                "score": 0.973,
+                "html": "<table><tr><td rowspan=\"2\">Model</td><td colspan=\"2\">Python</td><td colspan=\"3\">Javascript</td><td colspan=\"2\"></td><td colspan=\"2\">Ruby</td><td colspan=\"3\">Go</td></tr><tr><td>Prec.</td><td>Rec.</td><td>F1</td><td>Prec.</td><td>Rec.</td><td>F1</td><td>Prec.</td><td>Rec.</td><td>F1</td><td>Prec.</td><td>Rec.</td><td>F1</td></tr><tr><td>code2seq</td><td>1</td><td>1</td><td>1</td><td>-</td><td>1</td><td>1</td><td>=</td><td>1</td><td>1</td><td>1</td><td>1</td><td>-</td></tr><tr><td>GREAT</td><td>34.93</td><td>31.12</td><td>31.61</td><td>29.69</td><td>24.24</td><td>25.55</td><td>25.69</td><td>21.49</td><td>22.18</td><td>48.38</td><td>45.97</td><td>45.71</td></tr><tr><td>Ours w/o structure</td><td>36.87</td><td>32.17</td><td>32.97</td><td>31.30</td><td>25.03</td><td>26.64</td><td>31.43</td><td>25.34</td><td>26.63</td><td>49.78</td><td>46.73</td><td>46.69</td></tr><tr><td>Ours w/o pointer net</td><td>38.77</td><td>31.72</td><td>33.27</td><td>32.70</td><td>25.50</td><td>27.33</td><td>32.12</td><td>30.17</td><td>29.36</td><td>53.09</td><td>48.70</td><td>49.26</td></tr><tr><td>Ours</td><td>36.68</td><td>33.86</td><td>33.84</td><td>33.36</td><td>27.55</td><td>29.02</td><td>31.53</td><td>24.72</td><td>26.43</td><td>52.00</td><td>47.35</td><td>47.93</td></tr><tr><td>code2seq (Multilanguage)</td><td>-</td><td>=</td><td>=</td><td></td><td>=</td><td>=</td><td></td><td></td><td></td><td></td><td></td><td>-</td></tr><tr><td>GREAT (Multilanguage)</td><td>35.73</td><td>30.81</td><td>31.74</td><td>31.49</td><td>26.17</td><td>27.41</td><td>29.72</td><td>24.20</td><td>25.43</td><td>50.32</td><td>47.94</td><td>47.66</td></tr><tr><td>Ours w/o structure (Mult.)</td><td>36.78</td><td>29.92</td><td>31.58</td><td>32.60</td><td>26.02</td><td>27.74</td><td>31.71</td><td>26.07</td><td>27.24</td><td>51.91</td><td>47.58</td><td>48.15</td></tr><tr><td>Ours w/o pointer (Mult.)</td><td>37.18</td><td>30.52</td><td>32.04</td><td>33.95</td><td>25.92</td><td>28.11</td><td>32.76</td><td>25.04</td><td>27.01</td><td>53.50</td><td>48.54</td><td>49.35</td></tr><tr><td>Ours (Multilanguage)</td><td>38.10</td><td>33.32</td><td>34.18</td><td>34.29</td><td>28.69</td><td>30.08</td><td>33.30</td><td>28.33</td><td>29.29</td><td>53.86</td><td>50.46</td><td>50.61</td></tr><tr><td>Ours (Mult. + Finetune)</td><td>38.29</td><td>32.41</td><td>33.65</td><td>34.43</td><td>28.28</td><td>29.91</td><td>32.89</td><td>27.15</td><td>28.49</td><td>53.85</td><td>50.85</td><td></td></tr><tr><td>Ours (Mult.+ LMPretrain)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>50.81</td></tr><tr><td></td><td>38.97</td><td>34.77</td><td>35.34</td><td>35.23</td><td>30.26</td><td>31.38</td><td>33.73</td><td>29.15</td><td>29.94</td><td>55.31</td><td>52.03</td><td>52.13</td></tr></table>"
+            },
+            {
+                "category_id": 3,
+                "poly": [
+                    472,
+                    236,
+                    1229,
+                    236,
+                    1229,
+                    697,
+                    472,
+                    697
+                ],
+                "score": 0.968
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    298,
+                    1268,
+                    948,
+                    1268,
+                    948,
+                    1300,
+                    298,
+                    1300
+                ],
+                "score": 0.899
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    299,
+                    76,
+                    812,
+                    76,
+                    812,
+                    104,
+                    299,
+                    104
+                ],
+                "score": 0.892
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    293,
+                    1757,
+                    1313,
+                    1757,
+                    1313,
+                    1789,
+                    293,
+                    1789
+                ],
+                "score": 0.888
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    835,
+                    2088,
+                    865,
+                    2088,
+                    865,
+                    2112,
+                    835,
+                    2112
+                ],
+                "score": 0.85
+            },
+            {
+                "category_id": 4,
+                "poly": [
+                    410,
+                    733,
+                    1286,
+                    733,
+                    1286,
+                    767,
+                    410,
+                    767
+                ],
+                "score": 0.766
+            },
+            {
+                "category_id": 6,
+                "poly": [
+                    453,
+                    1177,
+                    1245,
+                    1177,
+                    1245,
+                    1209,
+                    453,
+                    1209
+                ],
+                "score": 0.651
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    299,
+                    1699,
+                    1209,
+                    1699,
+                    1209,
+                    1731,
+                    299,
+                    1731
+                ],
+                "score": 0.615
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1699,
+                    1209,
+                    1699,
+                    1209,
+                    1731,
+                    299,
+                    1731
+                ],
+                "score": 0.321
+            },
+            {
+                "category_id": 6,
+                "poly": [
+                    410,
+                    733,
+                    1286,
+                    733,
+                    1286,
+                    767,
+                    410,
+                    767
+                ],
+                "score": 0.14
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    453,
+                    1177,
+                    1245,
+                    1177,
+                    1245,
+                    1209,
+                    453,
+                    1209
+                ],
+                "score": 0.103
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    415,
+                    1106,
+                    433,
+                    1106,
+                    433,
+                    1123,
+                    415,
+                    1123
+                ],
+                "score": 0.59,
+                "latex": "^ +"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    416,
+                    1128,
+                    433,
+                    1128,
+                    433,
+                    1147,
+                    416,
+                    1147
+                ],
+                "score": 0.36,
+                "latex": "^ +"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    770.0,
+                    239.0,
+                    989.0,
+                    239.0,
+                    989.0,
+                    260.0,
+                    770.0,
+                    260.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1172.0,
+                    271.0,
+                    1213.0,
+                    271.0,
+                    1213.0,
+                    291.0,
+                    1172.0,
+                    291.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1172.0,
+                    288.0,
+                    1215.0,
+                    288.0,
+                    1215.0,
+                    312.0,
+                    1172.0,
+                    312.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    473.0,
+                    292.0,
+                    500.0,
+                    292.0,
+                    500.0,
+                    586.0,
+                    473.0,
+                    586.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    494.0,
+                    296.0,
+                    533.0,
+                    296.0,
+                    533.0,
+                    317.0,
+                    494.0,
+                    317.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1173.0,
+                    312.0,
+                    1207.0,
+                    312.0,
+                    1207.0,
+                    329.0,
+                    1173.0,
+                    329.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    494.0,
+                    348.0,
+                    533.0,
+                    348.0,
+                    533.0,
+                    368.0,
+                    494.0,
+                    368.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    493.0,
+                    397.0,
+                    534.0,
+                    397.0,
+                    534.0,
+                    422.0,
+                    493.0,
+                    422.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    493.0,
+                    449.0,
+                    534.0,
+                    449.0,
+                    534.0,
+                    473.0,
+                    493.0,
+                    473.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    493.0,
+                    502.0,
+                    534.0,
+                    502.0,
+                    534.0,
+                    525.0,
+                    493.0,
+                    525.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    494.0,
+                    553.0,
+                    535.0,
+                    553.0,
+                    535.0,
+                    577.0,
+                    494.0,
+                    577.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    504.0,
+                    607.0,
+                    532.0,
+                    607.0,
+                    532.0,
+                    625.0,
+                    504.0,
+                    625.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    593.0,
+                    622.0,
+                    613.0,
+                    622.0,
+                    613.0,
+                    696.0,
+                    593.0,
+                    696.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    734.0,
+                    620.0,
+                    753.0,
+                    620.0,
+                    753.0,
+                    646.0,
+                    734.0,
+                    646.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    869.0,
+                    620.0,
+                    889.0,
+                    620.0,
+                    889.0,
+                    675.0,
+                    869.0,
+                    675.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1006.0,
+                    620.0,
+                    1028.0,
+                    620.0,
+                    1028.0,
+                    661.0,
+                    1006.0,
+                    661.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1143.0,
+                    619.0,
+                    1162.0,
+                    619.0,
+                    1162.0,
+                    694.0,
+                    1143.0,
+                    694.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1266.0,
+                    952.0,
+                    1266.0,
+                    952.0,
+                    1304.0,
+                    295.0,
+                    1304.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    73.0,
+                    815.0,
+                    73.0,
+                    815.0,
+                    108.0,
+                    295.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    831.0,
+                    2085.0,
+                    869.0,
+                    2085.0,
+                    869.0,
+                    2124.0,
+                    831.0,
+                    2124.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    409.0,
+                    731.0,
+                    1290.0,
+                    731.0,
+                    1290.0,
+                    770.0,
+                    409.0,
+                    770.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    449.0,
+                    1172.0,
+                    1247.0,
+                    1172.0,
+                    1247.0,
+                    1215.0,
+                    449.0,
+                    1215.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1695.0,
+                    1213.0,
+                    1695.0,
+                    1213.0,
+                    1738.0,
+                    293.0,
+                    1738.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    409.0,
+                    731.0,
+                    1290.0,
+                    731.0,
+                    1290.0,
+                    770.0,
+                    409.0,
+                    770.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1327.0,
+                    1403.0,
+                    1327.0,
+                    1403.0,
+                    1361.0,
+                    294.0,
+                    1361.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1358.0,
+                    1407.0,
+                    1358.0,
+                    1407.0,
+                    1392.0,
+                    295.0,
+                    1392.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1387.0,
+                    1405.0,
+                    1387.0,
+                    1405.0,
+                    1422.0,
+                    295.0,
+                    1422.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1415.0,
+                    1406.0,
+                    1415.0,
+                    1406.0,
+                    1456.0,
+                    291.0,
+                    1456.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1448.0,
+                    1403.0,
+                    1448.0,
+                    1403.0,
+                    1483.0,
+                    294.0,
+                    1483.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1479.0,
+                    1405.0,
+                    1479.0,
+                    1405.0,
+                    1514.0,
+                    294.0,
+                    1514.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1510.0,
+                    1406.0,
+                    1510.0,
+                    1406.0,
+                    1545.0,
+                    294.0,
+                    1545.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1541.0,
+                    1406.0,
+                    1541.0,
+                    1406.0,
+                    1573.0,
+                    291.0,
+                    1573.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1572.0,
+                    1403.0,
+                    1572.0,
+                    1403.0,
+                    1603.0,
+                    295.0,
+                    1603.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1602.0,
+                    1406.0,
+                    1602.0,
+                    1406.0,
+                    1636.0,
+                    295.0,
+                    1636.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1631.0,
+                    669.0,
+                    1631.0,
+                    669.0,
+                    1665.0,
+                    296.0,
+                    1665.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1751.0,
+                    1321.0,
+                    1751.0,
+                    1321.0,
+                    1797.0,
+                    291.0,
+                    1797.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1695.0,
+                    1213.0,
+                    1695.0,
+                    1213.0,
+                    1738.0,
+                    293.0,
+                    1738.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    449.0,
+                    1172.0,
+                    1247.0,
+                    1172.0,
+                    1247.0,
+                    1215.0,
+                    449.0,
+                    1215.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 21,
+            "width": 1700,
+            "height": 2200
+        }
+    }
+]
\ No newline at end of file
diff --git a/parse/train/rJerHlrYwH/rJerHlrYwH.md b/parse/train/rJerHlrYwH/rJerHlrYwH.md
new file mode 100644
index 0000000000000000000000000000000000000000..9e976bb2c542b22bbfa2b334b47446ad5b7622b0
--- /dev/null
+++ b/parse/train/rJerHlrYwH/rJerHlrYwH.md
@@ -0,0 +1,298 @@
+# DATA-EFFICIENT IMAGE RECOGNITION WITH CONTRASTIVE PREDICTIVE CODING
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+Human observers can learn to recognize new categories of objects from a handful of examples, yet doing so with machine perception remains an open challenge. We hypothesize that data-efficient recognition is enabled by representations which make the variability in natural signals more predictable, as suggested by recent perceptual evidence. We therefore revisit and improve Contrastive Predictive Coding, a recently-proposed unsupervised learning framework, and arrive at a representation which enables generalization from small amounts of labeled data. When provided with only $1 \%$ of ImageNet labels (i.e. 13 per class), this model retains a strong classification performance, $73 \%$ Top-5 accuracy, outperforming supervised networks by $28 \%$ (a $65 \%$ relative improvement) and state-of-the-art semisupervised methods by $14 \%$ . We also find this representation to serve as a useful substrate for object detection on the PASCAL-VOC 2007 dataset, approaching the performance of representations trained with a fully annotated ImageNet dataset.
+
+# 1 INTRODUCTION
+
+Deep neural networks excel at perceptual tasks when labeled data are abundant, yet their performance degrades substantially when provided with limited supervision (Fig. 1, red). In contrast, humans and animals can quickly learn about new classes of objects from few examples (Landau et al., 1988; Markman, 1989). What accounts for this monumental difference in data-efficiency between biological and machine vision? While highly-structured representations (e.g. as proposed by Lake et al., 2015) may improve data-efficiency, it remains unclear how to program explicit structures that capture the enormous complexity of real visual scenes like those in ImageNet (Russakovsky et al., 2015). An alternative hypothesis has proposed that intelligent systems need not be structured a priori, but can instead learn about the structure of the world in an unsupervised manner (Barlow, 1989; Hinton et al., 1999; LeCun et al., 2015). Choosing an appropriate training objective is an open problem, but a promising guiding principle has emerged recently: good representations should make the spatio-temporal variability in natural signals more predictable. Indeed, human perceptual representations have been shown to linearize
+
+![](images/7b8ed316aeaae9bdfe3d3d7e12974b01335c33b7eb790b24e724753c0422fb2e.jpg)  
+Figure 1: Data-efficient image recognition with Contrastive Predictive Coding. With decreasing amounts of labeled data, supervised networks trained on pixels fail to generalize (red). When trained on unsupervised representations learned with CPC, these networks retain a much higher accuracy in this low-data regime (blue). Equivalently, the accuracy of supervised networks can be matched with significantly fewer labels.
+
+(or ‘straighten’) the temporal transformations found in natural videos, a property lacking from current supervised image recognition models (Henaff et al., 2019), and theories of both spatial and tem- ´ poral predictability have succeeded in describing properties of early visual areas (Rao & Ballard,
+
+1999; Palmer et al., 2015). In this work, we hypothesize that spatially predictable representations may allow artificial systems to benefit from human-like data-efficiency.
+
+Contrastive Predictive Coding (CPC, van den Oord et al., 2018) is an unsupervised objective which learns such predictable representations. CPC is a general technique that only requires in its definition that observations be ordered along e.g. temporal or spatial dimensions, and as such has been applied to a variety of different modalities including speech, natural language and images. This generality, combined with the strong performance of its representations in downstream linear classification tasks, makes CPC a promising candidate for investigating the efficacy of predictable representations for data-efficient image recognition.
+
+Our work makes the following contributions:
+
+• We revisit CPC in terms of its architecture and training methodology, and arrive at a new implementation of CPC with dramatically-improved ability to linearly separate image classes $+ 1 7 \%$ Top-1 ImageNet classification accuracy).   
+We then train deep networks on top of the resulting CPC representations using very few labeled images (e.g. $1 \%$ of the ImageNet dataset), and demonstrate test-time classification accuracy far above networks trained on raw pixels ( $73 \%$ Top-5 accuracy, a $28 \%$ absolute improvement), outperforming all other unsupervised representation learning methods $( + 1 5 \%$ Top-5 accuracy over the previous state-of-the-art (Zhai et al., 2019)). Surprisingly, this representation also surpasses supervised methods when given the entire ImageNet dataset $+ 1 \%$ Top-5 accuracy).   
+We isolate the contributions of different components of the final model to such downstream tasks. Interestingly, we find that linear classification accuracy is not always predictive of low-data classification accuracy, emphasizing the importance of this metric as a stand-alone benchmark for unsupervised learning.   
+• Finally, we assess the generality of CPC representations by transferring them to a new task and dataset: object detection on PASCAL-VOC 2007. Consistent with the results from the previous section, we find CPC to give state-of-the-art performance in this setting.
+
+# 2 EXPERIMENTAL SETUP
+
+We first review the CPC architecture and learning objective in section 2.1, before detailing how we use its resulting representations for image recognition tasks in section 2.2.
+
+# 2.1 CONTRASTIVE PREDICTIVE CODING
+
+Contrastive Predictive Coding as formulated in (van den Oord et al., 2018) learns representations by training neural networks to predict the representations of future observations from those of past ones. When applied to images, the original formulation of CPC operates by predicting the representations of patches below a certain position from those above it (Fig. 2, left). These predictions are evaluated using a contrastive loss, in which the network must correctly classify the ‘future’ representation amongst a set of unrelated ‘negative’ representations. This avoids trivial solutions such as representing all patches with a constant vector, as would be the case with a mean squared error loss.
+
+In the CPC architecture, each input image is first divided into a set of overlapping patches $\mathbf { \delta } _ { \mathbf { x } _ { i , j } }$ , each of which is encoded with a neural network $f _ { \theta }$ into a single vector $z _ { i , j } = f _ { \theta } ( \pmb { x } _ { i , j } )$ . To make predictions, a masked convolutional network $g _ { \phi }$ is then applied to the grid of feature vectors. The masks are such that the receptive field of each resulting context vector $c _ { i , j }$ only includes feature vectors that lie above it in the image (i.e. $\{ z _ { u , v } \} _ { u \leq i , v } )$ . The prediction task then consists o predicting ‘future’ feature vectors $z _ { i + k , j }$ from current context vectors $c _ { i , j }$ , where $k > 0$ . The predictions are made linearly: given a context vector $c _ { i , j }$ , a prediction length $k > 0$ , and a prediction matrix $W _ { k }$ , the predicted feature vector is $\hat { \boldsymbol { z } } _ { i + k , j } = \boldsymbol { W } _ { k } \boldsymbol { c } _ { i , j }$ .
+
+The quality of this prediction is then evaluated using a contrastive loss. Specifically, the goal is to correctly recognize the target $z _ { i + k , j }$ among a set of randomly sampled feature vectors $\{ z _ { l } \}$ from the dataset. We compute the probability assigned to the target using a softmax, and evaluate this probability using the usual cross-entropy loss. Summing this loss over locations and prediction offsets, we arrive at the CPC objective as defined in (van den Oord et al., 2018):
+
+![](images/e21408d1a55db66ba2cac6a3f4d98b0d1a13c2f1211e3956f93d67bae89bbaae.jpg)  
+Figure 2: Overview of the framework for semi-supervised learning with Contrastive Predictive Coding. Left: unsupervised pre-training with the spatial prediction task (See Section 2.1). First, an image is divided into a grid of overlapping patches. Each patch is encoded independently from the rest with a feature extractor (blue) which terminates with a mean-pooling operation, yielding a single feature vector for that patch. Doing so for all patches yields a field of such feature vectors (wireframe vectors). Feature vectors above a certain level (in this case, the center of the image) are then aggregated with a context network (red), yielding a row of context vectors which are used to linearly predict features vectors below. Right: using the CPC representation for a classification task. Having trained the encoder network, the context network (red) is discarded and replaced by a classifier network (green) which can be trained in a supervised manner. For some experiments, we also fine-tune the encoder network (blue) for the classification task. When applying the encoder to cropped patches (as opposed to the full image) we refer to it as a patched ResNet in the figure.
+
+$$
+\mathcal { L } _ { \mathrm { C P C } } = - \sum _ { i , j , k } \log p ( z _ { i + k , j } | \hat { z } _ { i + k , j } , \{ z _ { l } \} ) = - \sum _ { i , j , k } \log \frac { \exp ( \hat { z } _ { i + k , j } ^ { T } z _ { i + k , j } ) } { \exp ( \hat { z } _ { i + k , j } ^ { T } z _ { i + k , j } ) + \sum _ { l } \exp ( \hat { z } _ { i + k , j } ^ { T } z _ { l } ) }
+$$
+
+The negative samples $\left\{ z _ { l } \right\}$ are taken from other locations in the image and other images in the minibatch. This loss is called InfoNCE (van den Oord et al., 2018) as it is inspired by Noise-Contrastive Estimation (Gutmann $\&$ Hyvarinen, 2010; Mnih & Kavukcuoglu, 2013) and has been shown to ¨ maximize the mutual information between $\mathbf { } _ { c _ { i , j } }$ and $z _ { i + k , j }$ (van den Oord et al., 2018).
+
+# 2.2 EVALUATION PROTOCOL
+
+Having trained an encoder network $f _ { \theta }$ , a context network $g _ { \phi }$ , and a set of linear predictors $\{ W _ { k } \}$ using the CPC objective, we use the latents $z = f _ { \boldsymbol { \theta } } ( \pmb { x } )$ as a representation of new observations $x$ for downstream tasks, and discard the rest. We then train a model $h _ { \psi }$ to classify these representations given a dataset of labeled images. More formally, given a dataset of $N$ unlabeled images $\mathbb { D } _ { u } =$ $\left\{ x _ { n } \right\}$ , and a (potentially much smaller) dataset of $M$ labeled images $\mathbb { D } _ { l } = \{ x _ { m } , y _ { m } \}$ :
+
+$$
+\theta ^ { * } = \arg \operatorname* { m i n } _ { \theta } \frac { 1 } { N } \sum _ { n = 1 } ^ { N } \mathcal { L } _ { \mathrm { C P C } } [ f _ { \theta } ( x _ { n } ) ] , \quad \psi ^ { * } = \arg \operatorname* { m i n } _ { \psi } \frac { 1 } { M } \sum _ { m = 1 } ^ { M } \mathcal { L } _ { \mathrm { S u p } } [ h _ { \psi } \circ f _ { \theta ^ { * } } ( x _ { m } ) , y _ { m } ]
+$$
+
+In all cases, the dataset of unlabeled images $\mathbb { D } _ { u }$ we pre-train on is the full ImageNet ILSVRC 2012 training set (Russakovsky et al., 2015). We consider three labeled datasets $\mathbb { D } _ { l }$ for evaluation, each with an associated classifier $h _ { \psi }$ and supervised losse $\mathcal { L } _ { \mathrm { { S u p } } }$ (see Fig. 2, right). This protocol is sufficiently generic to allow us to later compare the CPC representation to other methods which have their own means of learning a feature extractor $f _ { \theta }$ .
+
+Linear classification is the standard benchmark for evaluating the quality of unsupervised image representations. In this regime, the classification network $h _ { \psi }$ is restricted to mean pooling followed by a single linear layer, and the parameters of $f _ { \theta }$ are kept fixed. The labeled dataset $\mathbb { D } _ { l }$ is the entire ImageNet dataset, and the supervised loss $\mathcal { L } _ { \mathrm { { S u p } } }$ is standard cross-entropy. We use the same dataaugmentation as in the unsupervised learning phase for training, and none at test time and evaluate with a single crop.
+
+Efficient classification directly tests whether the CPC representation enables visual learning from few labels. For this task, the classifier $h _ { \psi }$ is an arbitrary deep neural network (we use an 11-block ResNet architecture with 4096-dimensional feature maps and 1024-dimensional bottleneck layers). The labeled dataset $\mathbb { D } _ { l }$ is a subset of the ImageNet dataset: we investigated using $1 \%$ , $2 \%$ , $5 \%$ , $10 \%$ , $20 \%$ , $50 \%$ and $100 \%$ of the ImageNet dataset. The supervised loss $\mathcal { L } _ { \mathrm { { S u p } } }$ is again cross-entropy. In addition to random color-dropping we use the Inception data-augmentation scheme (Szegedy et al., 2014) for training, no augmentation at test-time and evaluate with a single crop.
+
+Transfer learning tests the generality of the representation by applying it to a new task and dataset. For this we chose image detection on the PASCAL-2007 dataset, a standard benchmark in computer vision (Everingham et al., 2007). As such $\mathbb { D } _ { l }$ is the entire PASCAL-2007 dataset (comprised of 5011 labeled images); $h _ { \psi }$ and $\mathcal { L } _ { \mathrm { { S u p } } }$ are the Faster-RCNN architecture and loss (Ren et al., 2015). In addition to color-dropping, we use scale-augmentation (Doersch et al., 2015) for training.
+
+For linear classification, we keep the feature extractor $f _ { \theta }$ fixed to assess the representation in absolute terms. For efficient classification and transfer learning, we additionally explore fine-tuning the feature extractor for the supervised objective. In this regime, we initialize the feature extractor and classifier with the solutions $\theta ^ { * } , \psi ^ { * }$ found in the previous learning phase, and train them both for the supervised objective. To ensure that the feature extractor does not deviate too much from the solution dictated by the CPC objective, we use a smaller learning rate and early-stopping.
+
+# 3 RELATED WORK
+
+Data-efficient learning has typically been approached by two complementary methods, both of which seek to make use of more plentiful unlabeled data: representation learning and semisupervised learning. The former formulates an objective to learn a feature extractor $f _ { \theta }$ in an unsupervised manner, whereas the latter directly constrains the classifier $h _ { \psi }$ using the unlabeled data.
+
+Representation learning saw early success using generative modeling (Kingma et al., 2014), but likelihood-based models have yet to generalize to more complex stimulus classes. Generative adversarial models have also been harnessed for representation learning (Donahue et al., 2016), and large-scale implementations have recently achieved corresponding gains in linear classification accuracy (Donahue & Simonyan, 2019).
+
+In contrast to generative models which require the reconstruction of observations, self-supervised techniques directly formulate tasks involving the learned representation. For example, simply asking a network to recognize the spatial layout of an image led to representations that transferred to popular vision tasks such as classification and detection (Doersch et al., 2015; Noroozi & Favaro, 2016). Other works showed that prediction of color (Zhang et al., 2016; Larsson et al., 2017) and image orientation (Gidaris et al., 2018), and invariance to data augmentation (Dosovitskiy et al., 2014) can provide useful self-supervised tasks. Beyond single images, works have leveraged video cues such as object tracking (Wang & Gupta, 2015), frame ordering (Misra et al., 2016), and object boundary cues (Li et al., 2016; Pathak et al., 2016). Non-visual information can be equally powerful; information about camera motion (Agrawal et al., 2015; Jayaraman & Grauman, 2015), scene geometry (Zamir et al., 2016), or sound (Arandjelovic & Zisserman, 2017; 2018) can all serve as natural sources of supervision.
+
+While many of these tasks require predicting fixed quantities computed from the data, another class of contrastive methods formulate their objectives in the learned representations themselves. CPC is a contrastive representation learning method that maximizes the mutual information between spatially removed latent representations with InfoNCE (van den Oord et al., 2018), a loss function based on Noise-Contrastive Estimation (Gutmann & Hyvarinen, 2010; Mnih & Kavukcuoglu, 2013). Two ¨ other methods have recently been proposed using the same loss function, but with different associated prediction tasks. Contrastive Multiview Coding (Tian et al., 2019) maximizes the mutual information between representations of different views of the same observation. Augmented Multiscale Deep InfoMax (AMDIM, Bachman et al., 2019) is most similar to CPC in that it makes predictions across space, but differs in that it also predicts representations across layers in the model. In addition, AMDIM limits the receptive field of its representation, but does this by constraining the number of spatial convolutions in the network architecture rather than using image patches.
+
+A common alternative approach for improving data efficiency is label-propagation (Zhu & Ghahramani, 2002), where a classifier is trained on a subset of labeled data, then used to label parts of the unlabeled dataset, after which the process is repeated. This label-propagation can either be discrete (as in pseudo-labeling, Lee, 2013) or continuous (as in entropy minimization, Grandvalet & Bengio, 2005). The predictions of this classifier are often constrained to be smooth with respect to certain deformations, such as data-augmentation (Xie et al., 2019) or adversarial perturbation (Miyato et al., 2018). Representation learning and semi-supervised learning have been shown to be complementary and can be combined to great effect (Zhai et al., 2019), which is why we focus solely on representation learning in this paper.
+
+# 4 RESULTS
+
+When asking whether CPC enables data-efficient learning, we wish to use the best possible representative of this model class. Unfortunately, purely unsupervised metrics tell us little about downstream performance, and implementation details have been shown to matter enormously (Doersch & Zisserman, 2017; Kolesnikov et al., 2019). Since many design choices (e.g. network architecture and datapreprocessing) have been previously evaluated using linear classification, we use this benchmark in section 4.1 to align the CPC model with best practices in representation learning and compare to published results. In section 4.2 we select the best performing model from the previous section and assess whether it enables efficient classification. We also investigate to what extent the first, more common metric (linear classification accuracy) is predictive of efficient classification. Finally, in section 4.3 we investigate the generality of our results through transfer learning to PASCAL-2007.
+
+# 4.1 FROM CPC V1 TO CPC V2
+
+The overarching principle behind our new model design is to increase the scale and efficiency of the encoder architecture while also maximizing the supervisory signal we obtain from each image. At the same time, it is important not to allow the network to solve the problem trivially, i.e., without learning semantics. To this end, we seek to remove low-level cues common across patches by augmenting individual patches independently, using standard stochastic data-processing techniques from supervised and self-supervised learning.
+
+We identify four axes for model capacity and task setup that could impact the model’s performance. The first axis increases model capacity by increasing depth and width, while the second improves training efficiency capacity by introducing layer normalization. The third axis increases task complexity by making predictions in all four directions, and the fourth does so by performing more extensive patch-based augmentation.
+
+Model capacity. Recent work has shown that networks and more effective training improves self-supervised learning (Doersch & Zisserman, 2017; Kolesnikov et al., 2019), but the original CPC model used only the first 3 stacks of a ResNet-101 (He et al., 2016a) architecture (i.e. a ResNet-92). Therefore, we converted the third residual stack of ResNet-101 (originally containing 23 blocks, 1024-dimensional feature maps, and 256-dimensional bottleneck layers), to use 46 blocks, with 4096-dimensional feature maps and 512-dimensional bottleneck layers. We call the resulting network ResNet-161. Consistent with prior results, this new architecture delivers better performance regardless of
+
+![](images/3eeded7c7663fc17771caa90292cc1343662124f1094d06f22d9ca255036f2a3.jpg)  
+Figure 3: Linear classification performance of new variants of CPC, which incrementally add a series of modifications. BU: bottum up spatial predictions. HF: randomly flipping patches horizontally. LN: layer normalization. RC: random color-dropping. TL: tuned prediction lengths. HP: horizontal spatial predictions. We use color to indicate the number of spatial predictions used (orange, green, blue for 1, 2 and 4 directions).
+
+Table 1: Linear classifier $h _ { \psi }$ trained with $100 \%$ of labels. Comparison to linear separability of other self-supervised methods. In all cases a feature extractor is optimized in an unsupervised manner, and a linear classifier is trained on top using all labels in the ImageNet dataset.   
+
+<table><tr><td>Method</td><td>Top-1</td><td>Top-5</td></tr><tr><td>Motion Segmentation (MS) (Pathak et al., 2016) Exemplar (Ex) (Dosovitskiy et al.,2014) Relative Position (RP) (Doersch et al.,2015) Colorization (Col) (Zhang et al., 2016) Combination of MS + Ex + RP+ Col (Doersch &amp; Zisserman,2017) CPC v1 (van den Oord et al., 2018) Rotation (Kolesnikov et al., 2019)</td><td>27.6 31.5 36.2 39.6 1 48.7 55.4</td><td>48.3 53.1 59.2 62.5 69.3 73.6</td></tr><tr><td>CMC (Tian et al., 2019) Local Aggregation (Zhuang et al., 2019)</td><td>60.1 60.2</td><td>82.8 1 =</td></tr><tr><td>BigBiGAN (Donahue &amp; Simonyan,2019) AMDIM (Bachman et al., 2019) CPC v2 (ours) 65.9</td><td>61.3 68.1</td><td>81.9</td></tr></table>
+
+other design choices. Interestingly, a larger architecture delivers larger improvements with more efficient training, more self-supervised losses, and more patch-based augmentations (Fig. 3, $+5 \%$ Top-1 accuracy with original training scheme, $+ 1 0 \%$ accuracy with new one).
+
+Layer normalization. Large architectures are more difficult to train efficiently. Early works on context prediction with patches used batch normalization (Ioffe & Szegedy, 2015; Doersch et al., 2015) to speed training. However, with CPC we find that batch normalization actually harms downstream performance of large models. We hypothesize that batch normalization allows large models to find a trivial solution to CPC: it introduces a dependency between patches (through the batch statistics) that can be exploited to bypass the constraints on the receptive field. We find that we can reclaim much of batch normalization’s training efficiency using layer normalization (Ba et al., 2016), which leads to a small gain for the smaller architecture $+ 1 \%$ accuracy over equivalent architectures that use neither normalization) and a larger gain for the larger architecture $( + 2 . 5 \%$ accuracy).
+
+Prediction lengths and directions. Larger architectures also run a greater risk of overfitting. We address this by asking more from the network: specifically, whereas van den Oord et al. (2018) predicted each patch using only context from spatially beneath it, we repeatedly predict the patch using context from above, to the right, and to the left, resulting in up to four times as many prediction tasks. Combining top-to-bottom with bottom-to-top helps both model architectures $42 \%$ accuracy for both), but using all 4 spatial directions only benefits the larger model (an additional $+ 1 . 5 \%$ for the larger model, ${ \bf - 1 \% }$ for the smaller), consistent with the idea that model capacity and amount of supervision must go hand-in-hand. We also hypothesized that prediction “length”—i.e. offset between the predicted patch and the aggregated context—might affect performance, as distant patches might lie on distinct objects, encouraging the network to memorize images. Indeed, limiting the range of the prediction length $k$ to $\{ 2 , 3 \}$ performed better than $\{ 2 , \ldots , 5 \}$ as was used originally $+ 1 \%$ for the larger model).
+
+Patch-based augmentation. If the network can solve CPC using low-level patterns (e.g. straight lines continuing between patches, chromatic aberration), it need not learn semantically meaningful content. Augmenting the low-level variability across patches can remove such low level cues. The original CPC model spatially jitters individual patches independently. We further this logic by adopting the ‘color dropping’ method of Doersch et al. (2015), which randomly drops two of the three color channels in each patch, and find it to delivers systematic gains $( + 1 \%$ for the small model, $+3 \%$ for the larger one). We also randomly flip patches horizontally, but find it only benefits the smaller model $( + 1 \% )$ .
+
+Combined. Cumulatively, these fairly straightforward implementation changes lead to a substantial improvement to the original CPC model $6 5 . 9 \%$ Top-1 accuracy, a $17 \%$ improvement), making it competitive with recent approaches and outperforming prior methods (see table 1). Interestingly, if we train the same patch-based architecture from scratch in a fully supervised manner, we obtain $6 6 . 4 \%$ Top-1 accuracy (with batch normalization; $6 2 . 5 \%$ without), suggesting that CPC is now nearly saturating the architecture’s representational power despite not using labels. These results illustrate how architecture and data have an outsized impact on the linear classification performance of self-supervised representations, and are interesting to compare with with previous results. For example, in AMDIM, different settings of data augmentation alone can result in a nearly $10 \%$ absolute increase in performance on ImageNet linear classification.
+
+# 4.2 EFFICIENT IMAGE CLASSIFICATION
+
+toWe now turn to our original question of whether CPC can enable data-efficient image recognition. We start by evaluating the performance of purely-supervised networks as the size of the labeled dataset $\mathbb { D } _ { l }$ varies from $1 \%$ to $100 \%$ of ImageNet, training separate classifiers on each subset. We found that a ResNet-152 to works best across all data-regimes (see Appendix). Despite our efforts to tune the supervised model for low-data classification (including network depth, regularization, and optimization parameters), the accuracy of the best model only reaches $4 4 . 1 \%$ Top-5 accuracy when trained on $1 \%$ of the dataset (compared to $9 3 . 9 \%$ when trained on the entire dataset, see Fig. 1, red).
+
+Contrastive Predictive Coding. We now address our central question of whether CPC enables data-efficient learning. We follow the same paradigm as for the supervised baseline (training and evaluating a separate classifier for each size subset), stacking a neural network classifier on top of the CPC latents $\begin{array} { r l r } { z } & { { } = } & { f _ { \theta } ( { \pmb x } ) } \end{array}$ rather than the raw image pixels $_ { \textbf { \em x } }$ (see section 2.2, efficient classification, and Appendix). This representation, which we selected for its improved linear classification performance (CPC v2 in Fig. 3), leads to a significant increase in data-efficiency compared to purely supervised networks (Fig. 1, blue curve). This classifier yields $7 2 . 9 \%$ Top-5 accuracy with only $1 \%$ of the labels, a $2 9 \%$ absolute improvement $65 \%$ relative) over purely-supervised methods. Surprisingly, when given the entire dataset, this classifier reaches $8 0 . 6 \% / 9 5 . 2 \%$ Top1/Top5 accuracy, surpassing our supervised baseline (ResNet-152: $7 8 . 0 \% / 9 3 . 9 \%$ accuracy) and published results (ResNet-200: $7 9 . 9 \% / 9 5 . 2 \%$ , He et al. (2016b)). We find similar results in all other data-regimes we considered (see Fig. 1).
+
+How important are the model specifications described in Section 4.1 for low-data classification? We hypothesized that predictable representations might enable data-efficient classifi
+
+![](images/106f2252ad377e16a329cfb21360459a72fdc1d09e4f745b26572da1cf6d5d14.jpg)  
+Figure 4: Relationship between linear classification accuracy and low-data classification, for different variants of the CPC model. Left: CPC variants with the same architecture but different training protocols. Orange, green, and blue dots correspond to CPC models making predictions in 1, 2, and 4 spatial directions respectively. Within a color group, different models correspond to other implementation details (e.g. layer norm and patch augmentation, and combinations thereof).
+
+cation, and therefore expect that increasing the amount of ‘predictability’ in the representation should also increase its ability to learn from small amounts of data. Fig. 4 shows evidence for this by ablating model parameters and comparing linear classification performance against low-data classification. Consistent with our hypothesis, increasing the number of spatial directions in the CPC prediction task (which increased linear classification performance) systematically increases low-data classification performance (Fig. 4, left, different color groups). As a control, we asked if all modifications that improve linear classification also improve low-data classification. We did not find evidence in favor of this: improvements in linear classification as a result of changing other model parameters (patch-based data-augmentation, layer normalization, and combinations thereof) seem uncorrelated to performance in other tasks (Fig. 4, left, within green group: $R ^ { 2 } = 0 . 1 7 , p = 0 . 3 6$ ). Different architectural specifications also produced different changes in both tasks (Fig. 4, right). Whereas increasing the depth of the encoding network greatly improves both metrics, increasing the network width (and therefore the number of features used for linear classification) only improves linear classification accuracy.
+
+Table 2: ResNet classifier $h _ { \psi }$ trained with $1 \%$ or $10 \%$ of labels. Comparison to other methods for semi-supervised learning using $1 \%$ or $10 \%$ of labeled data. Representation learning methods use a classifier to discriminate an unsupervised representation, and optimize it solely for the supervised objective on labeled data. Label-propagation methods on the other hand further constrain the classifier with smoothness and entropy criteria on unlabeled data, making the additional assumption that all training images fit into a single (unknown) testing category. $\dagger$ denotes methods implemented in this work, fixed and fine-tuned denote whether the feature extractor is allowed to accommodate the supervised objective.   
+
+<table><tr><td>Labeled data 1% 10% 100% Method Top-5 accuracy</td></tr><tr><td></td></tr><tr><td>Supervised baseline 44.1 82.1 93.9 Methods using label-propagation:</td></tr><tr><td>Pseudolabeling (Zhai et al., 2019) 51.6 82.4 VAT + Entropy Minimization (Zhai et al., 2019) 47.0 83.4 Unsup. Data Augmentation (Xie et al., 2019) 88.5</td></tr><tr><td>Rotation+ VAT+Ent.Min. (Zhai et al.,2019) 91.2 95.0 =</td></tr><tr><td>Methods using representation learning only:</td></tr><tr><td>Instance Discrimination (Wu et al., 2018) 39.2 77.4</td></tr><tr><td>Rotation (Zhai et al., 2019) 57.5 86.4</td></tr><tr><td>+ResNet trained on BigBiGAN (fixed) 55.2 78.8 87.0</td></tr><tr><td>+ResNet trained on AMDIM (fixed) 67.4 85.8 92.2</td></tr><tr><td>+ResNet trained on CPC v2 (fixed) 72.3 89.1 94.4 +ResNet trained on CPC v2 (fine-tuned) 72.9 89.5 95.2</td></tr></table>
+
+Other unsupervised representations. How well does the CPC representation compare to other representations that have been learned in an unsupervised manner? If predictable representations are uniquely suited for efficient classification, we would expect other methods within this family to perform similarly, and other model classes less so. Table 2 compares our best model with other works on efficient recognition. We consider three objectives from different model classes: self-supervised learning with rotation prediction (Zhai et al., 2019), large-scale adversarial feature learning (BigBiGAN, Donahue & Simonyan, 2019), and another contrastive prediction objective (AMDIM, Bachman et al., 2019). Zhai et al. (2019) evaluate the low-data classification performance of representations learned with rotation prediction using a similar paradigm and architecture (ResNet-152), hence we report their results directly. Given $1 \%$ of ImageNet, their method achieves $5 7 . 5 \%$ Top-5 accuracy, consistently with the reduced accuracy of a linear classifier ( $5 5 . 4 \%$ vs $6 5 . 9 \%$ for CPC)1.
+
+Because BigBiGAN and AMDIM achieve stronger linear classification accuracy than rotation prediction $6 1 . 3 \%$ and $6 8 . 1 \%$ Top-1 accuracy, respectively), we might expect better performance on efficient classification as well. Since their authors do not report results on efficient classification we evaluated these representations using the same paradigm we used for evaluating CPC, stacking a ResNet classifier on top of the $7 \times 7 \times 8 1 9 2$ latents of the BigBiGAN and the $7 \times 7 \times 2 5 6 0$ grid of feature vectors of AMDIM. We found fine-tuned representations to yield only marginal gains over fixed ones $7 2 . 9 \%$ compared to $7 2 . 3 \%$ Top-5 accuracy given $1 \%$ of labels), hence for simplicity we evaluate BigBiGAN and AMDIM on this task while keeping them fixed. We re-tune the hyper-parameters of the classifier (including optimization, regularization, etc.) for each of these representations separately. Although these methods achieve similar performance in terms of linear classification, we find them to achieve very different results in efficient classification. Given $1 \%$ of ImageNet, classifiers trained on top of BigBiGAN achieve $5 5 . 2 \%$ Top-5 accuracy, similarly to rotation prediction $( 5 7 . 5 \% )$ , despite its increased linear classification accuracy $( + 6 \%$ relative to rotation prediction). In contrast, AMDIM (which also belongs to the family of contrastive prediction methods) achieves $6 7 . 4 \%$ on this same task. Again, its increased linear classification accuracy did not entail an increase in data-efficiency. Nevertheless, in line with our initial hypothesis, we find that contrastive prediction methods such as CPC surpass other approaches in our efficient classification experiments, and that linear classification performance is not perfectly correlated with these results.
+
+Other semi-supervised techniques A separate class of methods for low-data classification attempts to propagate the knowledge extracted from the subset of labeled examples to unlabeled examples while being invariant to augmentation or other perturbations. These methods generally depend on the quality of the classifier’s predictions, and as such tend to fare well when given intermediate amounts of data. Although not sufficient in themselves (Unsupervised Data Augmentation (Xie et al., 2019), Virtual Adversarial Training (Miyato et al., 2018) and entropy minimization (Grandvalet & Bengio, 2005), and pseudo-labeling (Lee, 2013) achieve $8 5 . 8 \%$ , $8 3 . 4 \%$ , and $8 2 . 4 \%$ Top-5 accuracy with $10 \%$ of labels, compared to our $8 9 . 4 \%$ ) when combined with representation learning (e.g. rotation prediction Zhai et al., 2019) they can provide considerable gains $9 1 . 2 \%$ Top5 accuracy). It is therefore surprising that CPC representations alone can enable accuracy that is comparable to that of these methods, and investigating to what extent they can be combined would be an interesting topic of future work.
+
+# 4.3 TRANSFER LEARNING: IMAGE DETECTION ON PASCAL VOC 2007
+
+We next investigate transfer performance on object detection on the PASCAL-2007 dataset, which reflects the practical scenario where a representation must be trained on a dataset with different statistics than the dataset of interest. This dataset also tests the efficiency of the representation as it only contains 5011 labeled images to train from. In this setting, we replaced the neural network classifier $h _ { \psi }$ used previously with a Faster-RCNN (Ren et al., 2015) image detection architecture, and use the pre-trained feature extractor on ImageNet. As before, we first trained the Faster-RCNN model while keeping the feature extractor fixed, then fine-tuned the entire model end-to-end. Table 3 displays our results compared to other methods. Most competing methods, which optimize a single unsupervised objective on ImageNet before fine-tuning on PASCAL detection, attain around $65 \%$ mean average precision. Leveraging larger unlabeled datasets increases their performance up to $6 7 . 8 \%$ (Caron et al., 2019). Combining multiple forms of self-supervision enables them to reach $7 0 . 5 \%$ (Doersch & Zisserman, 2017). The proposed method, which learns only from ImageNet data using a single unsupervised objective, reaches $7 0 . 6 \%$ when equipped with a ResNet-101 feature extractor $f _ { \theta }$ (as for most competing methods (Doersch & Zisserman, 2017) but not all (Caron et al., 2018; 2019). Equipped with the more powerful ResNet-161 feature extractor $f _ { \theta }$ , our method reaches $7 2 . 7 \%$ . Importantly, this result is only $2 \%$ short of the performance attained by purely supervised transfer learning, which we obtain by using all ImageNet labels before transferring to PASCAL.
+
+# 5 DISCUSSION
+
+We asked whether CPC could enable data-efficient image recognition, and found that it indeed greatly improves the accuracy of classifiers and object detectors when given small amounts of labeled data. Surprisingly, CPC even improves results given ImageNet-scale labels. Our results show that there is still room for improvement using relatively straightforward changes such as augmentation, optimization, and network architecture. Furthermore, we found that the standard method for evaluating unsupervised representations—linear classification—is only partially predictive of efficient recognition performance, suggesting that further research should focus on efficient recognition as a standalone benchmark. Overall, these results open the door toward research on problems where data is naturally limited, e.g. medical imaging or robotics.
+
+Table 3: Faster-RCNN $h _ { \psi }$ trained with $100 \%$ of PASCAL labels. Comparison of PASCAL 2007 image detection accuracy to other transfer methods. The supervised baseline learns from the entire labeled ImageNet dataset and fine-tunes for PASCAL detection. The second class of methods learns from the same unlabeled images before transferring. All of these methods pre-train on the ImageNet dataset, except for DeeperCluster which learns from the larger, but uncurated, YFCC100M dataset (Thomee et al., 2015). All results are reported in terms of mean average precision (mAP). $\dagger$ denotes methods implemented in this work.   
+
+<table><tr><td>Method</td><td>mAP</td></tr><tr><td>Transfer from labeled data: Supervised - ResNet-152</td><td>74.7</td></tr><tr><td>Transfer from unlabeled data: Exemplar (Ex) (Dosovitskiy et al., 2014) Motion Segmentation (MS) (Pathak et al.,2016)</td><td>60.9</td></tr><tr><td>Colorization (Col) (Zhang et al.,2016) Relative Position (RP) (Doersch et al.,2015)</td><td>61.1 65.5</td></tr><tr><td>Combination of Ex + MS + Col +RP (Doersch &amp; Zisserman,2017)</td><td>66.8 70.5</td></tr><tr><td>Instance Discrimination (Wu et al., 2018)</td><td>65.4</td></tr><tr><td>Deep Cluster (Caron et al., 2018) Deeper Cluster (Caron et al., 2019)</td><td>65.9</td></tr></table>
+
+Furthermore, images are far from the only domain where unsupervised representation learning is important: for example, unsupervised learning is already a critical step in language (Mikolov et al., 2013; Devlin et al., 2018), and shows promise in domains like audio (van den Oord et al., 2018; Arandjelovic & Zisserman, 2018; 2017), video (Jing & Tian, 2018; Misra et al., 2016), and robotic manipulation (Pinto & Gupta, 2016; Pinto et al., 2016; Sermanet et al., 2018). Currently much self-supervised work builds upon tasks tailored for a specific domain (often images), which may not be easily adapted to other domains. Contrastive prediction methods, including the techniques suggested in this paper, are task agnostic and could therefore serve as a unifying framework for integrating these tasks and modalities. This generality is particularly useful given that many realworld environments are inherently multimodal, e.g. robotic environments which can have vision, audio, touch, proprioception, action, and more over long temporal sequences. Given the importance of increasing the amounts of self-supervision (via additional directions of prediction), integrating these modalities and tasks could lead to unsupervised representations which rival the efficiency and effectiveness of biological ones.
+
+# REFERENCES
+
+Pulkit Agrawal, Joao Carreira, and Jitendra Malik. Learning to see by moving. In ICCV, 2015.
+
+Relja Arandjelovic and Andrew Zisserman. Look, listen and learn. In Proceedings of the IEEE International Conference on Computer Vision, pp. 609–617, 2017.
+
+Relja Arandjelovic and Andrew Zisserman. Objects that sound. In Proceedings of the European Conference on Computer Vision (ECCV), pp. 435–451, 2018.
+
+Lei Jimmy Ba, Ryan Kiros, and Geoffrey E. Hinton. Layer normalization. CoRR, abs/1607.06450, 2016.
+
+Philip Bachman, R Devon Hjelm, and William Buchwalter. Learning representations by maximizing mutual information across views. arXiv preprint arXiv:1906.00910, 2019.
+
+H.B. Barlow. Unsupervised learning. Neural Computation, 1(3):295–311, 1989. doi: 10.1162/neco. 1989.1.3.295.
+
+Mathilde Caron, Piotr Bojanowski, Armand Joulin, and Matthijs Douze. Deep clustering for unsupervised learning of visual features. In The European Conference on Computer Vision (ECCV), September 2018.
+
+Mathilde Caron, Piotr Bojanowski, Julien Mairal, and Armand Joulin. Leveraging large-scale uncurated data for unsupervised pre-training of visual features. 2019.
+
+Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. BERT: pre-training of deep bidirectional transformers for language understanding. CoRR, abs/1810.04805, 2018.
+
+Carl Doersch and Andrew Zisserman. Multi-task self-supervised visual learning. In Proceedings of the IEEE International Conference on Computer Vision, pp. 2051–2060, 2017.
+
+Carl Doersch, Abhinav Gupta, and Alexei A Efros. Unsupervised visual representation learning by context prediction. In Proceedings of the IEEE International Conference on Computer Vision, pp. 1422–1430, 2015.
+
+Jeff Donahue and Karen Simonyan. Large scale adversarial representation learning. arXiv preprint arXiv:1907.02544, 2019.
+
+Jeff Donahue, Philipp Krahenb ¨ uhl, and Trevor Darrell. Adversarial feature learning. ¨ arXiv preprint arXiv:1605.09782, 2016.
+
+Alexey Dosovitskiy, Jost Tobias Springenberg, Martin Riedmiller, and Thomas Brox. Discriminative unsupervised feature learning with convolutional neural networks. In Advances in neural information processing systems, pp. 766–774, 2014.
+
+Mark Everingham, Luc Van Gool, Christopher KI Williams, John Winn, and Andrew Zisserman. The pascal visual object classes challenge 2007 (voc2007) results. 2007.
+
+Spyros Gidaris, Praveer Singh, and Nikos Komodakis. Unsupervised representation learning by predicting image rotations. arXiv preprint arXiv:1803.07728, 2018.
+
+Yves Grandvalet and Yoshua Bengio. Semi-supervised learning by entropy minimization. In Advances in neural information processing systems, pp. 529–536, 2005.
+
+Michael Gutmann and Aapo Hyvarinen. Noise-contrastive estimation: A new estimation principle ¨ for unnormalized statistical models. In Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, pp. 297–304, 2010.
+
+Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 770–778, 2016a.
+
+Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Identity mappings in deep residual networks. In European conference on computer vision, pp. 630–645. Springer, 2016b.
+
+G.E. Hinton, T.J. Sejnowski, H.H.M.I.C.N.L.T.J. Sejnowski, and T.A. Poggio. Unsupervised Learning: Foundations of Neural Computation. A Bradford Book. MIT Press, 1999. ISBN 9780262581684.
+
+Olivier J. Henaff, Robbe L. T. Goris, and Eero P. Simoncelli. Perceptual straightening of natural ´ videos. Nature Neuroscience, Apr 2019.
+
+Sergey Ioffe and Christian Szegedy. Batch normalization: Accelerating deep network training by reducing internal covariate shift. arXiv preprint arXiv:1502.03167, 2015.
+
+Dinesh Jayaraman and Kristen Grauman. Learning image representations tied to ego-motion. In ICCV, 2015.
+
+Longlong Jing and Yingli Tian. Self-supervised spatiotemporal feature learning by video geometric transformations. arXiv preprint arXiv:1811.11387, 2018.
+
+Durk P Kingma, Shakir Mohamed, Danilo Jimenez Rezende, and Max Welling. Semi-supervised learning with deep generative models. In Advances in neural information processing systems, pp. 3581–3589, 2014.
+
+Alexander Kolesnikov, Xiaohua Zhai, and Lucas Beyer. Revisiting self-supervised visual representation learning. CoRR, abs/1901.09005, 2019. URL http://arxiv.org/abs/1901.09005.
+
+Brenden M Lake, Ruslan Salakhutdinov, and Joshua B Tenenbaum. Human-level concept learning through probabilistic program induction. Science, 350(6266):1332–1338, 2015.
+
+Barbara Landau, Linda B Smith, and Susan S Jones. The importance of shape in early lexical learning. Cognitive development, 3(3):299–321, 1988.
+
+Gustav Larsson, Michael Maire, and Gregory Shakhnarovich. Colorization as a proxy task for visual understanding. In CVPR, pp. 6874–6883, 2017.
+
+Yann LeCun, Yoshua Bengio, and Geoffrey Hinton. Deep learning. nature, 521(7553):436, 2015.
+
+Dong-Hyun Lee. Pseudo-label: The simple and efficient semi-supervised learning method for deep neural networks. In Workshop on Challenges in Representation Learning, ICML, volume 3, pp. 2, 2013.
+
+Yin Li, Manohar Paluri, James M Rehg, and Piotr Dollar. Unsupervised learning of edges. In ´ CVPR, 2016.
+
+Ellen M Markman. Categorization and naming in children: Problems of induction. mit Press, 1989.
+
+Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg S Corrado, and Jeff Dean. Distributed representations of words and phrases and their compositionality. In C. J. C. Burges, L. Bottou, M. Welling, Z. Ghahramani, and K. Q. Weinberger (eds.), Advances in Neural Information Processing Systems 26, pp. 3111–3119. Curran Associates, Inc., 2013.
+
+Ishan Misra, C Lawrence Zitnick, and Martial Hebert. Shuffle and learn: unsupervised learning using temporal order verification. In ECCV, 2016.
+
+Takeru Miyato, Shin-ichi Maeda, Shin Ishii, and Masanori Koyama. Virtual adversarial training: a regularization method for supervised and semi-supervised learning. IEEE transactions on pattern analysis and machine intelligence, 2018.
+
+Andriy Mnih and Koray Kavukcuoglu. Learning word embeddings efficiently with noise-contrastive estimation. In Advances in neural information processing systems, pp. 2265–2273, 2013.
+
+Mehdi Noroozi and Paolo Favaro. Unsupervised learning of visual representations by solving jigsaw puzzles. In European Conference on Computer Vision, pp. 69–84. Springer, 2016.
+
+Stephanie E Palmer, Olivier Marre, Michael J Berry, and William Bialek. Predictive information in a sensory population. Proceedings of the National Academy of Sciences, 112(22):6908–6913, 2015.
+
+Deepak Pathak, Ross Girshick, Piotr Dollar, Trevor Darrell, and Bharath Hariharan. Learning fea-´ tures by watching objects move. arXiv preprint arXiv:1612.06370, 2016.
+
+Lerrel Pinto and Abhinav Gupta. Supersizing self-supervision: Learning to grasp from 50k tries and 700 robot hours. In ICRA, 2016.
+
+Lerrel Pinto, James Davidson, and Abhinav Gupta. Supervision via competition: Robot adversaries for learning tasks. arXiv preprint arXiv:1610.01685, 2016.
+
+Rajesh PN Rao and Dana H Ballard. Predictive coding in the visual cortex: a functional interpretation of some extra-classical receptive-field effects. Nature neuroscience, 2(1):79, 1999.
+
+Shaoqing Ren, Kaiming He, Ross Girshick, and Jian Sun. Faster r-cnn: Towards real-time object detection with region proposal networks. In Advances in neural information processing systems, pp. 91–99, 2015.
+
+Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang, Andrej Karpathy, Aditya Khosla, Michael Bernstein, et al. Imagenet large scale visual recognition challenge. International journal of computer vision, 115(3):211–252, 2015.
+
+Pierre Sermanet, Corey Lynch, Yevgen Chebotar, Jasmine Hsu, Eric Jang, Stefan Schaal, Sergey Levine, and Google Brain. Time-contrastive networks: Self-supervised learning from video. In 2018 IEEE International Conference on Robotics and Automation (ICRA), pp. 1134–1141. IEEE, 2018.
+
+Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov. Dropout: a simple way to prevent neural networks from overfitting. The journal of machine learning research, 15(1):1929–1958, 2014.
+
+Christian Szegedy, Wei Liu, Yangqing Jia, Pierre Sermanet, Scott E. Reed, Dragomir Anguelov, Dumitru Erhan, Vincent Vanhoucke, and Andrew Rabinovich. Going deeper with convolutions. CoRR, abs/1409.4842, 2014. URL http://arxiv.org/abs/1409.4842.
+
+Bart Thomee, David A Shamma, Gerald Friedland, Benjamin Elizalde, Karl Ni, Douglas Poland, Damian Borth, and Li-Jia Li. Yfcc100m: The new data in multimedia research. arXiv preprint arXiv:1503.01817, 2015.
+
+Yonglong Tian, Dilip Krishnan, and Phillip Isola. Contrastive multiview coding. arXiv preprint arXiv:1906.05849, 2019.
+
+Aaron van den Oord, Yazhe Li, and Oriol Vinyals. Representation learning with contrastive predictive coding. arXiv preprint arXiv:1807.03748, 2018.
+
+Xiaolong Wang and Abhinav Gupta. Unsupervised learning of visual representations using videos. In ICCV, 2015.
+
+Zhirong Wu, Yuanjun Xiong, Stella X Yu, and Dahua Lin. Unsupervised feature learning via nonparametric instance discrimination. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 3733–3742, 2018.
+
+Qizhe Xie, Zihang Dai, Eduard Hovy, Minh-Thang Luong, and Quoc V. Le. Unsupervised Data Augmentation. arXiv e-prints, art. arXiv:1904.12848, Apr 2019.
+
+Amir R Zamir, Tilman Wekel, Pulkit Agrawal, Colin Wei, Jitendra Malik, and Silvio Savarese. Generic 3D representation via pose estimation and matching. In ECCV, 2016.
+
+Xiaohua Zhai, Avital Oliver, Alexander Kolesnikov, and Lucas Beyer. $S ^ { 4 } L$ : Self-supervised semisupervised learning. arXiv preprint arXiv:1905.03670, 2019.
+
+Richard Zhang, Phillip Isola, and Alexei A Efros. Colorful image colorization. In European conference on computer vision, pp. 649–666. Springer, 2016.
+
+Xiaojin Zhu and Zoubin Ghahramani. Learning from labeled and unlabeled data with label propagation. In Technical Report CMU-CALD-02-107, Carnegie Mellon University, 2002.
+
+Chengxu Zhuang, Alex Lin Zhai, and Daniel Yamins. Local aggregation for unsupervised learning of visual embeddings. arXiv preprint arXiv:1903.12355, 2019.
+
+# A APPENDIX
+
+# A.1 ADDITIONAL RESULTS
+
+Table 4: Data efficient classification results with Top-1 accuracy.   
+
+<table><tr><td>Labeled data Method</td><td>1%</td><td>2%</td><td>5%</td><td>10% Top-1 accuracy</td><td>20%</td><td>50%</td><td>100%</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Supervised trained on pixels</td><td>23.1</td><td>34.8</td><td>50.2</td><td>60.0</td><td>67.6</td><td>74.4</td><td>78.0</td></tr><tr><td>ReseNet trained on CPC v2 (fine-tuned)</td><td>46.3</td><td>54.7</td><td>64.1</td><td>69.7</td><td>73.0</td><td>77.3</td><td>80.6</td></tr></table>
+
+Table 5: Data efficient classification results with Top-5 accuracy (data in Fig. 1).   
+
+<table><tr><td>Labeled data Method</td><td>1%</td><td>2%</td><td>5%</td><td>10% Top-5 accuracy</td><td>20%</td><td>50%</td><td>100%</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Supervised trained on pixels</td><td>44.1</td><td>59.9</td><td>75.2</td><td>82.1</td><td>87.9</td><td>91.8</td><td>93.8</td></tr><tr><td>ReseNet trained on CPC v2 (fine-tuned)</td><td>72.9</td><td>79.6</td><td>86.1</td><td>89.5</td><td>91.4</td><td>93.6</td><td>95.2</td></tr></table>
+
+# A.2 INFONCE IMPLEMENTATION
+
+For completeness, we provide pseudo-code for the main calculations involved in the InfoNCE objective, loosely modeled after Tensorflow operations. We suppose we have just calculated a set of latents $z _ { i , j } = f _ { \theta } ( \pmb { x } _ { i , j } )$ for $i , j \in \{ 1 , . . . , 7 \}$ , each one being e.g. a 4096-dimensional vector. Assuming we do so for a batch of $B$ images $\{ { \pmb x } \}$ , the set of latents is a tensor of size $B \times 7 \times 7 \times 4 0 9 6$ .
+
+def pixelCNN(latents): # latents: [B, H, W, D] cres $=$ latents cres_dim $=$ cres.shape[-1] for in range(5): c $=$ Conv2D(output_channels $= 2 5 6$ , kernel_shape $=$ (1, 1))(cres) c = ReLU(c) c = Conv2D(output_channels $= 2 5 6$ , kernel_shape $=$ (1, 3))(c) c = Pad(c, [[0, 0], [1, 0], [0, 0], [0, 0]]) c = Conv2D(output_channels $= 2 5 6$ , kernel_shape $=$ (2, 1), type $= ^ { \parallel }$ VALID')(c) c $=$ ReLU(c) c $=$ Conv2D(output_channels $=$ cres_dim, kernel_shape $=$ (1, 1))(c) cres $=$ cres + c cres $=$ ReLU(cres) return cres
+
+# A.3 LINEAR CLASSIFICATION
+
+• Model architecture: Having extracted $8 0 \mathrm { x } 8 0$ patches with a stride of $3 2 \mathrm { x } 3 2 $ from a $2 4 0 \times 2 4 0$ shaped input image, we end up with a grid of 6x6 features (each of which is obtained from our ResNet-161 architecture). This gives us a [6,6,4096] tensor for the image. We then use a Batch-Normalization layer to normalize the features (without scale parameter) followed by a 1x1 convolution mapping each feature in the grid to the 1000 logits for ImageNet classification. We then spatially-mean-pool these logits to end up with the final log probabilities for the linear classification.   
+• We use the Inception preprocessing (Szegedy et al., 2014) to extract $2 4 0 \times 2 4 0$ crops from the raw image. The image is divided into subcrops as per CPC data-preprocessing used for CPC pre-training.   
+• Optimization details: We use Adam Optimizer with a learning rate of 5e-4. We train the model on a batch size of 512 images with 32 images per core spread over 16 workers.
+
+A.4 EFFICIENT CLASSIFICATION: PURELY SUPERVISED
+
+In order to find the best model within this class, we vary the following hyperparameters:
+
+• Model architecture: We investigate using ResNet-50, ResNet-101, and ResNet-152 model architectures, all of them using the $\mathbf { \hat { v } } _ { \mathbf { \Delta } } 2 \mathbf { \hat { \mu } }$ variant (He et al., 2016b), and find larger architecture to perform better, even when given smaller amounts of data. We insert a DropOut layer before the final linear classification layer (Srivastava et al., 2014). • Data pre-processing: We use the Inception pre-processing pipeline (Szegedy et al., 2014). • Optimization details: We vary the learning rate in $\{ 0 . 0 5 , 0 . 1 , 0 . 2 \}$ , the weight decay logarithmically from $1 0 ^ { - 5 }$ to $1 0 ^ { - 2 }$ , the DropOut linearly from 0 to 1, and the batch size per worker in $\{ 1 6 , 3 2 \}$ .
+
+We chose the best performing model for each training subset $\mathbb { D } _ { l }$ of labeled ImageNet (using a separate validation set), and report its accuracy on the test set (i.e. the publicly available ILSVRC-2012 validation set).
\ No newline at end of file
diff --git a/parse/train/rJerHlrYwH/rJerHlrYwH_content_list.json b/parse/train/rJerHlrYwH/rJerHlrYwH_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..7ca5ef137f102419892bab9a2854d8534e8ed2af
--- /dev/null
+++ b/parse/train/rJerHlrYwH/rJerHlrYwH_content_list.json
@@ -0,0 +1,1615 @@
+[
+    {
+        "type": "text",
+        "text": "DATA-EFFICIENT IMAGE RECOGNITION WITH CONTRASTIVE PREDICTIVE CODING ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            98,
+            684,
+            146
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Anonymous authors Paper under double-blind review ",
+        "bbox": [
+            183,
+            170,
+            398,
+            198
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            234,
+            544,
+            251
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Human observers can learn to recognize new categories of objects from a handful of examples, yet doing so with machine perception remains an open challenge. We hypothesize that data-efficient recognition is enabled by representations which make the variability in natural signals more predictable, as suggested by recent perceptual evidence. We therefore revisit and improve Contrastive Predictive Coding, a recently-proposed unsupervised learning framework, and arrive at a representation which enables generalization from small amounts of labeled data. When provided with only $1 \\%$ of ImageNet labels (i.e. 13 per class), this model retains a strong classification performance, $73 \\%$ Top-5 accuracy, outperforming supervised networks by $28 \\%$ (a $65 \\%$ relative improvement) and state-of-the-art semisupervised methods by $14 \\%$ . We also find this representation to serve as a useful substrate for object detection on the PASCAL-VOC 2007 dataset, approaching the performance of representations trained with a fully annotated ImageNet dataset. ",
+        "bbox": [
+            233,
+            267,
+            764,
+            446
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            178,
+            476,
+            334,
+            492
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Deep neural networks excel at perceptual tasks when labeled data are abundant, yet their performance degrades substantially when provided with limited supervision (Fig. 1, red). In contrast, humans and animals can quickly learn about new classes of objects from few examples (Landau et al., 1988; Markman, 1989). What accounts for this monumental difference in data-efficiency between biological and machine vision? While highly-structured representations (e.g. as proposed by Lake et al., 2015) may improve data-efficiency, it remains unclear how to program explicit structures that capture the enormous complexity of real visual scenes like those in ImageNet (Russakovsky et al., 2015). An alternative hypothesis has proposed that intelligent systems need not be structured a priori, but can instead learn about the structure of the world in an unsupervised manner (Barlow, 1989; Hinton et al., 1999; LeCun et al., 2015). Choosing an appropriate training objective is an open problem, but a promising guiding principle has emerged recently: good representations should make the spatio-temporal variability in natural signals more predictable. Indeed, human perceptual representations have been shown to linearize ",
+        "bbox": [
+            174,
+            510,
+            483,
+            881
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/7b8ed316aeaae9bdfe3d3d7e12974b01335c33b7eb790b24e724753c0422fb2e.jpg",
+        "image_caption": [
+            "Figure 1: Data-efficient image recognition with Contrastive Predictive Coding. With decreasing amounts of labeled data, supervised networks trained on pixels fail to generalize (red). When trained on unsupervised representations learned with CPC, these networks retain a much higher accuracy in this low-data regime (blue). Equivalently, the accuracy of supervised networks can be matched with significantly fewer labels. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            500,
+            512,
+            820,
+            733
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "(or ‘straighten’) the temporal transformations found in natural videos, a property lacking from current supervised image recognition models (Henaff et al., 2019), and theories of both spatial and tem- ´ poral predictability have succeeded in describing properties of early visual areas (Rao & Ballard, ",
+        "bbox": [
+            176,
+            882,
+            823,
+            924
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1999; Palmer et al., 2015). In this work, we hypothesize that spatially predictable representations may allow artificial systems to benefit from human-like data-efficiency. ",
+        "bbox": [
+            171,
+            103,
+            823,
+            132
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Contrastive Predictive Coding (CPC, van den Oord et al., 2018) is an unsupervised objective which learns such predictable representations. CPC is a general technique that only requires in its definition that observations be ordered along e.g. temporal or spatial dimensions, and as such has been applied to a variety of different modalities including speech, natural language and images. This generality, combined with the strong performance of its representations in downstream linear classification tasks, makes CPC a promising candidate for investigating the efficacy of predictable representations for data-efficient image recognition. ",
+        "bbox": [
+            174,
+            138,
+            825,
+            236
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Our work makes the following contributions: ",
+        "bbox": [
+            174,
+            243,
+            468,
+            257
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "• We revisit CPC in terms of its architecture and training methodology, and arrive at a new implementation of CPC with dramatically-improved ability to linearly separate image classes $+ 1 7 \\%$ Top-1 ImageNet classification accuracy).   \nWe then train deep networks on top of the resulting CPC representations using very few labeled images (e.g. $1 \\%$ of the ImageNet dataset), and demonstrate test-time classification accuracy far above networks trained on raw pixels ( $73 \\%$ Top-5 accuracy, a $28 \\%$ absolute improvement), outperforming all other unsupervised representation learning methods $( + 1 5 \\%$ Top-5 accuracy over the previous state-of-the-art (Zhai et al., 2019)). Surprisingly, this representation also surpasses supervised methods when given the entire ImageNet dataset $+ 1 \\%$ Top-5 accuracy).   \nWe isolate the contributions of different components of the final model to such downstream tasks. Interestingly, we find that linear classification accuracy is not always predictive of low-data classification accuracy, emphasizing the importance of this metric as a stand-alone benchmark for unsupervised learning.   \n• Finally, we assess the generality of CPC representations by transferring them to a new task and dataset: object detection on PASCAL-VOC 2007. Consistent with the results from the previous section, we find CPC to give state-of-the-art performance in this setting. ",
+        "bbox": [
+            217,
+            270,
+            825,
+            522
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 EXPERIMENTAL SETUP ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            541,
+            398,
+            558
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We first review the CPC architecture and learning objective in section 2.1, before detailing how we use its resulting representations for image recognition tasks in section 2.2. ",
+        "bbox": [
+            176,
+            574,
+            825,
+            602
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1 CONTRASTIVE PREDICTIVE CODING ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            618,
+            467,
+            633
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Contrastive Predictive Coding as formulated in (van den Oord et al., 2018) learns representations by training neural networks to predict the representations of future observations from those of past ones. When applied to images, the original formulation of CPC operates by predicting the representations of patches below a certain position from those above it (Fig. 2, left). These predictions are evaluated using a contrastive loss, in which the network must correctly classify the ‘future’ representation amongst a set of unrelated ‘negative’ representations. This avoids trivial solutions such as representing all patches with a constant vector, as would be the case with a mean squared error loss. ",
+        "bbox": [
+            174,
+            645,
+            825,
+            742
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In the CPC architecture, each input image is first divided into a set of overlapping patches $\\mathbf { \\delta } _ { \\mathbf { x } _ { i , j } }$ , each of which is encoded with a neural network $f _ { \\theta }$ into a single vector $z _ { i , j } = f _ { \\theta } ( \\pmb { x } _ { i , j } )$ . To make predictions, a masked convolutional network $g _ { \\phi }$ is then applied to the grid of feature vectors. The masks are such that the receptive field of each resulting context vector $c _ { i , j }$ only includes feature vectors that lie above it in the image (i.e. $\\{ z _ { u , v } \\} _ { u \\leq i , v } )$ . The prediction task then consists o predicting ‘future’ feature vectors $z _ { i + k , j }$ from current context vectors $c _ { i , j }$ , where $k > 0$ . The predictions are made linearly: given a context vector $c _ { i , j }$ , a prediction length $k > 0$ , and a prediction matrix $W _ { k }$ , the predicted feature vector is $\\hat { \\boldsymbol { z } } _ { i + k , j } = \\boldsymbol { W } _ { k } \\boldsymbol { c } _ { i , j }$ . ",
+        "bbox": [
+            174,
+            750,
+            825,
+            862
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The quality of this prediction is then evaluated using a contrastive loss. Specifically, the goal is to correctly recognize the target $z _ { i + k , j }$ among a set of randomly sampled feature vectors $\\{ z _ { l } \\}$ from the dataset. We compute the probability assigned to the target using a softmax, and evaluate this probability using the usual cross-entropy loss. Summing this loss over locations and prediction offsets, we arrive at the CPC objective as defined in (van den Oord et al., 2018): ",
+        "bbox": [
+            174,
+            867,
+            823,
+            924
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/e21408d1a55db66ba2cac6a3f4d98b0d1a13c2f1211e3956f93d67bae89bbaae.jpg",
+        "image_caption": [
+            "Figure 2: Overview of the framework for semi-supervised learning with Contrastive Predictive Coding. Left: unsupervised pre-training with the spatial prediction task (See Section 2.1). First, an image is divided into a grid of overlapping patches. Each patch is encoded independently from the rest with a feature extractor (blue) which terminates with a mean-pooling operation, yielding a single feature vector for that patch. Doing so for all patches yields a field of such feature vectors (wireframe vectors). Feature vectors above a certain level (in this case, the center of the image) are then aggregated with a context network (red), yielding a row of context vectors which are used to linearly predict features vectors below. Right: using the CPC representation for a classification task. Having trained the encoder network, the context network (red) is discarded and replaced by a classifier network (green) which can be trained in a supervised manner. For some experiments, we also fine-tune the encoder network (blue) for the classification task. When applying the encoder to cropped patches (as opposed to the full image) we refer to it as a patched ResNet in the figure. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            174,
+            104,
+            823,
+            294
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            173,
+            486,
+            696,
+            502
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/7113b15debaadf2fc32b7ca0c3e55fb0689eecd2935810917cee824de20f6604.jpg",
+        "text": "$$\n\\mathcal { L } _ { \\mathrm { C P C } } = - \\sum _ { i , j , k } \\log p ( z _ { i + k , j } | \\hat { z } _ { i + k , j } , \\{ z _ { l } \\} ) = - \\sum _ { i , j , k } \\log \\frac { \\exp ( \\hat { z } _ { i + k , j } ^ { T } z _ { i + k , j } ) } { \\exp ( \\hat { z } _ { i + k , j } ^ { T } z _ { i + k , j } ) + \\sum _ { l } \\exp ( \\hat { z } _ { i + k , j } ^ { T } z _ { l } ) }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            186,
+            503,
+            808,
+            546
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The negative samples $\\left\\{ z _ { l } \\right\\}$ are taken from other locations in the image and other images in the minibatch. This loss is called InfoNCE (van den Oord et al., 2018) as it is inspired by Noise-Contrastive Estimation (Gutmann $\\&$ Hyvarinen, 2010; Mnih & Kavukcuoglu, 2013) and has been shown to ¨ maximize the mutual information between $\\mathbf { } _ { c _ { i , j } }$ and $z _ { i + k , j }$ (van den Oord et al., 2018). ",
+        "bbox": [
+            174,
+            547,
+            825,
+            606
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2 EVALUATION PROTOCOL ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            621,
+            383,
+            635
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Having trained an encoder network $f _ { \\theta }$ , a context network $g _ { \\phi }$ , and a set of linear predictors $\\{ W _ { k } \\}$ using the CPC objective, we use the latents $z = f _ { \\boldsymbol { \\theta } } ( \\pmb { x } )$ as a representation of new observations $x$ for downstream tasks, and discard the rest. We then train a model $h _ { \\psi }$ to classify these representations given a dataset of labeled images. More formally, given a dataset of $N$ unlabeled images $\\mathbb { D } _ { u } =$ $\\left\\{ x _ { n } \\right\\}$ , and a (potentially much smaller) dataset of $M$ labeled images $\\mathbb { D } _ { l } = \\{ x _ { m } , y _ { m } \\}$ : ",
+        "bbox": [
+            174,
+            646,
+            825,
+            717
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/c6df6158bc3640c41b4e80de8a77924da143cb3d171b2d5421986f303ad176ed.jpg",
+        "text": "$$\n\\theta ^ { * } = \\arg \\operatorname* { m i n } _ { \\theta } \\frac { 1 } { N } \\sum _ { n = 1 } ^ { N } \\mathcal { L } _ { \\mathrm { C P C } } [ f _ { \\theta } ( x _ { n } ) ] , \\quad \\psi ^ { * } = \\arg \\operatorname* { m i n } _ { \\psi } \\frac { 1 } { M } \\sum _ { m = 1 } ^ { M } \\mathcal { L } _ { \\mathrm { S u p } } [ h _ { \\psi } \\circ f _ { \\theta ^ { * } } ( x _ { m } ) , y _ { m } ]\n$$",
+        "text_format": "latex",
+        "bbox": [
+            217,
+            718,
+            781,
+            762
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In all cases, the dataset of unlabeled images $\\mathbb { D } _ { u }$ we pre-train on is the full ImageNet ILSVRC 2012 training set (Russakovsky et al., 2015). We consider three labeled datasets $\\mathbb { D } _ { l }$ for evaluation, each with an associated classifier $h _ { \\psi }$ and supervised losse $\\mathcal { L } _ { \\mathrm { { S u p } } }$ (see Fig. 2, right). This protocol is sufficiently generic to allow us to later compare the CPC representation to other methods which have their own means of learning a feature extractor $f _ { \\theta }$ . ",
+        "bbox": [
+            173,
+            763,
+            825,
+            834
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Linear classification is the standard benchmark for evaluating the quality of unsupervised image representations. In this regime, the classification network $h _ { \\psi }$ is restricted to mean pooling followed by a single linear layer, and the parameters of $f _ { \\theta }$ are kept fixed. The labeled dataset $\\mathbb { D } _ { l }$ is the entire ImageNet dataset, and the supervised loss $\\mathcal { L } _ { \\mathrm { { S u p } } }$ is standard cross-entropy. We use the same dataaugmentation as in the unsupervised learning phase for training, and none at test time and evaluate with a single crop. ",
+        "bbox": [
+            173,
+            839,
+            825,
+            924
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Efficient classification directly tests whether the CPC representation enables visual learning from few labels. For this task, the classifier $h _ { \\psi }$ is an arbitrary deep neural network (we use an 11-block ResNet architecture with 4096-dimensional feature maps and 1024-dimensional bottleneck layers). The labeled dataset $\\mathbb { D } _ { l }$ is a subset of the ImageNet dataset: we investigated using $1 \\%$ , $2 \\%$ , $5 \\%$ , $10 \\%$ , $20 \\%$ , $50 \\%$ and $100 \\%$ of the ImageNet dataset. The supervised loss $\\mathcal { L } _ { \\mathrm { { S u p } } }$ is again cross-entropy. In addition to random color-dropping we use the Inception data-augmentation scheme (Szegedy et al., 2014) for training, no augmentation at test-time and evaluate with a single crop. ",
+        "bbox": [
+            174,
+            103,
+            825,
+            202
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Transfer learning tests the generality of the representation by applying it to a new task and dataset. For this we chose image detection on the PASCAL-2007 dataset, a standard benchmark in computer vision (Everingham et al., 2007). As such $\\mathbb { D } _ { l }$ is the entire PASCAL-2007 dataset (comprised of 5011 labeled images); $h _ { \\psi }$ and $\\mathcal { L } _ { \\mathrm { { S u p } } }$ are the Faster-RCNN architecture and loss (Ren et al., 2015). In addition to color-dropping, we use scale-augmentation (Doersch et al., 2015) for training. ",
+        "bbox": [
+            174,
+            208,
+            825,
+            279
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "For linear classification, we keep the feature extractor $f _ { \\theta }$ fixed to assess the representation in absolute terms. For efficient classification and transfer learning, we additionally explore fine-tuning the feature extractor for the supervised objective. In this regime, we initialize the feature extractor and classifier with the solutions $\\theta ^ { * } , \\psi ^ { * }$ found in the previous learning phase, and train them both for the supervised objective. To ensure that the feature extractor does not deviate too much from the solution dictated by the CPC objective, we use a smaller learning rate and early-stopping. ",
+        "bbox": [
+            174,
+            285,
+            825,
+            368
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            402,
+            343,
+            419
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Data-efficient learning has typically been approached by two complementary methods, both of which seek to make use of more plentiful unlabeled data: representation learning and semisupervised learning. The former formulates an objective to learn a feature extractor $f _ { \\theta }$ in an unsupervised manner, whereas the latter directly constrains the classifier $h _ { \\psi }$ using the unlabeled data. ",
+        "bbox": [
+            174,
+            444,
+            823,
+            500
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Representation learning saw early success using generative modeling (Kingma et al., 2014), but likelihood-based models have yet to generalize to more complex stimulus classes. Generative adversarial models have also been harnessed for representation learning (Donahue et al., 2016), and large-scale implementations have recently achieved corresponding gains in linear classification accuracy (Donahue & Simonyan, 2019). ",
+        "bbox": [
+            174,
+            507,
+            823,
+            577
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In contrast to generative models which require the reconstruction of observations, self-supervised techniques directly formulate tasks involving the learned representation. For example, simply asking a network to recognize the spatial layout of an image led to representations that transferred to popular vision tasks such as classification and detection (Doersch et al., 2015; Noroozi & Favaro, 2016). Other works showed that prediction of color (Zhang et al., 2016; Larsson et al., 2017) and image orientation (Gidaris et al., 2018), and invariance to data augmentation (Dosovitskiy et al., 2014) can provide useful self-supervised tasks. Beyond single images, works have leveraged video cues such as object tracking (Wang & Gupta, 2015), frame ordering (Misra et al., 2016), and object boundary cues (Li et al., 2016; Pathak et al., 2016). Non-visual information can be equally powerful; information about camera motion (Agrawal et al., 2015; Jayaraman & Grauman, 2015), scene geometry (Zamir et al., 2016), or sound (Arandjelovic & Zisserman, 2017; 2018) can all serve as natural sources of supervision. ",
+        "bbox": [
+            174,
+            583,
+            825,
+            750
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "While many of these tasks require predicting fixed quantities computed from the data, another class of contrastive methods formulate their objectives in the learned representations themselves. CPC is a contrastive representation learning method that maximizes the mutual information between spatially removed latent representations with InfoNCE (van den Oord et al., 2018), a loss function based on Noise-Contrastive Estimation (Gutmann & Hyvarinen, 2010; Mnih & Kavukcuoglu, 2013). Two ¨ other methods have recently been proposed using the same loss function, but with different associated prediction tasks. Contrastive Multiview Coding (Tian et al., 2019) maximizes the mutual information between representations of different views of the same observation. Augmented Multiscale Deep InfoMax (AMDIM, Bachman et al., 2019) is most similar to CPC in that it makes predictions across space, but differs in that it also predicts representations across layers in the model. In addition, AMDIM limits the receptive field of its representation, but does this by constraining the number of spatial convolutions in the network architecture rather than using image patches. ",
+        "bbox": [
+            174,
+            757,
+            825,
+            924
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "A common alternative approach for improving data efficiency is label-propagation (Zhu & Ghahramani, 2002), where a classifier is trained on a subset of labeled data, then used to label parts of the unlabeled dataset, after which the process is repeated. This label-propagation can either be discrete (as in pseudo-labeling, Lee, 2013) or continuous (as in entropy minimization, Grandvalet & Bengio, 2005). The predictions of this classifier are often constrained to be smooth with respect to certain deformations, such as data-augmentation (Xie et al., 2019) or adversarial perturbation (Miyato et al., 2018). Representation learning and semi-supervised learning have been shown to be complementary and can be combined to great effect (Zhai et al., 2019), which is why we focus solely on representation learning in this paper. ",
+        "bbox": [
+            174,
+            103,
+            825,
+            229
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4 RESULTS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            251,
+            281,
+            267
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "When asking whether CPC enables data-efficient learning, we wish to use the best possible representative of this model class. Unfortunately, purely unsupervised metrics tell us little about downstream performance, and implementation details have been shown to matter enormously (Doersch & Zisserman, 2017; Kolesnikov et al., 2019). Since many design choices (e.g. network architecture and datapreprocessing) have been previously evaluated using linear classification, we use this benchmark in section 4.1 to align the CPC model with best practices in representation learning and compare to published results. In section 4.2 we select the best performing model from the previous section and assess whether it enables efficient classification. We also investigate to what extent the first, more common metric (linear classification accuracy) is predictive of efficient classification. Finally, in section 4.3 we investigate the generality of our results through transfer learning to PASCAL-2007. ",
+        "bbox": [
+            174,
+            284,
+            825,
+            422
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1 FROM CPC V1 TO CPC V2 ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            441,
+            400,
+            455
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The overarching principle behind our new model design is to increase the scale and efficiency of the encoder architecture while also maximizing the supervisory signal we obtain from each image. At the same time, it is important not to allow the network to solve the problem trivially, i.e., without learning semantics. To this end, we seek to remove low-level cues common across patches by augmenting individual patches independently, using standard stochastic data-processing techniques from supervised and self-supervised learning. ",
+        "bbox": [
+            174,
+            468,
+            825,
+            553
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We identify four axes for model capacity and task setup that could impact the model’s performance. The first axis increases model capacity by increasing depth and width, while the second improves training efficiency capacity by introducing layer normalization. The third axis increases task complexity by making predictions in all four directions, and the fourth does so by performing more extensive patch-based augmentation. ",
+        "bbox": [
+            174,
+            559,
+            485,
+            698
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Model capacity. Recent work has shown that networks and more effective training improves self-supervised learning (Doersch & Zisserman, 2017; Kolesnikov et al., 2019), but the original CPC model used only the first 3 stacks of a ResNet-101 (He et al., 2016a) architecture (i.e. a ResNet-92). Therefore, we converted the third residual stack of ResNet-101 (originally containing 23 blocks, 1024-dimensional feature maps, and 256-dimensional bottleneck layers), to use 46 blocks, with 4096-dimensional feature maps and 512-dimensional bottleneck layers. We call the resulting network ResNet-161. Consistent with prior results, this new architecture delivers better performance regardless of ",
+        "bbox": [
+            174,
+            715,
+            483,
+            922
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/3eeded7c7663fc17771caa90292cc1343662124f1094d06f22d9ca255036f2a3.jpg",
+        "image_caption": [
+            "Figure 3: Linear classification performance of new variants of CPC, which incrementally add a series of modifications. BU: bottum up spatial predictions. HF: randomly flipping patches horizontally. LN: layer normalization. RC: random color-dropping. TL: tuned prediction lengths. HP: horizontal spatial predictions. We use color to indicate the number of spatial predictions used (orange, green, blue for 1, 2 and 4 directions). "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            501,
+            566,
+            818,
+            777
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/fa1f65edaf71df9800daca9c26a7999e93d74856116a87cc357e08cc713a4be7.jpg",
+        "table_caption": [
+            "Table 1: Linear classifier $h _ { \\psi }$ trained with $100 \\%$ of labels. Comparison to linear separability of other self-supervised methods. In all cases a feature extractor is optimized in an unsupervised manner, and a linear classifier is trained on top using all labels in the ImageNet dataset. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Top-1</td><td>Top-5</td></tr><tr><td>Motion Segmentation (MS) (Pathak et al., 2016) Exemplar (Ex) (Dosovitskiy et al.,2014) Relative Position (RP) (Doersch et al.,2015) Colorization (Col) (Zhang et al., 2016) Combination of MS + Ex + RP+ Col (Doersch &amp; Zisserman,2017) CPC v1 (van den Oord et al., 2018) Rotation (Kolesnikov et al., 2019)</td><td>27.6 31.5 36.2 39.6 1 48.7 55.4</td><td>48.3 53.1 59.2 62.5 69.3 73.6</td></tr><tr><td>CMC (Tian et al., 2019) Local Aggregation (Zhuang et al., 2019)</td><td>60.1 60.2</td><td>82.8 1 =</td></tr><tr><td>BigBiGAN (Donahue &amp; Simonyan,2019) AMDIM (Bachman et al., 2019) CPC v2 (ours) 65.9</td><td>61.3 68.1</td><td>81.9</td></tr></table>",
+        "bbox": [
+            204,
+            159,
+            794,
+            371
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "other design choices. Interestingly, a larger architecture delivers larger improvements with more efficient training, more self-supervised losses, and more patch-based augmentations (Fig. 3, $+5 \\%$ Top-1 accuracy with original training scheme, $+ 1 0 \\%$ accuracy with new one). ",
+        "bbox": [
+            176,
+            410,
+            823,
+            452
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Layer normalization. Large architectures are more difficult to train efficiently. Early works on context prediction with patches used batch normalization (Ioffe & Szegedy, 2015; Doersch et al., 2015) to speed training. However, with CPC we find that batch normalization actually harms downstream performance of large models. We hypothesize that batch normalization allows large models to find a trivial solution to CPC: it introduces a dependency between patches (through the batch statistics) that can be exploited to bypass the constraints on the receptive field. We find that we can reclaim much of batch normalization’s training efficiency using layer normalization (Ba et al., 2016), which leads to a small gain for the smaller architecture $+ 1 \\%$ accuracy over equivalent architectures that use neither normalization) and a larger gain for the larger architecture $( + 2 . 5 \\%$ accuracy). ",
+        "bbox": [
+            174,
+            474,
+            825,
+            599
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Prediction lengths and directions. Larger architectures also run a greater risk of overfitting. We address this by asking more from the network: specifically, whereas van den Oord et al. (2018) predicted each patch using only context from spatially beneath it, we repeatedly predict the patch using context from above, to the right, and to the left, resulting in up to four times as many prediction tasks. Combining top-to-bottom with bottom-to-top helps both model architectures $42 \\%$ accuracy for both), but using all 4 spatial directions only benefits the larger model (an additional $+ 1 . 5 \\%$ for the larger model, ${ \\bf - 1 \\% }$ for the smaller), consistent with the idea that model capacity and amount of supervision must go hand-in-hand. We also hypothesized that prediction “length”—i.e. offset between the predicted patch and the aggregated context—might affect performance, as distant patches might lie on distinct objects, encouraging the network to memorize images. Indeed, limiting the range of the prediction length $k$ to $\\{ 2 , 3 \\}$ performed better than $\\{ 2 , \\ldots , 5 \\}$ as was used originally $+ 1 \\%$ for the larger model). ",
+        "bbox": [
+            173,
+            622,
+            825,
+            790
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Patch-based augmentation. If the network can solve CPC using low-level patterns (e.g. straight lines continuing between patches, chromatic aberration), it need not learn semantically meaningful content. Augmenting the low-level variability across patches can remove such low level cues. The original CPC model spatially jitters individual patches independently. We further this logic by adopting the ‘color dropping’ method of Doersch et al. (2015), which randomly drops two of the three color channels in each patch, and find it to delivers systematic gains $( + 1 \\%$ for the small model, $+3 \\%$ for the larger one). We also randomly flip patches horizontally, but find it only benefits the smaller model $( + 1 \\% )$ . ",
+        "bbox": [
+            174,
+            811,
+            825,
+            924
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Combined. Cumulatively, these fairly straightforward implementation changes lead to a substantial improvement to the original CPC model $6 5 . 9 \\%$ Top-1 accuracy, a $17 \\%$ improvement), making it competitive with recent approaches and outperforming prior methods (see table 1). Interestingly, if we train the same patch-based architecture from scratch in a fully supervised manner, we obtain $6 6 . 4 \\%$ Top-1 accuracy (with batch normalization; $6 2 . 5 \\%$ without), suggesting that CPC is now nearly saturating the architecture’s representational power despite not using labels. These results illustrate how architecture and data have an outsized impact on the linear classification performance of self-supervised representations, and are interesting to compare with with previous results. For example, in AMDIM, different settings of data augmentation alone can result in a nearly $10 \\%$ absolute increase in performance on ImageNet linear classification. ",
+        "bbox": [
+            173,
+            103,
+            825,
+            242
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.2 EFFICIENT IMAGE CLASSIFICATION ",
+        "text_level": 1,
+        "bbox": [
+            178,
+            262,
+            455,
+            276
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "toWe now turn to our original question of whether CPC can enable data-efficient image recognition. We start by evaluating the performance of purely-supervised networks as the size of the labeled dataset $\\mathbb { D } _ { l }$ varies from $1 \\%$ to $100 \\%$ of ImageNet, training separate classifiers on each subset. We found that a ResNet-152 to works best across all data-regimes (see Appendix). Despite our efforts to tune the supervised model for low-data classification (including network depth, regularization, and optimization parameters), the accuracy of the best model only reaches $4 4 . 1 \\%$ Top-5 accuracy when trained on $1 \\%$ of the dataset (compared to $9 3 . 9 \\%$ when trained on the entire dataset, see Fig. 1, red). ",
+        "bbox": [
+            174,
+            287,
+            825,
+            386
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Contrastive Predictive Coding. We now address our central question of whether CPC enables data-efficient learning. We follow the same paradigm as for the supervised baseline (training and evaluating a separate classifier for each size subset), stacking a neural network classifier on top of the CPC latents $\\begin{array} { r l r } { z } & { { } = } & { f _ { \\theta } ( { \\pmb x } ) } \\end{array}$ rather than the raw image pixels $_ { \\textbf { \\em x } }$ (see section 2.2, efficient classification, and Appendix). This representation, which we selected for its improved linear classification performance (CPC v2 in Fig. 3), leads to a significant increase in data-efficiency compared to purely supervised networks (Fig. 1, blue curve). This classifier yields $7 2 . 9 \\%$ Top-5 accuracy with only $1 \\%$ of the labels, a $2 9 \\%$ absolute improvement $65 \\%$ relative) over purely-supervised methods. Surprisingly, when given the entire dataset, this classifier reaches $8 0 . 6 \\% / 9 5 . 2 \\%$ Top1/Top5 accuracy, surpassing our supervised baseline (ResNet-152: $7 8 . 0 \\% / 9 3 . 9 \\%$ accuracy) and published results (ResNet-200: $7 9 . 9 \\% / 9 5 . 2 \\%$ , He et al. (2016b)). We find similar results in all other data-regimes we considered (see Fig. 1). ",
+        "bbox": [
+            174,
+            404,
+            483,
+            750
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "How important are the model specifications described in Section 4.1 for low-data classification? We hypothesized that predictable representations might enable data-efficient classifi",
+        "bbox": [
+            174,
+            757,
+            482,
+            813
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/106f2252ad377e16a329cfb21360459a72fdc1d09e4f745b26572da1cf6d5d14.jpg",
+        "image_caption": [
+            "Figure 4: Relationship between linear classification accuracy and low-data classification, for different variants of the CPC model. Left: CPC variants with the same architecture but different training protocols. Orange, green, and blue dots correspond to CPC models making predictions in 1, 2, and 4 spatial directions respectively. Within a color group, different models correspond to other implementation details (e.g. layer norm and patch augmentation, and combinations thereof). "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            503,
+            409,
+            810,
+            657
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "cation, and therefore expect that increasing the amount of ‘predictability’ in the representation should also increase its ability to learn from small amounts of data. Fig. 4 shows evidence for this by ablating model parameters and comparing linear classification performance against low-data classification. Consistent with our hypothesis, increasing the number of spatial directions in the CPC prediction task (which increased linear classification performance) systematically increases low-data classification performance (Fig. 4, left, different color groups). As a control, we asked if all modifications that improve linear classification also improve low-data classification. We did not find evidence in favor of this: improvements in linear classification as a result of changing other model parameters (patch-based data-augmentation, layer normalization, and combinations thereof) seem uncorrelated to performance in other tasks (Fig. 4, left, within green group: $R ^ { 2 } = 0 . 1 7 , p = 0 . 3 6$ ). Different architectural specifications also produced different changes in both tasks (Fig. 4, right). Whereas increasing the depth of the encoding network greatly improves both metrics, increasing the network width (and therefore the number of features used for linear classification) only improves linear classification accuracy. ",
+        "bbox": [
+            174,
+            813,
+            825,
+            924
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/e969618e28fc2ffa8c76067cea0310a604dd1bb350cd5a5534dd7265b81333a6.jpg",
+        "table_caption": [
+            "Table 2: ResNet classifier $h _ { \\psi }$ trained with $1 \\%$ or $10 \\%$ of labels. Comparison to other methods for semi-supervised learning using $1 \\%$ or $10 \\%$ of labeled data. Representation learning methods use a classifier to discriminate an unsupervised representation, and optimize it solely for the supervised objective on labeled data. Label-propagation methods on the other hand further constrain the classifier with smoothness and entropy criteria on unlabeled data, making the additional assumption that all training images fit into a single (unknown) testing category. $\\dagger$ denotes methods implemented in this work, fixed and fine-tuned denote whether the feature extractor is allowed to accommodate the supervised objective. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Labeled data 1% 10% 100% Method Top-5 accuracy</td></tr><tr><td></td></tr><tr><td>Supervised baseline 44.1 82.1 93.9 Methods using label-propagation:</td></tr><tr><td>Pseudolabeling (Zhai et al., 2019) 51.6 82.4 VAT + Entropy Minimization (Zhai et al., 2019) 47.0 83.4 Unsup. Data Augmentation (Xie et al., 2019) 88.5</td></tr><tr><td>Rotation+ VAT+Ent.Min. (Zhai et al.,2019) 91.2 95.0 =</td></tr><tr><td>Methods using representation learning only:</td></tr><tr><td>Instance Discrimination (Wu et al., 2018) 39.2 77.4</td></tr><tr><td>Rotation (Zhai et al., 2019) 57.5 86.4</td></tr><tr><td>+ResNet trained on BigBiGAN (fixed) 55.2 78.8 87.0</td></tr><tr><td>+ResNet trained on AMDIM (fixed) 67.4 85.8 92.2</td></tr><tr><td>+ResNet trained on CPC v2 (fixed) 72.3 89.1 94.4 +ResNet trained on CPC v2 (fine-tuned) 72.9 89.5 95.2</td></tr></table>",
+        "bbox": [
+            250,
+            228,
+            745,
+            487
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            531,
+            825,
+            614
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Other unsupervised representations. How well does the CPC representation compare to other representations that have been learned in an unsupervised manner? If predictable representations are uniquely suited for efficient classification, we would expect other methods within this family to perform similarly, and other model classes less so. Table 2 compares our best model with other works on efficient recognition. We consider three objectives from different model classes: self-supervised learning with rotation prediction (Zhai et al., 2019), large-scale adversarial feature learning (BigBiGAN, Donahue & Simonyan, 2019), and another contrastive prediction objective (AMDIM, Bachman et al., 2019). Zhai et al. (2019) evaluate the low-data classification performance of representations learned with rotation prediction using a similar paradigm and architecture (ResNet-152), hence we report their results directly. Given $1 \\%$ of ImageNet, their method achieves $5 7 . 5 \\%$ Top-5 accuracy, consistently with the reduced accuracy of a linear classifier ( $5 5 . 4 \\%$ vs $6 5 . 9 \\%$ for CPC)1. ",
+        "bbox": [
+            173,
+            631,
+            825,
+            796
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Because BigBiGAN and AMDIM achieve stronger linear classification accuracy than rotation prediction $6 1 . 3 \\%$ and $6 8 . 1 \\%$ Top-1 accuracy, respectively), we might expect better performance on efficient classification as well. Since their authors do not report results on efficient classification we evaluated these representations using the same paradigm we used for evaluating CPC, stacking a ResNet classifier on top of the $7 \\times 7 \\times 8 1 9 2$ latents of the BigBiGAN and the $7 \\times 7 \\times 2 5 6 0$ grid of feature vectors of AMDIM. We found fine-tuned representations to yield only marginal gains over fixed ones $7 2 . 9 \\%$ compared to $7 2 . 3 \\%$ Top-5 accuracy given $1 \\%$ of labels), hence for simplicity we evaluate BigBiGAN and AMDIM on this task while keeping them fixed. We re-tune the hyper-parameters of the classifier (including optimization, regularization, etc.) for each of these representations separately. Although these methods achieve similar performance in terms of linear classification, we find them to achieve very different results in efficient classification. Given $1 \\%$ of ImageNet, classifiers trained on top of BigBiGAN achieve $5 5 . 2 \\%$ Top-5 accuracy, similarly to rotation prediction $( 5 7 . 5 \\% )$ , despite its increased linear classification accuracy $( + 6 \\%$ relative to rotation prediction). In contrast, AMDIM (which also belongs to the family of contrastive prediction methods) achieves $6 7 . 4 \\%$ on this same task. Again, its increased linear classification accuracy did not entail an increase in data-efficiency. Nevertheless, in line with our initial hypothesis, we find that contrastive prediction methods such as CPC surpass other approaches in our efficient classification experiments, and that linear classification performance is not perfectly correlated with these results. ",
+        "bbox": [
+            173,
+            803,
+            825,
+            888
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            103,
+            825,
+            270
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Other semi-supervised techniques A separate class of methods for low-data classification attempts to propagate the knowledge extracted from the subset of labeled examples to unlabeled examples while being invariant to augmentation or other perturbations. These methods generally depend on the quality of the classifier’s predictions, and as such tend to fare well when given intermediate amounts of data. Although not sufficient in themselves (Unsupervised Data Augmentation (Xie et al., 2019), Virtual Adversarial Training (Miyato et al., 2018) and entropy minimization (Grandvalet & Bengio, 2005), and pseudo-labeling (Lee, 2013) achieve $8 5 . 8 \\%$ , $8 3 . 4 \\%$ , and $8 2 . 4 \\%$ Top-5 accuracy with $10 \\%$ of labels, compared to our $8 9 . 4 \\%$ ) when combined with representation learning (e.g. rotation prediction Zhai et al., 2019) they can provide considerable gains $9 1 . 2 \\%$ Top5 accuracy). It is therefore surprising that CPC representations alone can enable accuracy that is comparable to that of these methods, and investigating to what extent they can be combined would be an interesting topic of future work. ",
+        "bbox": [
+            174,
+            290,
+            823,
+            455
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4.3 TRANSFER LEARNING: IMAGE DETECTION ON PASCAL VOC 2007 ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            477,
+            681,
+            491
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We next investigate transfer performance on object detection on the PASCAL-2007 dataset, which reflects the practical scenario where a representation must be trained on a dataset with different statistics than the dataset of interest. This dataset also tests the efficiency of the representation as it only contains 5011 labeled images to train from. In this setting, we replaced the neural network classifier $h _ { \\psi }$ used previously with a Faster-RCNN (Ren et al., 2015) image detection architecture, and use the pre-trained feature extractor on ImageNet. As before, we first trained the Faster-RCNN model while keeping the feature extractor fixed, then fine-tuned the entire model end-to-end. Table 3 displays our results compared to other methods. Most competing methods, which optimize a single unsupervised objective on ImageNet before fine-tuning on PASCAL detection, attain around $65 \\%$ mean average precision. Leveraging larger unlabeled datasets increases their performance up to $6 7 . 8 \\%$ (Caron et al., 2019). Combining multiple forms of self-supervision enables them to reach $7 0 . 5 \\%$ (Doersch & Zisserman, 2017). The proposed method, which learns only from ImageNet data using a single unsupervised objective, reaches $7 0 . 6 \\%$ when equipped with a ResNet-101 feature extractor $f _ { \\theta }$ (as for most competing methods (Doersch & Zisserman, 2017) but not all (Caron et al., 2018; 2019). Equipped with the more powerful ResNet-161 feature extractor $f _ { \\theta }$ , our method reaches $7 2 . 7 \\%$ . Importantly, this result is only $2 \\%$ short of the performance attained by purely supervised transfer learning, which we obtain by using all ImageNet labels before transferring to PASCAL. ",
+        "bbox": [
+            174,
+            505,
+            825,
+            741
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5 DISCUSSION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            765,
+            310,
+            780
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We asked whether CPC could enable data-efficient image recognition, and found that it indeed greatly improves the accuracy of classifiers and object detectors when given small amounts of labeled data. Surprisingly, CPC even improves results given ImageNet-scale labels. Our results show that there is still room for improvement using relatively straightforward changes such as augmentation, optimization, and network architecture. Furthermore, we found that the standard method for evaluating unsupervised representations—linear classification—is only partially predictive of efficient recognition performance, suggesting that further research should focus on efficient recognition as a standalone benchmark. Overall, these results open the door toward research on problems where data is naturally limited, e.g. medical imaging or robotics. ",
+        "bbox": [
+            173,
+            799,
+            825,
+            924
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/d005a0a972800a539ffdecef950a4659796c2a8300a3ab9b860336449e53c88e.jpg",
+        "table_caption": [
+            "Table 3: Faster-RCNN $h _ { \\psi }$ trained with $100 \\%$ of PASCAL labels. Comparison of PASCAL 2007 image detection accuracy to other transfer methods. The supervised baseline learns from the entire labeled ImageNet dataset and fine-tunes for PASCAL detection. The second class of methods learns from the same unlabeled images before transferring. All of these methods pre-train on the ImageNet dataset, except for DeeperCluster which learns from the larger, but uncurated, YFCC100M dataset (Thomee et al., 2015). All results are reported in terms of mean average precision (mAP). $\\dagger$ denotes methods implemented in this work. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>mAP</td></tr><tr><td>Transfer from labeled data: Supervised - ResNet-152</td><td>74.7</td></tr><tr><td>Transfer from unlabeled data: Exemplar (Ex) (Dosovitskiy et al., 2014) Motion Segmentation (MS) (Pathak et al.,2016)</td><td>60.9</td></tr><tr><td>Colorization (Col) (Zhang et al.,2016) Relative Position (RP) (Doersch et al.,2015)</td><td>61.1 65.5</td></tr><tr><td>Combination of Ex + MS + Col +RP (Doersch &amp; Zisserman,2017)</td><td>66.8 70.5</td></tr><tr><td>Instance Discrimination (Wu et al., 2018)</td><td>65.4</td></tr><tr><td>Deep Cluster (Caron et al., 2018) Deeper Cluster (Caron et al., 2019)</td><td>65.9</td></tr></table>",
+        "bbox": [
+            240,
+            214,
+            758,
+            457
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Furthermore, images are far from the only domain where unsupervised representation learning is important: for example, unsupervised learning is already a critical step in language (Mikolov et al., 2013; Devlin et al., 2018), and shows promise in domains like audio (van den Oord et al., 2018; Arandjelovic & Zisserman, 2018; 2017), video (Jing & Tian, 2018; Misra et al., 2016), and robotic manipulation (Pinto & Gupta, 2016; Pinto et al., 2016; Sermanet et al., 2018). Currently much self-supervised work builds upon tasks tailored for a specific domain (often images), which may not be easily adapted to other domains. Contrastive prediction methods, including the techniques suggested in this paper, are task agnostic and could therefore serve as a unifying framework for integrating these tasks and modalities. This generality is particularly useful given that many realworld environments are inherently multimodal, e.g. robotic environments which can have vision, audio, touch, proprioception, action, and more over long temporal sequences. Given the importance of increasing the amounts of self-supervision (via additional directions of prediction), integrating these modalities and tasks could lead to unsupervised representations which rival the efficiency and effectiveness of biological ones. ",
+        "bbox": [
+            173,
+            486,
+            825,
+            680
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "REFERENCES ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            702,
+            285,
+            717
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Pulkit Agrawal, Joao Carreira, and Jitendra Malik. Learning to see by moving. In ICCV, 2015. ",
+        "bbox": [
+            171,
+            724,
+            794,
+            739
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Relja Arandjelovic and Andrew Zisserman. Look, listen and learn. In Proceedings of the IEEE International Conference on Computer Vision, pp. 609–617, 2017. ",
+        "bbox": [
+            173,
+            747,
+            823,
+            776
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Relja Arandjelovic and Andrew Zisserman. Objects that sound. In Proceedings of the European Conference on Computer Vision (ECCV), pp. 435–451, 2018. ",
+        "bbox": [
+            173,
+            784,
+            823,
+            813
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Lei Jimmy Ba, Ryan Kiros, and Geoffrey E. Hinton. Layer normalization. CoRR, abs/1607.06450, 2016. ",
+        "bbox": [
+            173,
+            820,
+            823,
+            849
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Philip Bachman, R Devon Hjelm, and William Buchwalter. Learning representations by maximizing mutual information across views. arXiv preprint arXiv:1906.00910, 2019. ",
+        "bbox": [
+            173,
+            858,
+            823,
+            887
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "H.B. Barlow. Unsupervised learning. Neural Computation, 1(3):295–311, 1989. doi: 10.1162/neco. 1989.1.3.295. ",
+        "bbox": [
+            174,
+            895,
+            821,
+            922
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Mathilde Caron, Piotr Bojanowski, Armand Joulin, and Matthijs Douze. Deep clustering for unsupervised learning of visual features. In The European Conference on Computer Vision (ECCV), September 2018. ",
+        "bbox": [
+            173,
+            103,
+            823,
+            146
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Mathilde Caron, Piotr Bojanowski, Julien Mairal, and Armand Joulin. Leveraging large-scale uncurated data for unsupervised pre-training of visual features. 2019. ",
+        "bbox": [
+            173,
+            156,
+            820,
+            185
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. BERT: pre-training of deep bidirectional transformers for language understanding. CoRR, abs/1810.04805, 2018. ",
+        "bbox": [
+            173,
+            195,
+            821,
+            224
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Carl Doersch and Andrew Zisserman. Multi-task self-supervised visual learning. In Proceedings of the IEEE International Conference on Computer Vision, pp. 2051–2060, 2017. ",
+        "bbox": [
+            174,
+            234,
+            823,
+            265
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Carl Doersch, Abhinav Gupta, and Alexei A Efros. Unsupervised visual representation learning by context prediction. In Proceedings of the IEEE International Conference on Computer Vision, pp. 1422–1430, 2015. ",
+        "bbox": [
+            173,
+            273,
+            826,
+            318
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Jeff Donahue and Karen Simonyan. Large scale adversarial representation learning. arXiv preprint arXiv:1907.02544, 2019. ",
+        "bbox": [
+            169,
+            327,
+            823,
+            357
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Jeff Donahue, Philipp Krahenb ¨ uhl, and Trevor Darrell. Adversarial feature learning. ¨ arXiv preprint arXiv:1605.09782, 2016. ",
+        "bbox": [
+            171,
+            367,
+            823,
+            396
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Alexey Dosovitskiy, Jost Tobias Springenberg, Martin Riedmiller, and Thomas Brox. Discriminative unsupervised feature learning with convolutional neural networks. In Advances in neural information processing systems, pp. 766–774, 2014. ",
+        "bbox": [
+            174,
+            406,
+            825,
+            450
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Mark Everingham, Luc Van Gool, Christopher KI Williams, John Winn, and Andrew Zisserman. The pascal visual object classes challenge 2007 (voc2007) results. 2007. ",
+        "bbox": [
+            178,
+            459,
+            823,
+            489
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Spyros Gidaris, Praveer Singh, and Nikos Komodakis. Unsupervised representation learning by predicting image rotations. arXiv preprint arXiv:1803.07728, 2018. ",
+        "bbox": [
+            174,
+            498,
+            823,
+            529
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Yves Grandvalet and Yoshua Bengio. Semi-supervised learning by entropy minimization. In Advances in neural information processing systems, pp. 529–536, 2005. ",
+        "bbox": [
+            171,
+            539,
+            823,
+            568
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Michael Gutmann and Aapo Hyvarinen. Noise-contrastive estimation: A new estimation principle ¨ for unnormalized statistical models. In Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, pp. 297–304, 2010. ",
+        "bbox": [
+            176,
+            577,
+            825,
+            621
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 770–778, 2016a. ",
+        "bbox": [
+            174,
+            631,
+            825,
+            674
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Identity mappings in deep residual networks. In European conference on computer vision, pp. 630–645. Springer, 2016b. ",
+        "bbox": [
+            173,
+            684,
+            825,
+            714
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "G.E. Hinton, T.J. Sejnowski, H.H.M.I.C.N.L.T.J. Sejnowski, and T.A. Poggio. Unsupervised Learning: Foundations of Neural Computation. A Bradford Book. MIT Press, 1999. ISBN 9780262581684. ",
+        "bbox": [
+            173,
+            723,
+            825,
+            766
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Olivier J. Henaff, Robbe L. T. Goris, and Eero P. Simoncelli. Perceptual straightening of natural ´ videos. Nature Neuroscience, Apr 2019. ",
+        "bbox": [
+            171,
+            776,
+            825,
+            806
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Sergey Ioffe and Christian Szegedy. Batch normalization: Accelerating deep network training by reducing internal covariate shift. arXiv preprint arXiv:1502.03167, 2015. ",
+        "bbox": [
+            171,
+            816,
+            823,
+            845
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Dinesh Jayaraman and Kristen Grauman. Learning image representations tied to ego-motion. In ICCV, 2015. ",
+        "bbox": [
+            171,
+            856,
+            823,
+            885
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Longlong Jing and Yingli Tian. Self-supervised spatiotemporal feature learning by video geometric transformations. arXiv preprint arXiv:1811.11387, 2018. ",
+        "bbox": [
+            173,
+            895,
+            821,
+            924
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Durk P Kingma, Shakir Mohamed, Danilo Jimenez Rezende, and Max Welling. Semi-supervised learning with deep generative models. In Advances in neural information processing systems, pp. 3581–3589, 2014. ",
+        "bbox": [
+            173,
+            103,
+            823,
+            146
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Alexander Kolesnikov, Xiaohua Zhai, and Lucas Beyer. Revisiting self-supervised visual representation learning. CoRR, abs/1901.09005, 2019. URL http://arxiv.org/abs/1901.09005. ",
+        "bbox": [
+            173,
+            155,
+            823,
+            184
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Brenden M Lake, Ruslan Salakhutdinov, and Joshua B Tenenbaum. Human-level concept learning through probabilistic program induction. Science, 350(6266):1332–1338, 2015. ",
+        "bbox": [
+            173,
+            193,
+            823,
+            222
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Barbara Landau, Linda B Smith, and Susan S Jones. The importance of shape in early lexical learning. Cognitive development, 3(3):299–321, 1988. ",
+        "bbox": [
+            171,
+            231,
+            823,
+            261
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Gustav Larsson, Michael Maire, and Gregory Shakhnarovich. Colorization as a proxy task for visual understanding. In CVPR, pp. 6874–6883, 2017. ",
+        "bbox": [
+            174,
+            268,
+            820,
+            299
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Yann LeCun, Yoshua Bengio, and Geoffrey Hinton. Deep learning. nature, 521(7553):436, 2015. ",
+        "bbox": [
+            173,
+            306,
+            810,
+            323
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Dong-Hyun Lee. Pseudo-label: The simple and efficient semi-supervised learning method for deep neural networks. In Workshop on Challenges in Representation Learning, ICML, volume 3, pp. 2, 2013. ",
+        "bbox": [
+            173,
+            332,
+            825,
+            375
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Yin Li, Manohar Paluri, James M Rehg, and Piotr Dollar. Unsupervised learning of edges. In ´ CVPR, 2016. ",
+        "bbox": [
+            174,
+            382,
+            821,
+            412
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Ellen M Markman. Categorization and naming in children: Problems of induction. mit Press, 1989. ",
+        "bbox": [
+            171,
+            421,
+            821,
+            438
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg S Corrado, and Jeff Dean. Distributed representations of words and phrases and their compositionality. In C. J. C. Burges, L. Bottou, M. Welling, Z. Ghahramani, and K. Q. Weinberger (eds.), Advances in Neural Information Processing Systems 26, pp. 3111–3119. Curran Associates, Inc., 2013. ",
+        "bbox": [
+            173,
+            444,
+            825,
+            502
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Ishan Misra, C Lawrence Zitnick, and Martial Hebert. Shuffle and learn: unsupervised learning using temporal order verification. In ECCV, 2016. ",
+        "bbox": [
+            174,
+            511,
+            823,
+            540
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Takeru Miyato, Shin-ichi Maeda, Shin Ishii, and Masanori Koyama. Virtual adversarial training: a regularization method for supervised and semi-supervised learning. IEEE transactions on pattern analysis and machine intelligence, 2018. ",
+        "bbox": [
+            173,
+            549,
+            825,
+            592
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Andriy Mnih and Koray Kavukcuoglu. Learning word embeddings efficiently with noise-contrastive estimation. In Advances in neural information processing systems, pp. 2265–2273, 2013. ",
+        "bbox": [
+            173,
+            601,
+            821,
+            631
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Mehdi Noroozi and Paolo Favaro. Unsupervised learning of visual representations by solving jigsaw puzzles. In European Conference on Computer Vision, pp. 69–84. Springer, 2016. ",
+        "bbox": [
+            173,
+            638,
+            821,
+            669
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Stephanie E Palmer, Olivier Marre, Michael J Berry, and William Bialek. Predictive information in a sensory population. Proceedings of the National Academy of Sciences, 112(22):6908–6913, 2015. ",
+        "bbox": [
+            178,
+            676,
+            823,
+            719
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Deepak Pathak, Ross Girshick, Piotr Dollar, Trevor Darrell, and Bharath Hariharan. Learning fea-´ tures by watching objects move. arXiv preprint arXiv:1612.06370, 2016. ",
+        "bbox": [
+            171,
+            728,
+            823,
+            758
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Lerrel Pinto and Abhinav Gupta. Supersizing self-supervision: Learning to grasp from 50k tries and 700 robot hours. In ICRA, 2016. ",
+        "bbox": [
+            171,
+            767,
+            825,
+            796
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Lerrel Pinto, James Davidson, and Abhinav Gupta. Supervision via competition: Robot adversaries for learning tasks. arXiv preprint arXiv:1610.01685, 2016. ",
+        "bbox": [
+            171,
+            805,
+            823,
+            834
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Rajesh PN Rao and Dana H Ballard. Predictive coding in the visual cortex: a functional interpretation of some extra-classical receptive-field effects. Nature neuroscience, 2(1):79, 1999. ",
+        "bbox": [
+            171,
+            843,
+            823,
+            872
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Shaoqing Ren, Kaiming He, Ross Girshick, and Jian Sun. Faster r-cnn: Towards real-time object detection with region proposal networks. In Advances in neural information processing systems, pp. 91–99, 2015. ",
+        "bbox": [
+            174,
+            881,
+            825,
+            924
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang, Andrej Karpathy, Aditya Khosla, Michael Bernstein, et al. Imagenet large scale visual recognition challenge. International journal of computer vision, 115(3):211–252, 2015. ",
+        "bbox": [
+            178,
+            103,
+            821,
+            146
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Pierre Sermanet, Corey Lynch, Yevgen Chebotar, Jasmine Hsu, Eric Jang, Stefan Schaal, Sergey Levine, and Google Brain. Time-contrastive networks: Self-supervised learning from video. In 2018 IEEE International Conference on Robotics and Automation (ICRA), pp. 1134–1141. IEEE, 2018. ",
+        "bbox": [
+            174,
+            155,
+            825,
+            210
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov. Dropout: a simple way to prevent neural networks from overfitting. The journal of machine learning research, 15(1):1929–1958, 2014. ",
+        "bbox": [
+            176,
+            219,
+            823,
+            263
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Christian Szegedy, Wei Liu, Yangqing Jia, Pierre Sermanet, Scott E. Reed, Dragomir Anguelov, Dumitru Erhan, Vincent Vanhoucke, and Andrew Rabinovich. Going deeper with convolutions. CoRR, abs/1409.4842, 2014. URL http://arxiv.org/abs/1409.4842. ",
+        "bbox": [
+            173,
+            271,
+            825,
+            315
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Bart Thomee, David A Shamma, Gerald Friedland, Benjamin Elizalde, Karl Ni, Douglas Poland, Damian Borth, and Li-Jia Li. Yfcc100m: The new data in multimedia research. arXiv preprint arXiv:1503.01817, 2015. ",
+        "bbox": [
+            174,
+            323,
+            823,
+            366
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Yonglong Tian, Dilip Krishnan, and Phillip Isola. Contrastive multiview coding. arXiv preprint arXiv:1906.05849, 2019. ",
+        "bbox": [
+            173,
+            375,
+            823,
+            404
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Aaron van den Oord, Yazhe Li, and Oriol Vinyals. Representation learning with contrastive predictive coding. arXiv preprint arXiv:1807.03748, 2018. ",
+        "bbox": [
+            173,
+            412,
+            823,
+            441
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Xiaolong Wang and Abhinav Gupta. Unsupervised learning of visual representations using videos. In ICCV, 2015. ",
+        "bbox": [
+            173,
+            450,
+            823,
+            479
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Zhirong Wu, Yuanjun Xiong, Stella X Yu, and Dahua Lin. Unsupervised feature learning via nonparametric instance discrimination. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 3733–3742, 2018. ",
+        "bbox": [
+            173,
+            488,
+            823,
+            531
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Qizhe Xie, Zihang Dai, Eduard Hovy, Minh-Thang Luong, and Quoc V. Le. Unsupervised Data Augmentation. arXiv e-prints, art. arXiv:1904.12848, Apr 2019. ",
+        "bbox": [
+            169,
+            540,
+            823,
+            569
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Amir R Zamir, Tilman Wekel, Pulkit Agrawal, Colin Wei, Jitendra Malik, and Silvio Savarese. Generic 3D representation via pose estimation and matching. In ECCV, 2016. ",
+        "bbox": [
+            169,
+            577,
+            821,
+            607
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Xiaohua Zhai, Avital Oliver, Alexander Kolesnikov, and Lucas Beyer. $S ^ { 4 } L$ : Self-supervised semisupervised learning. arXiv preprint arXiv:1905.03670, 2019. ",
+        "bbox": [
+            173,
+            614,
+            821,
+            645
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Richard Zhang, Phillip Isola, and Alexei A Efros. Colorful image colorization. In European conference on computer vision, pp. 649–666. Springer, 2016. ",
+        "bbox": [
+            173,
+            652,
+            821,
+            683
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Xiaojin Zhu and Zoubin Ghahramani. Learning from labeled and unlabeled data with label propagation. In Technical Report CMU-CALD-02-107, Carnegie Mellon University, 2002. ",
+        "bbox": [
+            171,
+            690,
+            821,
+            720
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Chengxu Zhuang, Alex Lin Zhai, and Daniel Yamins. Local aggregation for unsupervised learning of visual embeddings. arXiv preprint arXiv:1903.12355, 2019. ",
+        "bbox": [
+            173,
+            728,
+            823,
+            758
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "A APPENDIX ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            103,
+            299,
+            117
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "A.1 ADDITIONAL RESULTS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            133,
+            377,
+            148
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "table",
+        "img_path": "images/cd16abc0799fc70d1a375836e8cc04ff4651be0d7ba68507f20886a5866fd0b3.jpg",
+        "table_caption": [
+            "Table 4: Data efficient classification results with Top-1 accuracy. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Labeled data Method</td><td>1%</td><td>2%</td><td>5%</td><td>10% Top-1 accuracy</td><td>20%</td><td>50%</td><td>100%</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Supervised trained on pixels</td><td>23.1</td><td>34.8</td><td>50.2</td><td>60.0</td><td>67.6</td><td>74.4</td><td>78.0</td></tr><tr><td>ReseNet trained on CPC v2 (fine-tuned)</td><td>46.3</td><td>54.7</td><td>64.1</td><td>69.7</td><td>73.0</td><td>77.3</td><td>80.6</td></tr></table>",
+        "bbox": [
+            184,
+            193,
+            815,
+            267
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "table",
+        "img_path": "images/ef57c53b71083a6069724c7b7ef7e00273991c3de17438cac7824c7e459eff57.jpg",
+        "table_caption": [
+            "Table 5: Data efficient classification results with Top-5 accuracy (data in Fig. 1). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Labeled data Method</td><td>1%</td><td>2%</td><td>5%</td><td>10% Top-5 accuracy</td><td>20%</td><td>50%</td><td>100%</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Supervised trained on pixels</td><td>44.1</td><td>59.9</td><td>75.2</td><td>82.1</td><td>87.9</td><td>91.8</td><td>93.8</td></tr><tr><td>ReseNet trained on CPC v2 (fine-tuned)</td><td>72.9</td><td>79.6</td><td>86.1</td><td>89.5</td><td>91.4</td><td>93.6</td><td>95.2</td></tr></table>",
+        "bbox": [
+            184,
+            321,
+            815,
+            397
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "A.2 INFONCE IMPLEMENTATION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            429,
+            418,
+            444
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "For completeness, we provide pseudo-code for the main calculations involved in the InfoNCE objective, loosely modeled after Tensorflow operations. We suppose we have just calculated a set of latents $z _ { i , j } = f _ { \\theta } ( \\pmb { x } _ { i , j } )$ for $i , j \\in \\{ 1 , . . . , 7 \\}$ , each one being e.g. a 4096-dimensional vector. Assuming we do so for a batch of $B$ images $\\{ { \\pmb x } \\}$ , the set of latents is a tensor of size $B \\times 7 \\times 7 \\times 4 0 9 6$ . ",
+        "bbox": [
+            173,
+            455,
+            825,
+            512
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "def pixelCNN(latents): # latents: [B, H, W, D] cres $=$ latents cres_dim $=$ cres.shape[-1] for in range(5): c $=$ Conv2D(output_channels $= 2 5 6$ , kernel_shape $=$ (1, 1))(cres) c = ReLU(c) c = Conv2D(output_channels $= 2 5 6$ , kernel_shape $=$ (1, 3))(c) c = Pad(c, [[0, 0], [1, 0], [0, 0], [0, 0]]) c = Conv2D(output_channels $= 2 5 6$ , kernel_shape $=$ (2, 1), type $= ^ { \\parallel }$ VALID')(c) c $=$ ReLU(c) c $=$ Conv2D(output_channels $=$ cres_dim, kernel_shape $=$ (1, 1))(c) cres $=$ cres + c cres $=$ ReLU(cres) return cres ",
+        "bbox": [
+            176,
+            119,
+            663,
+            398
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "A.3 LINEAR CLASSIFICATION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            421,
+            392,
+            435
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "• Model architecture: Having extracted $8 0 \\mathrm { x } 8 0$ patches with a stride of $3 2 \\mathrm { x } 3 2 $ from a $2 4 0 \\times 2 4 0$ shaped input image, we end up with a grid of 6x6 features (each of which is obtained from our ResNet-161 architecture). This gives us a [6,6,4096] tensor for the image. We then use a Batch-Normalization layer to normalize the features (without scale parameter) followed by a 1x1 convolution mapping each feature in the grid to the 1000 logits for ImageNet classification. We then spatially-mean-pool these logits to end up with the final log probabilities for the linear classification.   \n• We use the Inception preprocessing (Szegedy et al., 2014) to extract $2 4 0 \\times 2 4 0$ crops from the raw image. The image is divided into subcrops as per CPC data-preprocessing used for CPC pre-training.   \n• Optimization details: We use Adam Optimizer with a learning rate of 5e-4. We train the model on a batch size of 512 images with 32 images per core spread over 16 workers. ",
+        "bbox": [
+            217,
+            443,
+            826,
+            619
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "A.4 EFFICIENT CLASSIFICATION: PURELY SUPERVISED ",
+        "bbox": [
+            174,
+            637,
+            565,
+            650
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "In order to find the best model within this class, we vary the following hyperparameters: ",
+        "bbox": [
+            171,
+            661,
+            750,
+            676
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "• Model architecture: We investigate using ResNet-50, ResNet-101, and ResNet-152 model architectures, all of them using the $\\mathbf { \\hat { v } } _ { \\mathbf { \\Delta } } 2 \\mathbf { \\hat { \\mu } }$ variant (He et al., 2016b), and find larger architecture to perform better, even when given smaller amounts of data. We insert a DropOut layer before the final linear classification layer (Srivastava et al., 2014). • Data pre-processing: We use the Inception pre-processing pipeline (Szegedy et al., 2014). • Optimization details: We vary the learning rate in $\\{ 0 . 0 5 , 0 . 1 , 0 . 2 \\}$ , the weight decay logarithmically from $1 0 ^ { - 5 }$ to $1 0 ^ { - 2 }$ , the DropOut linearly from 0 to 1, and the batch size per worker in $\\{ 1 6 , 3 2 \\}$ . ",
+        "bbox": [
+            217,
+            689,
+            823,
+            811
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "We chose the best performing model for each training subset $\\mathbb { D } _ { l }$ of labeled ImageNet (using a separate validation set), and report its accuracy on the test set (i.e. the publicly available ILSVRC-2012 validation set). ",
+        "bbox": [
+            178,
+            821,
+            825,
+            864
+        ],
+        "page_idx": 14
+    }
+]
\ No newline at end of file
diff --git a/parse/train/rJerHlrYwH/rJerHlrYwH_middle.json b/parse/train/rJerHlrYwH/rJerHlrYwH_middle.json
new file mode 100644
index 0000000000000000000000000000000000000000..6e522952034fbfd0d54cc28c42936e4afaba012f
--- /dev/null
+++ b/parse/train/rJerHlrYwH/rJerHlrYwH_middle.json
@@ -0,0 +1,43945 @@
+{
+    "pdf_info": [
+        {
+            "preproc_blocks": [
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        78,
+                        419,
+                        116
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                77,
+                                398,
+                                97
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        77,
+                                        398,
+                                        97
+                                    ],
+                                    "score": 1.0,
+                                    "content": "DATA-EFFICIENT IMAGE RECOGNITION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                98,
+                                420,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        98,
+                                        420,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "WITH CONTRASTIVE PREDICTIVE CODING",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        112,
+                        135,
+                        244,
+                        157
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                113,
+                                136,
+                                201,
+                                147
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        136,
+                                        201,
+                                        147
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Anonymous authors",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                112,
+                                146,
+                                245,
+                                158
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        112,
+                                        146,
+                                        245,
+                                        158
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Paper under double-blind review",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 2.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        278,
+                        186,
+                        333,
+                        199
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                276,
+                                186,
+                                335,
+                                200
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        276,
+                                        186,
+                                        335,
+                                        200
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ABSTRACT",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        143,
+                        212,
+                        468,
+                        354
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                141,
+                                212,
+                                469,
+                                225
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        212,
+                                        469,
+                                        225
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Human observers can learn to recognize new categories of objects from a hand-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                222,
+                                469,
+                                236
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        222,
+                                        469,
+                                        236
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ful of examples, yet doing so with machine perception remains an open challenge.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                233,
+                                470,
+                                246
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        233,
+                                        470,
+                                        246
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We hypothesize that data-efficient recognition is enabled by representations which",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                245,
+                                470,
+                                257
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        245,
+                                        470,
+                                        257
+                                    ],
+                                    "score": 1.0,
+                                    "content": "make the variability in natural signals more predictable, as suggested by recent",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                256,
+                                470,
+                                268
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        256,
+                                        470,
+                                        268
+                                    ],
+                                    "score": 1.0,
+                                    "content": "perceptual evidence. We therefore revisit and improve Contrastive Predictive Cod-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                267,
+                                469,
+                                279
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        267,
+                                        469,
+                                        279
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ing, a recently-proposed unsupervised learning framework, and arrive at a repre-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                278,
+                                469,
+                                289
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        278,
+                                        469,
+                                        289
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sentation which enables generalization from small amounts of labeled data. When",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                289,
+                                470,
+                                302
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        289,
+                                        222,
+                                        302
+                                    ],
+                                    "score": 1.0,
+                                    "content": "provided with only",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        222,
+                                        289,
+                                        237,
+                                        299
+                                    ],
+                                    "score": 0.86,
+                                    "content": "1 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        237,
+                                        289,
+                                        470,
+                                        302
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of ImageNet labels (i.e. 13 per class), this model retains",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                300,
+                                469,
+                                312
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        300,
+                                        290,
+                                        312
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a strong classification performance,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        291,
+                                        300,
+                                        311,
+                                        310
+                                    ],
+                                    "score": 0.86,
+                                    "content": "73 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        311,
+                                        300,
+                                        469,
+                                        312
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-5 accuracy, outperforming super-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                311,
+                                469,
+                                322
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        311,
+                                        218,
+                                        322
+                                    ],
+                                    "score": 1.0,
+                                    "content": "vised networks by",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        219,
+                                        311,
+                                        239,
+                                        321
+                                    ],
+                                    "score": 0.87,
+                                    "content": "28 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        239,
+                                        311,
+                                        251,
+                                        322
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(a",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        251,
+                                        311,
+                                        271,
+                                        321
+                                    ],
+                                    "score": 0.87,
+                                    "content": "65 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        271,
+                                        311,
+                                        469,
+                                        322
+                                    ],
+                                    "score": 1.0,
+                                    "content": "relative improvement) and state-of-the-art semi-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                322,
+                                470,
+                                334
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        322,
+                                        237,
+                                        334
+                                    ],
+                                    "score": 1.0,
+                                    "content": "supervised methods by",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        237,
+                                        322,
+                                        256,
+                                        332
+                                    ],
+                                    "score": 0.87,
+                                    "content": "14 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        256,
+                                        322,
+                                        470,
+                                        334
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". We also find this representation to serve as a useful",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                333,
+                                469,
+                                345
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        333,
+                                        469,
+                                        345
+                                    ],
+                                    "score": 1.0,
+                                    "content": "substrate for object detection on the PASCAL-VOC 2007 dataset, approaching the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                344,
+                                463,
+                                357
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        344,
+                                        463,
+                                        357
+                                    ],
+                                    "score": 1.0,
+                                    "content": "performance of representations trained with a fully annotated ImageNet dataset.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        109,
+                        377,
+                        205,
+                        390
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                376,
+                                208,
+                                393
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        376,
+                                        208,
+                                        393
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1 INTRODUCTION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        404,
+                        296,
+                        698
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                403,
+                                296,
+                                415
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        403,
+                                        296,
+                                        415
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Deep neural networks excel at perceptual tasks",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                413,
+                                297,
+                                426
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        413,
+                                        297,
+                                        426
+                                    ],
+                                    "score": 1.0,
+                                    "content": "when labeled data are abundant, yet their per-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                424,
+                                297,
+                                437
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        424,
+                                        297,
+                                        437
+                                    ],
+                                    "score": 1.0,
+                                    "content": "formance degrades substantially when provided",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                435,
+                                297,
+                                448
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        435,
+                                        297,
+                                        448
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with limited supervision (Fig. 1, red). In con-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                446,
+                                297,
+                                459
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        446,
+                                        297,
+                                        459
+                                    ],
+                                    "score": 1.0,
+                                    "content": "trast, humans and animals can quickly learn",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                457,
+                                297,
+                                469
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        457,
+                                        297,
+                                        469
+                                    ],
+                                    "score": 1.0,
+                                    "content": "about new classes of objects from few exam-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                468,
+                                297,
+                                480
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        468,
+                                        297,
+                                        480
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ples (Landau et al., 1988; Markman, 1989).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                479,
+                                297,
+                                491
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        479,
+                                        297,
+                                        491
+                                    ],
+                                    "score": 1.0,
+                                    "content": "What accounts for this monumental difference",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                490,
+                                297,
+                                502
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        490,
+                                        297,
+                                        502
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in data-efficiency between biological and ma-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                501,
+                                297,
+                                514
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        501,
+                                        297,
+                                        514
+                                    ],
+                                    "score": 1.0,
+                                    "content": "chine vision? While highly-structured repre-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                512,
+                                297,
+                                524
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        512,
+                                        297,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sentations (e.g. as proposed by Lake et al.,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                523,
+                                297,
+                                535
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        523,
+                                        297,
+                                        535
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2015) may improve data-efficiency, it remains",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                534,
+                                298,
+                                546
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        534,
+                                        298,
+                                        546
+                                    ],
+                                    "score": 1.0,
+                                    "content": "unclear how to program explicit structures that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                545,
+                                297,
+                                557
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        545,
+                                        297,
+                                        557
+                                    ],
+                                    "score": 1.0,
+                                    "content": "capture the enormous complexity of real visual",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                556,
+                                297,
+                                568
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        556,
+                                        297,
+                                        568
+                                    ],
+                                    "score": 1.0,
+                                    "content": "scenes like those in ImageNet (Russakovsky",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                566,
+                                298,
+                                579
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        566,
+                                        298,
+                                        579
+                                    ],
+                                    "score": 1.0,
+                                    "content": "et al., 2015). An alternative hypothesis has",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                578,
+                                298,
+                                590
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        578,
+                                        298,
+                                        590
+                                    ],
+                                    "score": 1.0,
+                                    "content": "proposed that intelligent systems need not be",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                590,
+                                297,
+                                600
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        590,
+                                        297,
+                                        600
+                                    ],
+                                    "score": 1.0,
+                                    "content": "structured a priori, but can instead learn about",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                601,
+                                297,
+                                612
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        601,
+                                        297,
+                                        612
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the structure of the world in an unsupervised",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                611,
+                                297,
+                                623
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        611,
+                                        297,
+                                        623
+                                    ],
+                                    "score": 1.0,
+                                    "content": "manner (Barlow, 1989; Hinton et al., 1999; Le-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                621,
+                                297,
+                                635
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        621,
+                                        297,
+                                        635
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Cun et al., 2015). Choosing an appropriate",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                633,
+                                298,
+                                645
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        633,
+                                        298,
+                                        645
+                                    ],
+                                    "score": 1.0,
+                                    "content": "training objective is an open problem, but a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                644,
+                                297,
+                                656
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        644,
+                                        297,
+                                        656
+                                    ],
+                                    "score": 1.0,
+                                    "content": "promising guiding principle has emerged re-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                655,
+                                297,
+                                666
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        655,
+                                        297,
+                                        666
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cently: good representations should make the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                666,
+                                297,
+                                678
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        666,
+                                        297,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "spatio-temporal variability in natural signals",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                677,
+                                297,
+                                689
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        677,
+                                        297,
+                                        689
+                                    ],
+                                    "score": 1.0,
+                                    "content": "more predictable. Indeed, human perceptual",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                688,
+                                297,
+                                699
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        688,
+                                        297,
+                                        699
+                                    ],
+                                    "score": 1.0,
+                                    "content": "representations have been shown to linearize",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        }
+                    ],
+                    "index": 32
+                },
+                {
+                    "type": "image",
+                    "bbox": [
+                        306,
+                        406,
+                        502,
+                        581
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                306,
+                                406,
+                                502,
+                                581
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        406,
+                                        502,
+                                        581
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                306,
+                                                406,
+                                                502,
+                                                581
+                                            ],
+                                            "score": 0.973,
+                                            "type": "image",
+                                            "image_path": "7b8ed316aeaae9bdfe3d3d7e12974b01335c33b7eb790b24e724753c0422fb2e.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 52.5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        406,
+                                        502,
+                                        418.5
+                                    ],
+                                    "spans": [],
+                                    "index": 46
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        418.5,
+                                        502,
+                                        431.0
+                                    ],
+                                    "spans": [],
+                                    "index": 47
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        431.0,
+                                        502,
+                                        443.5
+                                    ],
+                                    "spans": [],
+                                    "index": 48
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        443.5,
+                                        502,
+                                        456.0
+                                    ],
+                                    "spans": [],
+                                    "index": 49
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        456.0,
+                                        502,
+                                        468.5
+                                    ],
+                                    "spans": [],
+                                    "index": 50
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        468.5,
+                                        502,
+                                        481.0
+                                    ],
+                                    "spans": [],
+                                    "index": 51
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        481.0,
+                                        502,
+                                        493.5
+                                    ],
+                                    "spans": [],
+                                    "index": 52
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        493.5,
+                                        502,
+                                        506.0
+                                    ],
+                                    "spans": [],
+                                    "index": 53
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        506.0,
+                                        502,
+                                        518.5
+                                    ],
+                                    "spans": [],
+                                    "index": 54
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        518.5,
+                                        502,
+                                        531.0
+                                    ],
+                                    "spans": [],
+                                    "index": 55
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        531.0,
+                                        502,
+                                        543.5
+                                    ],
+                                    "spans": [],
+                                    "index": 56
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        543.5,
+                                        502,
+                                        556.0
+                                    ],
+                                    "spans": [],
+                                    "index": 57
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        556.0,
+                                        502,
+                                        568.5
+                                    ],
+                                    "spans": [],
+                                    "index": 58
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        568.5,
+                                        502,
+                                        581.0
+                                    ],
+                                    "spans": [],
+                                    "index": 59
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                304,
+                                586,
+                                504,
+                                684
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        586,
+                                        505,
+                                        597
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                304,
+                                                586,
+                                                505,
+                                                597
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 1: Data-efficient image recognition with",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 60
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        596,
+                                        505,
+                                        608
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                304,
+                                                596,
+                                                505,
+                                                608
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Contrastive Predictive Coding. With decreas-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 61
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        608,
+                                        505,
+                                        619
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                303,
+                                                608,
+                                                505,
+                                                619
+                                            ],
+                                            "score": 1.0,
+                                            "content": "ing amounts of labeled data, supervised networks",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 62
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        618,
+                                        505,
+                                        630
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                303,
+                                                618,
+                                                505,
+                                                630
+                                            ],
+                                            "score": 1.0,
+                                            "content": "trained on pixels fail to generalize (red). When",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 63
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        629,
+                                        505,
+                                        641
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                304,
+                                                629,
+                                                505,
+                                                641
+                                            ],
+                                            "score": 1.0,
+                                            "content": "trained on unsupervised representations learned",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 64
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        640,
+                                        506,
+                                        652
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                304,
+                                                640,
+                                                506,
+                                                652
+                                            ],
+                                            "score": 1.0,
+                                            "content": "with CPC, these networks retain a much higher",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 65
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        651,
+                                        505,
+                                        663
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                304,
+                                                651,
+                                                505,
+                                                663
+                                            ],
+                                            "score": 1.0,
+                                            "content": "accuracy in this low-data regime (blue). Equiva-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 66
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        662,
+                                        505,
+                                        674
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                304,
+                                                662,
+                                                505,
+                                                674
+                                            ],
+                                            "score": 1.0,
+                                            "content": "lently, the accuracy of supervised networks can be",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 67
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        673,
+                                        466,
+                                        685
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                303,
+                                                673,
+                                                466,
+                                                685
+                                            ],
+                                            "score": 1.0,
+                                            "content": "matched with significantly fewer labels.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 68
+                                }
+                            ],
+                            "index": 64
+                        }
+                    ],
+                    "index": 58.25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        699,
+                        504,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                699,
+                                504,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        699,
+                                        504,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(or ‘straighten’) the temporal transformations found in natural videos, a property lacking from cur-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 69
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                710,
+                                505,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        710,
+                                        505,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "rent supervised image recognition models (Henaff et al., 2019), and theories of both spatial and tem- ´",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 70
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                721,
+                                505,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        721,
+                                        505,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "poral predictability have succeeded in describing properties of early visual areas (Rao & Ballard,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 71
+                        }
+                    ],
+                    "index": 70
+                }
+            ],
+            "page_idx": 0,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        308,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                26,
+                                308,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        26,
+                                        308,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Under review as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        752,
+                        308,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                302,
+                                751,
+                                309,
+                                762
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        302,
+                                        751,
+                                        309,
+                                        762
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        78,
+                        419,
+                        116
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                77,
+                                398,
+                                97
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        77,
+                                        398,
+                                        97
+                                    ],
+                                    "score": 1.0,
+                                    "content": "DATA-EFFICIENT IMAGE RECOGNITION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                98,
+                                420,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        98,
+                                        420,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "WITH CONTRASTIVE PREDICTIVE CODING",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        112,
+                        135,
+                        244,
+                        157
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                113,
+                                136,
+                                201,
+                                147
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        136,
+                                        201,
+                                        147
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Anonymous authors",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                112,
+                                146,
+                                245,
+                                158
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        112,
+                                        146,
+                                        245,
+                                        158
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Paper under double-blind review",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 2.5,
+                    "bbox_fs": [
+                        112,
+                        136,
+                        245,
+                        158
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        278,
+                        186,
+                        333,
+                        199
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                276,
+                                186,
+                                335,
+                                200
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        276,
+                                        186,
+                                        335,
+                                        200
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ABSTRACT",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        143,
+                        212,
+                        468,
+                        354
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                141,
+                                212,
+                                469,
+                                225
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        212,
+                                        469,
+                                        225
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Human observers can learn to recognize new categories of objects from a hand-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                222,
+                                469,
+                                236
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        222,
+                                        469,
+                                        236
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ful of examples, yet doing so with machine perception remains an open challenge.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                233,
+                                470,
+                                246
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        233,
+                                        470,
+                                        246
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We hypothesize that data-efficient recognition is enabled by representations which",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                245,
+                                470,
+                                257
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        245,
+                                        470,
+                                        257
+                                    ],
+                                    "score": 1.0,
+                                    "content": "make the variability in natural signals more predictable, as suggested by recent",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                256,
+                                470,
+                                268
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        256,
+                                        470,
+                                        268
+                                    ],
+                                    "score": 1.0,
+                                    "content": "perceptual evidence. We therefore revisit and improve Contrastive Predictive Cod-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                267,
+                                469,
+                                279
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        267,
+                                        469,
+                                        279
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ing, a recently-proposed unsupervised learning framework, and arrive at a repre-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                278,
+                                469,
+                                289
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        278,
+                                        469,
+                                        289
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sentation which enables generalization from small amounts of labeled data. When",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                289,
+                                470,
+                                302
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        289,
+                                        222,
+                                        302
+                                    ],
+                                    "score": 1.0,
+                                    "content": "provided with only",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        222,
+                                        289,
+                                        237,
+                                        299
+                                    ],
+                                    "score": 0.86,
+                                    "content": "1 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        237,
+                                        289,
+                                        470,
+                                        302
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of ImageNet labels (i.e. 13 per class), this model retains",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                300,
+                                469,
+                                312
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        300,
+                                        290,
+                                        312
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a strong classification performance,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        291,
+                                        300,
+                                        311,
+                                        310
+                                    ],
+                                    "score": 0.86,
+                                    "content": "73 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        311,
+                                        300,
+                                        469,
+                                        312
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-5 accuracy, outperforming super-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                311,
+                                469,
+                                322
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        311,
+                                        218,
+                                        322
+                                    ],
+                                    "score": 1.0,
+                                    "content": "vised networks by",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        219,
+                                        311,
+                                        239,
+                                        321
+                                    ],
+                                    "score": 0.87,
+                                    "content": "28 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        239,
+                                        311,
+                                        251,
+                                        322
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(a",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        251,
+                                        311,
+                                        271,
+                                        321
+                                    ],
+                                    "score": 0.87,
+                                    "content": "65 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        271,
+                                        311,
+                                        469,
+                                        322
+                                    ],
+                                    "score": 1.0,
+                                    "content": "relative improvement) and state-of-the-art semi-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                322,
+                                470,
+                                334
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        322,
+                                        237,
+                                        334
+                                    ],
+                                    "score": 1.0,
+                                    "content": "supervised methods by",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        237,
+                                        322,
+                                        256,
+                                        332
+                                    ],
+                                    "score": 0.87,
+                                    "content": "14 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        256,
+                                        322,
+                                        470,
+                                        334
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". We also find this representation to serve as a useful",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                333,
+                                469,
+                                345
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        333,
+                                        469,
+                                        345
+                                    ],
+                                    "score": 1.0,
+                                    "content": "substrate for object detection on the PASCAL-VOC 2007 dataset, approaching the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                344,
+                                463,
+                                357
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        344,
+                                        463,
+                                        357
+                                    ],
+                                    "score": 1.0,
+                                    "content": "performance of representations trained with a fully annotated ImageNet dataset.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 11,
+                    "bbox_fs": [
+                        141,
+                        212,
+                        470,
+                        357
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        109,
+                        377,
+                        205,
+                        390
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                376,
+                                208,
+                                393
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        376,
+                                        208,
+                                        393
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1 INTRODUCTION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        404,
+                        296,
+                        698
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                403,
+                                296,
+                                415
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        403,
+                                        296,
+                                        415
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Deep neural networks excel at perceptual tasks",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                413,
+                                297,
+                                426
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        413,
+                                        297,
+                                        426
+                                    ],
+                                    "score": 1.0,
+                                    "content": "when labeled data are abundant, yet their per-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                424,
+                                297,
+                                437
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        424,
+                                        297,
+                                        437
+                                    ],
+                                    "score": 1.0,
+                                    "content": "formance degrades substantially when provided",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                435,
+                                297,
+                                448
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        435,
+                                        297,
+                                        448
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with limited supervision (Fig. 1, red). In con-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                446,
+                                297,
+                                459
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        446,
+                                        297,
+                                        459
+                                    ],
+                                    "score": 1.0,
+                                    "content": "trast, humans and animals can quickly learn",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                457,
+                                297,
+                                469
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        457,
+                                        297,
+                                        469
+                                    ],
+                                    "score": 1.0,
+                                    "content": "about new classes of objects from few exam-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                468,
+                                297,
+                                480
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        468,
+                                        297,
+                                        480
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ples (Landau et al., 1988; Markman, 1989).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                479,
+                                297,
+                                491
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        479,
+                                        297,
+                                        491
+                                    ],
+                                    "score": 1.0,
+                                    "content": "What accounts for this monumental difference",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                490,
+                                297,
+                                502
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        490,
+                                        297,
+                                        502
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in data-efficiency between biological and ma-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                501,
+                                297,
+                                514
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        501,
+                                        297,
+                                        514
+                                    ],
+                                    "score": 1.0,
+                                    "content": "chine vision? While highly-structured repre-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                512,
+                                297,
+                                524
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        512,
+                                        297,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sentations (e.g. as proposed by Lake et al.,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                523,
+                                297,
+                                535
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        523,
+                                        297,
+                                        535
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2015) may improve data-efficiency, it remains",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                534,
+                                298,
+                                546
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        534,
+                                        298,
+                                        546
+                                    ],
+                                    "score": 1.0,
+                                    "content": "unclear how to program explicit structures that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                545,
+                                297,
+                                557
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        545,
+                                        297,
+                                        557
+                                    ],
+                                    "score": 1.0,
+                                    "content": "capture the enormous complexity of real visual",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                556,
+                                297,
+                                568
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        556,
+                                        297,
+                                        568
+                                    ],
+                                    "score": 1.0,
+                                    "content": "scenes like those in ImageNet (Russakovsky",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                566,
+                                298,
+                                579
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        566,
+                                        298,
+                                        579
+                                    ],
+                                    "score": 1.0,
+                                    "content": "et al., 2015). An alternative hypothesis has",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                578,
+                                298,
+                                590
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        578,
+                                        298,
+                                        590
+                                    ],
+                                    "score": 1.0,
+                                    "content": "proposed that intelligent systems need not be",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                590,
+                                297,
+                                600
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        590,
+                                        297,
+                                        600
+                                    ],
+                                    "score": 1.0,
+                                    "content": "structured a priori, but can instead learn about",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                601,
+                                297,
+                                612
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        601,
+                                        297,
+                                        612
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the structure of the world in an unsupervised",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                611,
+                                297,
+                                623
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        611,
+                                        297,
+                                        623
+                                    ],
+                                    "score": 1.0,
+                                    "content": "manner (Barlow, 1989; Hinton et al., 1999; Le-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                621,
+                                297,
+                                635
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        621,
+                                        297,
+                                        635
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Cun et al., 2015). Choosing an appropriate",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                633,
+                                298,
+                                645
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        633,
+                                        298,
+                                        645
+                                    ],
+                                    "score": 1.0,
+                                    "content": "training objective is an open problem, but a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                644,
+                                297,
+                                656
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        644,
+                                        297,
+                                        656
+                                    ],
+                                    "score": 1.0,
+                                    "content": "promising guiding principle has emerged re-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                655,
+                                297,
+                                666
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        655,
+                                        297,
+                                        666
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cently: good representations should make the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                666,
+                                297,
+                                678
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        666,
+                                        297,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "spatio-temporal variability in natural signals",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                677,
+                                297,
+                                689
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        677,
+                                        297,
+                                        689
+                                    ],
+                                    "score": 1.0,
+                                    "content": "more predictable. Indeed, human perceptual",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                688,
+                                297,
+                                699
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        688,
+                                        297,
+                                        699
+                                    ],
+                                    "score": 1.0,
+                                    "content": "representations have been shown to linearize",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        }
+                    ],
+                    "index": 32,
+                    "bbox_fs": [
+                        105,
+                        403,
+                        298,
+                        699
+                    ]
+                },
+                {
+                    "type": "image",
+                    "bbox": [
+                        306,
+                        406,
+                        502,
+                        581
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                306,
+                                406,
+                                502,
+                                581
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        406,
+                                        502,
+                                        581
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                306,
+                                                406,
+                                                502,
+                                                581
+                                            ],
+                                            "score": 0.973,
+                                            "type": "image",
+                                            "image_path": "7b8ed316aeaae9bdfe3d3d7e12974b01335c33b7eb790b24e724753c0422fb2e.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 52.5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        406,
+                                        502,
+                                        418.5
+                                    ],
+                                    "spans": [],
+                                    "index": 46
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        418.5,
+                                        502,
+                                        431.0
+                                    ],
+                                    "spans": [],
+                                    "index": 47
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        431.0,
+                                        502,
+                                        443.5
+                                    ],
+                                    "spans": [],
+                                    "index": 48
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        443.5,
+                                        502,
+                                        456.0
+                                    ],
+                                    "spans": [],
+                                    "index": 49
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        456.0,
+                                        502,
+                                        468.5
+                                    ],
+                                    "spans": [],
+                                    "index": 50
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        468.5,
+                                        502,
+                                        481.0
+                                    ],
+                                    "spans": [],
+                                    "index": 51
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        481.0,
+                                        502,
+                                        493.5
+                                    ],
+                                    "spans": [],
+                                    "index": 52
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        493.5,
+                                        502,
+                                        506.0
+                                    ],
+                                    "spans": [],
+                                    "index": 53
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        506.0,
+                                        502,
+                                        518.5
+                                    ],
+                                    "spans": [],
+                                    "index": 54
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        518.5,
+                                        502,
+                                        531.0
+                                    ],
+                                    "spans": [],
+                                    "index": 55
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        531.0,
+                                        502,
+                                        543.5
+                                    ],
+                                    "spans": [],
+                                    "index": 56
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        543.5,
+                                        502,
+                                        556.0
+                                    ],
+                                    "spans": [],
+                                    "index": 57
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        556.0,
+                                        502,
+                                        568.5
+                                    ],
+                                    "spans": [],
+                                    "index": 58
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        568.5,
+                                        502,
+                                        581.0
+                                    ],
+                                    "spans": [],
+                                    "index": 59
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                304,
+                                586,
+                                504,
+                                684
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        586,
+                                        505,
+                                        597
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                304,
+                                                586,
+                                                505,
+                                                597
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 1: Data-efficient image recognition with",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 60
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        596,
+                                        505,
+                                        608
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                304,
+                                                596,
+                                                505,
+                                                608
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Contrastive Predictive Coding. With decreas-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 61
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        608,
+                                        505,
+                                        619
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                303,
+                                                608,
+                                                505,
+                                                619
+                                            ],
+                                            "score": 1.0,
+                                            "content": "ing amounts of labeled data, supervised networks",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 62
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        618,
+                                        505,
+                                        630
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                303,
+                                                618,
+                                                505,
+                                                630
+                                            ],
+                                            "score": 1.0,
+                                            "content": "trained on pixels fail to generalize (red). When",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 63
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        629,
+                                        505,
+                                        641
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                304,
+                                                629,
+                                                505,
+                                                641
+                                            ],
+                                            "score": 1.0,
+                                            "content": "trained on unsupervised representations learned",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 64
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        640,
+                                        506,
+                                        652
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                304,
+                                                640,
+                                                506,
+                                                652
+                                            ],
+                                            "score": 1.0,
+                                            "content": "with CPC, these networks retain a much higher",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 65
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        651,
+                                        505,
+                                        663
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                304,
+                                                651,
+                                                505,
+                                                663
+                                            ],
+                                            "score": 1.0,
+                                            "content": "accuracy in this low-data regime (blue). Equiva-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 66
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        662,
+                                        505,
+                                        674
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                304,
+                                                662,
+                                                505,
+                                                674
+                                            ],
+                                            "score": 1.0,
+                                            "content": "lently, the accuracy of supervised networks can be",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 67
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        673,
+                                        466,
+                                        685
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                303,
+                                                673,
+                                                466,
+                                                685
+                                            ],
+                                            "score": 1.0,
+                                            "content": "matched with significantly fewer labels.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 68
+                                }
+                            ],
+                            "index": 64
+                        }
+                    ],
+                    "index": 58.25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        699,
+                        504,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                699,
+                                504,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        699,
+                                        504,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(or ‘straighten’) the temporal transformations found in natural videos, a property lacking from cur-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 69
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                710,
+                                505,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        710,
+                                        505,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "rent supervised image recognition models (Henaff et al., 2019), and theories of both spatial and tem- ´",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 70
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                721,
+                                505,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        721,
+                                        505,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "poral predictability have succeeded in describing properties of early visual areas (Rao & Ballard,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 71
+                        }
+                    ],
+                    "index": 70,
+                    "bbox_fs": [
+                        105,
+                        699,
+                        505,
+                        733
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        82,
+                        504,
+                        105
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                81,
+                                505,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        81,
+                                        505,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1999; Palmer et al., 2015). In this work, we hypothesize that spatially predictable representations",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                92,
+                                393,
+                                108
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        92,
+                                        393,
+                                        108
+                                    ],
+                                    "score": 1.0,
+                                    "content": "may allow artificial systems to benefit from human-like data-efficiency.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        110,
+                        505,
+                        187
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                109,
+                                506,
+                                124
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        109,
+                                        506,
+                                        124
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Contrastive Predictive Coding (CPC, van den Oord et al., 2018) is an unsupervised objective which",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                122,
+                                505,
+                                133
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        122,
+                                        505,
+                                        133
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learns such predictable representations. CPC is a general technique that only requires in its definition",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                132,
+                                505,
+                                145
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        132,
+                                        505,
+                                        145
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that observations be ordered along e.g. temporal or spatial dimensions, and as such has been applied",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                143,
+                                505,
+                                156
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        143,
+                                        505,
+                                        156
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to a variety of different modalities including speech, natural language and images. This generality,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                154,
+                                505,
+                                167
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        154,
+                                        505,
+                                        167
+                                    ],
+                                    "score": 1.0,
+                                    "content": "combined with the strong performance of its representations in downstream linear classification",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                165,
+                                506,
+                                179
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        165,
+                                        506,
+                                        179
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tasks, makes CPC a promising candidate for investigating the efficacy of predictable representations",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                176,
+                                253,
+                                189
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        176,
+                                        253,
+                                        189
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for data-efficient image recognition.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        193,
+                        287,
+                        204
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                191,
+                                289,
+                                206
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        191,
+                                        289,
+                                        206
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Our work makes the following contributions:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        133,
+                        214,
+                        505,
+                        414
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                133,
+                                213,
+                                505,
+                                227
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        133,
+                                        213,
+                                        505,
+                                        227
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• We revisit CPC in terms of its architecture and training methodology, and arrive at a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                225,
+                                505,
+                                237
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        225,
+                                        505,
+                                        237
+                                    ],
+                                    "score": 1.0,
+                                    "content": "new implementation of CPC with dramatically-improved ability to linearly separate im-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                236,
+                                384,
+                                249
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        236,
+                                        191,
+                                        249
+                                    ],
+                                    "score": 1.0,
+                                    "content": "age classes",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        192,
+                                        236,
+                                        217,
+                                        247
+                                    ],
+                                    "score": 0.87,
+                                    "content": "+ 1 7 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        218,
+                                        236,
+                                        384,
+                                        249
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-1 ImageNet classification accuracy).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                138,
+                                251,
+                                505,
+                                263
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        138,
+                                        251,
+                                        505,
+                                        263
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We then train deep networks on top of the resulting CPC representations using very few la-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                261,
+                                505,
+                                276
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        261,
+                                        216,
+                                        276
+                                    ],
+                                    "score": 1.0,
+                                    "content": "beled images (e.g.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        216,
+                                        262,
+                                        230,
+                                        273
+                                    ],
+                                    "score": 0.85,
+                                    "content": "1 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        231,
+                                        261,
+                                        505,
+                                        276
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of the ImageNet dataset), and demonstrate test-time classification ac-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                273,
+                                505,
+                                285
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        273,
+                                        339,
+                                        285
+                                    ],
+                                    "score": 1.0,
+                                    "content": "curacy far above networks trained on raw pixels (",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        339,
+                                        273,
+                                        358,
+                                        284
+                                    ],
+                                    "score": 0.85,
+                                    "content": "73 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        359,
+                                        273,
+                                        432,
+                                        285
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-5 accuracy, a",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        432,
+                                        273,
+                                        452,
+                                        284
+                                    ],
+                                    "score": 0.88,
+                                    "content": "28 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        452,
+                                        273,
+                                        505,
+                                        285
+                                    ],
+                                    "score": 1.0,
+                                    "content": "absolute im-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                284,
+                                504,
+                                297
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        284,
+                                        477,
+                                        297
+                                    ],
+                                    "score": 1.0,
+                                    "content": "provement), outperforming all other unsupervised representation learning methods",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        477,
+                                        284,
+                                        504,
+                                        295
+                                    ],
+                                    "score": 0.87,
+                                    "content": "( + 1 5 \\%",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                295,
+                                506,
+                                308
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        295,
+                                        506,
+                                        308
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-5 accuracy over the previous state-of-the-art (Zhai et al., 2019)). Surprisingly, this",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                307,
+                                505,
+                                319
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        307,
+                                        505,
+                                        319
+                                    ],
+                                    "score": 1.0,
+                                    "content": "representation also surpasses supervised methods when given the entire ImageNet dataset",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                145,
+                                317,
+                                236,
+                                329
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        145,
+                                        317,
+                                        166,
+                                        328
+                                    ],
+                                    "score": 0.85,
+                                    "content": "+ 1 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        166,
+                                        317,
+                                        236,
+                                        329
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-5 accuracy).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                138,
+                                330,
+                                505,
+                                345
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        138,
+                                        330,
+                                        505,
+                                        345
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We isolate the contributions of different components of the final model to such downstream",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                343,
+                                505,
+                                355
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        343,
+                                        505,
+                                        355
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tasks. Interestingly, we find that linear classification accuracy is not always predictive of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                353,
+                                505,
+                                367
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        353,
+                                        505,
+                                        367
+                                    ],
+                                    "score": 1.0,
+                                    "content": "low-data classification accuracy, emphasizing the importance of this metric as a stand-alone",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                363,
+                                296,
+                                379
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        363,
+                                        296,
+                                        379
+                                    ],
+                                    "score": 1.0,
+                                    "content": "benchmark for unsupervised learning.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                135,
+                                379,
+                                506,
+                                393
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        135,
+                                        379,
+                                        506,
+                                        393
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• Finally, we assess the generality of CPC representations by transferring them to a new task",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                391,
+                                505,
+                                403
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        391,
+                                        505,
+                                        403
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and dataset: object detection on PASCAL-VOC 2007. Consistent with the results from the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                402,
+                                468,
+                                415
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        402,
+                                        468,
+                                        415
+                                    ],
+                                    "score": 1.0,
+                                    "content": "previous section, we find CPC to give state-of-the-art performance in this setting.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        429,
+                        244,
+                        442
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                428,
+                                245,
+                                444
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        428,
+                                        245,
+                                        444
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2 EXPERIMENTAL SETUP",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 27
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        455,
+                        505,
+                        477
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                453,
+                                505,
+                                468
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        453,
+                                        505,
+                                        468
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We first review the CPC architecture and learning objective in section 2.1, before detailing how we",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                466,
+                                405,
+                                478
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        466,
+                                        405,
+                                        478
+                                    ],
+                                    "score": 1.0,
+                                    "content": "use its resulting representations for image recognition tasks in section 2.2.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 28.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        490,
+                        286,
+                        502
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                490,
+                                287,
+                                503
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        490,
+                                        287,
+                                        503
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2.1 CONTRASTIVE PREDICTIVE CODING",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 30
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        511,
+                        505,
+                        588
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                510,
+                                505,
+                                524
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        510,
+                                        505,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Contrastive Predictive Coding as formulated in (van den Oord et al., 2018) learns representations",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                523,
+                                505,
+                                535
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        523,
+                                        505,
+                                        535
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by training neural networks to predict the representations of future observations from those of past",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                534,
+                                505,
+                                546
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        534,
+                                        505,
+                                        546
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ones. When applied to images, the original formulation of CPC operates by predicting the represen-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                545,
+                                505,
+                                556
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        545,
+                                        505,
+                                        556
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tations of patches below a certain position from those above it (Fig. 2, left). These predictions are",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                555,
+                                506,
+                                569
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        555,
+                                        506,
+                                        569
+                                    ],
+                                    "score": 1.0,
+                                    "content": "evaluated using a contrastive loss, in which the network must correctly classify the ‘future’ repre-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                566,
+                                505,
+                                578
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        566,
+                                        505,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sentation amongst a set of unrelated ‘negative’ representations. This avoids trivial solutions such as",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                577,
+                                506,
+                                591
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        577,
+                                        506,
+                                        591
+                                    ],
+                                    "score": 1.0,
+                                    "content": "representing all patches with a constant vector, as would be the case with a mean squared error loss.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 34
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        594,
+                        505,
+                        683
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                591,
+                                507,
+                                609
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        591,
+                                        484,
+                                        609
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In the CPC architecture, each input image is first divided into a set of overlapping patches",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        484,
+                                        596,
+                                        501,
+                                        606
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\mathbf { \\delta } _ { \\mathbf { x } _ { i , j } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        501,
+                                        591,
+                                        507,
+                                        609
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                604,
+                                506,
+                                618
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        604,
+                                        304,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": "each of which is encoded with a neural network",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        605,
+                                        315,
+                                        616
+                                    ],
+                                    "score": 0.88,
+                                    "content": "f _ { \\theta }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        315,
+                                        604,
+                                        397,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": "into a single vector",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        397,
+                                        605,
+                                        461,
+                                        618
+                                    ],
+                                    "score": 0.93,
+                                    "content": "z _ { i , j } = f _ { \\theta } ( \\pmb { x } _ { i , j } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        462,
+                                        604,
+                                        506,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". To make",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                615,
+                                506,
+                                629
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        615,
+                                        289,
+                                        629
+                                    ],
+                                    "score": 1.0,
+                                    "content": "predictions, a masked convolutional network",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        290,
+                                        618,
+                                        301,
+                                        628
+                                    ],
+                                    "score": 0.87,
+                                    "content": "g _ { \\phi }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        302,
+                                        615,
+                                        506,
+                                        629
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is then applied to the grid of feature vectors. The",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                627,
+                                506,
+                                640
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        627,
+                                        399,
+                                        640
+                                    ],
+                                    "score": 1.0,
+                                    "content": "masks are such that the receptive field of each resulting context vector",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        400,
+                                        628,
+                                        415,
+                                        639
+                                    ],
+                                    "score": 0.88,
+                                    "content": "c _ { i , j }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        415,
+                                        627,
+                                        506,
+                                        640
+                                    ],
+                                    "score": 1.0,
+                                    "content": "only includes feature",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                637,
+                                506,
+                                652
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        637,
+                                        268,
+                                        652
+                                    ],
+                                    "score": 1.0,
+                                    "content": "vectors that lie above it in the image (i.e.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        268,
+                                        638,
+                                        320,
+                                        650
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\{ z _ { u , v } \\} _ { u \\leq i , v } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        320,
+                                        637,
+                                        506,
+                                        652
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". The prediction task then consists o predicting",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                648,
+                                506,
+                                662
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        648,
+                                        201,
+                                        662
+                                    ],
+                                    "score": 1.0,
+                                    "content": "‘future’ feature vectors",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        202,
+                                        650,
+                                        227,
+                                        661
+                                    ],
+                                    "score": 0.9,
+                                    "content": "z _ { i + k , j }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        228,
+                                        648,
+                                        346,
+                                        662
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from current context vectors",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        346,
+                                        650,
+                                        361,
+                                        661
+                                    ],
+                                    "score": 0.88,
+                                    "content": "c _ { i , j }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        361,
+                                        648,
+                                        392,
+                                        662
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        393,
+                                        649,
+                                        419,
+                                        659
+                                    ],
+                                    "score": 0.9,
+                                    "content": "k > 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        420,
+                                        648,
+                                        506,
+                                        662
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". The predictions are",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                660,
+                                506,
+                                673
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        660,
+                                        260,
+                                        673
+                                    ],
+                                    "score": 1.0,
+                                    "content": "made linearly: given a context vector",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        260,
+                                        662,
+                                        275,
+                                        672
+                                    ],
+                                    "score": 0.86,
+                                    "content": "c _ { i , j }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        275,
+                                        660,
+                                        358,
+                                        673
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", a prediction length",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        358,
+                                        660,
+                                        384,
+                                        670
+                                    ],
+                                    "score": 0.9,
+                                    "content": "k > 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        385,
+                                        660,
+                                        486,
+                                        673
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and a prediction matrix",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        486,
+                                        660,
+                                        501,
+                                        671
+                                    ],
+                                    "score": 0.88,
+                                    "content": "W _ { k }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        501,
+                                        660,
+                                        506,
+                                        673
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                671,
+                                301,
+                                685
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        671,
+                                        227,
+                                        685
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the predicted feature vector is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        228,
+                                        672,
+                                        297,
+                                        683
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\hat { \\boldsymbol { z } } _ { i + k , j } = \\boldsymbol { W } _ { k } \\boldsymbol { c } _ { i , j }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        297,
+                                        671,
+                                        301,
+                                        685
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        }
+                    ],
+                    "index": 41.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        687,
+                        504,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                688,
+                                505,
+                                700
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        688,
+                                        505,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The quality of this prediction is then evaluated using a contrastive loss. Specifically, the goal is to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                699,
+                                506,
+                                711
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        699,
+                                        228,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "correctly recognize the target",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        229,
+                                        700,
+                                        254,
+                                        711
+                                    ],
+                                    "score": 0.82,
+                                    "content": "z _ { i + k , j }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        254,
+                                        699,
+                                        462,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "among a set of randomly sampled feature vectors",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        462,
+                                        699,
+                                        481,
+                                        711
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\{ z _ { l } \\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        482,
+                                        699,
+                                        506,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                709,
+                                506,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        709,
+                                        506,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the dataset. We compute the probability assigned to the target using a softmax, and evaluate this",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                721,
+                                505,
+                                734
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        721,
+                                        505,
+                                        734
+                                    ],
+                                    "score": 1.0,
+                                    "content": "probability using the usual cross-entropy loss. Summing this loss over locations and prediction",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        }
+                    ],
+                    "index": 47.5
+                }
+            ],
+            "page_idx": 1,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        308,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                25,
+                                309,
+                                39
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        25,
+                                        309,
+                                        39
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Under review as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        751,
+                        309,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                301,
+                                750,
+                                310,
+                                763
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        301,
+                                        750,
+                                        310,
+                                        763
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        82,
+                        504,
+                        105
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                81,
+                                505,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        81,
+                                        505,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1999; Palmer et al., 2015). In this work, we hypothesize that spatially predictable representations",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                92,
+                                393,
+                                108
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        92,
+                                        393,
+                                        108
+                                    ],
+                                    "score": 1.0,
+                                    "content": "may allow artificial systems to benefit from human-like data-efficiency.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5,
+                    "bbox_fs": [
+                        105,
+                        81,
+                        505,
+                        108
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        110,
+                        505,
+                        187
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                109,
+                                506,
+                                124
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        109,
+                                        506,
+                                        124
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Contrastive Predictive Coding (CPC, van den Oord et al., 2018) is an unsupervised objective which",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                122,
+                                505,
+                                133
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        122,
+                                        505,
+                                        133
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learns such predictable representations. CPC is a general technique that only requires in its definition",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                132,
+                                505,
+                                145
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        132,
+                                        505,
+                                        145
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that observations be ordered along e.g. temporal or spatial dimensions, and as such has been applied",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                143,
+                                505,
+                                156
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        143,
+                                        505,
+                                        156
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to a variety of different modalities including speech, natural language and images. This generality,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                154,
+                                505,
+                                167
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        154,
+                                        505,
+                                        167
+                                    ],
+                                    "score": 1.0,
+                                    "content": "combined with the strong performance of its representations in downstream linear classification",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                165,
+                                506,
+                                179
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        165,
+                                        506,
+                                        179
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tasks, makes CPC a promising candidate for investigating the efficacy of predictable representations",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                176,
+                                253,
+                                189
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        176,
+                                        253,
+                                        189
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for data-efficient image recognition.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 5,
+                    "bbox_fs": [
+                        105,
+                        109,
+                        506,
+                        189
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        193,
+                        287,
+                        204
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                191,
+                                289,
+                                206
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        191,
+                                        289,
+                                        206
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Our work makes the following contributions:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 9,
+                    "bbox_fs": [
+                        105,
+                        191,
+                        289,
+                        206
+                    ]
+                },
+                {
+                    "type": "list",
+                    "bbox": [
+                        133,
+                        214,
+                        505,
+                        414
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                133,
+                                213,
+                                505,
+                                227
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        133,
+                                        213,
+                                        505,
+                                        227
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• We revisit CPC in terms of its architecture and training methodology, and arrive at a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                225,
+                                505,
+                                237
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        225,
+                                        505,
+                                        237
+                                    ],
+                                    "score": 1.0,
+                                    "content": "new implementation of CPC with dramatically-improved ability to linearly separate im-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                236,
+                                384,
+                                249
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        236,
+                                        191,
+                                        249
+                                    ],
+                                    "score": 1.0,
+                                    "content": "age classes",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        192,
+                                        236,
+                                        217,
+                                        247
+                                    ],
+                                    "score": 0.87,
+                                    "content": "+ 1 7 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        218,
+                                        236,
+                                        384,
+                                        249
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-1 ImageNet classification accuracy).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                138,
+                                251,
+                                505,
+                                263
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        138,
+                                        251,
+                                        505,
+                                        263
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We then train deep networks on top of the resulting CPC representations using very few la-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                261,
+                                505,
+                                276
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        261,
+                                        216,
+                                        276
+                                    ],
+                                    "score": 1.0,
+                                    "content": "beled images (e.g.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        216,
+                                        262,
+                                        230,
+                                        273
+                                    ],
+                                    "score": 0.85,
+                                    "content": "1 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        231,
+                                        261,
+                                        505,
+                                        276
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of the ImageNet dataset), and demonstrate test-time classification ac-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                273,
+                                505,
+                                285
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        273,
+                                        339,
+                                        285
+                                    ],
+                                    "score": 1.0,
+                                    "content": "curacy far above networks trained on raw pixels (",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        339,
+                                        273,
+                                        358,
+                                        284
+                                    ],
+                                    "score": 0.85,
+                                    "content": "73 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        359,
+                                        273,
+                                        432,
+                                        285
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-5 accuracy, a",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        432,
+                                        273,
+                                        452,
+                                        284
+                                    ],
+                                    "score": 0.88,
+                                    "content": "28 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        452,
+                                        273,
+                                        505,
+                                        285
+                                    ],
+                                    "score": 1.0,
+                                    "content": "absolute im-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                284,
+                                504,
+                                297
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        284,
+                                        477,
+                                        297
+                                    ],
+                                    "score": 1.0,
+                                    "content": "provement), outperforming all other unsupervised representation learning methods",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        477,
+                                        284,
+                                        504,
+                                        295
+                                    ],
+                                    "score": 0.87,
+                                    "content": "( + 1 5 \\%",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                295,
+                                506,
+                                308
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        295,
+                                        506,
+                                        308
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-5 accuracy over the previous state-of-the-art (Zhai et al., 2019)). Surprisingly, this",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                307,
+                                505,
+                                319
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        307,
+                                        505,
+                                        319
+                                    ],
+                                    "score": 1.0,
+                                    "content": "representation also surpasses supervised methods when given the entire ImageNet dataset",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                145,
+                                317,
+                                236,
+                                329
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        145,
+                                        317,
+                                        166,
+                                        328
+                                    ],
+                                    "score": 0.85,
+                                    "content": "+ 1 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        166,
+                                        317,
+                                        236,
+                                        329
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-5 accuracy).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                138,
+                                330,
+                                505,
+                                345
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        138,
+                                        330,
+                                        505,
+                                        345
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We isolate the contributions of different components of the final model to such downstream",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                343,
+                                505,
+                                355
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        343,
+                                        505,
+                                        355
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tasks. Interestingly, we find that linear classification accuracy is not always predictive of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                353,
+                                505,
+                                367
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        353,
+                                        505,
+                                        367
+                                    ],
+                                    "score": 1.0,
+                                    "content": "low-data classification accuracy, emphasizing the importance of this metric as a stand-alone",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                363,
+                                296,
+                                379
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        363,
+                                        296,
+                                        379
+                                    ],
+                                    "score": 1.0,
+                                    "content": "benchmark for unsupervised learning.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                135,
+                                379,
+                                506,
+                                393
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        135,
+                                        379,
+                                        506,
+                                        393
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• Finally, we assess the generality of CPC representations by transferring them to a new task",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                391,
+                                505,
+                                403
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        391,
+                                        505,
+                                        403
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and dataset: object detection on PASCAL-VOC 2007. Consistent with the results from the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                402,
+                                468,
+                                415
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        402,
+                                        468,
+                                        415
+                                    ],
+                                    "score": 1.0,
+                                    "content": "previous section, we find CPC to give state-of-the-art performance in this setting.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26,
+                            "is_list_end_line": true
+                        }
+                    ],
+                    "index": 18,
+                    "bbox_fs": [
+                        133,
+                        213,
+                        506,
+                        415
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        429,
+                        244,
+                        442
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                428,
+                                245,
+                                444
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        428,
+                                        245,
+                                        444
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2 EXPERIMENTAL SETUP",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 27
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        455,
+                        505,
+                        477
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                453,
+                                505,
+                                468
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        453,
+                                        505,
+                                        468
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We first review the CPC architecture and learning objective in section 2.1, before detailing how we",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                466,
+                                405,
+                                478
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        466,
+                                        405,
+                                        478
+                                    ],
+                                    "score": 1.0,
+                                    "content": "use its resulting representations for image recognition tasks in section 2.2.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 28.5,
+                    "bbox_fs": [
+                        105,
+                        453,
+                        505,
+                        478
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        490,
+                        286,
+                        502
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                490,
+                                287,
+                                503
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        490,
+                                        287,
+                                        503
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2.1 CONTRASTIVE PREDICTIVE CODING",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 30
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        511,
+                        505,
+                        588
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                510,
+                                505,
+                                524
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        510,
+                                        505,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Contrastive Predictive Coding as formulated in (van den Oord et al., 2018) learns representations",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                523,
+                                505,
+                                535
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        523,
+                                        505,
+                                        535
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by training neural networks to predict the representations of future observations from those of past",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                534,
+                                505,
+                                546
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        534,
+                                        505,
+                                        546
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ones. When applied to images, the original formulation of CPC operates by predicting the represen-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                545,
+                                505,
+                                556
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        545,
+                                        505,
+                                        556
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tations of patches below a certain position from those above it (Fig. 2, left). These predictions are",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                555,
+                                506,
+                                569
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        555,
+                                        506,
+                                        569
+                                    ],
+                                    "score": 1.0,
+                                    "content": "evaluated using a contrastive loss, in which the network must correctly classify the ‘future’ repre-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                566,
+                                505,
+                                578
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        566,
+                                        505,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sentation amongst a set of unrelated ‘negative’ representations. This avoids trivial solutions such as",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                577,
+                                506,
+                                591
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        577,
+                                        506,
+                                        591
+                                    ],
+                                    "score": 1.0,
+                                    "content": "representing all patches with a constant vector, as would be the case with a mean squared error loss.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 34,
+                    "bbox_fs": [
+                        105,
+                        510,
+                        506,
+                        591
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        594,
+                        505,
+                        683
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                591,
+                                507,
+                                609
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        591,
+                                        484,
+                                        609
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In the CPC architecture, each input image is first divided into a set of overlapping patches",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        484,
+                                        596,
+                                        501,
+                                        606
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\mathbf { \\delta } _ { \\mathbf { x } _ { i , j } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        501,
+                                        591,
+                                        507,
+                                        609
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                604,
+                                506,
+                                618
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        604,
+                                        304,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": "each of which is encoded with a neural network",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        605,
+                                        315,
+                                        616
+                                    ],
+                                    "score": 0.88,
+                                    "content": "f _ { \\theta }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        315,
+                                        604,
+                                        397,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": "into a single vector",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        397,
+                                        605,
+                                        461,
+                                        618
+                                    ],
+                                    "score": 0.93,
+                                    "content": "z _ { i , j } = f _ { \\theta } ( \\pmb { x } _ { i , j } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        462,
+                                        604,
+                                        506,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". To make",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                615,
+                                506,
+                                629
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        615,
+                                        289,
+                                        629
+                                    ],
+                                    "score": 1.0,
+                                    "content": "predictions, a masked convolutional network",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        290,
+                                        618,
+                                        301,
+                                        628
+                                    ],
+                                    "score": 0.87,
+                                    "content": "g _ { \\phi }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        302,
+                                        615,
+                                        506,
+                                        629
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is then applied to the grid of feature vectors. The",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                627,
+                                506,
+                                640
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        627,
+                                        399,
+                                        640
+                                    ],
+                                    "score": 1.0,
+                                    "content": "masks are such that the receptive field of each resulting context vector",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        400,
+                                        628,
+                                        415,
+                                        639
+                                    ],
+                                    "score": 0.88,
+                                    "content": "c _ { i , j }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        415,
+                                        627,
+                                        506,
+                                        640
+                                    ],
+                                    "score": 1.0,
+                                    "content": "only includes feature",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                637,
+                                506,
+                                652
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        637,
+                                        268,
+                                        652
+                                    ],
+                                    "score": 1.0,
+                                    "content": "vectors that lie above it in the image (i.e.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        268,
+                                        638,
+                                        320,
+                                        650
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\{ z _ { u , v } \\} _ { u \\leq i , v } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        320,
+                                        637,
+                                        506,
+                                        652
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". The prediction task then consists o predicting",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                648,
+                                506,
+                                662
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        648,
+                                        201,
+                                        662
+                                    ],
+                                    "score": 1.0,
+                                    "content": "‘future’ feature vectors",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        202,
+                                        650,
+                                        227,
+                                        661
+                                    ],
+                                    "score": 0.9,
+                                    "content": "z _ { i + k , j }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        228,
+                                        648,
+                                        346,
+                                        662
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from current context vectors",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        346,
+                                        650,
+                                        361,
+                                        661
+                                    ],
+                                    "score": 0.88,
+                                    "content": "c _ { i , j }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        361,
+                                        648,
+                                        392,
+                                        662
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        393,
+                                        649,
+                                        419,
+                                        659
+                                    ],
+                                    "score": 0.9,
+                                    "content": "k > 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        420,
+                                        648,
+                                        506,
+                                        662
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". The predictions are",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                660,
+                                506,
+                                673
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        660,
+                                        260,
+                                        673
+                                    ],
+                                    "score": 1.0,
+                                    "content": "made linearly: given a context vector",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        260,
+                                        662,
+                                        275,
+                                        672
+                                    ],
+                                    "score": 0.86,
+                                    "content": "c _ { i , j }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        275,
+                                        660,
+                                        358,
+                                        673
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", a prediction length",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        358,
+                                        660,
+                                        384,
+                                        670
+                                    ],
+                                    "score": 0.9,
+                                    "content": "k > 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        385,
+                                        660,
+                                        486,
+                                        673
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and a prediction matrix",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        486,
+                                        660,
+                                        501,
+                                        671
+                                    ],
+                                    "score": 0.88,
+                                    "content": "W _ { k }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        501,
+                                        660,
+                                        506,
+                                        673
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                671,
+                                301,
+                                685
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        671,
+                                        227,
+                                        685
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the predicted feature vector is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        228,
+                                        672,
+                                        297,
+                                        683
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\hat { \\boldsymbol { z } } _ { i + k , j } = \\boldsymbol { W } _ { k } \\boldsymbol { c } _ { i , j }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        297,
+                                        671,
+                                        301,
+                                        685
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        }
+                    ],
+                    "index": 41.5,
+                    "bbox_fs": [
+                        104,
+                        591,
+                        507,
+                        685
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        687,
+                        504,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                688,
+                                505,
+                                700
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        688,
+                                        505,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The quality of this prediction is then evaluated using a contrastive loss. Specifically, the goal is to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                699,
+                                506,
+                                711
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        699,
+                                        228,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "correctly recognize the target",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        229,
+                                        700,
+                                        254,
+                                        711
+                                    ],
+                                    "score": 0.82,
+                                    "content": "z _ { i + k , j }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        254,
+                                        699,
+                                        462,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "among a set of randomly sampled feature vectors",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        462,
+                                        699,
+                                        481,
+                                        711
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\{ z _ { l } \\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        482,
+                                        699,
+                                        506,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                709,
+                                506,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        709,
+                                        506,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the dataset. We compute the probability assigned to the target using a softmax, and evaluate this",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                721,
+                                505,
+                                734
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        721,
+                                        505,
+                                        734
+                                    ],
+                                    "score": 1.0,
+                                    "content": "probability using the usual cross-entropy loss. Summing this loss over locations and prediction",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                385,
+                                427,
+                                399
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        385,
+                                        427,
+                                        399
+                                    ],
+                                    "score": 1.0,
+                                    "content": "offsets, we arrive at the CPC objective as defined in (van den Oord et al., 2018):",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 47.5,
+                    "bbox_fs": [
+                        105,
+                        688,
+                        506,
+                        734
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "image",
+                    "bbox": [
+                        107,
+                        83,
+                        504,
+                        233
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                107,
+                                83,
+                                504,
+                                233
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        83,
+                                        504,
+                                        233
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                107,
+                                                83,
+                                                504,
+                                                233
+                                            ],
+                                            "score": 0.97,
+                                            "type": "image",
+                                            "image_path": "e21408d1a55db66ba2cac6a3f4d98b0d1a13c2f1211e3956f93d67bae89bbaae.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        83,
+                                        504,
+                                        133.0
+                                    ],
+                                    "spans": [],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        107,
+                                        133.0,
+                                        504,
+                                        183.0
+                                    ],
+                                    "spans": [],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        107,
+                                        183.0,
+                                        504,
+                                        233.0
+                                    ],
+                                    "spans": [],
+                                    "index": 2
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                106,
+                                237,
+                                506,
+                                369
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        237,
+                                        506,
+                                        249
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                237,
+                                                506,
+                                                249
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 2: Overview of the framework for semi-supervised learning with Contrastive Predictive",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        248,
+                                        505,
+                                        261
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                248,
+                                                505,
+                                                261
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Coding. Left: unsupervised pre-training with the spatial prediction task (See Section 2.1). First,",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        259,
+                                        506,
+                                        272
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                259,
+                                                506,
+                                                272
+                                            ],
+                                            "score": 1.0,
+                                            "content": "an image is divided into a grid of overlapping patches. Each patch is encoded independently from",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 5
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        269,
+                                        506,
+                                        283
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                269,
+                                                506,
+                                                283
+                                            ],
+                                            "score": 1.0,
+                                            "content": "the rest with a feature extractor (blue) which terminates with a mean-pooling operation, yielding a",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 6
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        281,
+                                        506,
+                                        294
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                281,
+                                                506,
+                                                294
+                                            ],
+                                            "score": 1.0,
+                                            "content": "single feature vector for that patch. Doing so for all patches yields a field of such feature vectors",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 7
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        292,
+                                        505,
+                                        304
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                292,
+                                                505,
+                                                304
+                                            ],
+                                            "score": 1.0,
+                                            "content": "(wireframe vectors). Feature vectors above a certain level (in this case, the center of the image)",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 8
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        303,
+                                        506,
+                                        315
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                303,
+                                                506,
+                                                315
+                                            ],
+                                            "score": 1.0,
+                                            "content": "are then aggregated with a context network (red), yielding a row of context vectors which are used",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 9
+                                },
+                                {
+                                    "bbox": [
+                                        104,
+                                        313,
+                                        506,
+                                        326
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                104,
+                                                313,
+                                                506,
+                                                326
+                                            ],
+                                            "score": 1.0,
+                                            "content": "to linearly predict features vectors below. Right: using the CPC representation for a classification",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 10
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        324,
+                                        506,
+                                        338
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                324,
+                                                506,
+                                                338
+                                            ],
+                                            "score": 1.0,
+                                            "content": "task. Having trained the encoder network, the context network (red) is discarded and replaced by a",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 11
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        335,
+                                        506,
+                                        349
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                335,
+                                                506,
+                                                349
+                                            ],
+                                            "score": 1.0,
+                                            "content": "classifier network (green) which can be trained in a supervised manner. For some experiments, we",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 12
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        347,
+                                        505,
+                                        358
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                347,
+                                                505,
+                                                358
+                                            ],
+                                            "score": 1.0,
+                                            "content": "also fine-tune the encoder network (blue) for the classification task. When applying the encoder to",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 13
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        358,
+                                        485,
+                                        370
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                358,
+                                                485,
+                                                370
+                                            ],
+                                            "score": 1.0,
+                                            "content": "cropped patches (as opposed to the full image) we refer to it as a patched ResNet in the figure.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 14
+                                }
+                            ],
+                            "index": 8.5
+                        }
+                    ],
+                    "index": 4.75
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        385,
+                        426,
+                        398
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                385,
+                                427,
+                                399
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        385,
+                                        427,
+                                        399
+                                    ],
+                                    "score": 1.0,
+                                    "content": "offsets, we arrive at the CPC objective as defined in (van den Oord et al., 2018):",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        114,
+                        399,
+                        495,
+                        433
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                114,
+                                399,
+                                495,
+                                433
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        399,
+                                        495,
+                                        433
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\mathcal { L } _ { \\mathrm { C P C } } = - \\sum _ { i , j , k } \\log p ( z _ { i + k , j } | \\hat { z } _ { i + k , j } , \\{ z _ { l } \\} ) = - \\sum _ { i , j , k } \\log \\frac { \\exp ( \\hat { z } _ { i + k , j } ^ { T } z _ { i + k , j } ) } { \\exp ( \\hat { z } _ { i + k , j } ^ { T } z _ { i + k , j } ) + \\sum _ { l } \\exp ( \\hat { z } _ { i + k , j } ^ { T } z _ { l } ) }",
+                                    "type": "interline_equation",
+                                    "image_path": "7113b15debaadf2fc32b7ca0c3e55fb0689eecd2935810917cee824de20f6604.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                114,
+                                399,
+                                495,
+                                410.3333333333333
+                            ],
+                            "spans": [],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                410.3333333333333,
+                                495,
+                                421.66666666666663
+                            ],
+                            "spans": [],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                421.66666666666663,
+                                495,
+                                432.99999999999994
+                            ],
+                            "spans": [],
+                            "index": 18
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        434,
+                        505,
+                        480
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                434,
+                                505,
+                                447
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        434,
+                                        194,
+                                        447
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The negative samples",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        195,
+                                        435,
+                                        214,
+                                        447
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\left\\{ z _ { l } \\right\\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        214,
+                                        434,
+                                        505,
+                                        447
+                                    ],
+                                    "score": 1.0,
+                                    "content": "are taken from other locations in the image and other images in the mini-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                446,
+                                506,
+                                459
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        446,
+                                        506,
+                                        459
+                                    ],
+                                    "score": 1.0,
+                                    "content": "batch. This loss is called InfoNCE (van den Oord et al., 2018) as it is inspired by Noise-Contrastive",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                457,
+                                505,
+                                469
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        457,
+                                        197,
+                                        469
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Estimation (Gutmann",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        198,
+                                        457,
+                                        207,
+                                        467
+                                    ],
+                                    "score": 0.43,
+                                    "content": "\\&",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        208,
+                                        457,
+                                        505,
+                                        469
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Hyvarinen, 2010; Mnih & Kavukcuoglu, 2013) and has been shown to ¨",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                468,
+                                452,
+                                481
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        468,
+                                        278,
+                                        481
+                                    ],
+                                    "score": 1.0,
+                                    "content": "maximize the mutual information between",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        278,
+                                        470,
+                                        294,
+                                        480
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\mathbf { } _ { c _ { i , j } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        294,
+                                        468,
+                                        312,
+                                        481
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        312,
+                                        469,
+                                        339,
+                                        480
+                                    ],
+                                    "score": 0.9,
+                                    "content": "z _ { i + k , j }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        339,
+                                        468,
+                                        452,
+                                        481
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(van den Oord et al., 2018).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 20.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        492,
+                        235,
+                        503
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                492,
+                                236,
+                                505
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        492,
+                                        236,
+                                        505
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2.2 EVALUATION PROTOCOL",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 23
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        512,
+                        505,
+                        568
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                512,
+                                504,
+                                525
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        512,
+                                        252,
+                                        525
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Having trained an encoder network",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        252,
+                                        513,
+                                        262,
+                                        524
+                                    ],
+                                    "score": 0.87,
+                                    "content": "f _ { \\theta }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        263,
+                                        512,
+                                        342,
+                                        525
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", a context network",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        342,
+                                        515,
+                                        353,
+                                        525
+                                    ],
+                                    "score": 0.86,
+                                    "content": "g _ { \\phi }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        353,
+                                        512,
+                                        477,
+                                        525
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and a set of linear predictors",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        477,
+                                        513,
+                                        504,
+                                        525
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\{ W _ { k } \\}",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                524,
+                                505,
+                                536
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        524,
+                                        279,
+                                        536
+                                    ],
+                                    "score": 1.0,
+                                    "content": "using the CPC objective, we use the latents",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        279,
+                                        524,
+                                        323,
+                                        536
+                                    ],
+                                    "score": 0.93,
+                                    "content": "z = f _ { \\boldsymbol { \\theta } } ( \\pmb { x } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        323,
+                                        524,
+                                        483,
+                                        536
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as a representation of new observations",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        483,
+                                        527,
+                                        490,
+                                        534
+                                    ],
+                                    "score": 0.78,
+                                    "content": "x",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        490,
+                                        524,
+                                        505,
+                                        536
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                533,
+                                505,
+                                547
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        533,
+                                        360,
+                                        547
+                                    ],
+                                    "score": 1.0,
+                                    "content": "downstream tasks, and discard the rest. We then train a model",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        360,
+                                        535,
+                                        373,
+                                        547
+                                    ],
+                                    "score": 0.9,
+                                    "content": "h _ { \\psi }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        374,
+                                        533,
+                                        505,
+                                        547
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to classify these representations",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                545,
+                                505,
+                                559
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        545,
+                                        391,
+                                        559
+                                    ],
+                                    "score": 1.0,
+                                    "content": "given a dataset of labeled images. More formally, given a dataset of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        392,
+                                        546,
+                                        402,
+                                        556
+                                    ],
+                                    "score": 0.82,
+                                    "content": "N",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        402,
+                                        545,
+                                        477,
+                                        559
+                                    ],
+                                    "score": 1.0,
+                                    "content": "unlabeled images",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        478,
+                                        546,
+                                        505,
+                                        557
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\mathbb { D } _ { u } =",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                555,
+                                450,
+                                571
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        556,
+                                        128,
+                                        569
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\left\\{ x _ { n } \\right\\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        129,
+                                        555,
+                                        306,
+                                        571
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and a (potentially much smaller) dataset of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        557,
+                                        317,
+                                        567
+                                    ],
+                                    "score": 0.85,
+                                    "content": "M",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        318,
+                                        555,
+                                        380,
+                                        571
+                                    ],
+                                    "score": 1.0,
+                                    "content": "labeled images",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        381,
+                                        556,
+                                        446,
+                                        569
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\mathbb { D } _ { l } = \\{ x _ { m } , y _ { m } \\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        446,
+                                        555,
+                                        450,
+                                        571
+                                    ],
+                                    "score": 1.0,
+                                    "content": ":",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 26
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        133,
+                        569,
+                        478,
+                        604
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                133,
+                                569,
+                                478,
+                                604
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        133,
+                                        569,
+                                        478,
+                                        604
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\theta ^ { * } = \\arg \\operatorname* { m i n } _ { \\theta } \\frac { 1 } { N } \\sum _ { n = 1 } ^ { N } \\mathcal { L } _ { \\mathrm { C P C } } [ f _ { \\theta } ( x _ { n } ) ] , \\quad \\psi ^ { * } = \\arg \\operatorname* { m i n } _ { \\psi } \\frac { 1 } { M } \\sum _ { m = 1 } ^ { M } \\mathcal { L } _ { \\mathrm { S u p } } [ h _ { \\psi } \\circ f _ { \\theta ^ { * } } ( x _ { m } ) , y _ { m } ]",
+                                    "type": "interline_equation",
+                                    "image_path": "c6df6158bc3640c41b4e80de8a77924da143cb3d171b2d5421986f303ad176ed.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 30,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                133,
+                                569,
+                                478,
+                                580.6666666666666
+                            ],
+                            "spans": [],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                133,
+                                580.6666666666666,
+                                478,
+                                592.3333333333333
+                            ],
+                            "spans": [],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                133,
+                                592.3333333333333,
+                                478,
+                                603.9999999999999
+                            ],
+                            "spans": [],
+                            "index": 31
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        605,
+                        505,
+                        661
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                604,
+                                506,
+                                618
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        604,
+                                        295,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In all cases, the dataset of unlabeled images",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        295,
+                                        605,
+                                        309,
+                                        616
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\mathbb { D } _ { u }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        309,
+                                        604,
+                                        506,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": "we pre-train on is the full ImageNet ILSVRC",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                615,
+                                505,
+                                628
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        615,
+                                        431,
+                                        628
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2012 training set (Russakovsky et al., 2015). We consider three labeled datasets",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        431,
+                                        616,
+                                        443,
+                                        627
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\mathbb { D } _ { l }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        443,
+                                        615,
+                                        505,
+                                        628
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for evaluation,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                627,
+                                506,
+                                640
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        627,
+                                        244,
+                                        640
+                                    ],
+                                    "score": 1.0,
+                                    "content": "each with an associated classifier",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        245,
+                                        627,
+                                        258,
+                                        639
+                                    ],
+                                    "score": 0.9,
+                                    "content": "h _ { \\psi }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        258,
+                                        627,
+                                        347,
+                                        640
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and supervised losse",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        347,
+                                        627,
+                                        367,
+                                        639
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\mathcal { L } _ { \\mathrm { { S u p } } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        367,
+                                        627,
+                                        506,
+                                        640
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(see Fig. 2, right). This protocol",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                637,
+                                506,
+                                650
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        637,
+                                        506,
+                                        650
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is sufficiently generic to allow us to later compare the CPC representation to other methods which",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                648,
+                                330,
+                                662
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        648,
+                                        316,
+                                        662
+                                    ],
+                                    "score": 1.0,
+                                    "content": "have their own means of learning a feature extractor",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        317,
+                                        649,
+                                        326,
+                                        660
+                                    ],
+                                    "score": 0.87,
+                                    "content": "f _ { \\theta }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        327,
+                                        648,
+                                        330,
+                                        662
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 34
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        665,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                664,
+                                505,
+                                679
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        664,
+                                        505,
+                                        679
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Linear classification is the standard benchmark for evaluating the quality of unsupervised image",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                677,
+                                505,
+                                689
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        677,
+                                        336,
+                                        689
+                                    ],
+                                    "score": 1.0,
+                                    "content": "representations. In this regime, the classification network",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        337,
+                                        677,
+                                        350,
+                                        689
+                                    ],
+                                    "score": 0.89,
+                                    "content": "h _ { \\psi }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        350,
+                                        677,
+                                        505,
+                                        689
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is restricted to mean pooling followed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                687,
+                                506,
+                                701
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        687,
+                                        291,
+                                        701
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by a single linear layer, and the parameters of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        291,
+                                        688,
+                                        302,
+                                        699
+                                    ],
+                                    "score": 0.88,
+                                    "content": "f _ { \\theta }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        302,
+                                        687,
+                                        442,
+                                        701
+                                    ],
+                                    "score": 1.0,
+                                    "content": "are kept fixed. The labeled dataset",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        443,
+                                        688,
+                                        455,
+                                        699
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\mathbb { D } _ { l }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        455,
+                                        687,
+                                        506,
+                                        701
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the entire",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                698,
+                                505,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        698,
+                                        280,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ImageNet dataset, and the supervised loss",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        281,
+                                        700,
+                                        300,
+                                        711
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\mathcal { L } _ { \\mathrm { { S u p } } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        300,
+                                        698,
+                                        505,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is standard cross-entropy. We use the same data-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                710,
+                                506,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        710,
+                                        506,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "augmentation as in the unsupervised learning phase for training, and none at test time and evaluate",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                720,
+                                183,
+                                734
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        720,
+                                        183,
+                                        734
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with a single crop.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        }
+                    ],
+                    "index": 39.5
+                }
+            ],
+            "page_idx": 2,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        308,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                25,
+                                309,
+                                39
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        25,
+                                        309,
+                                        39
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Under review as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        751,
+                        309,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                301,
+                                750,
+                                310,
+                                762
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        301,
+                                        750,
+                                        310,
+                                        762
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "image",
+                    "bbox": [
+                        107,
+                        83,
+                        504,
+                        233
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                107,
+                                83,
+                                504,
+                                233
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        83,
+                                        504,
+                                        233
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                107,
+                                                83,
+                                                504,
+                                                233
+                                            ],
+                                            "score": 0.97,
+                                            "type": "image",
+                                            "image_path": "e21408d1a55db66ba2cac6a3f4d98b0d1a13c2f1211e3956f93d67bae89bbaae.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        83,
+                                        504,
+                                        133.0
+                                    ],
+                                    "spans": [],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        107,
+                                        133.0,
+                                        504,
+                                        183.0
+                                    ],
+                                    "spans": [],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        107,
+                                        183.0,
+                                        504,
+                                        233.0
+                                    ],
+                                    "spans": [],
+                                    "index": 2
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                106,
+                                237,
+                                506,
+                                369
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        237,
+                                        506,
+                                        249
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                237,
+                                                506,
+                                                249
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 2: Overview of the framework for semi-supervised learning with Contrastive Predictive",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        248,
+                                        505,
+                                        261
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                248,
+                                                505,
+                                                261
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Coding. Left: unsupervised pre-training with the spatial prediction task (See Section 2.1). First,",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        259,
+                                        506,
+                                        272
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                259,
+                                                506,
+                                                272
+                                            ],
+                                            "score": 1.0,
+                                            "content": "an image is divided into a grid of overlapping patches. Each patch is encoded independently from",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 5
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        269,
+                                        506,
+                                        283
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                269,
+                                                506,
+                                                283
+                                            ],
+                                            "score": 1.0,
+                                            "content": "the rest with a feature extractor (blue) which terminates with a mean-pooling operation, yielding a",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 6
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        281,
+                                        506,
+                                        294
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                281,
+                                                506,
+                                                294
+                                            ],
+                                            "score": 1.0,
+                                            "content": "single feature vector for that patch. Doing so for all patches yields a field of such feature vectors",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 7
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        292,
+                                        505,
+                                        304
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                292,
+                                                505,
+                                                304
+                                            ],
+                                            "score": 1.0,
+                                            "content": "(wireframe vectors). Feature vectors above a certain level (in this case, the center of the image)",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 8
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        303,
+                                        506,
+                                        315
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                303,
+                                                506,
+                                                315
+                                            ],
+                                            "score": 1.0,
+                                            "content": "are then aggregated with a context network (red), yielding a row of context vectors which are used",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 9
+                                },
+                                {
+                                    "bbox": [
+                                        104,
+                                        313,
+                                        506,
+                                        326
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                104,
+                                                313,
+                                                506,
+                                                326
+                                            ],
+                                            "score": 1.0,
+                                            "content": "to linearly predict features vectors below. Right: using the CPC representation for a classification",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 10
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        324,
+                                        506,
+                                        338
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                324,
+                                                506,
+                                                338
+                                            ],
+                                            "score": 1.0,
+                                            "content": "task. Having trained the encoder network, the context network (red) is discarded and replaced by a",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 11
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        335,
+                                        506,
+                                        349
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                335,
+                                                506,
+                                                349
+                                            ],
+                                            "score": 1.0,
+                                            "content": "classifier network (green) which can be trained in a supervised manner. For some experiments, we",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 12
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        347,
+                                        505,
+                                        358
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                347,
+                                                505,
+                                                358
+                                            ],
+                                            "score": 1.0,
+                                            "content": "also fine-tune the encoder network (blue) for the classification task. When applying the encoder to",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 13
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        358,
+                                        485,
+                                        370
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                358,
+                                                485,
+                                                370
+                                            ],
+                                            "score": 1.0,
+                                            "content": "cropped patches (as opposed to the full image) we refer to it as a patched ResNet in the figure.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 14
+                                }
+                            ],
+                            "index": 8.5
+                        }
+                    ],
+                    "index": 4.75
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        385,
+                        426,
+                        398
+                    ],
+                    "lines": [],
+                    "index": 15,
+                    "bbox_fs": [
+                        106,
+                        385,
+                        427,
+                        399
+                    ],
+                    "lines_deleted": true
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        114,
+                        399,
+                        495,
+                        433
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                114,
+                                399,
+                                495,
+                                433
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        399,
+                                        495,
+                                        433
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\mathcal { L } _ { \\mathrm { C P C } } = - \\sum _ { i , j , k } \\log p ( z _ { i + k , j } | \\hat { z } _ { i + k , j } , \\{ z _ { l } \\} ) = - \\sum _ { i , j , k } \\log \\frac { \\exp ( \\hat { z } _ { i + k , j } ^ { T } z _ { i + k , j } ) } { \\exp ( \\hat { z } _ { i + k , j } ^ { T } z _ { i + k , j } ) + \\sum _ { l } \\exp ( \\hat { z } _ { i + k , j } ^ { T } z _ { l } ) }",
+                                    "type": "interline_equation",
+                                    "image_path": "7113b15debaadf2fc32b7ca0c3e55fb0689eecd2935810917cee824de20f6604.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                114,
+                                399,
+                                495,
+                                410.3333333333333
+                            ],
+                            "spans": [],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                410.3333333333333,
+                                495,
+                                421.66666666666663
+                            ],
+                            "spans": [],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                421.66666666666663,
+                                495,
+                                432.99999999999994
+                            ],
+                            "spans": [],
+                            "index": 18
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        434,
+                        505,
+                        480
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                434,
+                                505,
+                                447
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        434,
+                                        194,
+                                        447
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The negative samples",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        195,
+                                        435,
+                                        214,
+                                        447
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\left\\{ z _ { l } \\right\\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        214,
+                                        434,
+                                        505,
+                                        447
+                                    ],
+                                    "score": 1.0,
+                                    "content": "are taken from other locations in the image and other images in the mini-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                446,
+                                506,
+                                459
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        446,
+                                        506,
+                                        459
+                                    ],
+                                    "score": 1.0,
+                                    "content": "batch. This loss is called InfoNCE (van den Oord et al., 2018) as it is inspired by Noise-Contrastive",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                457,
+                                505,
+                                469
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        457,
+                                        197,
+                                        469
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Estimation (Gutmann",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        198,
+                                        457,
+                                        207,
+                                        467
+                                    ],
+                                    "score": 0.43,
+                                    "content": "\\&",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        208,
+                                        457,
+                                        505,
+                                        469
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Hyvarinen, 2010; Mnih & Kavukcuoglu, 2013) and has been shown to ¨",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                468,
+                                452,
+                                481
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        468,
+                                        278,
+                                        481
+                                    ],
+                                    "score": 1.0,
+                                    "content": "maximize the mutual information between",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        278,
+                                        470,
+                                        294,
+                                        480
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\mathbf { } _ { c _ { i , j } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        294,
+                                        468,
+                                        312,
+                                        481
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        312,
+                                        469,
+                                        339,
+                                        480
+                                    ],
+                                    "score": 0.9,
+                                    "content": "z _ { i + k , j }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        339,
+                                        468,
+                                        452,
+                                        481
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(van den Oord et al., 2018).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 20.5,
+                    "bbox_fs": [
+                        105,
+                        434,
+                        506,
+                        481
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        492,
+                        235,
+                        503
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                492,
+                                236,
+                                505
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        492,
+                                        236,
+                                        505
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2.2 EVALUATION PROTOCOL",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 23
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        512,
+                        505,
+                        568
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                512,
+                                504,
+                                525
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        512,
+                                        252,
+                                        525
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Having trained an encoder network",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        252,
+                                        513,
+                                        262,
+                                        524
+                                    ],
+                                    "score": 0.87,
+                                    "content": "f _ { \\theta }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        263,
+                                        512,
+                                        342,
+                                        525
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", a context network",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        342,
+                                        515,
+                                        353,
+                                        525
+                                    ],
+                                    "score": 0.86,
+                                    "content": "g _ { \\phi }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        353,
+                                        512,
+                                        477,
+                                        525
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and a set of linear predictors",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        477,
+                                        513,
+                                        504,
+                                        525
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\{ W _ { k } \\}",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                524,
+                                505,
+                                536
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        524,
+                                        279,
+                                        536
+                                    ],
+                                    "score": 1.0,
+                                    "content": "using the CPC objective, we use the latents",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        279,
+                                        524,
+                                        323,
+                                        536
+                                    ],
+                                    "score": 0.93,
+                                    "content": "z = f _ { \\boldsymbol { \\theta } } ( \\pmb { x } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        323,
+                                        524,
+                                        483,
+                                        536
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as a representation of new observations",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        483,
+                                        527,
+                                        490,
+                                        534
+                                    ],
+                                    "score": 0.78,
+                                    "content": "x",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        490,
+                                        524,
+                                        505,
+                                        536
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                533,
+                                505,
+                                547
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        533,
+                                        360,
+                                        547
+                                    ],
+                                    "score": 1.0,
+                                    "content": "downstream tasks, and discard the rest. We then train a model",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        360,
+                                        535,
+                                        373,
+                                        547
+                                    ],
+                                    "score": 0.9,
+                                    "content": "h _ { \\psi }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        374,
+                                        533,
+                                        505,
+                                        547
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to classify these representations",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                545,
+                                505,
+                                559
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        545,
+                                        391,
+                                        559
+                                    ],
+                                    "score": 1.0,
+                                    "content": "given a dataset of labeled images. More formally, given a dataset of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        392,
+                                        546,
+                                        402,
+                                        556
+                                    ],
+                                    "score": 0.82,
+                                    "content": "N",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        402,
+                                        545,
+                                        477,
+                                        559
+                                    ],
+                                    "score": 1.0,
+                                    "content": "unlabeled images",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        478,
+                                        546,
+                                        505,
+                                        557
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\mathbb { D } _ { u } =",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                555,
+                                450,
+                                571
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        556,
+                                        128,
+                                        569
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\left\\{ x _ { n } \\right\\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        129,
+                                        555,
+                                        306,
+                                        571
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and a (potentially much smaller) dataset of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        557,
+                                        317,
+                                        567
+                                    ],
+                                    "score": 0.85,
+                                    "content": "M",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        318,
+                                        555,
+                                        380,
+                                        571
+                                    ],
+                                    "score": 1.0,
+                                    "content": "labeled images",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        381,
+                                        556,
+                                        446,
+                                        569
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\mathbb { D } _ { l } = \\{ x _ { m } , y _ { m } \\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        446,
+                                        555,
+                                        450,
+                                        571
+                                    ],
+                                    "score": 1.0,
+                                    "content": ":",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 26,
+                    "bbox_fs": [
+                        105,
+                        512,
+                        505,
+                        571
+                    ]
+                },
+                {
+                    "type": "interline_equation",
+                    "bbox": [
+                        133,
+                        569,
+                        478,
+                        604
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                133,
+                                569,
+                                478,
+                                604
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        133,
+                                        569,
+                                        478,
+                                        604
+                                    ],
+                                    "score": 0.94,
+                                    "content": "\\theta ^ { * } = \\arg \\operatorname* { m i n } _ { \\theta } \\frac { 1 } { N } \\sum _ { n = 1 } ^ { N } \\mathcal { L } _ { \\mathrm { C P C } } [ f _ { \\theta } ( x _ { n } ) ] , \\quad \\psi ^ { * } = \\arg \\operatorname* { m i n } _ { \\psi } \\frac { 1 } { M } \\sum _ { m = 1 } ^ { M } \\mathcal { L } _ { \\mathrm { S u p } } [ h _ { \\psi } \\circ f _ { \\theta ^ { * } } ( x _ { m } ) , y _ { m } ]",
+                                    "type": "interline_equation",
+                                    "image_path": "c6df6158bc3640c41b4e80de8a77924da143cb3d171b2d5421986f303ad176ed.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 30,
+                    "virtual_lines": [
+                        {
+                            "bbox": [
+                                133,
+                                569,
+                                478,
+                                580.6666666666666
+                            ],
+                            "spans": [],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                133,
+                                580.6666666666666,
+                                478,
+                                592.3333333333333
+                            ],
+                            "spans": [],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                133,
+                                592.3333333333333,
+                                478,
+                                603.9999999999999
+                            ],
+                            "spans": [],
+                            "index": 31
+                        }
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        605,
+                        505,
+                        661
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                604,
+                                506,
+                                618
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        604,
+                                        295,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In all cases, the dataset of unlabeled images",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        295,
+                                        605,
+                                        309,
+                                        616
+                                    ],
+                                    "score": 0.89,
+                                    "content": "\\mathbb { D } _ { u }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        309,
+                                        604,
+                                        506,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": "we pre-train on is the full ImageNet ILSVRC",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                615,
+                                505,
+                                628
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        615,
+                                        431,
+                                        628
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2012 training set (Russakovsky et al., 2015). We consider three labeled datasets",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        431,
+                                        616,
+                                        443,
+                                        627
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\mathbb { D } _ { l }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        443,
+                                        615,
+                                        505,
+                                        628
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for evaluation,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                627,
+                                506,
+                                640
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        627,
+                                        244,
+                                        640
+                                    ],
+                                    "score": 1.0,
+                                    "content": "each with an associated classifier",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        245,
+                                        627,
+                                        258,
+                                        639
+                                    ],
+                                    "score": 0.9,
+                                    "content": "h _ { \\psi }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        258,
+                                        627,
+                                        347,
+                                        640
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and supervised losse",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        347,
+                                        627,
+                                        367,
+                                        639
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\mathcal { L } _ { \\mathrm { { S u p } } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        367,
+                                        627,
+                                        506,
+                                        640
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(see Fig. 2, right). This protocol",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                637,
+                                506,
+                                650
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        637,
+                                        506,
+                                        650
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is sufficiently generic to allow us to later compare the CPC representation to other methods which",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                648,
+                                330,
+                                662
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        648,
+                                        316,
+                                        662
+                                    ],
+                                    "score": 1.0,
+                                    "content": "have their own means of learning a feature extractor",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        317,
+                                        649,
+                                        326,
+                                        660
+                                    ],
+                                    "score": 0.87,
+                                    "content": "f _ { \\theta }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        327,
+                                        648,
+                                        330,
+                                        662
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 34,
+                    "bbox_fs": [
+                        104,
+                        604,
+                        506,
+                        662
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        665,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                664,
+                                505,
+                                679
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        664,
+                                        505,
+                                        679
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Linear classification is the standard benchmark for evaluating the quality of unsupervised image",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                677,
+                                505,
+                                689
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        677,
+                                        336,
+                                        689
+                                    ],
+                                    "score": 1.0,
+                                    "content": "representations. In this regime, the classification network",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        337,
+                                        677,
+                                        350,
+                                        689
+                                    ],
+                                    "score": 0.89,
+                                    "content": "h _ { \\psi }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        350,
+                                        677,
+                                        505,
+                                        689
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is restricted to mean pooling followed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                687,
+                                506,
+                                701
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        687,
+                                        291,
+                                        701
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by a single linear layer, and the parameters of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        291,
+                                        688,
+                                        302,
+                                        699
+                                    ],
+                                    "score": 0.88,
+                                    "content": "f _ { \\theta }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        302,
+                                        687,
+                                        442,
+                                        701
+                                    ],
+                                    "score": 1.0,
+                                    "content": "are kept fixed. The labeled dataset",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        443,
+                                        688,
+                                        455,
+                                        699
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\mathbb { D } _ { l }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        455,
+                                        687,
+                                        506,
+                                        701
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the entire",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                698,
+                                505,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        698,
+                                        280,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ImageNet dataset, and the supervised loss",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        281,
+                                        700,
+                                        300,
+                                        711
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\mathcal { L } _ { \\mathrm { { S u p } } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        300,
+                                        698,
+                                        505,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is standard cross-entropy. We use the same data-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                710,
+                                506,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        710,
+                                        506,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "augmentation as in the unsupervised learning phase for training, and none at test time and evaluate",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                720,
+                                183,
+                                734
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        720,
+                                        183,
+                                        734
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with a single crop.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        }
+                    ],
+                    "index": 39.5,
+                    "bbox_fs": [
+                        104,
+                        664,
+                        506,
+                        734
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        82,
+                        505,
+                        160
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                82,
+                                505,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        82,
+                                        505,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Efficient classification directly tests whether the CPC representation enables visual learning from",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                92,
+                                505,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        92,
+                                        262,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "few labels. For this task, the classifier",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        262,
+                                        94,
+                                        275,
+                                        106
+                                    ],
+                                    "score": 0.89,
+                                    "content": "h _ { \\psi }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        276,
+                                        92,
+                                        505,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is an arbitrary deep neural network (we use an 11-block",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                104,
+                                505,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        104,
+                                        505,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ResNet architecture with 4096-dimensional feature maps and 1024-dimensional bottleneck layers).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                115,
+                                505,
+                                128
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        115,
+                                        185,
+                                        128
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The labeled dataset",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        185,
+                                        116,
+                                        196,
+                                        126
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\mathbb { D } _ { l }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        197,
+                                        115,
+                                        428,
+                                        128
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is a subset of the ImageNet dataset: we investigated using",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        428,
+                                        115,
+                                        442,
+                                        126
+                                    ],
+                                    "score": 0.76,
+                                    "content": "1 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        442,
+                                        115,
+                                        445,
+                                        128
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        445,
+                                        115,
+                                        460,
+                                        126
+                                    ],
+                                    "score": 0.77,
+                                    "content": "2 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        460,
+                                        115,
+                                        463,
+                                        128
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        463,
+                                        115,
+                                        478,
+                                        126
+                                    ],
+                                    "score": 0.78,
+                                    "content": "5 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        478,
+                                        115,
+                                        482,
+                                        128
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        482,
+                                        115,
+                                        501,
+                                        126
+                                    ],
+                                    "score": 0.83,
+                                    "content": "10 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        501,
+                                        115,
+                                        505,
+                                        128
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                125,
+                                506,
+                                140
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        126,
+                                        126,
+                                        137
+                                    ],
+                                    "score": 0.84,
+                                    "content": "20 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        126,
+                                        125,
+                                        129,
+                                        140
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        130,
+                                        126,
+                                        150,
+                                        137
+                                    ],
+                                    "score": 0.86,
+                                    "content": "50 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        150,
+                                        125,
+                                        169,
+                                        140
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        169,
+                                        127,
+                                        193,
+                                        137
+                                    ],
+                                    "score": 0.87,
+                                    "content": "100 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        194,
+                                        125,
+                                        379,
+                                        140
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of the ImageNet dataset. The supervised loss",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        379,
+                                        127,
+                                        399,
+                                        138
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\mathcal { L } _ { \\mathrm { { S u p } } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        399,
+                                        125,
+                                        506,
+                                        140
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is again cross-entropy. In",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                136,
+                                505,
+                                151
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        136,
+                                        505,
+                                        151
+                                    ],
+                                    "score": 1.0,
+                                    "content": "addition to random color-dropping we use the Inception data-augmentation scheme (Szegedy et al.,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                148,
+                                426,
+                                162
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        148,
+                                        426,
+                                        162
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2014) for training, no augmentation at test-time and evaluate with a single crop.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        165,
+                        505,
+                        221
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                165,
+                                505,
+                                178
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        165,
+                                        505,
+                                        178
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Transfer learning tests the generality of the representation by applying it to a new task and dataset.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                176,
+                                505,
+                                188
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        176,
+                                        505,
+                                        188
+                                    ],
+                                    "score": 1.0,
+                                    "content": "For this we chose image detection on the PASCAL-2007 dataset, a standard benchmark in computer",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                187,
+                                506,
+                                200
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        187,
+                                        284,
+                                        200
+                                    ],
+                                    "score": 1.0,
+                                    "content": "vision (Everingham et al., 2007). As such",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        285,
+                                        187,
+                                        296,
+                                        198
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\mathbb { D } _ { l }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        297,
+                                        187,
+                                        506,
+                                        200
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the entire PASCAL-2007 dataset (comprised of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                197,
+                                506,
+                                212
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        197,
+                                        196,
+                                        212
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5011 labeled images);",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        197,
+                                        198,
+                                        209,
+                                        210
+                                    ],
+                                    "score": 0.88,
+                                    "content": "h _ { \\psi }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        210,
+                                        197,
+                                        228,
+                                        212
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        228,
+                                        199,
+                                        248,
+                                        210
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\mathcal { L } _ { \\mathrm { { S u p } } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        248,
+                                        197,
+                                        506,
+                                        212
+                                    ],
+                                    "score": 1.0,
+                                    "content": "are the Faster-RCNN architecture and loss (Ren et al., 2015). In",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                208,
+                                466,
+                                223
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        208,
+                                        466,
+                                        223
+                                    ],
+                                    "score": 1.0,
+                                    "content": "addition to color-dropping, we use scale-augmentation (Doersch et al., 2015) for training.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        226,
+                        505,
+                        292
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                226,
+                                505,
+                                239
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        226,
+                                        331,
+                                        239
+                                    ],
+                                    "score": 1.0,
+                                    "content": "For linear classification, we keep the feature extractor",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        332,
+                                        226,
+                                        342,
+                                        238
+                                    ],
+                                    "score": 0.34,
+                                    "content": "f _ { \\theta }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        342,
+                                        226,
+                                        505,
+                                        239
+                                    ],
+                                    "score": 1.0,
+                                    "content": "fixed to assess the representation in ab-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                235,
+                                506,
+                                251
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        235,
+                                        506,
+                                        251
+                                    ],
+                                    "score": 1.0,
+                                    "content": "solute terms. For efficient classification and transfer learning, we additionally explore fine-tuning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                248,
+                                505,
+                                259
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        248,
+                                        505,
+                                        259
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the feature extractor for the supervised objective. In this regime, we initialize the feature extractor",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                259,
+                                506,
+                                271
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        259,
+                                        234,
+                                        271
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and classifier with the solutions",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        234,
+                                        259,
+                                        260,
+                                        270
+                                    ],
+                                    "score": 0.4,
+                                    "content": "\\theta ^ { * } , \\psi ^ { * }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        261,
+                                        259,
+                                        506,
+                                        271
+                                    ],
+                                    "score": 1.0,
+                                    "content": "found in the previous learning phase, and train them both for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                270,
+                                505,
+                                281
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        270,
+                                        505,
+                                        281
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the supervised objective. To ensure that the feature extractor does not deviate too much from the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                280,
+                                465,
+                                294
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        280,
+                                        465,
+                                        294
+                                    ],
+                                    "score": 1.0,
+                                    "content": "solution dictated by the CPC objective, we use a smaller learning rate and early-stopping.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 14.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        319,
+                        210,
+                        332
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                318,
+                                213,
+                                334
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        318,
+                                        213,
+                                        334
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3 RELATED WORK",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        352,
+                        504,
+                        396
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                352,
+                                506,
+                                365
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        352,
+                                        506,
+                                        365
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Data-efficient learning has typically been approached by two complementary methods, both of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                363,
+                                505,
+                                375
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        363,
+                                        505,
+                                        375
+                                    ],
+                                    "score": 1.0,
+                                    "content": "which seek to make use of more plentiful unlabeled data: representation learning and semi-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                374,
+                                505,
+                                386
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        375,
+                                        452,
+                                        386
+                                    ],
+                                    "score": 1.0,
+                                    "content": "supervised learning. The former formulates an objective to learn a feature extractor",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        453,
+                                        374,
+                                        463,
+                                        385
+                                    ],
+                                    "score": 0.87,
+                                    "content": "f _ { \\theta }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        464,
+                                        375,
+                                        505,
+                                        386
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in an un-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                385,
+                                504,
+                                398
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        385,
+                                        387,
+                                        398
+                                    ],
+                                    "score": 1.0,
+                                    "content": "supervised manner, whereas the latter directly constrains the classifier",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        387,
+                                        385,
+                                        400,
+                                        397
+                                    ],
+                                    "score": 0.89,
+                                    "content": "h _ { \\psi }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        401,
+                                        385,
+                                        504,
+                                        398
+                                    ],
+                                    "score": 1.0,
+                                    "content": "using the unlabeled data.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 20.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        402,
+                        504,
+                        457
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                402,
+                                506,
+                                415
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        402,
+                                        506,
+                                        415
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Representation learning saw early success using generative modeling (Kingma et al., 2014), but",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                412,
+                                505,
+                                425
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        412,
+                                        505,
+                                        425
+                                    ],
+                                    "score": 1.0,
+                                    "content": "likelihood-based models have yet to generalize to more complex stimulus classes. Generative ad-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                424,
+                                505,
+                                436
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        424,
+                                        505,
+                                        436
+                                    ],
+                                    "score": 1.0,
+                                    "content": "versarial models have also been harnessed for representation learning (Donahue et al., 2016), and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                434,
+                                506,
+                                448
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        434,
+                                        506,
+                                        448
+                                    ],
+                                    "score": 1.0,
+                                    "content": "large-scale implementations have recently achieved corresponding gains in linear classification ac-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                446,
+                                261,
+                                459
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        446,
+                                        261,
+                                        459
+                                    ],
+                                    "score": 1.0,
+                                    "content": "curacy (Donahue & Simonyan, 2019).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        462,
+                        505,
+                        594
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                462,
+                                505,
+                                476
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        462,
+                                        505,
+                                        476
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In contrast to generative models which require the reconstruction of observations, self-supervised",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                473,
+                                505,
+                                487
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        473,
+                                        505,
+                                        487
+                                    ],
+                                    "score": 1.0,
+                                    "content": "techniques directly formulate tasks involving the learned representation. For example, simply ask-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                485,
+                                505,
+                                497
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        485,
+                                        505,
+                                        497
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ing a network to recognize the spatial layout of an image led to representations that transferred to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                495,
+                                506,
+                                509
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        495,
+                                        506,
+                                        509
+                                    ],
+                                    "score": 1.0,
+                                    "content": "popular vision tasks such as classification and detection (Doersch et al., 2015; Noroozi & Favaro,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                506,
+                                505,
+                                519
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        506,
+                                        505,
+                                        519
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2016). Other works showed that prediction of color (Zhang et al., 2016; Larsson et al., 2017) and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                518,
+                                505,
+                                530
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        518,
+                                        505,
+                                        530
+                                    ],
+                                    "score": 1.0,
+                                    "content": "image orientation (Gidaris et al., 2018), and invariance to data augmentation (Dosovitskiy et al.,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                528,
+                                505,
+                                541
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        528,
+                                        505,
+                                        541
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2014) can provide useful self-supervised tasks. Beyond single images, works have leveraged video",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                540,
+                                505,
+                                552
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        540,
+                                        505,
+                                        552
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cues such as object tracking (Wang & Gupta, 2015), frame ordering (Misra et al., 2016), and object",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                550,
+                                505,
+                                564
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        550,
+                                        505,
+                                        564
+                                    ],
+                                    "score": 1.0,
+                                    "content": "boundary cues (Li et al., 2016; Pathak et al., 2016). Non-visual information can be equally power-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                560,
+                                505,
+                                574
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        560,
+                                        505,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ful; information about camera motion (Agrawal et al., 2015; Jayaraman & Grauman, 2015), scene",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                572,
+                                506,
+                                585
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        572,
+                                        506,
+                                        585
+                                    ],
+                                    "score": 1.0,
+                                    "content": "geometry (Zamir et al., 2016), or sound (Arandjelovic & Zisserman, 2017; 2018) can all serve as",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                584,
+                                230,
+                                595
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        584,
+                                        230,
+                                        595
+                                    ],
+                                    "score": 1.0,
+                                    "content": "natural sources of supervision.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 33.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        600,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                599,
+                                506,
+                                613
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        599,
+                                        506,
+                                        613
+                                    ],
+                                    "score": 1.0,
+                                    "content": "While many of these tasks require predicting fixed quantities computed from the data, another class",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                611,
+                                505,
+                                622
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        611,
+                                        505,
+                                        622
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of contrastive methods formulate their objectives in the learned representations themselves. CPC is",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                622,
+                                505,
+                                635
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        622,
+                                        505,
+                                        635
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a contrastive representation learning method that maximizes the mutual information between spa-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                633,
+                                505,
+                                645
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        633,
+                                        505,
+                                        645
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tially removed latent representations with InfoNCE (van den Oord et al., 2018), a loss function based",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                645,
+                                505,
+                                655
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        645,
+                                        505,
+                                        655
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on Noise-Contrastive Estimation (Gutmann & Hyvarinen, 2010; Mnih & Kavukcuoglu, 2013). Two ¨",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                655,
+                                505,
+                                667
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        655,
+                                        505,
+                                        667
+                                    ],
+                                    "score": 1.0,
+                                    "content": "other methods have recently been proposed using the same loss function, but with different associ-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                666,
+                                505,
+                                678
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        666,
+                                        505,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ated prediction tasks. Contrastive Multiview Coding (Tian et al., 2019) maximizes the mutual infor-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                677,
+                                505,
+                                689
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        677,
+                                        505,
+                                        689
+                                    ],
+                                    "score": 1.0,
+                                    "content": "mation between representations of different views of the same observation. Augmented Multiscale",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                687,
+                                505,
+                                701
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        687,
+                                        505,
+                                        701
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Deep InfoMax (AMDIM, Bachman et al., 2019) is most similar to CPC in that it makes predic-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                699,
+                                505,
+                                711
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        699,
+                                        505,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tions across space, but differs in that it also predicts representations across layers in the model. In",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                709,
+                                506,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        709,
+                                        506,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "addition, AMDIM limits the receptive field of its representation, but does this by constraining the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                721,
+                                473,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        721,
+                                        473,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "number of spatial convolutions in the network architecture rather than using image patches.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 51
+                        }
+                    ],
+                    "index": 45.5
+                }
+            ],
+            "page_idx": 3,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        308,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                26,
+                                308,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        26,
+                                        308,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Under review as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        752,
+                        308,
+                        759
+                    ],
+                    "lines": []
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        82,
+                        505,
+                        160
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                82,
+                                505,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        82,
+                                        505,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Efficient classification directly tests whether the CPC representation enables visual learning from",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                92,
+                                505,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        92,
+                                        262,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "few labels. For this task, the classifier",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        262,
+                                        94,
+                                        275,
+                                        106
+                                    ],
+                                    "score": 0.89,
+                                    "content": "h _ { \\psi }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        276,
+                                        92,
+                                        505,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is an arbitrary deep neural network (we use an 11-block",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                104,
+                                505,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        104,
+                                        505,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ResNet architecture with 4096-dimensional feature maps and 1024-dimensional bottleneck layers).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                115,
+                                505,
+                                128
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        115,
+                                        185,
+                                        128
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The labeled dataset",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        185,
+                                        116,
+                                        196,
+                                        126
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\mathbb { D } _ { l }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        197,
+                                        115,
+                                        428,
+                                        128
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is a subset of the ImageNet dataset: we investigated using",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        428,
+                                        115,
+                                        442,
+                                        126
+                                    ],
+                                    "score": 0.76,
+                                    "content": "1 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        442,
+                                        115,
+                                        445,
+                                        128
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        445,
+                                        115,
+                                        460,
+                                        126
+                                    ],
+                                    "score": 0.77,
+                                    "content": "2 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        460,
+                                        115,
+                                        463,
+                                        128
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        463,
+                                        115,
+                                        478,
+                                        126
+                                    ],
+                                    "score": 0.78,
+                                    "content": "5 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        478,
+                                        115,
+                                        482,
+                                        128
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        482,
+                                        115,
+                                        501,
+                                        126
+                                    ],
+                                    "score": 0.83,
+                                    "content": "10 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        501,
+                                        115,
+                                        505,
+                                        128
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                125,
+                                506,
+                                140
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        126,
+                                        126,
+                                        137
+                                    ],
+                                    "score": 0.84,
+                                    "content": "20 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        126,
+                                        125,
+                                        129,
+                                        140
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        130,
+                                        126,
+                                        150,
+                                        137
+                                    ],
+                                    "score": 0.86,
+                                    "content": "50 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        150,
+                                        125,
+                                        169,
+                                        140
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        169,
+                                        127,
+                                        193,
+                                        137
+                                    ],
+                                    "score": 0.87,
+                                    "content": "100 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        194,
+                                        125,
+                                        379,
+                                        140
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of the ImageNet dataset. The supervised loss",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        379,
+                                        127,
+                                        399,
+                                        138
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\mathcal { L } _ { \\mathrm { { S u p } } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        399,
+                                        125,
+                                        506,
+                                        140
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is again cross-entropy. In",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                136,
+                                505,
+                                151
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        136,
+                                        505,
+                                        151
+                                    ],
+                                    "score": 1.0,
+                                    "content": "addition to random color-dropping we use the Inception data-augmentation scheme (Szegedy et al.,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                148,
+                                426,
+                                162
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        148,
+                                        426,
+                                        162
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2014) for training, no augmentation at test-time and evaluate with a single crop.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 3,
+                    "bbox_fs": [
+                        105,
+                        82,
+                        506,
+                        162
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        165,
+                        505,
+                        221
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                165,
+                                505,
+                                178
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        165,
+                                        505,
+                                        178
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Transfer learning tests the generality of the representation by applying it to a new task and dataset.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                176,
+                                505,
+                                188
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        176,
+                                        505,
+                                        188
+                                    ],
+                                    "score": 1.0,
+                                    "content": "For this we chose image detection on the PASCAL-2007 dataset, a standard benchmark in computer",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                187,
+                                506,
+                                200
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        187,
+                                        284,
+                                        200
+                                    ],
+                                    "score": 1.0,
+                                    "content": "vision (Everingham et al., 2007). As such",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        285,
+                                        187,
+                                        296,
+                                        198
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\mathbb { D } _ { l }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        297,
+                                        187,
+                                        506,
+                                        200
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the entire PASCAL-2007 dataset (comprised of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                197,
+                                506,
+                                212
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        197,
+                                        196,
+                                        212
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5011 labeled images);",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        197,
+                                        198,
+                                        209,
+                                        210
+                                    ],
+                                    "score": 0.88,
+                                    "content": "h _ { \\psi }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        210,
+                                        197,
+                                        228,
+                                        212
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        228,
+                                        199,
+                                        248,
+                                        210
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\mathcal { L } _ { \\mathrm { { S u p } } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        248,
+                                        197,
+                                        506,
+                                        212
+                                    ],
+                                    "score": 1.0,
+                                    "content": "are the Faster-RCNN architecture and loss (Ren et al., 2015). In",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                208,
+                                466,
+                                223
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        208,
+                                        466,
+                                        223
+                                    ],
+                                    "score": 1.0,
+                                    "content": "addition to color-dropping, we use scale-augmentation (Doersch et al., 2015) for training.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 9,
+                    "bbox_fs": [
+                        105,
+                        165,
+                        506,
+                        223
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        226,
+                        505,
+                        292
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                226,
+                                505,
+                                239
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        226,
+                                        331,
+                                        239
+                                    ],
+                                    "score": 1.0,
+                                    "content": "For linear classification, we keep the feature extractor",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        332,
+                                        226,
+                                        342,
+                                        238
+                                    ],
+                                    "score": 0.34,
+                                    "content": "f _ { \\theta }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        342,
+                                        226,
+                                        505,
+                                        239
+                                    ],
+                                    "score": 1.0,
+                                    "content": "fixed to assess the representation in ab-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                235,
+                                506,
+                                251
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        235,
+                                        506,
+                                        251
+                                    ],
+                                    "score": 1.0,
+                                    "content": "solute terms. For efficient classification and transfer learning, we additionally explore fine-tuning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                248,
+                                505,
+                                259
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        248,
+                                        505,
+                                        259
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the feature extractor for the supervised objective. In this regime, we initialize the feature extractor",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                259,
+                                506,
+                                271
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        259,
+                                        234,
+                                        271
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and classifier with the solutions",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        234,
+                                        259,
+                                        260,
+                                        270
+                                    ],
+                                    "score": 0.4,
+                                    "content": "\\theta ^ { * } , \\psi ^ { * }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        261,
+                                        259,
+                                        506,
+                                        271
+                                    ],
+                                    "score": 1.0,
+                                    "content": "found in the previous learning phase, and train them both for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                270,
+                                505,
+                                281
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        270,
+                                        505,
+                                        281
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the supervised objective. To ensure that the feature extractor does not deviate too much from the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                280,
+                                465,
+                                294
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        280,
+                                        465,
+                                        294
+                                    ],
+                                    "score": 1.0,
+                                    "content": "solution dictated by the CPC objective, we use a smaller learning rate and early-stopping.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 14.5,
+                    "bbox_fs": [
+                        105,
+                        226,
+                        506,
+                        294
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        319,
+                        210,
+                        332
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                318,
+                                213,
+                                334
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        318,
+                                        213,
+                                        334
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3 RELATED WORK",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        352,
+                        504,
+                        396
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                352,
+                                506,
+                                365
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        352,
+                                        506,
+                                        365
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Data-efficient learning has typically been approached by two complementary methods, both of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                363,
+                                505,
+                                375
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        363,
+                                        505,
+                                        375
+                                    ],
+                                    "score": 1.0,
+                                    "content": "which seek to make use of more plentiful unlabeled data: representation learning and semi-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                374,
+                                505,
+                                386
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        375,
+                                        452,
+                                        386
+                                    ],
+                                    "score": 1.0,
+                                    "content": "supervised learning. The former formulates an objective to learn a feature extractor",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        453,
+                                        374,
+                                        463,
+                                        385
+                                    ],
+                                    "score": 0.87,
+                                    "content": "f _ { \\theta }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        464,
+                                        375,
+                                        505,
+                                        386
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in an un-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                385,
+                                504,
+                                398
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        385,
+                                        387,
+                                        398
+                                    ],
+                                    "score": 1.0,
+                                    "content": "supervised manner, whereas the latter directly constrains the classifier",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        387,
+                                        385,
+                                        400,
+                                        397
+                                    ],
+                                    "score": 0.89,
+                                    "content": "h _ { \\psi }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        401,
+                                        385,
+                                        504,
+                                        398
+                                    ],
+                                    "score": 1.0,
+                                    "content": "using the unlabeled data.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 20.5,
+                    "bbox_fs": [
+                        105,
+                        352,
+                        506,
+                        398
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        402,
+                        504,
+                        457
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                402,
+                                506,
+                                415
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        402,
+                                        506,
+                                        415
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Representation learning saw early success using generative modeling (Kingma et al., 2014), but",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                412,
+                                505,
+                                425
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        412,
+                                        505,
+                                        425
+                                    ],
+                                    "score": 1.0,
+                                    "content": "likelihood-based models have yet to generalize to more complex stimulus classes. Generative ad-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                424,
+                                505,
+                                436
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        424,
+                                        505,
+                                        436
+                                    ],
+                                    "score": 1.0,
+                                    "content": "versarial models have also been harnessed for representation learning (Donahue et al., 2016), and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                434,
+                                506,
+                                448
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        434,
+                                        506,
+                                        448
+                                    ],
+                                    "score": 1.0,
+                                    "content": "large-scale implementations have recently achieved corresponding gains in linear classification ac-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                446,
+                                261,
+                                459
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        446,
+                                        261,
+                                        459
+                                    ],
+                                    "score": 1.0,
+                                    "content": "curacy (Donahue & Simonyan, 2019).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 25,
+                    "bbox_fs": [
+                        105,
+                        402,
+                        506,
+                        459
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        462,
+                        505,
+                        594
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                462,
+                                505,
+                                476
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        462,
+                                        505,
+                                        476
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In contrast to generative models which require the reconstruction of observations, self-supervised",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                473,
+                                505,
+                                487
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        473,
+                                        505,
+                                        487
+                                    ],
+                                    "score": 1.0,
+                                    "content": "techniques directly formulate tasks involving the learned representation. For example, simply ask-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                485,
+                                505,
+                                497
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        485,
+                                        505,
+                                        497
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ing a network to recognize the spatial layout of an image led to representations that transferred to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                495,
+                                506,
+                                509
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        495,
+                                        506,
+                                        509
+                                    ],
+                                    "score": 1.0,
+                                    "content": "popular vision tasks such as classification and detection (Doersch et al., 2015; Noroozi & Favaro,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                506,
+                                505,
+                                519
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        506,
+                                        505,
+                                        519
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2016). Other works showed that prediction of color (Zhang et al., 2016; Larsson et al., 2017) and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                518,
+                                505,
+                                530
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        518,
+                                        505,
+                                        530
+                                    ],
+                                    "score": 1.0,
+                                    "content": "image orientation (Gidaris et al., 2018), and invariance to data augmentation (Dosovitskiy et al.,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                528,
+                                505,
+                                541
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        528,
+                                        505,
+                                        541
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2014) can provide useful self-supervised tasks. Beyond single images, works have leveraged video",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                540,
+                                505,
+                                552
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        540,
+                                        505,
+                                        552
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cues such as object tracking (Wang & Gupta, 2015), frame ordering (Misra et al., 2016), and object",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                550,
+                                505,
+                                564
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        550,
+                                        505,
+                                        564
+                                    ],
+                                    "score": 1.0,
+                                    "content": "boundary cues (Li et al., 2016; Pathak et al., 2016). Non-visual information can be equally power-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                560,
+                                505,
+                                574
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        560,
+                                        505,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ful; information about camera motion (Agrawal et al., 2015; Jayaraman & Grauman, 2015), scene",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                572,
+                                506,
+                                585
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        572,
+                                        506,
+                                        585
+                                    ],
+                                    "score": 1.0,
+                                    "content": "geometry (Zamir et al., 2016), or sound (Arandjelovic & Zisserman, 2017; 2018) can all serve as",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                584,
+                                230,
+                                595
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        584,
+                                        230,
+                                        595
+                                    ],
+                                    "score": 1.0,
+                                    "content": "natural sources of supervision.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 33.5,
+                    "bbox_fs": [
+                        104,
+                        462,
+                        506,
+                        595
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        600,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                599,
+                                506,
+                                613
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        599,
+                                        506,
+                                        613
+                                    ],
+                                    "score": 1.0,
+                                    "content": "While many of these tasks require predicting fixed quantities computed from the data, another class",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                611,
+                                505,
+                                622
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        611,
+                                        505,
+                                        622
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of contrastive methods formulate their objectives in the learned representations themselves. CPC is",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                622,
+                                505,
+                                635
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        622,
+                                        505,
+                                        635
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a contrastive representation learning method that maximizes the mutual information between spa-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                633,
+                                505,
+                                645
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        633,
+                                        505,
+                                        645
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tially removed latent representations with InfoNCE (van den Oord et al., 2018), a loss function based",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                645,
+                                505,
+                                655
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        645,
+                                        505,
+                                        655
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on Noise-Contrastive Estimation (Gutmann & Hyvarinen, 2010; Mnih & Kavukcuoglu, 2013). Two ¨",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                655,
+                                505,
+                                667
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        655,
+                                        505,
+                                        667
+                                    ],
+                                    "score": 1.0,
+                                    "content": "other methods have recently been proposed using the same loss function, but with different associ-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                666,
+                                505,
+                                678
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        666,
+                                        505,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ated prediction tasks. Contrastive Multiview Coding (Tian et al., 2019) maximizes the mutual infor-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                677,
+                                505,
+                                689
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        677,
+                                        505,
+                                        689
+                                    ],
+                                    "score": 1.0,
+                                    "content": "mation between representations of different views of the same observation. Augmented Multiscale",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                687,
+                                505,
+                                701
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        687,
+                                        505,
+                                        701
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Deep InfoMax (AMDIM, Bachman et al., 2019) is most similar to CPC in that it makes predic-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                699,
+                                505,
+                                711
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        699,
+                                        505,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tions across space, but differs in that it also predicts representations across layers in the model. In",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                709,
+                                506,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        709,
+                                        506,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "addition, AMDIM limits the receptive field of its representation, but does this by constraining the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                721,
+                                473,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        721,
+                                        473,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "number of spatial convolutions in the network architecture rather than using image patches.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 51
+                        }
+                    ],
+                    "index": 45.5,
+                    "bbox_fs": [
+                        105,
+                        599,
+                        506,
+                        733
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        82,
+                        505,
+                        182
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                82,
+                                504,
+                                94
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        82,
+                                        504,
+                                        94
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A common alternative approach for improving data efficiency is label-propagation (Zhu & Ghahra-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                94,
+                                505,
+                                105
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        94,
+                                        505,
+                                        105
+                                    ],
+                                    "score": 1.0,
+                                    "content": "mani, 2002), where a classifier is trained on a subset of labeled data, then used to label parts of the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                104,
+                                505,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        104,
+                                        505,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "unlabeled dataset, after which the process is repeated. This label-propagation can either be discrete",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                114,
+                                505,
+                                129
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        114,
+                                        505,
+                                        129
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(as in pseudo-labeling, Lee, 2013) or continuous (as in entropy minimization, Grandvalet & Bengio,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                126,
+                                505,
+                                139
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        126,
+                                        505,
+                                        139
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2005). The predictions of this classifier are often constrained to be smooth with respect to cer-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                138,
+                                504,
+                                150
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        138,
+                                        504,
+                                        150
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tain deformations, such as data-augmentation (Xie et al., 2019) or adversarial perturbation (Miyato",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                148,
+                                505,
+                                161
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        148,
+                                        505,
+                                        161
+                                    ],
+                                    "score": 1.0,
+                                    "content": "et al., 2018). Representation learning and semi-supervised learning have been shown to be comple-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                158,
+                                505,
+                                172
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        158,
+                                        505,
+                                        172
+                                    ],
+                                    "score": 1.0,
+                                    "content": "mentary and can be combined to great effect (Zhai et al., 2019), which is why we focus solely on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                171,
+                                253,
+                                183
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        171,
+                                        253,
+                                        183
+                                    ],
+                                    "score": 1.0,
+                                    "content": "representation learning in this paper.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        199,
+                        172,
+                        212
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                197,
+                                174,
+                                214
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        197,
+                                        174,
+                                        214
+                                    ],
+                                    "score": 1.0,
+                                    "content": "4 RESULTS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        225,
+                        505,
+                        335
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                225,
+                                505,
+                                238
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        225,
+                                        505,
+                                        238
+                                    ],
+                                    "score": 1.0,
+                                    "content": "When asking whether CPC enables data-efficient learning, we wish to use the best possible represen-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                236,
+                                505,
+                                249
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        236,
+                                        505,
+                                        249
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tative of this model class. Unfortunately, purely unsupervised metrics tell us little about downstream",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                247,
+                                505,
+                                259
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        247,
+                                        505,
+                                        259
+                                    ],
+                                    "score": 1.0,
+                                    "content": "performance, and implementation details have been shown to matter enormously (Doersch & Zisser-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                258,
+                                505,
+                                271
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        258,
+                                        505,
+                                        271
+                                    ],
+                                    "score": 1.0,
+                                    "content": "man, 2017; Kolesnikov et al., 2019). Since many design choices (e.g. network architecture and data-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                269,
+                                505,
+                                281
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        269,
+                                        505,
+                                        281
+                                    ],
+                                    "score": 1.0,
+                                    "content": "preprocessing) have been previously evaluated using linear classification, we use this benchmark",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                280,
+                                505,
+                                293
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        280,
+                                        505,
+                                        293
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in section 4.1 to align the CPC model with best practices in representation learning and compare to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                290,
+                                506,
+                                304
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        290,
+                                        506,
+                                        304
+                                    ],
+                                    "score": 1.0,
+                                    "content": "published results. In section 4.2 we select the best performing model from the previous section and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                302,
+                                506,
+                                315
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        302,
+                                        506,
+                                        315
+                                    ],
+                                    "score": 1.0,
+                                    "content": "assess whether it enables efficient classification. We also investigate to what extent the first, more",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                314,
+                                505,
+                                325
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        314,
+                                        505,
+                                        325
+                                    ],
+                                    "score": 1.0,
+                                    "content": "common metric (linear classification accuracy) is predictive of efficient classification. Finally, in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                324,
+                                505,
+                                336
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        324,
+                                        505,
+                                        336
+                                    ],
+                                    "score": 1.0,
+                                    "content": "section 4.3 we investigate the generality of our results through transfer learning to PASCAL-2007.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 14.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        350,
+                        245,
+                        361
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                348,
+                                247,
+                                363
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        348,
+                                        247,
+                                        363
+                                    ],
+                                    "score": 1.0,
+                                    "content": "4.1 FROM CPC V1 TO CPC V2",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 20
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        371,
+                        505,
+                        438
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                372,
+                                505,
+                                383
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        372,
+                                        505,
+                                        383
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The overarching principle behind our new model design is to increase the scale and efficiency of the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                383,
+                                505,
+                                394
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        383,
+                                        505,
+                                        394
+                                    ],
+                                    "score": 1.0,
+                                    "content": "encoder architecture while also maximizing the supervisory signal we obtain from each image. At",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                394,
+                                505,
+                                405
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        394,
+                                        505,
+                                        405
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the same time, it is important not to allow the network to solve the problem trivially, i.e., without",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                404,
+                                505,
+                                417
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        404,
+                                        505,
+                                        417
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning semantics. To this end, we seek to remove low-level cues common across patches by",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                416,
+                                505,
+                                429
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        416,
+                                        505,
+                                        429
+                                    ],
+                                    "score": 1.0,
+                                    "content": "augmenting individual patches independently, using standard stochastic data-processing techniques",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                424,
+                                291,
+                                441
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        424,
+                                        291,
+                                        441
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from supervised and self-supervised learning.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 23.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        443,
+                        297,
+                        553
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                442,
+                                297,
+                                456
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        442,
+                                        297,
+                                        456
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We identify four axes for model capacity and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                455,
+                                297,
+                                466
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        455,
+                                        297,
+                                        466
+                                    ],
+                                    "score": 1.0,
+                                    "content": "task setup that could impact the model’s perfor-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                465,
+                                297,
+                                478
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        465,
+                                        297,
+                                        478
+                                    ],
+                                    "score": 1.0,
+                                    "content": "mance. The first axis increases model capacity",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                476,
+                                297,
+                                488
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        476,
+                                        297,
+                                        488
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by increasing depth and width, while the second",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                488,
+                                296,
+                                499
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        488,
+                                        296,
+                                        499
+                                    ],
+                                    "score": 1.0,
+                                    "content": "improves training efficiency capacity by intro-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                498,
+                                297,
+                                510
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        498,
+                                        297,
+                                        510
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ducing layer normalization. The third axis in-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                509,
+                                297,
+                                521
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        509,
+                                        297,
+                                        521
+                                    ],
+                                    "score": 1.0,
+                                    "content": "creases task complexity by making predictions",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                519,
+                                297,
+                                532
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        519,
+                                        297,
+                                        532
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in all four directions, and the fourth does so by",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                531,
+                                297,
+                                544
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        531,
+                                        297,
+                                        544
+                                    ],
+                                    "score": 1.0,
+                                    "content": "performing more extensive patch-based aug-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                542,
+                                154,
+                                553
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        542,
+                                        154,
+                                        553
+                                    ],
+                                    "score": 1.0,
+                                    "content": "mentation.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 31.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        567,
+                        296,
+                        731
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                567,
+                                297,
+                                578
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        567,
+                                        297,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Model capacity. Recent work has shown that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                577,
+                                297,
+                                591
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        577,
+                                        297,
+                                        591
+                                    ],
+                                    "score": 1.0,
+                                    "content": "networks and more effective training improves",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                589,
+                                297,
+                                601
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        589,
+                                        297,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": "self-supervised learning (Doersch & Zisser-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                600,
+                                297,
+                                612
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        600,
+                                        297,
+                                        612
+                                    ],
+                                    "score": 1.0,
+                                    "content": "man, 2017; Kolesnikov et al., 2019), but the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                611,
+                                297,
+                                622
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        611,
+                                        297,
+                                        622
+                                    ],
+                                    "score": 1.0,
+                                    "content": "original CPC model used only the first 3 stacks",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                622,
+                                297,
+                                633
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        622,
+                                        297,
+                                        633
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of a ResNet-101 (He et al., 2016a) architecture",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 51
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                633,
+                                297,
+                                644
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        633,
+                                        297,
+                                        644
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(i.e. a ResNet-92). Therefore, we converted the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 52
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                643,
+                                297,
+                                655
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        643,
+                                        297,
+                                        655
+                                    ],
+                                    "score": 1.0,
+                                    "content": "third residual stack of ResNet-101 (originally",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 53
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                655,
+                                297,
+                                667
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        655,
+                                        297,
+                                        667
+                                    ],
+                                    "score": 1.0,
+                                    "content": "containing 23 blocks, 1024-dimensional feature",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 54
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                666,
+                                297,
+                                678
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        666,
+                                        297,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "maps, and 256-dimensional bottleneck layers),",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 55
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                677,
+                                297,
+                                688
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        677,
+                                        297,
+                                        688
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to use 46 blocks, with 4096-dimensional fea-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 56
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                687,
+                                297,
+                                700
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        687,
+                                        297,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ture maps and 512-dimensional bottleneck lay-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 57
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                699,
+                                297,
+                                710
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        699,
+                                        297,
+                                        710
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ers. We call the resulting network ResNet-161.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 58
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                709,
+                                297,
+                                721
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        709,
+                                        297,
+                                        721
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Consistent with prior results, this new architec-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 59
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                720,
+                                298,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        720,
+                                        298,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ture delivers better performance regardless of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 60
+                        }
+                    ],
+                    "index": 53
+                },
+                {
+                    "type": "image",
+                    "bbox": [
+                        307,
+                        449,
+                        501,
+                        616
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                307,
+                                449,
+                                501,
+                                616
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        307,
+                                        449,
+                                        501,
+                                        616
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                307,
+                                                449,
+                                                501,
+                                                616
+                                            ],
+                                            "score": 0.97,
+                                            "type": "image",
+                                            "image_path": "3eeded7c7663fc17771caa90292cc1343662124f1094d06f22d9ca255036f2a3.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 43,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        307,
+                                        449,
+                                        501,
+                                        461.84615384615387
+                                    ],
+                                    "spans": [],
+                                    "index": 37
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        461.84615384615387,
+                                        501,
+                                        474.69230769230774
+                                    ],
+                                    "spans": [],
+                                    "index": 38
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        474.69230769230774,
+                                        501,
+                                        487.5384615384616
+                                    ],
+                                    "spans": [],
+                                    "index": 39
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        487.5384615384616,
+                                        501,
+                                        500.3846153846155
+                                    ],
+                                    "spans": [],
+                                    "index": 40
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        500.3846153846155,
+                                        501,
+                                        513.2307692307693
+                                    ],
+                                    "spans": [],
+                                    "index": 41
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        513.2307692307693,
+                                        501,
+                                        526.0769230769231
+                                    ],
+                                    "spans": [],
+                                    "index": 42
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        526.0769230769231,
+                                        501,
+                                        538.9230769230769
+                                    ],
+                                    "spans": [],
+                                    "index": 43
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        538.9230769230769,
+                                        501,
+                                        551.7692307692307
+                                    ],
+                                    "spans": [],
+                                    "index": 44
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        551.7692307692307,
+                                        501,
+                                        564.6153846153845
+                                    ],
+                                    "spans": [],
+                                    "index": 45
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        564.6153846153845,
+                                        501,
+                                        577.4615384615383
+                                    ],
+                                    "spans": [],
+                                    "index": 61
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        577.4615384615383,
+                                        501,
+                                        590.3076923076922
+                                    ],
+                                    "spans": [],
+                                    "index": 62
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        590.3076923076922,
+                                        501,
+                                        603.153846153846
+                                    ],
+                                    "spans": [],
+                                    "index": 63
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        603.153846153846,
+                                        501,
+                                        615.9999999999998
+                                    ],
+                                    "spans": [],
+                                    "index": 64
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                304,
+                                620,
+                                504,
+                                719
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        620,
+                                        506,
+                                        632
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                304,
+                                                620,
+                                                506,
+                                                632
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 3: Linear classification performance of",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 65
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        631,
+                                        506,
+                                        643
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                303,
+                                                631,
+                                                506,
+                                                643
+                                            ],
+                                            "score": 1.0,
+                                            "content": "new variants of CPC, which incrementally add a",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 66
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        642,
+                                        505,
+                                        654
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                304,
+                                                642,
+                                                505,
+                                                654
+                                            ],
+                                            "score": 1.0,
+                                            "content": "series of modifications. BU: bottum up spatial",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 67
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        653,
+                                        505,
+                                        665
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                303,
+                                                653,
+                                                505,
+                                                665
+                                            ],
+                                            "score": 1.0,
+                                            "content": "predictions. HF: randomly flipping patches hor-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 68
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        664,
+                                        505,
+                                        675
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                304,
+                                                664,
+                                                505,
+                                                675
+                                            ],
+                                            "score": 1.0,
+                                            "content": "izontally. LN: layer normalization. RC: random",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 69
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        675,
+                                        505,
+                                        686
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                303,
+                                                675,
+                                                505,
+                                                686
+                                            ],
+                                            "score": 1.0,
+                                            "content": "color-dropping. TL: tuned prediction lengths. HP:",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 70
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        686,
+                                        505,
+                                        697
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                304,
+                                                686,
+                                                505,
+                                                697
+                                            ],
+                                            "score": 1.0,
+                                            "content": "horizontal spatial predictions. We use color to in-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 71
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        697,
+                                        505,
+                                        709
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                304,
+                                                697,
+                                                505,
+                                                709
+                                            ],
+                                            "score": 1.0,
+                                            "content": "dicate the number of spatial predictions used (or-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 72
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        708,
+                                        478,
+                                        719
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                303,
+                                                708,
+                                                478,
+                                                719
+                                            ],
+                                            "score": 1.0,
+                                            "content": "ange, green, blue for 1, 2 and 4 directions).",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 73
+                                }
+                            ],
+                            "index": 69
+                        }
+                    ],
+                    "index": 56.0
+                }
+            ],
+            "page_idx": 4,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        308,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                26,
+                                308,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        26,
+                                        308,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Under review as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        751,
+                        308,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                302,
+                                750,
+                                309,
+                                763
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        302,
+                                        750,
+                                        309,
+                                        763
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        82,
+                        505,
+                        182
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                82,
+                                504,
+                                94
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        82,
+                                        504,
+                                        94
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A common alternative approach for improving data efficiency is label-propagation (Zhu & Ghahra-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                94,
+                                505,
+                                105
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        94,
+                                        505,
+                                        105
+                                    ],
+                                    "score": 1.0,
+                                    "content": "mani, 2002), where a classifier is trained on a subset of labeled data, then used to label parts of the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                104,
+                                505,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        104,
+                                        505,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "unlabeled dataset, after which the process is repeated. This label-propagation can either be discrete",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                114,
+                                505,
+                                129
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        114,
+                                        505,
+                                        129
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(as in pseudo-labeling, Lee, 2013) or continuous (as in entropy minimization, Grandvalet & Bengio,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                126,
+                                505,
+                                139
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        126,
+                                        505,
+                                        139
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2005). The predictions of this classifier are often constrained to be smooth with respect to cer-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                138,
+                                504,
+                                150
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        138,
+                                        504,
+                                        150
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tain deformations, such as data-augmentation (Xie et al., 2019) or adversarial perturbation (Miyato",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                148,
+                                505,
+                                161
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        148,
+                                        505,
+                                        161
+                                    ],
+                                    "score": 1.0,
+                                    "content": "et al., 2018). Representation learning and semi-supervised learning have been shown to be comple-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                158,
+                                505,
+                                172
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        158,
+                                        505,
+                                        172
+                                    ],
+                                    "score": 1.0,
+                                    "content": "mentary and can be combined to great effect (Zhai et al., 2019), which is why we focus solely on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                171,
+                                253,
+                                183
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        171,
+                                        253,
+                                        183
+                                    ],
+                                    "score": 1.0,
+                                    "content": "representation learning in this paper.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 4,
+                    "bbox_fs": [
+                        105,
+                        82,
+                        505,
+                        183
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        199,
+                        172,
+                        212
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                197,
+                                174,
+                                214
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        197,
+                                        174,
+                                        214
+                                    ],
+                                    "score": 1.0,
+                                    "content": "4 RESULTS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        225,
+                        505,
+                        335
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                225,
+                                505,
+                                238
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        225,
+                                        505,
+                                        238
+                                    ],
+                                    "score": 1.0,
+                                    "content": "When asking whether CPC enables data-efficient learning, we wish to use the best possible represen-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                236,
+                                505,
+                                249
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        236,
+                                        505,
+                                        249
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tative of this model class. Unfortunately, purely unsupervised metrics tell us little about downstream",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                247,
+                                505,
+                                259
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        247,
+                                        505,
+                                        259
+                                    ],
+                                    "score": 1.0,
+                                    "content": "performance, and implementation details have been shown to matter enormously (Doersch & Zisser-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                258,
+                                505,
+                                271
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        258,
+                                        505,
+                                        271
+                                    ],
+                                    "score": 1.0,
+                                    "content": "man, 2017; Kolesnikov et al., 2019). Since many design choices (e.g. network architecture and data-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                269,
+                                505,
+                                281
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        269,
+                                        505,
+                                        281
+                                    ],
+                                    "score": 1.0,
+                                    "content": "preprocessing) have been previously evaluated using linear classification, we use this benchmark",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                280,
+                                505,
+                                293
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        280,
+                                        505,
+                                        293
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in section 4.1 to align the CPC model with best practices in representation learning and compare to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                290,
+                                506,
+                                304
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        290,
+                                        506,
+                                        304
+                                    ],
+                                    "score": 1.0,
+                                    "content": "published results. In section 4.2 we select the best performing model from the previous section and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                302,
+                                506,
+                                315
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        302,
+                                        506,
+                                        315
+                                    ],
+                                    "score": 1.0,
+                                    "content": "assess whether it enables efficient classification. We also investigate to what extent the first, more",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                314,
+                                505,
+                                325
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        314,
+                                        505,
+                                        325
+                                    ],
+                                    "score": 1.0,
+                                    "content": "common metric (linear classification accuracy) is predictive of efficient classification. Finally, in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                324,
+                                505,
+                                336
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        324,
+                                        505,
+                                        336
+                                    ],
+                                    "score": 1.0,
+                                    "content": "section 4.3 we investigate the generality of our results through transfer learning to PASCAL-2007.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 14.5,
+                    "bbox_fs": [
+                        104,
+                        225,
+                        506,
+                        336
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        350,
+                        245,
+                        361
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                348,
+                                247,
+                                363
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        348,
+                                        247,
+                                        363
+                                    ],
+                                    "score": 1.0,
+                                    "content": "4.1 FROM CPC V1 TO CPC V2",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 20
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        371,
+                        505,
+                        438
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                372,
+                                505,
+                                383
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        372,
+                                        505,
+                                        383
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The overarching principle behind our new model design is to increase the scale and efficiency of the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                383,
+                                505,
+                                394
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        383,
+                                        505,
+                                        394
+                                    ],
+                                    "score": 1.0,
+                                    "content": "encoder architecture while also maximizing the supervisory signal we obtain from each image. At",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                394,
+                                505,
+                                405
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        394,
+                                        505,
+                                        405
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the same time, it is important not to allow the network to solve the problem trivially, i.e., without",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                404,
+                                505,
+                                417
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        404,
+                                        505,
+                                        417
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning semantics. To this end, we seek to remove low-level cues common across patches by",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                416,
+                                505,
+                                429
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        416,
+                                        505,
+                                        429
+                                    ],
+                                    "score": 1.0,
+                                    "content": "augmenting individual patches independently, using standard stochastic data-processing techniques",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                424,
+                                291,
+                                441
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        424,
+                                        291,
+                                        441
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from supervised and self-supervised learning.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 23.5,
+                    "bbox_fs": [
+                        105,
+                        372,
+                        505,
+                        441
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        443,
+                        297,
+                        553
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                442,
+                                297,
+                                456
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        442,
+                                        297,
+                                        456
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We identify four axes for model capacity and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                455,
+                                297,
+                                466
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        455,
+                                        297,
+                                        466
+                                    ],
+                                    "score": 1.0,
+                                    "content": "task setup that could impact the model’s perfor-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                465,
+                                297,
+                                478
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        465,
+                                        297,
+                                        478
+                                    ],
+                                    "score": 1.0,
+                                    "content": "mance. The first axis increases model capacity",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                476,
+                                297,
+                                488
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        476,
+                                        297,
+                                        488
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by increasing depth and width, while the second",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                488,
+                                296,
+                                499
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        488,
+                                        296,
+                                        499
+                                    ],
+                                    "score": 1.0,
+                                    "content": "improves training efficiency capacity by intro-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                498,
+                                297,
+                                510
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        498,
+                                        297,
+                                        510
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ducing layer normalization. The third axis in-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                509,
+                                297,
+                                521
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        509,
+                                        297,
+                                        521
+                                    ],
+                                    "score": 1.0,
+                                    "content": "creases task complexity by making predictions",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                519,
+                                297,
+                                532
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        519,
+                                        297,
+                                        532
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in all four directions, and the fourth does so by",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                531,
+                                297,
+                                544
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        531,
+                                        297,
+                                        544
+                                    ],
+                                    "score": 1.0,
+                                    "content": "performing more extensive patch-based aug-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                542,
+                                154,
+                                553
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        542,
+                                        154,
+                                        553
+                                    ],
+                                    "score": 1.0,
+                                    "content": "mentation.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 31.5,
+                    "bbox_fs": [
+                        105,
+                        442,
+                        297,
+                        553
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        567,
+                        296,
+                        731
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                567,
+                                297,
+                                578
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        567,
+                                        297,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Model capacity. Recent work has shown that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                577,
+                                297,
+                                591
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        577,
+                                        297,
+                                        591
+                                    ],
+                                    "score": 1.0,
+                                    "content": "networks and more effective training improves",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                589,
+                                297,
+                                601
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        589,
+                                        297,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": "self-supervised learning (Doersch & Zisser-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                600,
+                                297,
+                                612
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        600,
+                                        297,
+                                        612
+                                    ],
+                                    "score": 1.0,
+                                    "content": "man, 2017; Kolesnikov et al., 2019), but the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                611,
+                                297,
+                                622
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        611,
+                                        297,
+                                        622
+                                    ],
+                                    "score": 1.0,
+                                    "content": "original CPC model used only the first 3 stacks",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                622,
+                                297,
+                                633
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        622,
+                                        297,
+                                        633
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of a ResNet-101 (He et al., 2016a) architecture",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 51
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                633,
+                                297,
+                                644
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        633,
+                                        297,
+                                        644
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(i.e. a ResNet-92). Therefore, we converted the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 52
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                643,
+                                297,
+                                655
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        643,
+                                        297,
+                                        655
+                                    ],
+                                    "score": 1.0,
+                                    "content": "third residual stack of ResNet-101 (originally",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 53
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                655,
+                                297,
+                                667
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        655,
+                                        297,
+                                        667
+                                    ],
+                                    "score": 1.0,
+                                    "content": "containing 23 blocks, 1024-dimensional feature",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 54
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                666,
+                                297,
+                                678
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        666,
+                                        297,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "maps, and 256-dimensional bottleneck layers),",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 55
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                677,
+                                297,
+                                688
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        677,
+                                        297,
+                                        688
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to use 46 blocks, with 4096-dimensional fea-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 56
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                687,
+                                297,
+                                700
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        687,
+                                        297,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ture maps and 512-dimensional bottleneck lay-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 57
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                699,
+                                297,
+                                710
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        699,
+                                        297,
+                                        710
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ers. We call the resulting network ResNet-161.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 58
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                709,
+                                297,
+                                721
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        709,
+                                        297,
+                                        721
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Consistent with prior results, this new architec-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 59
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                720,
+                                298,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        720,
+                                        298,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ture delivers better performance regardless of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 60
+                        }
+                    ],
+                    "index": 53,
+                    "bbox_fs": [
+                        105,
+                        567,
+                        298,
+                        733
+                    ]
+                },
+                {
+                    "type": "image",
+                    "bbox": [
+                        307,
+                        449,
+                        501,
+                        616
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                307,
+                                449,
+                                501,
+                                616
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        307,
+                                        449,
+                                        501,
+                                        616
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                307,
+                                                449,
+                                                501,
+                                                616
+                                            ],
+                                            "score": 0.97,
+                                            "type": "image",
+                                            "image_path": "3eeded7c7663fc17771caa90292cc1343662124f1094d06f22d9ca255036f2a3.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 43,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        307,
+                                        449,
+                                        501,
+                                        461.84615384615387
+                                    ],
+                                    "spans": [],
+                                    "index": 37
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        461.84615384615387,
+                                        501,
+                                        474.69230769230774
+                                    ],
+                                    "spans": [],
+                                    "index": 38
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        474.69230769230774,
+                                        501,
+                                        487.5384615384616
+                                    ],
+                                    "spans": [],
+                                    "index": 39
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        487.5384615384616,
+                                        501,
+                                        500.3846153846155
+                                    ],
+                                    "spans": [],
+                                    "index": 40
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        500.3846153846155,
+                                        501,
+                                        513.2307692307693
+                                    ],
+                                    "spans": [],
+                                    "index": 41
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        513.2307692307693,
+                                        501,
+                                        526.0769230769231
+                                    ],
+                                    "spans": [],
+                                    "index": 42
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        526.0769230769231,
+                                        501,
+                                        538.9230769230769
+                                    ],
+                                    "spans": [],
+                                    "index": 43
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        538.9230769230769,
+                                        501,
+                                        551.7692307692307
+                                    ],
+                                    "spans": [],
+                                    "index": 44
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        551.7692307692307,
+                                        501,
+                                        564.6153846153845
+                                    ],
+                                    "spans": [],
+                                    "index": 45
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        564.6153846153845,
+                                        501,
+                                        577.4615384615383
+                                    ],
+                                    "spans": [],
+                                    "index": 61
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        577.4615384615383,
+                                        501,
+                                        590.3076923076922
+                                    ],
+                                    "spans": [],
+                                    "index": 62
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        590.3076923076922,
+                                        501,
+                                        603.153846153846
+                                    ],
+                                    "spans": [],
+                                    "index": 63
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        603.153846153846,
+                                        501,
+                                        615.9999999999998
+                                    ],
+                                    "spans": [],
+                                    "index": 64
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                304,
+                                620,
+                                504,
+                                719
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        620,
+                                        506,
+                                        632
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                304,
+                                                620,
+                                                506,
+                                                632
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 3: Linear classification performance of",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 65
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        631,
+                                        506,
+                                        643
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                303,
+                                                631,
+                                                506,
+                                                643
+                                            ],
+                                            "score": 1.0,
+                                            "content": "new variants of CPC, which incrementally add a",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 66
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        642,
+                                        505,
+                                        654
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                304,
+                                                642,
+                                                505,
+                                                654
+                                            ],
+                                            "score": 1.0,
+                                            "content": "series of modifications. BU: bottum up spatial",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 67
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        653,
+                                        505,
+                                        665
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                303,
+                                                653,
+                                                505,
+                                                665
+                                            ],
+                                            "score": 1.0,
+                                            "content": "predictions. HF: randomly flipping patches hor-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 68
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        664,
+                                        505,
+                                        675
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                304,
+                                                664,
+                                                505,
+                                                675
+                                            ],
+                                            "score": 1.0,
+                                            "content": "izontally. LN: layer normalization. RC: random",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 69
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        675,
+                                        505,
+                                        686
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                303,
+                                                675,
+                                                505,
+                                                686
+                                            ],
+                                            "score": 1.0,
+                                            "content": "color-dropping. TL: tuned prediction lengths. HP:",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 70
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        686,
+                                        505,
+                                        697
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                304,
+                                                686,
+                                                505,
+                                                697
+                                            ],
+                                            "score": 1.0,
+                                            "content": "horizontal spatial predictions. We use color to in-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 71
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        697,
+                                        505,
+                                        709
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                304,
+                                                697,
+                                                505,
+                                                709
+                                            ],
+                                            "score": 1.0,
+                                            "content": "dicate the number of spatial predictions used (or-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 72
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        708,
+                                        478,
+                                        719
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                303,
+                                                708,
+                                                478,
+                                                719
+                                            ],
+                                            "score": 1.0,
+                                            "content": "ange, green, blue for 1, 2 and 4 directions).",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 73
+                                }
+                            ],
+                            "index": 69
+                        }
+                    ],
+                    "index": 56.0
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "table",
+                    "bbox": [
+                        125,
+                        126,
+                        486,
+                        294
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                107,
+                                89,
+                                504,
+                                123
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        88,
+                                        505,
+                                        102
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                88,
+                                                218,
+                                                102
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 1: Linear classifier",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
+                                                218,
+                                                90,
+                                                231,
+                                                101
+                                            ],
+                                            "score": 0.89,
+                                            "content": "h _ { \\psi }",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
+                                                232,
+                                                88,
+                                                291,
+                                                102
+                                            ],
+                                            "score": 1.0,
+                                            "content": "trained with",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
+                                                291,
+                                                89,
+                                                317,
+                                                100
+                                            ],
+                                            "score": 0.86,
+                                            "content": "100 \\%",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
+                                                318,
+                                                88,
+                                                505,
+                                                102
+                                            ],
+                                            "score": 1.0,
+                                            "content": "of labels. Comparison to linear separability",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        101,
+                                        506,
+                                        113
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                101,
+                                                506,
+                                                113
+                                            ],
+                                            "score": 1.0,
+                                            "content": "of other self-supervised methods. In all cases a feature extractor is optimized in an unsupervised",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        111,
+                                        456,
+                                        124
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                111,
+                                                456,
+                                                124
+                                            ],
+                                            "score": 1.0,
+                                            "content": "manner, and a linear classifier is trained on top using all labels in the ImageNet dataset.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 2
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                125,
+                                126,
+                                486,
+                                294
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        125,
+                                        126,
+                                        486,
+                                        294
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                125,
+                                                126,
+                                                486,
+                                                294
+                                            ],
+                                            "score": 0.974,
+                                            "html": "<table><tr><td>Method</td><td>Top-1</td><td>Top-5</td></tr><tr><td>Motion Segmentation (MS) (Pathak et al., 2016) Exemplar (Ex) (Dosovitskiy et al.,2014) Relative Position (RP) (Doersch et al.,2015) Colorization (Col) (Zhang et al., 2016) Combination of MS + Ex + RP+ Col (Doersch &amp; Zisserman,2017) CPC v1 (van den Oord et al., 2018) Rotation (Kolesnikov et al., 2019)</td><td>27.6 31.5 36.2 39.6 1 48.7 55.4</td><td>48.3 53.1 59.2 62.5 69.3 73.6</td></tr><tr><td>CMC (Tian et al., 2019) Local Aggregation (Zhuang et al., 2019)</td><td>60.1 60.2</td><td>82.8 1 =</td></tr><tr><td>BigBiGAN (Donahue &amp; Simonyan,2019) AMDIM (Bachman et al., 2019) CPC v2 (ours) 65.9</td><td>61.3 68.1</td><td>81.9</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "fa1f65edaf71df9800daca9c26a7999e93d74856116a87cc357e08cc713a4be7.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 4,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        125,
+                                        126,
+                                        486,
+                                        182.0
+                                    ],
+                                    "spans": [],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        125,
+                                        182.0,
+                                        486,
+                                        238.0
+                                    ],
+                                    "spans": [],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        125,
+                                        238.0,
+                                        486,
+                                        294.0
+                                    ],
+                                    "spans": [],
+                                    "index": 5
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        325,
+                        504,
+                        358
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                324,
+                                506,
+                                338
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        324,
+                                        506,
+                                        338
+                                    ],
+                                    "score": 1.0,
+                                    "content": "other design choices. Interestingly, a larger architecture delivers larger improvements with more",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                335,
+                                503,
+                                349
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        335,
+                                        481,
+                                        349
+                                    ],
+                                    "score": 1.0,
+                                    "content": "efficient training, more self-supervised losses, and more patch-based augmentations (Fig. 3,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        482,
+                                        336,
+                                        503,
+                                        347
+                                    ],
+                                    "score": 0.84,
+                                    "content": "+5 \\%",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                347,
+                                420,
+                                360
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        347,
+                                        292,
+                                        360
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-1 accuracy with original training scheme,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        292,
+                                        347,
+                                        318,
+                                        357
+                                    ],
+                                    "score": 0.88,
+                                    "content": "+ 1 0 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        319,
+                                        347,
+                                        420,
+                                        360
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accuracy with new one).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        376,
+                        505,
+                        475
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                376,
+                                505,
+                                388
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        376,
+                                        505,
+                                        388
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Layer normalization. Large architectures are more difficult to train efficiently. Early works on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                387,
+                                506,
+                                400
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        387,
+                                        506,
+                                        400
+                                    ],
+                                    "score": 1.0,
+                                    "content": "context prediction with patches used batch normalization (Ioffe & Szegedy, 2015; Doersch et al.,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                397,
+                                504,
+                                411
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        397,
+                                        504,
+                                        411
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2015) to speed training. However, with CPC we find that batch normalization actually harms down-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                409,
+                                505,
+                                422
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        409,
+                                        505,
+                                        422
+                                    ],
+                                    "score": 1.0,
+                                    "content": "stream performance of large models. We hypothesize that batch normalization allows large models",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                420,
+                                505,
+                                432
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        420,
+                                        505,
+                                        432
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to find a trivial solution to CPC: it introduces a dependency between patches (through the batch",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                431,
+                                505,
+                                444
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        431,
+                                        505,
+                                        444
+                                    ],
+                                    "score": 1.0,
+                                    "content": "statistics) that can be exploited to bypass the constraints on the receptive field. We find that we can",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                442,
+                                505,
+                                455
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        442,
+                                        505,
+                                        455
+                                    ],
+                                    "score": 1.0,
+                                    "content": "reclaim much of batch normalization’s training efficiency using layer normalization (Ba et al., 2016),",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                452,
+                                505,
+                                466
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        452,
+                                        328,
+                                        466
+                                    ],
+                                    "score": 1.0,
+                                    "content": "which leads to a small gain for the smaller architecture",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        328,
+                                        453,
+                                        349,
+                                        464
+                                    ],
+                                    "score": 0.87,
+                                    "content": "+ 1 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        350,
+                                        452,
+                                        505,
+                                        466
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accuracy over equivalent architectures",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                462,
+                                481,
+                                478
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        462,
+                                        406,
+                                        478
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that use neither normalization) and a larger gain for the larger architecture",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        406,
+                                        464,
+                                        436,
+                                        475
+                                    ],
+                                    "score": 0.87,
+                                    "content": "( + 2 . 5 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        436,
+                                        462,
+                                        481,
+                                        478
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accuracy).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        493,
+                        505,
+                        626
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                493,
+                                505,
+                                506
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        493,
+                                        505,
+                                        506
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Prediction lengths and directions. Larger architectures also run a greater risk of overfitting. We",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                505,
+                                505,
+                                517
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        505,
+                                        505,
+                                        517
+                                    ],
+                                    "score": 1.0,
+                                    "content": "address this by asking more from the network: specifically, whereas van den Oord et al. (2018) pre-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                514,
+                                505,
+                                529
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        514,
+                                        505,
+                                        529
+                                    ],
+                                    "score": 1.0,
+                                    "content": "dicted each patch using only context from spatially beneath it, we repeatedly predict the patch using",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                527,
+                                505,
+                                539
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        527,
+                                        505,
+                                        539
+                                    ],
+                                    "score": 1.0,
+                                    "content": "context from above, to the right, and to the left, resulting in up to four times as many prediction",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                536,
+                                505,
+                                551
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        536,
+                                        443,
+                                        551
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tasks. Combining top-to-bottom with bottom-to-top helps both model architectures",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        443,
+                                        538,
+                                        465,
+                                        548
+                                    ],
+                                    "score": 0.87,
+                                    "content": "42 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        466,
+                                        536,
+                                        505,
+                                        551
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accuracy",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                548,
+                                505,
+                                560
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        548,
+                                        460,
+                                        560
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for both), but using all 4 spatial directions only benefits the larger model (an additional",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        460,
+                                        549,
+                                        489,
+                                        559
+                                    ],
+                                    "score": 0.9,
+                                    "content": "+ 1 . 5 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        489,
+                                        548,
+                                        505,
+                                        560
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                560,
+                                506,
+                                572
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        560,
+                                        177,
+                                        572
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the larger model,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        177,
+                                        560,
+                                        196,
+                                        570
+                                    ],
+                                    "score": 0.85,
+                                    "content": "{ \\bf - 1 \\% }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        197,
+                                        560,
+                                        506,
+                                        572
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for the smaller), consistent with the idea that model capacity and amount of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                570,
+                                505,
+                                582
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        570,
+                                        505,
+                                        582
+                                    ],
+                                    "score": 1.0,
+                                    "content": "supervision must go hand-in-hand. We also hypothesized that prediction “length”—i.e. offset be-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                582,
+                                505,
+                                594
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        582,
+                                        505,
+                                        594
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tween the predicted patch and the aggregated context—might affect performance, as distant patches",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                592,
+                                505,
+                                605
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        592,
+                                        505,
+                                        605
+                                    ],
+                                    "score": 1.0,
+                                    "content": "might lie on distinct objects, encouraging the network to memorize images. Indeed, limiting the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                603,
+                                505,
+                                617
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        603,
+                                        230,
+                                        617
+                                    ],
+                                    "score": 1.0,
+                                    "content": "range of the prediction length",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        230,
+                                        604,
+                                        237,
+                                        613
+                                    ],
+                                    "score": 0.8,
+                                    "content": "k",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        237,
+                                        603,
+                                        249,
+                                        617
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        250,
+                                        603,
+                                        275,
+                                        615
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\{ 2 , 3 \\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        275,
+                                        603,
+                                        367,
+                                        617
+                                    ],
+                                    "score": 1.0,
+                                    "content": "performed better than",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        368,
+                                        603,
+                                        411,
+                                        615
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\{ 2 , \\ldots , 5 \\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        411,
+                                        603,
+                                        505,
+                                        617
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as was used originally",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                110,
+                                614,
+                                220,
+                                627
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        614,
+                                        131,
+                                        625
+                                    ],
+                                    "score": 0.86,
+                                    "content": "+ 1 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        132,
+                                        614,
+                                        220,
+                                        627
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for the larger model).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 23.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        643,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                643,
+                                505,
+                                657
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        643,
+                                        505,
+                                        657
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Patch-based augmentation. If the network can solve CPC using low-level patterns (e.g. straight",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                655,
+                                505,
+                                668
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        655,
+                                        505,
+                                        668
+                                    ],
+                                    "score": 1.0,
+                                    "content": "lines continuing between patches, chromatic aberration), it need not learn semantically meaning-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                666,
+                                506,
+                                679
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        666,
+                                        506,
+                                        679
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ful content. Augmenting the low-level variability across patches can remove such low level cues.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                676,
+                                505,
+                                690
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        676,
+                                        505,
+                                        690
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The original CPC model spatially jitters individual patches independently. We further this logic by",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                688,
+                                505,
+                                700
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        688,
+                                        505,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "adopting the ‘color dropping’ method of Doersch et al. (2015), which randomly drops two of the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                698,
+                                505,
+                                711
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        698,
+                                        399,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "three color channels in each patch, and find it to delivers systematic gains",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        400,
+                                        699,
+                                        422,
+                                        709
+                                    ],
+                                    "score": 0.86,
+                                    "content": "( + 1 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        422,
+                                        698,
+                                        505,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for the small model,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                709,
+                                506,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        710,
+                                        128,
+                                        720
+                                    ],
+                                    "score": 0.87,
+                                    "content": "+3 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        128,
+                                        709,
+                                        506,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for the larger one). We also randomly flip patches horizontally, but find it only benefits the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                720,
+                                199,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        720,
+                                        166,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "smaller model",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        166,
+                                        721,
+                                        194,
+                                        732
+                                    ],
+                                    "score": 0.9,
+                                    "content": "( + 1 \\% )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        194,
+                                        720,
+                                        199,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 33.5
+                }
+            ],
+            "page_idx": 5,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        308,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                25,
+                                308,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        25,
+                                        308,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Under review as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        752,
+                        308,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                302,
+                                751,
+                                309,
+                                762
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        302,
+                                        751,
+                                        309,
+                                        762
+                                    ],
+                                    "score": 1.0,
+                                    "content": "6",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "table",
+                    "bbox": [
+                        125,
+                        126,
+                        486,
+                        294
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                107,
+                                89,
+                                504,
+                                123
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        88,
+                                        505,
+                                        102
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                88,
+                                                218,
+                                                102
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 1: Linear classifier",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
+                                                218,
+                                                90,
+                                                231,
+                                                101
+                                            ],
+                                            "score": 0.89,
+                                            "content": "h _ { \\psi }",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
+                                                232,
+                                                88,
+                                                291,
+                                                102
+                                            ],
+                                            "score": 1.0,
+                                            "content": "trained with",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
+                                                291,
+                                                89,
+                                                317,
+                                                100
+                                            ],
+                                            "score": 0.86,
+                                            "content": "100 \\%",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
+                                                318,
+                                                88,
+                                                505,
+                                                102
+                                            ],
+                                            "score": 1.0,
+                                            "content": "of labels. Comparison to linear separability",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        101,
+                                        506,
+                                        113
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                101,
+                                                506,
+                                                113
+                                            ],
+                                            "score": 1.0,
+                                            "content": "of other self-supervised methods. In all cases a feature extractor is optimized in an unsupervised",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        111,
+                                        456,
+                                        124
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                111,
+                                                456,
+                                                124
+                                            ],
+                                            "score": 1.0,
+                                            "content": "manner, and a linear classifier is trained on top using all labels in the ImageNet dataset.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 2
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                125,
+                                126,
+                                486,
+                                294
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        125,
+                                        126,
+                                        486,
+                                        294
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                125,
+                                                126,
+                                                486,
+                                                294
+                                            ],
+                                            "score": 0.974,
+                                            "html": "<table><tr><td>Method</td><td>Top-1</td><td>Top-5</td></tr><tr><td>Motion Segmentation (MS) (Pathak et al., 2016) Exemplar (Ex) (Dosovitskiy et al.,2014) Relative Position (RP) (Doersch et al.,2015) Colorization (Col) (Zhang et al., 2016) Combination of MS + Ex + RP+ Col (Doersch &amp; Zisserman,2017) CPC v1 (van den Oord et al., 2018) Rotation (Kolesnikov et al., 2019)</td><td>27.6 31.5 36.2 39.6 1 48.7 55.4</td><td>48.3 53.1 59.2 62.5 69.3 73.6</td></tr><tr><td>CMC (Tian et al., 2019) Local Aggregation (Zhuang et al., 2019)</td><td>60.1 60.2</td><td>82.8 1 =</td></tr><tr><td>BigBiGAN (Donahue &amp; Simonyan,2019) AMDIM (Bachman et al., 2019) CPC v2 (ours) 65.9</td><td>61.3 68.1</td><td>81.9</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "fa1f65edaf71df9800daca9c26a7999e93d74856116a87cc357e08cc713a4be7.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 4,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        125,
+                                        126,
+                                        486,
+                                        182.0
+                                    ],
+                                    "spans": [],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        125,
+                                        182.0,
+                                        486,
+                                        238.0
+                                    ],
+                                    "spans": [],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        125,
+                                        238.0,
+                                        486,
+                                        294.0
+                                    ],
+                                    "spans": [],
+                                    "index": 5
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        325,
+                        504,
+                        358
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                324,
+                                506,
+                                338
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        324,
+                                        506,
+                                        338
+                                    ],
+                                    "score": 1.0,
+                                    "content": "other design choices. Interestingly, a larger architecture delivers larger improvements with more",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                335,
+                                503,
+                                349
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        335,
+                                        481,
+                                        349
+                                    ],
+                                    "score": 1.0,
+                                    "content": "efficient training, more self-supervised losses, and more patch-based augmentations (Fig. 3,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        482,
+                                        336,
+                                        503,
+                                        347
+                                    ],
+                                    "score": 0.84,
+                                    "content": "+5 \\%",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                347,
+                                420,
+                                360
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        347,
+                                        292,
+                                        360
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-1 accuracy with original training scheme,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        292,
+                                        347,
+                                        318,
+                                        357
+                                    ],
+                                    "score": 0.88,
+                                    "content": "+ 1 0 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        319,
+                                        347,
+                                        420,
+                                        360
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accuracy with new one).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 7,
+                    "bbox_fs": [
+                        105,
+                        324,
+                        506,
+                        360
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        376,
+                        505,
+                        475
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                376,
+                                505,
+                                388
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        376,
+                                        505,
+                                        388
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Layer normalization. Large architectures are more difficult to train efficiently. Early works on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                387,
+                                506,
+                                400
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        387,
+                                        506,
+                                        400
+                                    ],
+                                    "score": 1.0,
+                                    "content": "context prediction with patches used batch normalization (Ioffe & Szegedy, 2015; Doersch et al.,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                397,
+                                504,
+                                411
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        397,
+                                        504,
+                                        411
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2015) to speed training. However, with CPC we find that batch normalization actually harms down-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                409,
+                                505,
+                                422
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        409,
+                                        505,
+                                        422
+                                    ],
+                                    "score": 1.0,
+                                    "content": "stream performance of large models. We hypothesize that batch normalization allows large models",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                420,
+                                505,
+                                432
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        420,
+                                        505,
+                                        432
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to find a trivial solution to CPC: it introduces a dependency between patches (through the batch",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                431,
+                                505,
+                                444
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        431,
+                                        505,
+                                        444
+                                    ],
+                                    "score": 1.0,
+                                    "content": "statistics) that can be exploited to bypass the constraints on the receptive field. We find that we can",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                442,
+                                505,
+                                455
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        442,
+                                        505,
+                                        455
+                                    ],
+                                    "score": 1.0,
+                                    "content": "reclaim much of batch normalization’s training efficiency using layer normalization (Ba et al., 2016),",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                452,
+                                505,
+                                466
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        452,
+                                        328,
+                                        466
+                                    ],
+                                    "score": 1.0,
+                                    "content": "which leads to a small gain for the smaller architecture",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        328,
+                                        453,
+                                        349,
+                                        464
+                                    ],
+                                    "score": 0.87,
+                                    "content": "+ 1 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        350,
+                                        452,
+                                        505,
+                                        466
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accuracy over equivalent architectures",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                462,
+                                481,
+                                478
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        462,
+                                        406,
+                                        478
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that use neither normalization) and a larger gain for the larger architecture",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        406,
+                                        464,
+                                        436,
+                                        475
+                                    ],
+                                    "score": 0.87,
+                                    "content": "( + 2 . 5 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        436,
+                                        462,
+                                        481,
+                                        478
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accuracy).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 13,
+                    "bbox_fs": [
+                        105,
+                        376,
+                        506,
+                        478
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        493,
+                        505,
+                        626
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                493,
+                                505,
+                                506
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        493,
+                                        505,
+                                        506
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Prediction lengths and directions. Larger architectures also run a greater risk of overfitting. We",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                505,
+                                505,
+                                517
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        505,
+                                        505,
+                                        517
+                                    ],
+                                    "score": 1.0,
+                                    "content": "address this by asking more from the network: specifically, whereas van den Oord et al. (2018) pre-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                514,
+                                505,
+                                529
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        514,
+                                        505,
+                                        529
+                                    ],
+                                    "score": 1.0,
+                                    "content": "dicted each patch using only context from spatially beneath it, we repeatedly predict the patch using",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                527,
+                                505,
+                                539
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        527,
+                                        505,
+                                        539
+                                    ],
+                                    "score": 1.0,
+                                    "content": "context from above, to the right, and to the left, resulting in up to four times as many prediction",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                536,
+                                505,
+                                551
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        536,
+                                        443,
+                                        551
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tasks. Combining top-to-bottom with bottom-to-top helps both model architectures",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        443,
+                                        538,
+                                        465,
+                                        548
+                                    ],
+                                    "score": 0.87,
+                                    "content": "42 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        466,
+                                        536,
+                                        505,
+                                        551
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accuracy",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                548,
+                                505,
+                                560
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        548,
+                                        460,
+                                        560
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for both), but using all 4 spatial directions only benefits the larger model (an additional",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        460,
+                                        549,
+                                        489,
+                                        559
+                                    ],
+                                    "score": 0.9,
+                                    "content": "+ 1 . 5 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        489,
+                                        548,
+                                        505,
+                                        560
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                560,
+                                506,
+                                572
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        560,
+                                        177,
+                                        572
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the larger model,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        177,
+                                        560,
+                                        196,
+                                        570
+                                    ],
+                                    "score": 0.85,
+                                    "content": "{ \\bf - 1 \\% }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        197,
+                                        560,
+                                        506,
+                                        572
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for the smaller), consistent with the idea that model capacity and amount of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                570,
+                                505,
+                                582
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        570,
+                                        505,
+                                        582
+                                    ],
+                                    "score": 1.0,
+                                    "content": "supervision must go hand-in-hand. We also hypothesized that prediction “length”—i.e. offset be-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                582,
+                                505,
+                                594
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        582,
+                                        505,
+                                        594
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tween the predicted patch and the aggregated context—might affect performance, as distant patches",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                592,
+                                505,
+                                605
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        592,
+                                        505,
+                                        605
+                                    ],
+                                    "score": 1.0,
+                                    "content": "might lie on distinct objects, encouraging the network to memorize images. Indeed, limiting the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                603,
+                                505,
+                                617
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        603,
+                                        230,
+                                        617
+                                    ],
+                                    "score": 1.0,
+                                    "content": "range of the prediction length",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        230,
+                                        604,
+                                        237,
+                                        613
+                                    ],
+                                    "score": 0.8,
+                                    "content": "k",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        237,
+                                        603,
+                                        249,
+                                        617
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        250,
+                                        603,
+                                        275,
+                                        615
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\{ 2 , 3 \\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        275,
+                                        603,
+                                        367,
+                                        617
+                                    ],
+                                    "score": 1.0,
+                                    "content": "performed better than",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        368,
+                                        603,
+                                        411,
+                                        615
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\{ 2 , \\ldots , 5 \\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        411,
+                                        603,
+                                        505,
+                                        617
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as was used originally",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                110,
+                                614,
+                                220,
+                                627
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        614,
+                                        131,
+                                        625
+                                    ],
+                                    "score": 0.86,
+                                    "content": "+ 1 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        132,
+                                        614,
+                                        220,
+                                        627
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for the larger model).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 23.5,
+                    "bbox_fs": [
+                        104,
+                        493,
+                        506,
+                        627
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        643,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                643,
+                                505,
+                                657
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        643,
+                                        505,
+                                        657
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Patch-based augmentation. If the network can solve CPC using low-level patterns (e.g. straight",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                655,
+                                505,
+                                668
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        655,
+                                        505,
+                                        668
+                                    ],
+                                    "score": 1.0,
+                                    "content": "lines continuing between patches, chromatic aberration), it need not learn semantically meaning-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                666,
+                                506,
+                                679
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        666,
+                                        506,
+                                        679
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ful content. Augmenting the low-level variability across patches can remove such low level cues.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                676,
+                                505,
+                                690
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        676,
+                                        505,
+                                        690
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The original CPC model spatially jitters individual patches independently. We further this logic by",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                688,
+                                505,
+                                700
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        688,
+                                        505,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "adopting the ‘color dropping’ method of Doersch et al. (2015), which randomly drops two of the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                698,
+                                505,
+                                711
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        698,
+                                        399,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "three color channels in each patch, and find it to delivers systematic gains",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        400,
+                                        699,
+                                        422,
+                                        709
+                                    ],
+                                    "score": 0.86,
+                                    "content": "( + 1 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        422,
+                                        698,
+                                        505,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for the small model,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                709,
+                                506,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        710,
+                                        128,
+                                        720
+                                    ],
+                                    "score": 0.87,
+                                    "content": "+3 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        128,
+                                        709,
+                                        506,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for the larger one). We also randomly flip patches horizontally, but find it only benefits the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                720,
+                                199,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        720,
+                                        166,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "smaller model",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        166,
+                                        721,
+                                        194,
+                                        732
+                                    ],
+                                    "score": 0.9,
+                                    "content": "( + 1 \\% )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        194,
+                                        720,
+                                        199,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 33.5,
+                    "bbox_fs": [
+                        105,
+                        643,
+                        506,
+                        733
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        82,
+                        505,
+                        192
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                82,
+                                505,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        82,
+                                        505,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Combined. Cumulatively, these fairly straightforward implementation changes lead to a substan-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                93,
+                                505,
+                                107
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        93,
+                                        288,
+                                        107
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tial improvement to the original CPC model",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        94,
+                                        316,
+                                        105
+                                    ],
+                                    "score": 0.83,
+                                    "content": "6 5 . 9 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        316,
+                                        93,
+                                        390,
+                                        107
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-1 accuracy, a",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        390,
+                                        94,
+                                        410,
+                                        104
+                                    ],
+                                    "score": 0.87,
+                                    "content": "17 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        410,
+                                        93,
+                                        505,
+                                        107
+                                    ],
+                                    "score": 1.0,
+                                    "content": "improvement), making",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                103,
+                                505,
+                                118
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        103,
+                                        505,
+                                        118
+                                    ],
+                                    "score": 1.0,
+                                    "content": "it competitive with recent approaches and outperforming prior methods (see table 1). Interestingly,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                114,
+                                505,
+                                128
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        114,
+                                        505,
+                                        128
+                                    ],
+                                    "score": 1.0,
+                                    "content": "if we train the same patch-based architecture from scratch in a fully supervised manner, we ob-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                126,
+                                505,
+                                139
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        126,
+                                        124,
+                                        139
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tain",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        124,
+                                        126,
+                                        151,
+                                        137
+                                    ],
+                                    "score": 0.86,
+                                    "content": "6 6 . 4 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        152,
+                                        126,
+                                        325,
+                                        139
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-1 accuracy (with batch normalization;",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        325,
+                                        126,
+                                        352,
+                                        137
+                                    ],
+                                    "score": 0.87,
+                                    "content": "6 2 . 5 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        352,
+                                        126,
+                                        505,
+                                        139
+                                    ],
+                                    "score": 1.0,
+                                    "content": "without), suggesting that CPC is now",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                137,
+                                505,
+                                150
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        137,
+                                        505,
+                                        150
+                                    ],
+                                    "score": 1.0,
+                                    "content": "nearly saturating the architecture’s representational power despite not using labels. These results",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                148,
+                                505,
+                                162
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        148,
+                                        505,
+                                        162
+                                    ],
+                                    "score": 1.0,
+                                    "content": "illustrate how architecture and data have an outsized impact on the linear classification performance",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                159,
+                                505,
+                                172
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        159,
+                                        505,
+                                        172
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of self-supervised representations, and are interesting to compare with with previous results. For ex-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                169,
+                                506,
+                                183
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        169,
+                                        449,
+                                        183
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ample, in AMDIM, different settings of data augmentation alone can result in a nearly",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        449,
+                                        171,
+                                        468,
+                                        181
+                                    ],
+                                    "score": 0.85,
+                                    "content": "10 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        469,
+                                        169,
+                                        506,
+                                        183
+                                    ],
+                                    "score": 1.0,
+                                    "content": "absolute",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                181,
+                                340,
+                                193
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        181,
+                                        340,
+                                        193
+                                    ],
+                                    "score": 1.0,
+                                    "content": "increase in performance on ImageNet linear classification.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 4.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        109,
+                        208,
+                        279,
+                        219
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                208,
+                                281,
+                                220
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        208,
+                                        281,
+                                        220
+                                    ],
+                                    "score": 1.0,
+                                    "content": "4.2 EFFICIENT IMAGE CLASSIFICATION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        228,
+                        505,
+                        306
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                229,
+                                505,
+                                241
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        229,
+                                        505,
+                                        241
+                                    ],
+                                    "score": 1.0,
+                                    "content": "toWe now turn to our original question of whether CPC can enable data-efficient image recognition.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                239,
+                                506,
+                                253
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        239,
+                                        506,
+                                        253
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We start by evaluating the performance of purely-supervised networks as the size of the labeled",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                251,
+                                505,
+                                263
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        251,
+                                        137,
+                                        263
+                                    ],
+                                    "score": 1.0,
+                                    "content": "dataset",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        137,
+                                        251,
+                                        149,
+                                        262
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\mathbb { D } _ { l }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        149,
+                                        251,
+                                        200,
+                                        263
+                                    ],
+                                    "score": 1.0,
+                                    "content": "varies from",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        200,
+                                        251,
+                                        214,
+                                        261
+                                    ],
+                                    "score": 0.84,
+                                    "content": "1 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        215,
+                                        251,
+                                        227,
+                                        263
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        228,
+                                        251,
+                                        252,
+                                        262
+                                    ],
+                                    "score": 0.87,
+                                    "content": "100 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        252,
+                                        251,
+                                        505,
+                                        263
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of ImageNet, training separate classifiers on each subset. We",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                261,
+                                506,
+                                275
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        261,
+                                        506,
+                                        275
+                                    ],
+                                    "score": 1.0,
+                                    "content": "found that a ResNet-152 to works best across all data-regimes (see Appendix). Despite our efforts to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                272,
+                                505,
+                                286
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        272,
+                                        505,
+                                        286
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tune the supervised model for low-data classification (including network depth, regularization, and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                284,
+                                505,
+                                296
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        284,
+                                        388,
+                                        296
+                                    ],
+                                    "score": 1.0,
+                                    "content": "optimization parameters), the accuracy of the best model only reaches",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        389,
+                                        284,
+                                        416,
+                                        294
+                                    ],
+                                    "score": 0.86,
+                                    "content": "4 4 . 1 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        416,
+                                        284,
+                                        505,
+                                        296
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-5 accuracy when",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                295,
+                                505,
+                                307
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        295,
+                                        149,
+                                        307
+                                    ],
+                                    "score": 1.0,
+                                    "content": "trained on",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        149,
+                                        295,
+                                        163,
+                                        305
+                                    ],
+                                    "score": 0.84,
+                                    "content": "1 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        164,
+                                        295,
+                                        274,
+                                        307
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of the dataset (compared to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        275,
+                                        295,
+                                        302,
+                                        306
+                                    ],
+                                    "score": 0.86,
+                                    "content": "9 3 . 9 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        302,
+                                        295,
+                                        505,
+                                        307
+                                    ],
+                                    "score": 1.0,
+                                    "content": "when trained on the entire dataset, see Fig. 1, red).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        320,
+                        296,
+                        594
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                320,
+                                297,
+                                332
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        320,
+                                        297,
+                                        332
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Contrastive Predictive Coding. We now ad-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                331,
+                                297,
+                                343
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        331,
+                                        297,
+                                        343
+                                    ],
+                                    "score": 1.0,
+                                    "content": "dress our central question of whether CPC en-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                342,
+                                297,
+                                354
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        342,
+                                        297,
+                                        354
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ables data-efficient learning. We follow the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                353,
+                                297,
+                                365
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        353,
+                                        297,
+                                        365
+                                    ],
+                                    "score": 1.0,
+                                    "content": "same paradigm as for the supervised base-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                363,
+                                297,
+                                377
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        363,
+                                        297,
+                                        377
+                                    ],
+                                    "score": 1.0,
+                                    "content": "line (training and evaluating a separate clas-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                374,
+                                297,
+                                387
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        374,
+                                        297,
+                                        387
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sifier for each size subset), stacking a neu-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                386,
+                                297,
+                                398
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        386,
+                                        297,
+                                        398
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ral network classifier on top of the CPC la-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                397,
+                                297,
+                                409
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        397,
+                                        130,
+                                        409
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tents",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        131,
+                                        397,
+                                        186,
+                                        408
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\begin{array} { r l r } { z } & { { } = } & { f _ { \\theta } ( { \\pmb x } ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        187,
+                                        397,
+                                        297,
+                                        409
+                                    ],
+                                    "score": 1.0,
+                                    "content": "rather than the raw im-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                408,
+                                298,
+                                420
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        408,
+                                        153,
+                                        420
+                                    ],
+                                    "score": 1.0,
+                                    "content": "age pixels",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        154,
+                                        410,
+                                        162,
+                                        418
+                                    ],
+                                    "score": 0.74,
+                                    "content": "_ { \\textbf { \\em x } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        162,
+                                        408,
+                                        298,
+                                        420
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(see section 2.2, efficient clas-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                418,
+                                297,
+                                431
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        418,
+                                        297,
+                                        431
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sification, and Appendix). This representa-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                429,
+                                297,
+                                441
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        429,
+                                        297,
+                                        441
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tion, which we selected for its improved linear",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                441,
+                                297,
+                                453
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        441,
+                                        297,
+                                        453
+                                    ],
+                                    "score": 1.0,
+                                    "content": "classification performance (CPC v2 in Fig. 3),",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                451,
+                                297,
+                                464
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        451,
+                                        297,
+                                        464
+                                    ],
+                                    "score": 1.0,
+                                    "content": "leads to a significant increase in data-efficiency",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                463,
+                                297,
+                                475
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        463,
+                                        297,
+                                        475
+                                    ],
+                                    "score": 1.0,
+                                    "content": "compared to purely supervised networks (Fig.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                473,
+                                296,
+                                486
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        473,
+                                        268,
+                                        486
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1, blue curve). This classifier yields",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        268,
+                                        474,
+                                        296,
+                                        484
+                                    ],
+                                    "score": 0.85,
+                                    "content": "7 2 . 9 \\%",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                484,
+                                297,
+                                496
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        484,
+                                        220,
+                                        496
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-5 accuracy with only",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        220,
+                                        485,
+                                        235,
+                                        495
+                                    ],
+                                    "score": 0.85,
+                                    "content": "1 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        236,
+                                        484,
+                                        297,
+                                        496
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of the labels,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                495,
+                                297,
+                                507
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        495,
+                                        115,
+                                        507
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        115,
+                                        496,
+                                        136,
+                                        506
+                                    ],
+                                    "score": 0.87,
+                                    "content": "2 9 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        136,
+                                        495,
+                                        238,
+                                        507
+                                    ],
+                                    "score": 1.0,
+                                    "content": "absolute improvement",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        239,
+                                        496,
+                                        258,
+                                        506
+                                    ],
+                                    "score": 0.83,
+                                    "content": "65 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        259,
+                                        495,
+                                        297,
+                                        507
+                                    ],
+                                    "score": 1.0,
+                                    "content": "relative)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                506,
+                                297,
+                                519
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        506,
+                                        297,
+                                        519
+                                    ],
+                                    "score": 1.0,
+                                    "content": "over purely-supervised methods. Surprisingly,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                517,
+                                297,
+                                528
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        517,
+                                        297,
+                                        528
+                                    ],
+                                    "score": 1.0,
+                                    "content": "when given the entire dataset, this classifier",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                528,
+                                297,
+                                540
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        528,
+                                        139,
+                                        540
+                                    ],
+                                    "score": 1.0,
+                                    "content": "reaches",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        139,
+                                        528,
+                                        194,
+                                        539
+                                    ],
+                                    "score": 0.9,
+                                    "content": "8 0 . 6 \\% / 9 5 . 2 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        194,
+                                        528,
+                                        297,
+                                        540
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top1/Top5 accuracy, sur-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                540,
+                                297,
+                                550
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        540,
+                                        297,
+                                        550
+                                    ],
+                                    "score": 1.0,
+                                    "content": "passing our supervised baseline (ResNet-152:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                549,
+                                297,
+                                562
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        550,
+                                        162,
+                                        561
+                                    ],
+                                    "score": 0.89,
+                                    "content": "7 8 . 0 \\% / 9 3 . 9 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        163,
+                                        549,
+                                        297,
+                                        562
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accuracy) and published results",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                560,
+                                297,
+                                574
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        560,
+                                        163,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(ResNet-200:",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        163,
+                                        561,
+                                        218,
+                                        572
+                                    ],
+                                    "score": 0.86,
+                                    "content": "7 9 . 9 \\% / 9 5 . 2 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        219,
+                                        560,
+                                        297,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", He et al. (2016b)).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                571,
+                                297,
+                                584
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        571,
+                                        297,
+                                        584
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We find similar results in all other data-regimes",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                582,
+                                217,
+                                595
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        582,
+                                        217,
+                                        595
+                                    ],
+                                    "score": 1.0,
+                                    "content": "we considered (see Fig. 1).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        }
+                    ],
+                    "index": 30
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        600,
+                        295,
+                        644
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                600,
+                                296,
+                                612
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        600,
+                                        296,
+                                        612
+                                    ],
+                                    "score": 1.0,
+                                    "content": "How important are the model specifications de-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                611,
+                                297,
+                                623
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        611,
+                                        297,
+                                        623
+                                    ],
+                                    "score": 1.0,
+                                    "content": "scribed in Section 4.1 for low-data classifica-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                622,
+                                297,
+                                633
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        622,
+                                        297,
+                                        633
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tion? We hypothesized that predictable repre-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                633,
+                                297,
+                                644
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        633,
+                                        297,
+                                        644
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sentations might enable data-efficient classifi-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        }
+                    ],
+                    "index": 44.5
+                },
+                {
+                    "type": "image",
+                    "bbox": [
+                        308,
+                        324,
+                        496,
+                        521
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                308,
+                                324,
+                                496,
+                                521
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        308,
+                                        324,
+                                        496,
+                                        521
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                308,
+                                                324,
+                                                496,
+                                                521
+                                            ],
+                                            "score": 0.97,
+                                            "type": "image",
+                                            "image_path": "106f2252ad377e16a329cfb21360459a72fdc1d09e4f745b26572da1cf6d5d14.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 54.5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        308,
+                                        324,
+                                        496,
+                                        336.3125
+                                    ],
+                                    "spans": [],
+                                    "index": 47
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        336.3125,
+                                        496,
+                                        348.625
+                                    ],
+                                    "spans": [],
+                                    "index": 48
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        348.625,
+                                        496,
+                                        360.9375
+                                    ],
+                                    "spans": [],
+                                    "index": 49
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        360.9375,
+                                        496,
+                                        373.25
+                                    ],
+                                    "spans": [],
+                                    "index": 50
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        373.25,
+                                        496,
+                                        385.5625
+                                    ],
+                                    "spans": [],
+                                    "index": 51
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        385.5625,
+                                        496,
+                                        397.875
+                                    ],
+                                    "spans": [],
+                                    "index": 52
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        397.875,
+                                        496,
+                                        410.1875
+                                    ],
+                                    "spans": [],
+                                    "index": 53
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        410.1875,
+                                        496,
+                                        422.5
+                                    ],
+                                    "spans": [],
+                                    "index": 54
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        422.5,
+                                        496,
+                                        434.8125
+                                    ],
+                                    "spans": [],
+                                    "index": 55
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        434.8125,
+                                        496,
+                                        447.125
+                                    ],
+                                    "spans": [],
+                                    "index": 56
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        447.125,
+                                        496,
+                                        459.4375
+                                    ],
+                                    "spans": [],
+                                    "index": 57
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        459.4375,
+                                        496,
+                                        471.75
+                                    ],
+                                    "spans": [],
+                                    "index": 58
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        471.75,
+                                        496,
+                                        484.0625
+                                    ],
+                                    "spans": [],
+                                    "index": 59
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        484.0625,
+                                        496,
+                                        496.375
+                                    ],
+                                    "spans": [],
+                                    "index": 60
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        496.375,
+                                        496,
+                                        508.6875
+                                    ],
+                                    "spans": [],
+                                    "index": 61
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        508.6875,
+                                        496,
+                                        521.0
+                                    ],
+                                    "spans": [],
+                                    "index": 62
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                304,
+                                526,
+                                504,
+                                636
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        526,
+                                        505,
+                                        537
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                304,
+                                                526,
+                                                505,
+                                                537
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 4: Relationship between linear classifica-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 63
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        537,
+                                        505,
+                                        548
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                303,
+                                                537,
+                                                505,
+                                                548
+                                            ],
+                                            "score": 1.0,
+                                            "content": "tion accuracy and low-data classification, for dif-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 64
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        548,
+                                        505,
+                                        559
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                304,
+                                                548,
+                                                505,
+                                                559
+                                            ],
+                                            "score": 1.0,
+                                            "content": "ferent variants of the CPC model. Left: CPC vari-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 65
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        559,
+                                        505,
+                                        570
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                304,
+                                                559,
+                                                505,
+                                                570
+                                            ],
+                                            "score": 1.0,
+                                            "content": "ants with the same architecture but different train-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 66
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        570,
+                                        505,
+                                        581
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                303,
+                                                570,
+                                                505,
+                                                581
+                                            ],
+                                            "score": 1.0,
+                                            "content": "ing protocols. Orange, green, and blue dots cor-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 67
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        581,
+                                        505,
+                                        593
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                303,
+                                                581,
+                                                505,
+                                                593
+                                            ],
+                                            "score": 1.0,
+                                            "content": "respond to CPC models making predictions in 1,",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 68
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        592,
+                                        506,
+                                        604
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                303,
+                                                592,
+                                                506,
+                                                604
+                                            ],
+                                            "score": 1.0,
+                                            "content": "2, and 4 spatial directions respectively. Within a",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 69
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        603,
+                                        505,
+                                        614
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                303,
+                                                603,
+                                                505,
+                                                614
+                                            ],
+                                            "score": 1.0,
+                                            "content": "color group, different models correspond to other",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 70
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        613,
+                                        506,
+                                        626
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                303,
+                                                613,
+                                                506,
+                                                626
+                                            ],
+                                            "score": 1.0,
+                                            "content": "implementation details (e.g. layer norm and patch",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 71
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        625,
+                                        473,
+                                        636
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                303,
+                                                625,
+                                                473,
+                                                636
+                                            ],
+                                            "score": 1.0,
+                                            "content": "augmentation, and combinations thereof).",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 72
+                                }
+                            ],
+                            "index": 67.5
+                        }
+                    ],
+                    "index": 61.0
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        644,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                644,
+                                505,
+                                656
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        644,
+                                        505,
+                                        656
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cation, and therefore expect that increasing the amount of ‘predictability’ in the representation",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 73
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                655,
+                                505,
+                                666
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        655,
+                                        505,
+                                        666
+                                    ],
+                                    "score": 1.0,
+                                    "content": "should also increase its ability to learn from small amounts of data. Fig. 4 shows evidence for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 74
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                666,
+                                505,
+                                678
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        666,
+                                        505,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "this by ablating model parameters and comparing linear classification performance against low-data",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 75
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                677,
+                                505,
+                                689
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        677,
+                                        505,
+                                        689
+                                    ],
+                                    "score": 1.0,
+                                    "content": "classification. Consistent with our hypothesis, increasing the number of spatial directions in the CPC",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 76
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                687,
+                                506,
+                                700
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        687,
+                                        506,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "prediction task (which increased linear classification performance) systematically increases low-data",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 77
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                699,
+                                505,
+                                711
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        699,
+                                        505,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "classification performance (Fig. 4, left, different color groups). As a control, we asked if all mod-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 78
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                710,
+                                505,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        710,
+                                        505,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ifications that improve linear classification also improve low-data classification. We did not find",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 79
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                721,
+                                505,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        721,
+                                        505,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "evidence in favor of this: improvements in linear classification as a result of changing other model",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 80
+                        }
+                    ],
+                    "index": 76.5
+                }
+            ],
+            "page_idx": 6,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        308,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                26,
+                                308,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        26,
+                                        308,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Under review as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        303,
+                        751,
+                        309,
+                        759
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                302,
+                                750,
+                                309,
+                                762
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        302,
+                                        750,
+                                        309,
+                                        762
+                                    ],
+                                    "score": 1.0,
+                                    "content": "7",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        82,
+                        505,
+                        192
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                82,
+                                505,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        82,
+                                        505,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Combined. Cumulatively, these fairly straightforward implementation changes lead to a substan-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                93,
+                                505,
+                                107
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        93,
+                                        288,
+                                        107
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tial improvement to the original CPC model",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        94,
+                                        316,
+                                        105
+                                    ],
+                                    "score": 0.83,
+                                    "content": "6 5 . 9 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        316,
+                                        93,
+                                        390,
+                                        107
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-1 accuracy, a",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        390,
+                                        94,
+                                        410,
+                                        104
+                                    ],
+                                    "score": 0.87,
+                                    "content": "17 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        410,
+                                        93,
+                                        505,
+                                        107
+                                    ],
+                                    "score": 1.0,
+                                    "content": "improvement), making",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                103,
+                                505,
+                                118
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        103,
+                                        505,
+                                        118
+                                    ],
+                                    "score": 1.0,
+                                    "content": "it competitive with recent approaches and outperforming prior methods (see table 1). Interestingly,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                114,
+                                505,
+                                128
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        114,
+                                        505,
+                                        128
+                                    ],
+                                    "score": 1.0,
+                                    "content": "if we train the same patch-based architecture from scratch in a fully supervised manner, we ob-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                126,
+                                505,
+                                139
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        126,
+                                        124,
+                                        139
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tain",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        124,
+                                        126,
+                                        151,
+                                        137
+                                    ],
+                                    "score": 0.86,
+                                    "content": "6 6 . 4 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        152,
+                                        126,
+                                        325,
+                                        139
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-1 accuracy (with batch normalization;",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        325,
+                                        126,
+                                        352,
+                                        137
+                                    ],
+                                    "score": 0.87,
+                                    "content": "6 2 . 5 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        352,
+                                        126,
+                                        505,
+                                        139
+                                    ],
+                                    "score": 1.0,
+                                    "content": "without), suggesting that CPC is now",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                137,
+                                505,
+                                150
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        137,
+                                        505,
+                                        150
+                                    ],
+                                    "score": 1.0,
+                                    "content": "nearly saturating the architecture’s representational power despite not using labels. These results",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                148,
+                                505,
+                                162
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        148,
+                                        505,
+                                        162
+                                    ],
+                                    "score": 1.0,
+                                    "content": "illustrate how architecture and data have an outsized impact on the linear classification performance",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                159,
+                                505,
+                                172
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        159,
+                                        505,
+                                        172
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of self-supervised representations, and are interesting to compare with with previous results. For ex-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                169,
+                                506,
+                                183
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        169,
+                                        449,
+                                        183
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ample, in AMDIM, different settings of data augmentation alone can result in a nearly",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        449,
+                                        171,
+                                        468,
+                                        181
+                                    ],
+                                    "score": 0.85,
+                                    "content": "10 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        469,
+                                        169,
+                                        506,
+                                        183
+                                    ],
+                                    "score": 1.0,
+                                    "content": "absolute",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                181,
+                                340,
+                                193
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        181,
+                                        340,
+                                        193
+                                    ],
+                                    "score": 1.0,
+                                    "content": "increase in performance on ImageNet linear classification.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 4.5,
+                    "bbox_fs": [
+                        104,
+                        82,
+                        506,
+                        193
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        109,
+                        208,
+                        279,
+                        219
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                208,
+                                281,
+                                220
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        208,
+                                        281,
+                                        220
+                                    ],
+                                    "score": 1.0,
+                                    "content": "4.2 EFFICIENT IMAGE CLASSIFICATION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        228,
+                        505,
+                        306
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                229,
+                                505,
+                                241
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        229,
+                                        505,
+                                        241
+                                    ],
+                                    "score": 1.0,
+                                    "content": "toWe now turn to our original question of whether CPC can enable data-efficient image recognition.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                239,
+                                506,
+                                253
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        239,
+                                        506,
+                                        253
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We start by evaluating the performance of purely-supervised networks as the size of the labeled",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                251,
+                                505,
+                                263
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        251,
+                                        137,
+                                        263
+                                    ],
+                                    "score": 1.0,
+                                    "content": "dataset",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        137,
+                                        251,
+                                        149,
+                                        262
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\mathbb { D } _ { l }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        149,
+                                        251,
+                                        200,
+                                        263
+                                    ],
+                                    "score": 1.0,
+                                    "content": "varies from",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        200,
+                                        251,
+                                        214,
+                                        261
+                                    ],
+                                    "score": 0.84,
+                                    "content": "1 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        215,
+                                        251,
+                                        227,
+                                        263
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        228,
+                                        251,
+                                        252,
+                                        262
+                                    ],
+                                    "score": 0.87,
+                                    "content": "100 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        252,
+                                        251,
+                                        505,
+                                        263
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of ImageNet, training separate classifiers on each subset. We",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                261,
+                                506,
+                                275
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        261,
+                                        506,
+                                        275
+                                    ],
+                                    "score": 1.0,
+                                    "content": "found that a ResNet-152 to works best across all data-regimes (see Appendix). Despite our efforts to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                272,
+                                505,
+                                286
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        272,
+                                        505,
+                                        286
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tune the supervised model for low-data classification (including network depth, regularization, and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                284,
+                                505,
+                                296
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        284,
+                                        388,
+                                        296
+                                    ],
+                                    "score": 1.0,
+                                    "content": "optimization parameters), the accuracy of the best model only reaches",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        389,
+                                        284,
+                                        416,
+                                        294
+                                    ],
+                                    "score": 0.86,
+                                    "content": "4 4 . 1 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        416,
+                                        284,
+                                        505,
+                                        296
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-5 accuracy when",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                295,
+                                505,
+                                307
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        295,
+                                        149,
+                                        307
+                                    ],
+                                    "score": 1.0,
+                                    "content": "trained on",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        149,
+                                        295,
+                                        163,
+                                        305
+                                    ],
+                                    "score": 0.84,
+                                    "content": "1 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        164,
+                                        295,
+                                        274,
+                                        307
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of the dataset (compared to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        275,
+                                        295,
+                                        302,
+                                        306
+                                    ],
+                                    "score": 0.86,
+                                    "content": "9 3 . 9 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        302,
+                                        295,
+                                        505,
+                                        307
+                                    ],
+                                    "score": 1.0,
+                                    "content": "when trained on the entire dataset, see Fig. 1, red).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 14,
+                    "bbox_fs": [
+                        105,
+                        229,
+                        506,
+                        307
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        320,
+                        296,
+                        594
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                320,
+                                297,
+                                332
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        320,
+                                        297,
+                                        332
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Contrastive Predictive Coding. We now ad-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                331,
+                                297,
+                                343
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        331,
+                                        297,
+                                        343
+                                    ],
+                                    "score": 1.0,
+                                    "content": "dress our central question of whether CPC en-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                342,
+                                297,
+                                354
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        342,
+                                        297,
+                                        354
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ables data-efficient learning. We follow the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                353,
+                                297,
+                                365
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        353,
+                                        297,
+                                        365
+                                    ],
+                                    "score": 1.0,
+                                    "content": "same paradigm as for the supervised base-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                363,
+                                297,
+                                377
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        363,
+                                        297,
+                                        377
+                                    ],
+                                    "score": 1.0,
+                                    "content": "line (training and evaluating a separate clas-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                374,
+                                297,
+                                387
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        374,
+                                        297,
+                                        387
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sifier for each size subset), stacking a neu-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                386,
+                                297,
+                                398
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        386,
+                                        297,
+                                        398
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ral network classifier on top of the CPC la-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                397,
+                                297,
+                                409
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        397,
+                                        130,
+                                        409
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tents",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        131,
+                                        397,
+                                        186,
+                                        408
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\begin{array} { r l r } { z } & { { } = } & { f _ { \\theta } ( { \\pmb x } ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        187,
+                                        397,
+                                        297,
+                                        409
+                                    ],
+                                    "score": 1.0,
+                                    "content": "rather than the raw im-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                408,
+                                298,
+                                420
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        408,
+                                        153,
+                                        420
+                                    ],
+                                    "score": 1.0,
+                                    "content": "age pixels",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        154,
+                                        410,
+                                        162,
+                                        418
+                                    ],
+                                    "score": 0.74,
+                                    "content": "_ { \\textbf { \\em x } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        162,
+                                        408,
+                                        298,
+                                        420
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(see section 2.2, efficient clas-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                418,
+                                297,
+                                431
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        418,
+                                        297,
+                                        431
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sification, and Appendix). This representa-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                429,
+                                297,
+                                441
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        429,
+                                        297,
+                                        441
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tion, which we selected for its improved linear",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                441,
+                                297,
+                                453
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        441,
+                                        297,
+                                        453
+                                    ],
+                                    "score": 1.0,
+                                    "content": "classification performance (CPC v2 in Fig. 3),",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                451,
+                                297,
+                                464
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        451,
+                                        297,
+                                        464
+                                    ],
+                                    "score": 1.0,
+                                    "content": "leads to a significant increase in data-efficiency",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                463,
+                                297,
+                                475
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        463,
+                                        297,
+                                        475
+                                    ],
+                                    "score": 1.0,
+                                    "content": "compared to purely supervised networks (Fig.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                473,
+                                296,
+                                486
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        473,
+                                        268,
+                                        486
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1, blue curve). This classifier yields",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        268,
+                                        474,
+                                        296,
+                                        484
+                                    ],
+                                    "score": 0.85,
+                                    "content": "7 2 . 9 \\%",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                484,
+                                297,
+                                496
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        484,
+                                        220,
+                                        496
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-5 accuracy with only",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        220,
+                                        485,
+                                        235,
+                                        495
+                                    ],
+                                    "score": 0.85,
+                                    "content": "1 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        236,
+                                        484,
+                                        297,
+                                        496
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of the labels,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                495,
+                                297,
+                                507
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        495,
+                                        115,
+                                        507
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        115,
+                                        496,
+                                        136,
+                                        506
+                                    ],
+                                    "score": 0.87,
+                                    "content": "2 9 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        136,
+                                        495,
+                                        238,
+                                        507
+                                    ],
+                                    "score": 1.0,
+                                    "content": "absolute improvement",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        239,
+                                        496,
+                                        258,
+                                        506
+                                    ],
+                                    "score": 0.83,
+                                    "content": "65 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        259,
+                                        495,
+                                        297,
+                                        507
+                                    ],
+                                    "score": 1.0,
+                                    "content": "relative)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                506,
+                                297,
+                                519
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        506,
+                                        297,
+                                        519
+                                    ],
+                                    "score": 1.0,
+                                    "content": "over purely-supervised methods. Surprisingly,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                517,
+                                297,
+                                528
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        517,
+                                        297,
+                                        528
+                                    ],
+                                    "score": 1.0,
+                                    "content": "when given the entire dataset, this classifier",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                528,
+                                297,
+                                540
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        528,
+                                        139,
+                                        540
+                                    ],
+                                    "score": 1.0,
+                                    "content": "reaches",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        139,
+                                        528,
+                                        194,
+                                        539
+                                    ],
+                                    "score": 0.9,
+                                    "content": "8 0 . 6 \\% / 9 5 . 2 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        194,
+                                        528,
+                                        297,
+                                        540
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top1/Top5 accuracy, sur-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                540,
+                                297,
+                                550
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        540,
+                                        297,
+                                        550
+                                    ],
+                                    "score": 1.0,
+                                    "content": "passing our supervised baseline (ResNet-152:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                549,
+                                297,
+                                562
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        550,
+                                        162,
+                                        561
+                                    ],
+                                    "score": 0.89,
+                                    "content": "7 8 . 0 \\% / 9 3 . 9 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        163,
+                                        549,
+                                        297,
+                                        562
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accuracy) and published results",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                560,
+                                297,
+                                574
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        560,
+                                        163,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(ResNet-200:",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        163,
+                                        561,
+                                        218,
+                                        572
+                                    ],
+                                    "score": 0.86,
+                                    "content": "7 9 . 9 \\% / 9 5 . 2 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        219,
+                                        560,
+                                        297,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", He et al. (2016b)).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                571,
+                                297,
+                                584
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        571,
+                                        297,
+                                        584
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We find similar results in all other data-regimes",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                582,
+                                217,
+                                595
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        582,
+                                        217,
+                                        595
+                                    ],
+                                    "score": 1.0,
+                                    "content": "we considered (see Fig. 1).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        }
+                    ],
+                    "index": 30,
+                    "bbox_fs": [
+                        105,
+                        320,
+                        298,
+                        595
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        600,
+                        295,
+                        644
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                600,
+                                296,
+                                612
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        600,
+                                        296,
+                                        612
+                                    ],
+                                    "score": 1.0,
+                                    "content": "How important are the model specifications de-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                611,
+                                297,
+                                623
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        611,
+                                        297,
+                                        623
+                                    ],
+                                    "score": 1.0,
+                                    "content": "scribed in Section 4.1 for low-data classifica-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                622,
+                                297,
+                                633
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        622,
+                                        297,
+                                        633
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tion? We hypothesized that predictable repre-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                633,
+                                297,
+                                644
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        633,
+                                        297,
+                                        644
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sentations might enable data-efficient classifi-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        }
+                    ],
+                    "index": 44.5,
+                    "bbox_fs": [
+                        105,
+                        600,
+                        297,
+                        644
+                    ]
+                },
+                {
+                    "type": "image",
+                    "bbox": [
+                        308,
+                        324,
+                        496,
+                        521
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                308,
+                                324,
+                                496,
+                                521
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        308,
+                                        324,
+                                        496,
+                                        521
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                308,
+                                                324,
+                                                496,
+                                                521
+                                            ],
+                                            "score": 0.97,
+                                            "type": "image",
+                                            "image_path": "106f2252ad377e16a329cfb21360459a72fdc1d09e4f745b26572da1cf6d5d14.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 54.5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        308,
+                                        324,
+                                        496,
+                                        336.3125
+                                    ],
+                                    "spans": [],
+                                    "index": 47
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        336.3125,
+                                        496,
+                                        348.625
+                                    ],
+                                    "spans": [],
+                                    "index": 48
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        348.625,
+                                        496,
+                                        360.9375
+                                    ],
+                                    "spans": [],
+                                    "index": 49
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        360.9375,
+                                        496,
+                                        373.25
+                                    ],
+                                    "spans": [],
+                                    "index": 50
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        373.25,
+                                        496,
+                                        385.5625
+                                    ],
+                                    "spans": [],
+                                    "index": 51
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        385.5625,
+                                        496,
+                                        397.875
+                                    ],
+                                    "spans": [],
+                                    "index": 52
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        397.875,
+                                        496,
+                                        410.1875
+                                    ],
+                                    "spans": [],
+                                    "index": 53
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        410.1875,
+                                        496,
+                                        422.5
+                                    ],
+                                    "spans": [],
+                                    "index": 54
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        422.5,
+                                        496,
+                                        434.8125
+                                    ],
+                                    "spans": [],
+                                    "index": 55
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        434.8125,
+                                        496,
+                                        447.125
+                                    ],
+                                    "spans": [],
+                                    "index": 56
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        447.125,
+                                        496,
+                                        459.4375
+                                    ],
+                                    "spans": [],
+                                    "index": 57
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        459.4375,
+                                        496,
+                                        471.75
+                                    ],
+                                    "spans": [],
+                                    "index": 58
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        471.75,
+                                        496,
+                                        484.0625
+                                    ],
+                                    "spans": [],
+                                    "index": 59
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        484.0625,
+                                        496,
+                                        496.375
+                                    ],
+                                    "spans": [],
+                                    "index": 60
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        496.375,
+                                        496,
+                                        508.6875
+                                    ],
+                                    "spans": [],
+                                    "index": 61
+                                },
+                                {
+                                    "bbox": [
+                                        308,
+                                        508.6875,
+                                        496,
+                                        521.0
+                                    ],
+                                    "spans": [],
+                                    "index": 62
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                304,
+                                526,
+                                504,
+                                636
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        526,
+                                        505,
+                                        537
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                304,
+                                                526,
+                                                505,
+                                                537
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 4: Relationship between linear classifica-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 63
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        537,
+                                        505,
+                                        548
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                303,
+                                                537,
+                                                505,
+                                                548
+                                            ],
+                                            "score": 1.0,
+                                            "content": "tion accuracy and low-data classification, for dif-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 64
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        548,
+                                        505,
+                                        559
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                304,
+                                                548,
+                                                505,
+                                                559
+                                            ],
+                                            "score": 1.0,
+                                            "content": "ferent variants of the CPC model. Left: CPC vari-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 65
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        559,
+                                        505,
+                                        570
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                304,
+                                                559,
+                                                505,
+                                                570
+                                            ],
+                                            "score": 1.0,
+                                            "content": "ants with the same architecture but different train-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 66
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        570,
+                                        505,
+                                        581
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                303,
+                                                570,
+                                                505,
+                                                581
+                                            ],
+                                            "score": 1.0,
+                                            "content": "ing protocols. Orange, green, and blue dots cor-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 67
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        581,
+                                        505,
+                                        593
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                303,
+                                                581,
+                                                505,
+                                                593
+                                            ],
+                                            "score": 1.0,
+                                            "content": "respond to CPC models making predictions in 1,",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 68
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        592,
+                                        506,
+                                        604
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                303,
+                                                592,
+                                                506,
+                                                604
+                                            ],
+                                            "score": 1.0,
+                                            "content": "2, and 4 spatial directions respectively. Within a",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 69
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        603,
+                                        505,
+                                        614
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                303,
+                                                603,
+                                                505,
+                                                614
+                                            ],
+                                            "score": 1.0,
+                                            "content": "color group, different models correspond to other",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 70
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        613,
+                                        506,
+                                        626
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                303,
+                                                613,
+                                                506,
+                                                626
+                                            ],
+                                            "score": 1.0,
+                                            "content": "implementation details (e.g. layer norm and patch",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 71
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        625,
+                                        473,
+                                        636
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                303,
+                                                625,
+                                                473,
+                                                636
+                                            ],
+                                            "score": 1.0,
+                                            "content": "augmentation, and combinations thereof).",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 72
+                                }
+                            ],
+                            "index": 67.5
+                        }
+                    ],
+                    "index": 61.0
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        644,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                644,
+                                505,
+                                656
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        644,
+                                        505,
+                                        656
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cation, and therefore expect that increasing the amount of ‘predictability’ in the representation",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 73
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                655,
+                                505,
+                                666
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        655,
+                                        505,
+                                        666
+                                    ],
+                                    "score": 1.0,
+                                    "content": "should also increase its ability to learn from small amounts of data. Fig. 4 shows evidence for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 74
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                666,
+                                505,
+                                678
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        666,
+                                        505,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "this by ablating model parameters and comparing linear classification performance against low-data",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 75
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                677,
+                                505,
+                                689
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        677,
+                                        505,
+                                        689
+                                    ],
+                                    "score": 1.0,
+                                    "content": "classification. Consistent with our hypothesis, increasing the number of spatial directions in the CPC",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 76
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                687,
+                                506,
+                                700
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        687,
+                                        506,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "prediction task (which increased linear classification performance) systematically increases low-data",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 77
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                699,
+                                505,
+                                711
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        699,
+                                        505,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "classification performance (Fig. 4, left, different color groups). As a control, we asked if all mod-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 78
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                710,
+                                505,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        710,
+                                        505,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ifications that improve linear classification also improve low-data classification. We did not find",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 79
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                721,
+                                505,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        721,
+                                        505,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "evidence in favor of this: improvements in linear classification as a result of changing other model",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 80
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                421,
+                                506,
+                                434
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        421,
+                                        506,
+                                        434
+                                    ],
+                                    "score": 1.0,
+                                    "content": "parameters (patch-based data-augmentation, layer normalization, and combinations thereof) seem",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                432,
+                                505,
+                                445
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        432,
+                                        411,
+                                        445
+                                    ],
+                                    "score": 1.0,
+                                    "content": "uncorrelated to performance in other tasks (Fig. 4, left, within green group:",
+                                    "type": "text",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        412,
+                                        432,
+                                        498,
+                                        444
+                                    ],
+                                    "score": 0.78,
+                                    "content": "R ^ { 2 } = 0 . 1 7 , p = 0 . 3 6",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        499,
+                                        432,
+                                        505,
+                                        445
+                                    ],
+                                    "score": 1.0,
+                                    "content": ").",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                443,
+                                504,
+                                456
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        443,
+                                        504,
+                                        456
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Different architectural specifications also produced different changes in both tasks (Fig. 4, right).",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                453,
+                                505,
+                                467
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        453,
+                                        505,
+                                        467
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Whereas increasing the depth of the encoding network greatly improves both metrics, increasing the",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                464,
+                                506,
+                                479
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        464,
+                                        506,
+                                        479
+                                    ],
+                                    "score": 1.0,
+                                    "content": "network width (and therefore the number of features used for linear classification) only improves",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                475,
+                                226,
+                                489
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        475,
+                                        226,
+                                        489
+                                    ],
+                                    "score": 1.0,
+                                    "content": "linear classification accuracy.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 76.5,
+                    "bbox_fs": [
+                        105,
+                        644,
+                        506,
+                        732
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "table",
+                    "bbox": [
+                        153,
+                        181,
+                        456,
+                        386
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                106,
+                                88,
+                                505,
+                                177
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        89,
+                                        505,
+                                        101
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                89,
+                                                216,
+                                                101
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 2: ResNet classifier",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
+                                                217,
+                                                90,
+                                                229,
+                                                101
+                                            ],
+                                            "score": 0.89,
+                                            "content": "h _ { \\psi }",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
+                                                230,
+                                                89,
+                                                286,
+                                                101
+                                            ],
+                                            "score": 1.0,
+                                            "content": "trained with",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
+                                                287,
+                                                90,
+                                                303,
+                                                100
+                                            ],
+                                            "score": 0.85,
+                                            "content": "1 \\%",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
+                                                303,
+                                                89,
+                                                317,
+                                                101
+                                            ],
+                                            "score": 1.0,
+                                            "content": "or",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                90,
+                                                338,
+                                                100
+                                            ],
+                                            "score": 0.85,
+                                            "content": "10 \\%",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
+                                                339,
+                                                89,
+                                                505,
+                                                101
+                                            ],
+                                            "score": 1.0,
+                                            "content": "of labels. Comparison to other methods",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        101,
+                                        505,
+                                        113
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                101,
+                                                250,
+                                                113
+                                            ],
+                                            "score": 1.0,
+                                            "content": "for semi-supervised learning using",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
+                                                250,
+                                                101,
+                                                265,
+                                                111
+                                            ],
+                                            "score": 0.84,
+                                            "content": "1 \\%",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
+                                                266,
+                                                101,
+                                                279,
+                                                113
+                                            ],
+                                            "score": 1.0,
+                                            "content": "or",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
+                                                279,
+                                                101,
+                                                298,
+                                                111
+                                            ],
+                                            "score": 0.88,
+                                            "content": "10 \\%",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
+                                                299,
+                                                101,
+                                                505,
+                                                113
+                                            ],
+                                            "score": 1.0,
+                                            "content": "of labeled data. Representation learning methods",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        110,
+                                        505,
+                                        125
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                110,
+                                                505,
+                                                125
+                                            ],
+                                            "score": 1.0,
+                                            "content": "use a classifier to discriminate an unsupervised representation, and optimize it solely for the super-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 2
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        123,
+                                        505,
+                                        135
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                123,
+                                                505,
+                                                135
+                                            ],
+                                            "score": 1.0,
+                                            "content": "vised objective on labeled data. Label-propagation methods on the other hand further constrain the",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        133,
+                                        505,
+                                        145
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                133,
+                                                505,
+                                                145
+                                            ],
+                                            "score": 1.0,
+                                            "content": "classifier with smoothness and entropy criteria on unlabeled data, making the additional assumption",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        144,
+                                        505,
+                                        156
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                144,
+                                                374,
+                                                156
+                                            ],
+                                            "score": 1.0,
+                                            "content": "that all training images fit into a single (unknown) testing category.",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
+                                                375,
+                                                145,
+                                                381,
+                                                156
+                                            ],
+                                            "score": 0.76,
+                                            "content": "\\dagger",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
+                                                381,
+                                                144,
+                                                505,
+                                                156
+                                            ],
+                                            "score": 1.0,
+                                            "content": "denotes methods implemented",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 5
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        155,
+                                        505,
+                                        168
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                155,
+                                                505,
+                                                168
+                                            ],
+                                            "score": 1.0,
+                                            "content": "in this work, fixed and fine-tuned denote whether the feature extractor is allowed to accommodate",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 6
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        165,
+                                        208,
+                                        179
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                165,
+                                                208,
+                                                179
+                                            ],
+                                            "score": 1.0,
+                                            "content": "the supervised objective.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 7
+                                }
+                            ],
+                            "index": 3.5
+                        },
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                153,
+                                181,
+                                456,
+                                386
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        153,
+                                        181,
+                                        456,
+                                        386
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                153,
+                                                181,
+                                                456,
+                                                386
+                                            ],
+                                            "score": 0.91,
+                                            "html": "<table><tr><td>Labeled data 1% 10% 100% Method Top-5 accuracy</td></tr><tr><td></td></tr><tr><td>Supervised baseline 44.1 82.1 93.9 Methods using label-propagation:</td></tr><tr><td>Pseudolabeling (Zhai et al., 2019) 51.6 82.4 VAT + Entropy Minimization (Zhai et al., 2019) 47.0 83.4 Unsup. Data Augmentation (Xie et al., 2019) 88.5</td></tr><tr><td>Rotation+ VAT+Ent.Min. (Zhai et al.,2019) 91.2 95.0 =</td></tr><tr><td>Methods using representation learning only:</td></tr><tr><td>Instance Discrimination (Wu et al., 2018) 39.2 77.4</td></tr><tr><td>Rotation (Zhai et al., 2019) 57.5 86.4</td></tr><tr><td>+ResNet trained on BigBiGAN (fixed) 55.2 78.8 87.0</td></tr><tr><td>+ResNet trained on AMDIM (fixed) 67.4 85.8 92.2</td></tr><tr><td>+ResNet trained on CPC v2 (fixed) 72.3 89.1 94.4 +ResNet trained on CPC v2 (fine-tuned) 72.9 89.5 95.2</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "e969618e28fc2ffa8c76067cea0310a604dd1bb350cd5a5534dd7265b81333a6.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 15,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        153,
+                                        181,
+                                        456,
+                                        194.66666666666666
+                                    ],
+                                    "spans": [],
+                                    "index": 8
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        194.66666666666666,
+                                        456,
+                                        208.33333333333331
+                                    ],
+                                    "spans": [],
+                                    "index": 9
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        208.33333333333331,
+                                        456,
+                                        221.99999999999997
+                                    ],
+                                    "spans": [],
+                                    "index": 10
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        221.99999999999997,
+                                        456,
+                                        235.66666666666663
+                                    ],
+                                    "spans": [],
+                                    "index": 11
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        235.66666666666663,
+                                        456,
+                                        249.3333333333333
+                                    ],
+                                    "spans": [],
+                                    "index": 12
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        249.3333333333333,
+                                        456,
+                                        262.99999999999994
+                                    ],
+                                    "spans": [],
+                                    "index": 13
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        262.99999999999994,
+                                        456,
+                                        276.66666666666663
+                                    ],
+                                    "spans": [],
+                                    "index": 14
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        276.66666666666663,
+                                        456,
+                                        290.3333333333333
+                                    ],
+                                    "spans": [],
+                                    "index": 15
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        290.3333333333333,
+                                        456,
+                                        304.0
+                                    ],
+                                    "spans": [],
+                                    "index": 16
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        304.0,
+                                        456,
+                                        317.6666666666667
+                                    ],
+                                    "spans": [],
+                                    "index": 17
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        317.6666666666667,
+                                        456,
+                                        331.33333333333337
+                                    ],
+                                    "spans": [],
+                                    "index": 18
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        331.33333333333337,
+                                        456,
+                                        345.00000000000006
+                                    ],
+                                    "spans": [],
+                                    "index": 19
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        345.00000000000006,
+                                        456,
+                                        358.66666666666674
+                                    ],
+                                    "spans": [],
+                                    "index": 20
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        358.66666666666674,
+                                        456,
+                                        372.3333333333334
+                                    ],
+                                    "spans": [],
+                                    "index": 21
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        372.3333333333334,
+                                        456,
+                                        386.0000000000001
+                                    ],
+                                    "spans": [],
+                                    "index": 22
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9.25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        421,
+                        505,
+                        487
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                421,
+                                506,
+                                434
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        421,
+                                        506,
+                                        434
+                                    ],
+                                    "score": 1.0,
+                                    "content": "parameters (patch-based data-augmentation, layer normalization, and combinations thereof) seem",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                432,
+                                505,
+                                445
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        432,
+                                        411,
+                                        445
+                                    ],
+                                    "score": 1.0,
+                                    "content": "uncorrelated to performance in other tasks (Fig. 4, left, within green group:",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        412,
+                                        432,
+                                        498,
+                                        444
+                                    ],
+                                    "score": 0.78,
+                                    "content": "R ^ { 2 } = 0 . 1 7 , p = 0 . 3 6",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        499,
+                                        432,
+                                        505,
+                                        445
+                                    ],
+                                    "score": 1.0,
+                                    "content": ").",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                443,
+                                504,
+                                456
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        443,
+                                        504,
+                                        456
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Different architectural specifications also produced different changes in both tasks (Fig. 4, right).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                453,
+                                505,
+                                467
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        453,
+                                        505,
+                                        467
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Whereas increasing the depth of the encoding network greatly improves both metrics, increasing the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                464,
+                                506,
+                                479
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        464,
+                                        506,
+                                        479
+                                    ],
+                                    "score": 1.0,
+                                    "content": "network width (and therefore the number of features used for linear classification) only improves",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                475,
+                                226,
+                                489
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        475,
+                                        226,
+                                        489
+                                    ],
+                                    "score": 1.0,
+                                    "content": "linear classification accuracy.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 25.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        500,
+                        505,
+                        631
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                500,
+                                505,
+                                512
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        500,
+                                        505,
+                                        512
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Other unsupervised representations. How well does the CPC representation compare to other",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                510,
+                                506,
+                                523
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        510,
+                                        506,
+                                        523
+                                    ],
+                                    "score": 1.0,
+                                    "content": "representations that have been learned in an unsupervised manner? If predictable representations",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                522,
+                                504,
+                                534
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        522,
+                                        504,
+                                        534
+                                    ],
+                                    "score": 1.0,
+                                    "content": "are uniquely suited for efficient classification, we would expect other methods within this fam-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                533,
+                                505,
+                                545
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        533,
+                                        505,
+                                        545
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ily to perform similarly, and other model classes less so. Table 2 compares our best model with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                543,
+                                505,
+                                556
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        543,
+                                        505,
+                                        556
+                                    ],
+                                    "score": 1.0,
+                                    "content": "other works on efficient recognition. We consider three objectives from different model classes:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                554,
+                                505,
+                                568
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        554,
+                                        505,
+                                        568
+                                    ],
+                                    "score": 1.0,
+                                    "content": "self-supervised learning with rotation prediction (Zhai et al., 2019), large-scale adversarial feature",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                565,
+                                505,
+                                578
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        565,
+                                        505,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning (BigBiGAN, Donahue & Simonyan, 2019), and another contrastive prediction objective",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                576,
+                                505,
+                                589
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        576,
+                                        505,
+                                        589
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(AMDIM, Bachman et al., 2019). Zhai et al. (2019) evaluate the low-data classification perfor-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                587,
+                                505,
+                                600
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        587,
+                                        505,
+                                        600
+                                    ],
+                                    "score": 1.0,
+                                    "content": "mance of representations learned with rotation prediction using a similar paradigm and architecture",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                597,
+                                504,
+                                610
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        597,
+                                        344,
+                                        610
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(ResNet-152), hence we report their results directly. Given",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        344,
+                                        598,
+                                        359,
+                                        609
+                                    ],
+                                    "score": 0.85,
+                                    "content": "1 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        359,
+                                        597,
+                                        504,
+                                        610
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of ImageNet, their method achieves",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                608,
+                                504,
+                                622
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        609,
+                                        133,
+                                        620
+                                    ],
+                                    "score": 0.85,
+                                    "content": "5 7 . 5 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        134,
+                                        608,
+                                        438,
+                                        622
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-5 accuracy, consistently with the reduced accuracy of a linear classifier (",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        438,
+                                        609,
+                                        465,
+                                        620
+                                    ],
+                                    "score": 0.82,
+                                    "content": "5 5 . 4 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        465,
+                                        608,
+                                        477,
+                                        622
+                                    ],
+                                    "score": 1.0,
+                                    "content": "vs",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        477,
+                                        609,
+                                        504,
+                                        620
+                                    ],
+                                    "score": 0.85,
+                                    "content": "6 5 . 9 \\%",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                619,
+                                152,
+                                632
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        619,
+                                        152,
+                                        632
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for CPC)1.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        }
+                    ],
+                    "index": 34.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        636,
+                        505,
+                        704
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                636,
+                                505,
+                                650
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        636,
+                                        505,
+                                        650
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Because BigBiGAN and AMDIM achieve stronger linear classification accuracy than rotation pre-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                648,
+                                506,
+                                661
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        648,
+                                        140,
+                                        661
+                                    ],
+                                    "score": 1.0,
+                                    "content": "diction",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        141,
+                                        648,
+                                        168,
+                                        659
+                                    ],
+                                    "score": 0.83,
+                                    "content": "6 1 . 3 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        168,
+                                        648,
+                                        187,
+                                        661
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        188,
+                                        648,
+                                        215,
+                                        659
+                                    ],
+                                    "score": 0.86,
+                                    "content": "6 8 . 1 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        216,
+                                        648,
+                                        506,
+                                        661
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-1 accuracy, respectively), we might expect better performance on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                658,
+                                506,
+                                672
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        658,
+                                        506,
+                                        672
+                                    ],
+                                    "score": 1.0,
+                                    "content": "efficient classification as well. Since their authors do not report results on efficient classification we",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                670,
+                                506,
+                                683
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        670,
+                                        506,
+                                        683
+                                    ],
+                                    "score": 1.0,
+                                    "content": "evaluated these representations using the same paradigm we used for evaluating CPC, stacking a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                680,
+                                505,
+                                694
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        680,
+                                        228,
+                                        694
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ResNet classifier on top of the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        229,
+                                        681,
+                                        276,
+                                        691
+                                    ],
+                                    "score": 0.9,
+                                    "content": "7 \\times 7 \\times 8 1 9 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        276,
+                                        680,
+                                        410,
+                                        694
+                                    ],
+                                    "score": 1.0,
+                                    "content": "latents of the BigBiGAN and the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        410,
+                                        681,
+                                        457,
+                                        692
+                                    ],
+                                    "score": 0.9,
+                                    "content": "7 \\times 7 \\times 2 5 6 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        457,
+                                        680,
+                                        505,
+                                        694
+                                    ],
+                                    "score": 1.0,
+                                    "content": "grid of fea-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                692,
+                                505,
+                                705
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        692,
+                                        505,
+                                        705
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ture vectors of AMDIM. We found fine-tuned representations to yield only marginal gains over fixed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        }
+                    ],
+                    "index": 43.5
+                }
+            ],
+            "page_idx": 7,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        712,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                118,
+                                710,
+                                505,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        118,
+                                        710,
+                                        505,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1Although note that linear classification accuracy is reported using a separate model that was designed for",
+                                    "type": "text"
+                                }
+                            ]
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                721,
+                                318,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        721,
+                                        318,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "linear classification performance (Kolesnikov et al., 2019)",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        308,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                25,
+                                308,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        25,
+                                        308,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Under review as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        752,
+                        308,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                301,
+                                750,
+                                310,
+                                762
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        301,
+                                        750,
+                                        310,
+                                        762
+                                    ],
+                                    "score": 1.0,
+                                    "content": "",
+                                    "type": "text",
+                                    "height": 12,
+                                    "width": 9
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "table",
+                    "bbox": [
+                        153,
+                        181,
+                        456,
+                        386
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                106,
+                                88,
+                                505,
+                                177
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        89,
+                                        505,
+                                        101
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                89,
+                                                216,
+                                                101
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 2: ResNet classifier",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
+                                                217,
+                                                90,
+                                                229,
+                                                101
+                                            ],
+                                            "score": 0.89,
+                                            "content": "h _ { \\psi }",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
+                                                230,
+                                                89,
+                                                286,
+                                                101
+                                            ],
+                                            "score": 1.0,
+                                            "content": "trained with",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
+                                                287,
+                                                90,
+                                                303,
+                                                100
+                                            ],
+                                            "score": 0.85,
+                                            "content": "1 \\%",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
+                                                303,
+                                                89,
+                                                317,
+                                                101
+                                            ],
+                                            "score": 1.0,
+                                            "content": "or",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                90,
+                                                338,
+                                                100
+                                            ],
+                                            "score": 0.85,
+                                            "content": "10 \\%",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
+                                                339,
+                                                89,
+                                                505,
+                                                101
+                                            ],
+                                            "score": 1.0,
+                                            "content": "of labels. Comparison to other methods",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        101,
+                                        505,
+                                        113
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                101,
+                                                250,
+                                                113
+                                            ],
+                                            "score": 1.0,
+                                            "content": "for semi-supervised learning using",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
+                                                250,
+                                                101,
+                                                265,
+                                                111
+                                            ],
+                                            "score": 0.84,
+                                            "content": "1 \\%",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
+                                                266,
+                                                101,
+                                                279,
+                                                113
+                                            ],
+                                            "score": 1.0,
+                                            "content": "or",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
+                                                279,
+                                                101,
+                                                298,
+                                                111
+                                            ],
+                                            "score": 0.88,
+                                            "content": "10 \\%",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
+                                                299,
+                                                101,
+                                                505,
+                                                113
+                                            ],
+                                            "score": 1.0,
+                                            "content": "of labeled data. Representation learning methods",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        110,
+                                        505,
+                                        125
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                110,
+                                                505,
+                                                125
+                                            ],
+                                            "score": 1.0,
+                                            "content": "use a classifier to discriminate an unsupervised representation, and optimize it solely for the super-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 2
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        123,
+                                        505,
+                                        135
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                123,
+                                                505,
+                                                135
+                                            ],
+                                            "score": 1.0,
+                                            "content": "vised objective on labeled data. Label-propagation methods on the other hand further constrain the",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        133,
+                                        505,
+                                        145
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                133,
+                                                505,
+                                                145
+                                            ],
+                                            "score": 1.0,
+                                            "content": "classifier with smoothness and entropy criteria on unlabeled data, making the additional assumption",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        144,
+                                        505,
+                                        156
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                144,
+                                                374,
+                                                156
+                                            ],
+                                            "score": 1.0,
+                                            "content": "that all training images fit into a single (unknown) testing category.",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
+                                                375,
+                                                145,
+                                                381,
+                                                156
+                                            ],
+                                            "score": 0.76,
+                                            "content": "\\dagger",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
+                                                381,
+                                                144,
+                                                505,
+                                                156
+                                            ],
+                                            "score": 1.0,
+                                            "content": "denotes methods implemented",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 5
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        155,
+                                        505,
+                                        168
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                155,
+                                                505,
+                                                168
+                                            ],
+                                            "score": 1.0,
+                                            "content": "in this work, fixed and fine-tuned denote whether the feature extractor is allowed to accommodate",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 6
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        165,
+                                        208,
+                                        179
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                165,
+                                                208,
+                                                179
+                                            ],
+                                            "score": 1.0,
+                                            "content": "the supervised objective.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 7
+                                }
+                            ],
+                            "index": 3.5
+                        },
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                153,
+                                181,
+                                456,
+                                386
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        153,
+                                        181,
+                                        456,
+                                        386
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                153,
+                                                181,
+                                                456,
+                                                386
+                                            ],
+                                            "score": 0.91,
+                                            "html": "<table><tr><td>Labeled data 1% 10% 100% Method Top-5 accuracy</td></tr><tr><td></td></tr><tr><td>Supervised baseline 44.1 82.1 93.9 Methods using label-propagation:</td></tr><tr><td>Pseudolabeling (Zhai et al., 2019) 51.6 82.4 VAT + Entropy Minimization (Zhai et al., 2019) 47.0 83.4 Unsup. Data Augmentation (Xie et al., 2019) 88.5</td></tr><tr><td>Rotation+ VAT+Ent.Min. (Zhai et al.,2019) 91.2 95.0 =</td></tr><tr><td>Methods using representation learning only:</td></tr><tr><td>Instance Discrimination (Wu et al., 2018) 39.2 77.4</td></tr><tr><td>Rotation (Zhai et al., 2019) 57.5 86.4</td></tr><tr><td>+ResNet trained on BigBiGAN (fixed) 55.2 78.8 87.0</td></tr><tr><td>+ResNet trained on AMDIM (fixed) 67.4 85.8 92.2</td></tr><tr><td>+ResNet trained on CPC v2 (fixed) 72.3 89.1 94.4 +ResNet trained on CPC v2 (fine-tuned) 72.9 89.5 95.2</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "e969618e28fc2ffa8c76067cea0310a604dd1bb350cd5a5534dd7265b81333a6.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 15,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        153,
+                                        181,
+                                        456,
+                                        194.66666666666666
+                                    ],
+                                    "spans": [],
+                                    "index": 8
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        194.66666666666666,
+                                        456,
+                                        208.33333333333331
+                                    ],
+                                    "spans": [],
+                                    "index": 9
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        208.33333333333331,
+                                        456,
+                                        221.99999999999997
+                                    ],
+                                    "spans": [],
+                                    "index": 10
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        221.99999999999997,
+                                        456,
+                                        235.66666666666663
+                                    ],
+                                    "spans": [],
+                                    "index": 11
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        235.66666666666663,
+                                        456,
+                                        249.3333333333333
+                                    ],
+                                    "spans": [],
+                                    "index": 12
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        249.3333333333333,
+                                        456,
+                                        262.99999999999994
+                                    ],
+                                    "spans": [],
+                                    "index": 13
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        262.99999999999994,
+                                        456,
+                                        276.66666666666663
+                                    ],
+                                    "spans": [],
+                                    "index": 14
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        276.66666666666663,
+                                        456,
+                                        290.3333333333333
+                                    ],
+                                    "spans": [],
+                                    "index": 15
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        290.3333333333333,
+                                        456,
+                                        304.0
+                                    ],
+                                    "spans": [],
+                                    "index": 16
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        304.0,
+                                        456,
+                                        317.6666666666667
+                                    ],
+                                    "spans": [],
+                                    "index": 17
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        317.6666666666667,
+                                        456,
+                                        331.33333333333337
+                                    ],
+                                    "spans": [],
+                                    "index": 18
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        331.33333333333337,
+                                        456,
+                                        345.00000000000006
+                                    ],
+                                    "spans": [],
+                                    "index": 19
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        345.00000000000006,
+                                        456,
+                                        358.66666666666674
+                                    ],
+                                    "spans": [],
+                                    "index": 20
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        358.66666666666674,
+                                        456,
+                                        372.3333333333334
+                                    ],
+                                    "spans": [],
+                                    "index": 21
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        372.3333333333334,
+                                        456,
+                                        386.0000000000001
+                                    ],
+                                    "spans": [],
+                                    "index": 22
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9.25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        421,
+                        505,
+                        487
+                    ],
+                    "lines": [],
+                    "index": 25.5,
+                    "bbox_fs": [
+                        104,
+                        421,
+                        506,
+                        489
+                    ],
+                    "lines_deleted": true
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        500,
+                        505,
+                        631
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                500,
+                                505,
+                                512
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        500,
+                                        505,
+                                        512
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Other unsupervised representations. How well does the CPC representation compare to other",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                510,
+                                506,
+                                523
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        510,
+                                        506,
+                                        523
+                                    ],
+                                    "score": 1.0,
+                                    "content": "representations that have been learned in an unsupervised manner? If predictable representations",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                522,
+                                504,
+                                534
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        522,
+                                        504,
+                                        534
+                                    ],
+                                    "score": 1.0,
+                                    "content": "are uniquely suited for efficient classification, we would expect other methods within this fam-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                533,
+                                505,
+                                545
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        533,
+                                        505,
+                                        545
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ily to perform similarly, and other model classes less so. Table 2 compares our best model with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                543,
+                                505,
+                                556
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        543,
+                                        505,
+                                        556
+                                    ],
+                                    "score": 1.0,
+                                    "content": "other works on efficient recognition. We consider three objectives from different model classes:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                554,
+                                505,
+                                568
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        554,
+                                        505,
+                                        568
+                                    ],
+                                    "score": 1.0,
+                                    "content": "self-supervised learning with rotation prediction (Zhai et al., 2019), large-scale adversarial feature",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                565,
+                                505,
+                                578
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        565,
+                                        505,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning (BigBiGAN, Donahue & Simonyan, 2019), and another contrastive prediction objective",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                576,
+                                505,
+                                589
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        576,
+                                        505,
+                                        589
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(AMDIM, Bachman et al., 2019). Zhai et al. (2019) evaluate the low-data classification perfor-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                587,
+                                505,
+                                600
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        587,
+                                        505,
+                                        600
+                                    ],
+                                    "score": 1.0,
+                                    "content": "mance of representations learned with rotation prediction using a similar paradigm and architecture",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                597,
+                                504,
+                                610
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        597,
+                                        344,
+                                        610
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(ResNet-152), hence we report their results directly. Given",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        344,
+                                        598,
+                                        359,
+                                        609
+                                    ],
+                                    "score": 0.85,
+                                    "content": "1 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        359,
+                                        597,
+                                        504,
+                                        610
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of ImageNet, their method achieves",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                608,
+                                504,
+                                622
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        609,
+                                        133,
+                                        620
+                                    ],
+                                    "score": 0.85,
+                                    "content": "5 7 . 5 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        134,
+                                        608,
+                                        438,
+                                        622
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-5 accuracy, consistently with the reduced accuracy of a linear classifier (",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        438,
+                                        609,
+                                        465,
+                                        620
+                                    ],
+                                    "score": 0.82,
+                                    "content": "5 5 . 4 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        465,
+                                        608,
+                                        477,
+                                        622
+                                    ],
+                                    "score": 1.0,
+                                    "content": "vs",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        477,
+                                        609,
+                                        504,
+                                        620
+                                    ],
+                                    "score": 0.85,
+                                    "content": "6 5 . 9 \\%",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                619,
+                                152,
+                                632
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        619,
+                                        152,
+                                        632
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for CPC)1.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        }
+                    ],
+                    "index": 34.5,
+                    "bbox_fs": [
+                        104,
+                        500,
+                        506,
+                        632
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        636,
+                        505,
+                        704
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                636,
+                                505,
+                                650
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        636,
+                                        505,
+                                        650
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Because BigBiGAN and AMDIM achieve stronger linear classification accuracy than rotation pre-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                648,
+                                506,
+                                661
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        648,
+                                        140,
+                                        661
+                                    ],
+                                    "score": 1.0,
+                                    "content": "diction",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        141,
+                                        648,
+                                        168,
+                                        659
+                                    ],
+                                    "score": 0.83,
+                                    "content": "6 1 . 3 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        168,
+                                        648,
+                                        187,
+                                        661
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        188,
+                                        648,
+                                        215,
+                                        659
+                                    ],
+                                    "score": 0.86,
+                                    "content": "6 8 . 1 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        216,
+                                        648,
+                                        506,
+                                        661
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-1 accuracy, respectively), we might expect better performance on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                658,
+                                506,
+                                672
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        658,
+                                        506,
+                                        672
+                                    ],
+                                    "score": 1.0,
+                                    "content": "efficient classification as well. Since their authors do not report results on efficient classification we",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                670,
+                                506,
+                                683
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        670,
+                                        506,
+                                        683
+                                    ],
+                                    "score": 1.0,
+                                    "content": "evaluated these representations using the same paradigm we used for evaluating CPC, stacking a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                680,
+                                505,
+                                694
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        680,
+                                        228,
+                                        694
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ResNet classifier on top of the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        229,
+                                        681,
+                                        276,
+                                        691
+                                    ],
+                                    "score": 0.9,
+                                    "content": "7 \\times 7 \\times 8 1 9 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        276,
+                                        680,
+                                        410,
+                                        694
+                                    ],
+                                    "score": 1.0,
+                                    "content": "latents of the BigBiGAN and the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        410,
+                                        681,
+                                        457,
+                                        692
+                                    ],
+                                    "score": 0.9,
+                                    "content": "7 \\times 7 \\times 2 5 6 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        457,
+                                        680,
+                                        505,
+                                        694
+                                    ],
+                                    "score": 1.0,
+                                    "content": "grid of fea-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                692,
+                                505,
+                                705
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        692,
+                                        505,
+                                        705
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ture vectors of AMDIM. We found fine-tuned representations to yield only marginal gains over fixed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                83,
+                                505,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        83,
+                                        130,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ones",
+                                    "type": "text",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        131,
+                                        83,
+                                        158,
+                                        93
+                                    ],
+                                    "score": 0.84,
+                                    "content": "7 2 . 9 \\%",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        158,
+                                        83,
+                                        209,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "compared to",
+                                    "type": "text",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        210,
+                                        83,
+                                        237,
+                                        93
+                                    ],
+                                    "score": 0.89,
+                                    "content": "7 2 . 3 \\%",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        237,
+                                        83,
+                                        325,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-5 accuracy given",
+                                    "type": "text",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        325,
+                                        83,
+                                        340,
+                                        93
+                                    ],
+                                    "score": 0.86,
+                                    "content": "1 \\%",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        340,
+                                        83,
+                                        505,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of labels), hence for simplicity we evalu-",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                93,
+                                505,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        93,
+                                        505,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ate BigBiGAN and AMDIM on this task while keeping them fixed. We re-tune the hyper-parameters",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                104,
+                                505,
+                                118
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        104,
+                                        505,
+                                        118
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of the classifier (including optimization, regularization, etc.) for each of these representations sep-",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                115,
+                                506,
+                                128
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        115,
+                                        506,
+                                        128
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arately. Although these methods achieve similar performance in terms of linear classification, we",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                126,
+                                505,
+                                139
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        126,
+                                        411,
+                                        139
+                                    ],
+                                    "score": 1.0,
+                                    "content": "find them to achieve very different results in efficient classification. Given",
+                                    "type": "text",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        411,
+                                        127,
+                                        426,
+                                        137
+                                    ],
+                                    "score": 0.84,
+                                    "content": "1 \\%",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        426,
+                                        126,
+                                        505,
+                                        139
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of ImageNet, clas-",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                137,
+                                505,
+                                150
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        137,
+                                        284,
+                                        150
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sifiers trained on top of BigBiGAN achieve",
+                                    "type": "text",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        284,
+                                        137,
+                                        312,
+                                        148
+                                    ],
+                                    "score": 0.88,
+                                    "content": "5 5 . 2 \\%",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        312,
+                                        137,
+                                        505,
+                                        150
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-5 accuracy, similarly to rotation prediction",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                149,
+                                505,
+                                161
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        149,
+                                        140,
+                                        160
+                                    ],
+                                    "score": 0.87,
+                                    "content": "( 5 7 . 5 \\% )",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        140,
+                                        149,
+                                        354,
+                                        161
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", despite its increased linear classification accuracy",
+                                    "type": "text",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        354,
+                                        149,
+                                        375,
+                                        159
+                                    ],
+                                    "score": 0.87,
+                                    "content": "( + 6 \\%",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        376,
+                                        149,
+                                        505,
+                                        161
+                                    ],
+                                    "score": 1.0,
+                                    "content": "relative to rotation prediction).",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                159,
+                                505,
+                                171
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        159,
+                                        505,
+                                        171
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In contrast, AMDIM (which also belongs to the family of contrastive prediction methods) achieves",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                170,
+                                505,
+                                183
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        171,
+                                        134,
+                                        181
+                                    ],
+                                    "score": 0.88,
+                                    "content": "6 7 . 4 \\%",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        134,
+                                        170,
+                                        505,
+                                        183
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on this same task. Again, its increased linear classification accuracy did not entail an increase",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                181,
+                                505,
+                                194
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        181,
+                                        505,
+                                        194
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in data-efficiency. Nevertheless, in line with our initial hypothesis, we find that contrastive predic-",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                192,
+                                505,
+                                205
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        192,
+                                        505,
+                                        205
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tion methods such as CPC surpass other approaches in our efficient classification experiments, and",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                203,
+                                435,
+                                216
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        203,
+                                        435,
+                                        216
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that linear classification performance is not perfectly correlated with these results.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 43.5,
+                    "bbox_fs": [
+                        105,
+                        636,
+                        506,
+                        705
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        82,
+                        505,
+                        214
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                83,
+                                505,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        83,
+                                        130,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ones",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        131,
+                                        83,
+                                        158,
+                                        93
+                                    ],
+                                    "score": 0.84,
+                                    "content": "7 2 . 9 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        158,
+                                        83,
+                                        209,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "compared to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        210,
+                                        83,
+                                        237,
+                                        93
+                                    ],
+                                    "score": 0.89,
+                                    "content": "7 2 . 3 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        237,
+                                        83,
+                                        325,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-5 accuracy given",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        325,
+                                        83,
+                                        340,
+                                        93
+                                    ],
+                                    "score": 0.86,
+                                    "content": "1 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        340,
+                                        83,
+                                        505,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of labels), hence for simplicity we evalu-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                93,
+                                505,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        93,
+                                        505,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ate BigBiGAN and AMDIM on this task while keeping them fixed. We re-tune the hyper-parameters",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                104,
+                                505,
+                                118
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        104,
+                                        505,
+                                        118
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of the classifier (including optimization, regularization, etc.) for each of these representations sep-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                115,
+                                506,
+                                128
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        115,
+                                        506,
+                                        128
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arately. Although these methods achieve similar performance in terms of linear classification, we",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                126,
+                                505,
+                                139
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        126,
+                                        411,
+                                        139
+                                    ],
+                                    "score": 1.0,
+                                    "content": "find them to achieve very different results in efficient classification. Given",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        411,
+                                        127,
+                                        426,
+                                        137
+                                    ],
+                                    "score": 0.84,
+                                    "content": "1 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        426,
+                                        126,
+                                        505,
+                                        139
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of ImageNet, clas-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                137,
+                                505,
+                                150
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        137,
+                                        284,
+                                        150
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sifiers trained on top of BigBiGAN achieve",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        284,
+                                        137,
+                                        312,
+                                        148
+                                    ],
+                                    "score": 0.88,
+                                    "content": "5 5 . 2 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        312,
+                                        137,
+                                        505,
+                                        150
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-5 accuracy, similarly to rotation prediction",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                149,
+                                505,
+                                161
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        149,
+                                        140,
+                                        160
+                                    ],
+                                    "score": 0.87,
+                                    "content": "( 5 7 . 5 \\% )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        140,
+                                        149,
+                                        354,
+                                        161
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", despite its increased linear classification accuracy",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        354,
+                                        149,
+                                        375,
+                                        159
+                                    ],
+                                    "score": 0.87,
+                                    "content": "( + 6 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        376,
+                                        149,
+                                        505,
+                                        161
+                                    ],
+                                    "score": 1.0,
+                                    "content": "relative to rotation prediction).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                159,
+                                505,
+                                171
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        159,
+                                        505,
+                                        171
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In contrast, AMDIM (which also belongs to the family of contrastive prediction methods) achieves",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                170,
+                                505,
+                                183
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        171,
+                                        134,
+                                        181
+                                    ],
+                                    "score": 0.88,
+                                    "content": "6 7 . 4 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        134,
+                                        170,
+                                        505,
+                                        183
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on this same task. Again, its increased linear classification accuracy did not entail an increase",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                181,
+                                505,
+                                194
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        181,
+                                        505,
+                                        194
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in data-efficiency. Nevertheless, in line with our initial hypothesis, we find that contrastive predic-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                192,
+                                505,
+                                205
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        192,
+                                        505,
+                                        205
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tion methods such as CPC surpass other approaches in our efficient classification experiments, and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                203,
+                                435,
+                                216
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        203,
+                                        435,
+                                        216
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that linear classification performance is not perfectly correlated with these results.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 5.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        230,
+                        504,
+                        361
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                230,
+                                506,
+                                243
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        230,
+                                        506,
+                                        243
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Other semi-supervised techniques A separate class of methods for low-data classification at-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                241,
+                                506,
+                                253
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        241,
+                                        506,
+                                        253
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tempts to propagate the knowledge extracted from the subset of labeled examples to unlabeled",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                252,
+                                504,
+                                264
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        252,
+                                        504,
+                                        264
+                                    ],
+                                    "score": 1.0,
+                                    "content": "examples while being invariant to augmentation or other perturbations. These methods generally",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                263,
+                                504,
+                                275
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        263,
+                                        504,
+                                        275
+                                    ],
+                                    "score": 1.0,
+                                    "content": "depend on the quality of the classifier’s predictions, and as such tend to fare well when given in-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                273,
+                                505,
+                                287
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        273,
+                                        505,
+                                        287
+                                    ],
+                                    "score": 1.0,
+                                    "content": "termediate amounts of data. Although not sufficient in themselves (Unsupervised Data Augmenta-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                284,
+                                506,
+                                297
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        284,
+                                        506,
+                                        297
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tion (Xie et al., 2019), Virtual Adversarial Training (Miyato et al., 2018) and entropy minimization",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                295,
+                                504,
+                                308
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        296,
+                                        397,
+                                        308
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(Grandvalet & Bengio, 2005), and pseudo-labeling (Lee, 2013) achieve",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        397,
+                                        296,
+                                        424,
+                                        306
+                                    ],
+                                    "score": 0.86,
+                                    "content": "8 5 . 8 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        424,
+                                        296,
+                                        428,
+                                        308
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        428,
+                                        296,
+                                        455,
+                                        306
+                                    ],
+                                    "score": 0.83,
+                                    "content": "8 3 . 4 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        455,
+                                        296,
+                                        477,
+                                        308
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        477,
+                                        295,
+                                        504,
+                                        306
+                                    ],
+                                    "score": 0.86,
+                                    "content": "8 2 . 4 \\%",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                306,
+                                506,
+                                320
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        306,
+                                        193,
+                                        320
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-5 accuracy with",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        193,
+                                        307,
+                                        213,
+                                        317
+                                    ],
+                                    "score": 0.87,
+                                    "content": "10 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        213,
+                                        306,
+                                        325,
+                                        320
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of labels, compared to our",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        325,
+                                        307,
+                                        353,
+                                        317
+                                    ],
+                                    "score": 0.88,
+                                    "content": "8 9 . 4 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        353,
+                                        306,
+                                        506,
+                                        320
+                                    ],
+                                    "score": 1.0,
+                                    "content": ") when combined with representation",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                317,
+                                506,
+                                331
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        317,
+                                        455,
+                                        331
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning (e.g. rotation prediction Zhai et al., 2019) they can provide considerable gains",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        455,
+                                        318,
+                                        483,
+                                        329
+                                    ],
+                                    "score": 0.8,
+                                    "content": "9 1 . 2 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        483,
+                                        317,
+                                        506,
+                                        331
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                329,
+                                506,
+                                341
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        329,
+                                        506,
+                                        341
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5 accuracy). It is therefore surprising that CPC representations alone can enable accuracy that is",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                339,
+                                506,
+                                353
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        339,
+                                        506,
+                                        353
+                                    ],
+                                    "score": 1.0,
+                                    "content": "comparable to that of these methods, and investigating to what extent they can be combined would",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                351,
+                                259,
+                                362
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        351,
+                                        259,
+                                        362
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be an interesting topic of future work.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 17.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        378,
+                        417,
+                        389
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                378,
+                                419,
+                                391
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        378,
+                                        419,
+                                        391
+                                    ],
+                                    "score": 1.0,
+                                    "content": "4.3 TRANSFER LEARNING: IMAGE DETECTION ON PASCAL VOC 2007",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 24
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        400,
+                        505,
+                        587
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                400,
+                                505,
+                                413
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        400,
+                                        505,
+                                        413
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We next investigate transfer performance on object detection on the PASCAL-2007 dataset, which",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                411,
+                                506,
+                                424
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        411,
+                                        506,
+                                        424
+                                    ],
+                                    "score": 1.0,
+                                    "content": "reflects the practical scenario where a representation must be trained on a dataset with different",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                421,
+                                506,
+                                435
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        421,
+                                        506,
+                                        435
+                                    ],
+                                    "score": 1.0,
+                                    "content": "statistics than the dataset of interest. This dataset also tests the efficiency of the representation as",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                434,
+                                504,
+                                445
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        434,
+                                        504,
+                                        445
+                                    ],
+                                    "score": 1.0,
+                                    "content": "it only contains 5011 labeled images to train from. In this setting, we replaced the neural network",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                443,
+                                505,
+                                456
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        443,
+                                        145,
+                                        456
+                                    ],
+                                    "score": 1.0,
+                                    "content": "classifier",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        145,
+                                        444,
+                                        158,
+                                        456
+                                    ],
+                                    "score": 0.9,
+                                    "content": "h _ { \\psi }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        158,
+                                        443,
+                                        505,
+                                        456
+                                    ],
+                                    "score": 1.0,
+                                    "content": "used previously with a Faster-RCNN (Ren et al., 2015) image detection architecture,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                455,
+                                505,
+                                467
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        455,
+                                        505,
+                                        467
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and use the pre-trained feature extractor on ImageNet. As before, we first trained the Faster-RCNN",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                466,
+                                506,
+                                479
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        466,
+                                        506,
+                                        479
+                                    ],
+                                    "score": 1.0,
+                                    "content": "model while keeping the feature extractor fixed, then fine-tuned the entire model end-to-end. Table",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                476,
+                                506,
+                                489
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        476,
+                                        506,
+                                        489
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3 displays our results compared to other methods. Most competing methods, which optimize a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                487,
+                                506,
+                                502
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        487,
+                                        506,
+                                        502
+                                    ],
+                                    "score": 1.0,
+                                    "content": "single unsupervised objective on ImageNet before fine-tuning on PASCAL detection, attain around",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                498,
+                                506,
+                                513
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        499,
+                                        126,
+                                        509
+                                    ],
+                                    "score": 0.86,
+                                    "content": "65 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        127,
+                                        498,
+                                        506,
+                                        513
+                                    ],
+                                    "score": 1.0,
+                                    "content": "mean average precision. Leveraging larger unlabeled datasets increases their performance up",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                509,
+                                505,
+                                522
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        509,
+                                        117,
+                                        522
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        117,
+                                        510,
+                                        144,
+                                        520
+                                    ],
+                                    "score": 0.86,
+                                    "content": "6 7 . 8 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        144,
+                                        509,
+                                        505,
+                                        522
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(Caron et al., 2019). Combining multiple forms of self-supervision enables them to reach",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                519,
+                                506,
+                                534
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        521,
+                                        134,
+                                        532
+                                    ],
+                                    "score": 0.86,
+                                    "content": "7 0 . 5 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        134,
+                                        519,
+                                        506,
+                                        534
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(Doersch & Zisserman, 2017). The proposed method, which learns only from ImageNet data",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                532,
+                                506,
+                                545
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        532,
+                                        299,
+                                        545
+                                    ],
+                                    "score": 1.0,
+                                    "content": "using a single unsupervised objective, reaches",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        299,
+                                        532,
+                                        327,
+                                        542
+                                    ],
+                                    "score": 0.87,
+                                    "content": "7 0 . 6 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        327,
+                                        532,
+                                        506,
+                                        545
+                                    ],
+                                    "score": 1.0,
+                                    "content": "when equipped with a ResNet-101 feature",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                542,
+                                505,
+                                555
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        542,
+                                        144,
+                                        555
+                                    ],
+                                    "score": 1.0,
+                                    "content": "extractor",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        145,
+                                        543,
+                                        155,
+                                        554
+                                    ],
+                                    "score": 0.86,
+                                    "content": "f _ { \\theta }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        155,
+                                        542,
+                                        505,
+                                        555
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(as for most competing methods (Doersch & Zisserman, 2017) but not all (Caron et al.,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                553,
+                                505,
+                                566
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        553,
+                                        411,
+                                        566
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2018; 2019). Equipped with the more powerful ResNet-161 feature extractor",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        411,
+                                        554,
+                                        421,
+                                        565
+                                    ],
+                                    "score": 0.89,
+                                    "content": "f _ { \\theta }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        422,
+                                        553,
+                                        505,
+                                        566
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", our method reaches",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                563,
+                                505,
+                                577
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        565,
+                                        133,
+                                        575
+                                    ],
+                                    "score": 0.87,
+                                    "content": "7 2 . 7 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        134,
+                                        563,
+                                        264,
+                                        577
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Importantly, this result is only",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        264,
+                                        565,
+                                        279,
+                                        575
+                                    ],
+                                    "score": 0.84,
+                                    "content": "2 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        280,
+                                        563,
+                                        505,
+                                        577
+                                    ],
+                                    "score": 1.0,
+                                    "content": "short of the performance attained by purely supervised",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                576,
+                                491,
+                                588
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        576,
+                                        491,
+                                        588
+                                    ],
+                                    "score": 1.0,
+                                    "content": "transfer learning, which we obtain by using all ImageNet labels before transferring to PASCAL.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        }
+                    ],
+                    "index": 33
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        606,
+                        190,
+                        618
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                605,
+                                192,
+                                621
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        605,
+                                        192,
+                                        621
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5 DISCUSSION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        }
+                    ],
+                    "index": 42
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        633,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                632,
+                                505,
+                                646
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        632,
+                                        505,
+                                        646
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We asked whether CPC could enable data-efficient image recognition, and found that it indeed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                644,
+                                505,
+                                656
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        644,
+                                        505,
+                                        656
+                                    ],
+                                    "score": 1.0,
+                                    "content": "greatly improves the accuracy of classifiers and object detectors when given small amounts of la-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                654,
+                                505,
+                                668
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        654,
+                                        505,
+                                        668
+                                    ],
+                                    "score": 1.0,
+                                    "content": "beled data. Surprisingly, CPC even improves results given ImageNet-scale labels. Our results show",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                666,
+                                505,
+                                678
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        666,
+                                        505,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that there is still room for improvement using relatively straightforward changes such as augmenta-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                677,
+                                505,
+                                689
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        677,
+                                        505,
+                                        689
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tion, optimization, and network architecture. Furthermore, we found that the standard method for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                687,
+                                505,
+                                700
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        687,
+                                        505,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "evaluating unsupervised representations—linear classification—is only partially predictive of effi-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                699,
+                                505,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        699,
+                                        505,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cient recognition performance, suggesting that further research should focus on efficient recognition",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                708,
+                                506,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        708,
+                                        506,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as a standalone benchmark. Overall, these results open the door toward research on problems where",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                720,
+                                340,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        720,
+                                        340,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "data is naturally limited, e.g. medical imaging or robotics.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 51
+                        }
+                    ],
+                    "index": 47
+                }
+            ],
+            "page_idx": 8,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        308,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                26,
+                                308,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        26,
+                                        308,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Under review as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        752,
+                        308,
+                        759
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                302,
+                                751,
+                                309,
+                                762
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        302,
+                                        751,
+                                        309,
+                                        762
+                                    ],
+                                    "score": 1.0,
+                                    "content": "9",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        82,
+                        505,
+                        214
+                    ],
+                    "lines": [],
+                    "index": 5.5,
+                    "bbox_fs": [
+                        105,
+                        83,
+                        506,
+                        216
+                    ],
+                    "lines_deleted": true
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        230,
+                        504,
+                        361
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                230,
+                                506,
+                                243
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        230,
+                                        506,
+                                        243
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Other semi-supervised techniques A separate class of methods for low-data classification at-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                241,
+                                506,
+                                253
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        241,
+                                        506,
+                                        253
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tempts to propagate the knowledge extracted from the subset of labeled examples to unlabeled",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                252,
+                                504,
+                                264
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        252,
+                                        504,
+                                        264
+                                    ],
+                                    "score": 1.0,
+                                    "content": "examples while being invariant to augmentation or other perturbations. These methods generally",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                263,
+                                504,
+                                275
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        263,
+                                        504,
+                                        275
+                                    ],
+                                    "score": 1.0,
+                                    "content": "depend on the quality of the classifier’s predictions, and as such tend to fare well when given in-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                273,
+                                505,
+                                287
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        273,
+                                        505,
+                                        287
+                                    ],
+                                    "score": 1.0,
+                                    "content": "termediate amounts of data. Although not sufficient in themselves (Unsupervised Data Augmenta-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                284,
+                                506,
+                                297
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        284,
+                                        506,
+                                        297
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tion (Xie et al., 2019), Virtual Adversarial Training (Miyato et al., 2018) and entropy minimization",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                295,
+                                504,
+                                308
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        296,
+                                        397,
+                                        308
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(Grandvalet & Bengio, 2005), and pseudo-labeling (Lee, 2013) achieve",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        397,
+                                        296,
+                                        424,
+                                        306
+                                    ],
+                                    "score": 0.86,
+                                    "content": "8 5 . 8 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        424,
+                                        296,
+                                        428,
+                                        308
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        428,
+                                        296,
+                                        455,
+                                        306
+                                    ],
+                                    "score": 0.83,
+                                    "content": "8 3 . 4 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        455,
+                                        296,
+                                        477,
+                                        308
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        477,
+                                        295,
+                                        504,
+                                        306
+                                    ],
+                                    "score": 0.86,
+                                    "content": "8 2 . 4 \\%",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                306,
+                                506,
+                                320
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        306,
+                                        193,
+                                        320
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-5 accuracy with",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        193,
+                                        307,
+                                        213,
+                                        317
+                                    ],
+                                    "score": 0.87,
+                                    "content": "10 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        213,
+                                        306,
+                                        325,
+                                        320
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of labels, compared to our",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        325,
+                                        307,
+                                        353,
+                                        317
+                                    ],
+                                    "score": 0.88,
+                                    "content": "8 9 . 4 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        353,
+                                        306,
+                                        506,
+                                        320
+                                    ],
+                                    "score": 1.0,
+                                    "content": ") when combined with representation",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                317,
+                                506,
+                                331
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        317,
+                                        455,
+                                        331
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning (e.g. rotation prediction Zhai et al., 2019) they can provide considerable gains",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        455,
+                                        318,
+                                        483,
+                                        329
+                                    ],
+                                    "score": 0.8,
+                                    "content": "9 1 . 2 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        483,
+                                        317,
+                                        506,
+                                        331
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Top-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                329,
+                                506,
+                                341
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        329,
+                                        506,
+                                        341
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5 accuracy). It is therefore surprising that CPC representations alone can enable accuracy that is",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                339,
+                                506,
+                                353
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        339,
+                                        506,
+                                        353
+                                    ],
+                                    "score": 1.0,
+                                    "content": "comparable to that of these methods, and investigating to what extent they can be combined would",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                351,
+                                259,
+                                362
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        351,
+                                        259,
+                                        362
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be an interesting topic of future work.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 17.5,
+                    "bbox_fs": [
+                        105,
+                        230,
+                        506,
+                        362
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        378,
+                        417,
+                        389
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                378,
+                                419,
+                                391
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        378,
+                                        419,
+                                        391
+                                    ],
+                                    "score": 1.0,
+                                    "content": "4.3 TRANSFER LEARNING: IMAGE DETECTION ON PASCAL VOC 2007",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 24
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        400,
+                        505,
+                        587
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                400,
+                                505,
+                                413
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        400,
+                                        505,
+                                        413
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We next investigate transfer performance on object detection on the PASCAL-2007 dataset, which",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                411,
+                                506,
+                                424
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        411,
+                                        506,
+                                        424
+                                    ],
+                                    "score": 1.0,
+                                    "content": "reflects the practical scenario where a representation must be trained on a dataset with different",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                421,
+                                506,
+                                435
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        421,
+                                        506,
+                                        435
+                                    ],
+                                    "score": 1.0,
+                                    "content": "statistics than the dataset of interest. This dataset also tests the efficiency of the representation as",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                434,
+                                504,
+                                445
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        434,
+                                        504,
+                                        445
+                                    ],
+                                    "score": 1.0,
+                                    "content": "it only contains 5011 labeled images to train from. In this setting, we replaced the neural network",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                443,
+                                505,
+                                456
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        443,
+                                        145,
+                                        456
+                                    ],
+                                    "score": 1.0,
+                                    "content": "classifier",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        145,
+                                        444,
+                                        158,
+                                        456
+                                    ],
+                                    "score": 0.9,
+                                    "content": "h _ { \\psi }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        158,
+                                        443,
+                                        505,
+                                        456
+                                    ],
+                                    "score": 1.0,
+                                    "content": "used previously with a Faster-RCNN (Ren et al., 2015) image detection architecture,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                455,
+                                505,
+                                467
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        455,
+                                        505,
+                                        467
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and use the pre-trained feature extractor on ImageNet. As before, we first trained the Faster-RCNN",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                466,
+                                506,
+                                479
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        466,
+                                        506,
+                                        479
+                                    ],
+                                    "score": 1.0,
+                                    "content": "model while keeping the feature extractor fixed, then fine-tuned the entire model end-to-end. Table",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                476,
+                                506,
+                                489
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        476,
+                                        506,
+                                        489
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3 displays our results compared to other methods. Most competing methods, which optimize a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                487,
+                                506,
+                                502
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        487,
+                                        506,
+                                        502
+                                    ],
+                                    "score": 1.0,
+                                    "content": "single unsupervised objective on ImageNet before fine-tuning on PASCAL detection, attain around",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                498,
+                                506,
+                                513
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        499,
+                                        126,
+                                        509
+                                    ],
+                                    "score": 0.86,
+                                    "content": "65 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        127,
+                                        498,
+                                        506,
+                                        513
+                                    ],
+                                    "score": 1.0,
+                                    "content": "mean average precision. Leveraging larger unlabeled datasets increases their performance up",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                509,
+                                505,
+                                522
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        509,
+                                        117,
+                                        522
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        117,
+                                        510,
+                                        144,
+                                        520
+                                    ],
+                                    "score": 0.86,
+                                    "content": "6 7 . 8 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        144,
+                                        509,
+                                        505,
+                                        522
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(Caron et al., 2019). Combining multiple forms of self-supervision enables them to reach",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                519,
+                                506,
+                                534
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        521,
+                                        134,
+                                        532
+                                    ],
+                                    "score": 0.86,
+                                    "content": "7 0 . 5 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        134,
+                                        519,
+                                        506,
+                                        534
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(Doersch & Zisserman, 2017). The proposed method, which learns only from ImageNet data",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                532,
+                                506,
+                                545
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        532,
+                                        299,
+                                        545
+                                    ],
+                                    "score": 1.0,
+                                    "content": "using a single unsupervised objective, reaches",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        299,
+                                        532,
+                                        327,
+                                        542
+                                    ],
+                                    "score": 0.87,
+                                    "content": "7 0 . 6 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        327,
+                                        532,
+                                        506,
+                                        545
+                                    ],
+                                    "score": 1.0,
+                                    "content": "when equipped with a ResNet-101 feature",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                542,
+                                505,
+                                555
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        542,
+                                        144,
+                                        555
+                                    ],
+                                    "score": 1.0,
+                                    "content": "extractor",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        145,
+                                        543,
+                                        155,
+                                        554
+                                    ],
+                                    "score": 0.86,
+                                    "content": "f _ { \\theta }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        155,
+                                        542,
+                                        505,
+                                        555
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(as for most competing methods (Doersch & Zisserman, 2017) but not all (Caron et al.,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                553,
+                                505,
+                                566
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        553,
+                                        411,
+                                        566
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2018; 2019). Equipped with the more powerful ResNet-161 feature extractor",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        411,
+                                        554,
+                                        421,
+                                        565
+                                    ],
+                                    "score": 0.89,
+                                    "content": "f _ { \\theta }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        422,
+                                        553,
+                                        505,
+                                        566
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", our method reaches",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                563,
+                                505,
+                                577
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        565,
+                                        133,
+                                        575
+                                    ],
+                                    "score": 0.87,
+                                    "content": "7 2 . 7 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        134,
+                                        563,
+                                        264,
+                                        577
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Importantly, this result is only",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        264,
+                                        565,
+                                        279,
+                                        575
+                                    ],
+                                    "score": 0.84,
+                                    "content": "2 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        280,
+                                        563,
+                                        505,
+                                        577
+                                    ],
+                                    "score": 1.0,
+                                    "content": "short of the performance attained by purely supervised",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                576,
+                                491,
+                                588
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        576,
+                                        491,
+                                        588
+                                    ],
+                                    "score": 1.0,
+                                    "content": "transfer learning, which we obtain by using all ImageNet labels before transferring to PASCAL.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        }
+                    ],
+                    "index": 33,
+                    "bbox_fs": [
+                        104,
+                        400,
+                        506,
+                        588
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        606,
+                        190,
+                        618
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                605,
+                                192,
+                                621
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        605,
+                                        192,
+                                        621
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5 DISCUSSION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        }
+                    ],
+                    "index": 42
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        633,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                632,
+                                505,
+                                646
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        632,
+                                        505,
+                                        646
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We asked whether CPC could enable data-efficient image recognition, and found that it indeed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                644,
+                                505,
+                                656
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        644,
+                                        505,
+                                        656
+                                    ],
+                                    "score": 1.0,
+                                    "content": "greatly improves the accuracy of classifiers and object detectors when given small amounts of la-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                654,
+                                505,
+                                668
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        654,
+                                        505,
+                                        668
+                                    ],
+                                    "score": 1.0,
+                                    "content": "beled data. Surprisingly, CPC even improves results given ImageNet-scale labels. Our results show",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                666,
+                                505,
+                                678
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        666,
+                                        505,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that there is still room for improvement using relatively straightforward changes such as augmenta-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                677,
+                                505,
+                                689
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        677,
+                                        505,
+                                        689
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tion, optimization, and network architecture. Furthermore, we found that the standard method for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                687,
+                                505,
+                                700
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        687,
+                                        505,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "evaluating unsupervised representations—linear classification—is only partially predictive of effi-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                699,
+                                505,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        699,
+                                        505,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cient recognition performance, suggesting that further research should focus on efficient recognition",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                708,
+                                506,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        708,
+                                        506,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as a standalone benchmark. Overall, these results open the door toward research on problems where",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                720,
+                                340,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        720,
+                                        340,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "data is naturally limited, e.g. medical imaging or robotics.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 51
+                        }
+                    ],
+                    "index": 47,
+                    "bbox_fs": [
+                        105,
+                        632,
+                        506,
+                        733
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "table",
+                    "bbox": [
+                        147,
+                        170,
+                        464,
+                        362
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                106,
+                                89,
+                                505,
+                                166
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        89,
+                                        505,
+                                        101
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                89,
+                                                202,
+                                                101
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 3: Faster-RCNN",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
+                                                203,
+                                                90,
+                                                216,
+                                                101
+                                            ],
+                                            "score": 0.88,
+                                            "content": "h _ { \\psi }",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
+                                                216,
+                                                89,
+                                                271,
+                                                101
+                                            ],
+                                            "score": 1.0,
+                                            "content": "trained with",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
+                                                271,
+                                                89,
+                                                297,
+                                                100
+                                            ],
+                                            "score": 0.86,
+                                            "content": "100 \\%",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
+                                                298,
+                                                89,
+                                                505,
+                                                101
+                                            ],
+                                            "score": 1.0,
+                                            "content": "of PASCAL labels. Comparison of PASCAL 2007",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        100,
+                                        505,
+                                        113
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                100,
+                                                505,
+                                                113
+                                            ],
+                                            "score": 1.0,
+                                            "content": "image detection accuracy to other transfer methods. The supervised baseline learns from the entire",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        111,
+                                        505,
+                                        123
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                111,
+                                                505,
+                                                123
+                                            ],
+                                            "score": 1.0,
+                                            "content": "labeled ImageNet dataset and fine-tunes for PASCAL detection. The second class of methods learns",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 2
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        123,
+                                        505,
+                                        134
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                123,
+                                                505,
+                                                134
+                                            ],
+                                            "score": 1.0,
+                                            "content": "from the same unlabeled images before transferring. All of these methods pre-train on the ImageNet",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        133,
+                                        505,
+                                        146
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                133,
+                                                505,
+                                                146
+                                            ],
+                                            "score": 1.0,
+                                            "content": "dataset, except for DeeperCluster which learns from the larger, but uncurated, YFCC100M dataset",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        144,
+                                        505,
+                                        157
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                144,
+                                                464,
+                                                157
+                                            ],
+                                            "score": 1.0,
+                                            "content": "(Thomee et al., 2015). All results are reported in terms of mean average precision (mAP).",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
+                                                465,
+                                                145,
+                                                471,
+                                                156
+                                            ],
+                                            "score": 0.73,
+                                            "content": "\\dagger",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
+                                                472,
+                                                144,
+                                                505,
+                                                157
+                                            ],
+                                            "score": 1.0,
+                                            "content": "denotes",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 5
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        156,
+                                        249,
+                                        167
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                156,
+                                                249,
+                                                167
+                                            ],
+                                            "score": 1.0,
+                                            "content": "methods implemented in this work.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 6
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                147,
+                                170,
+                                464,
+                                362
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        147,
+                                        170,
+                                        464,
+                                        362
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                147,
+                                                170,
+                                                464,
+                                                362
+                                            ],
+                                            "score": 0.527,
+                                            "html": "<table><tr><td>Method</td><td>mAP</td></tr><tr><td>Transfer from labeled data: Supervised - ResNet-152</td><td>74.7</td></tr><tr><td>Transfer from unlabeled data: Exemplar (Ex) (Dosovitskiy et al., 2014) Motion Segmentation (MS) (Pathak et al.,2016)</td><td>60.9</td></tr><tr><td>Colorization (Col) (Zhang et al.,2016) Relative Position (RP) (Doersch et al.,2015)</td><td>61.1 65.5</td></tr><tr><td>Combination of Ex + MS + Col +RP (Doersch &amp; Zisserman,2017)</td><td>66.8 70.5</td></tr><tr><td>Instance Discrimination (Wu et al., 2018)</td><td>65.4</td></tr><tr><td>Deep Cluster (Caron et al., 2018) Deeper Cluster (Caron et al., 2019)</td><td>65.9</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "d005a0a972800a539ffdecef950a4659796c2a8300a3ab9b860336449e53c88e.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 8,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        147,
+                                        170,
+                                        464,
+                                        234.0
+                                    ],
+                                    "spans": [],
+                                    "index": 7
+                                },
+                                {
+                                    "bbox": [
+                                        147,
+                                        234.0,
+                                        464,
+                                        298.0
+                                    ],
+                                    "spans": [],
+                                    "index": 8
+                                },
+                                {
+                                    "bbox": [
+                                        147,
+                                        298.0,
+                                        464,
+                                        362.0
+                                    ],
+                                    "spans": [],
+                                    "index": 9
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        385,
+                        505,
+                        539
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                385,
+                                505,
+                                398
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        385,
+                                        505,
+                                        398
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Furthermore, images are far from the only domain where unsupervised representation learning is",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                397,
+                                505,
+                                409
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        397,
+                                        505,
+                                        409
+                                    ],
+                                    "score": 1.0,
+                                    "content": "important: for example, unsupervised learning is already a critical step in language (Mikolov et al.,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                407,
+                                505,
+                                420
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        407,
+                                        505,
+                                        420
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2013; Devlin et al., 2018), and shows promise in domains like audio (van den Oord et al., 2018;",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                419,
+                                505,
+                                430
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        419,
+                                        505,
+                                        430
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Arandjelovic & Zisserman, 2018; 2017), video (Jing & Tian, 2018; Misra et al., 2016), and robotic",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                430,
+                                505,
+                                442
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        430,
+                                        505,
+                                        442
+                                    ],
+                                    "score": 1.0,
+                                    "content": "manipulation (Pinto & Gupta, 2016; Pinto et al., 2016; Sermanet et al., 2018). Currently much",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                439,
+                                505,
+                                453
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        439,
+                                        505,
+                                        453
+                                    ],
+                                    "score": 1.0,
+                                    "content": "self-supervised work builds upon tasks tailored for a specific domain (often images), which may",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                450,
+                                506,
+                                465
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        450,
+                                        506,
+                                        465
+                                    ],
+                                    "score": 1.0,
+                                    "content": "not be easily adapted to other domains. Contrastive prediction methods, including the techniques",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                462,
+                                506,
+                                475
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        462,
+                                        506,
+                                        475
+                                    ],
+                                    "score": 1.0,
+                                    "content": "suggested in this paper, are task agnostic and could therefore serve as a unifying framework for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                474,
+                                505,
+                                486
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        474,
+                                        505,
+                                        486
+                                    ],
+                                    "score": 1.0,
+                                    "content": "integrating these tasks and modalities. This generality is particularly useful given that many real-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                484,
+                                505,
+                                497
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        484,
+                                        505,
+                                        497
+                                    ],
+                                    "score": 1.0,
+                                    "content": "world environments are inherently multimodal, e.g. robotic environments which can have vision,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                495,
+                                505,
+                                508
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        495,
+                                        505,
+                                        508
+                                    ],
+                                    "score": 1.0,
+                                    "content": "audio, touch, proprioception, action, and more over long temporal sequences. Given the importance",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                505,
+                                506,
+                                520
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        505,
+                                        506,
+                                        520
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of increasing the amounts of self-supervision (via additional directions of prediction), integrating",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                517,
+                                506,
+                                530
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        517,
+                                        506,
+                                        530
+                                    ],
+                                    "score": 1.0,
+                                    "content": "these modalities and tasks could lead to unsupervised representations which rival the efficiency and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                528,
+                                237,
+                                541
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        528,
+                                        237,
+                                        541
+                                    ],
+                                    "score": 1.0,
+                                    "content": "effectiveness of biological ones.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 16.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        556,
+                        175,
+                        568
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                555,
+                                176,
+                                569
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        555,
+                                        176,
+                                        569
+                                    ],
+                                    "score": 1.0,
+                                    "content": "REFERENCES",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 24
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        574,
+                        486,
+                        586
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                572,
+                                487,
+                                588
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        572,
+                                        487,
+                                        588
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Pulkit Agrawal, Joao Carreira, and Jitendra Malik. Learning to see by moving. In ICCV, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        592,
+                        504,
+                        615
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                592,
+                                505,
+                                605
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        592,
+                                        505,
+                                        605
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Relja Arandjelovic and Andrew Zisserman. Look, listen and learn. In Proceedings of the IEEE",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                603,
+                                384,
+                                616
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        603,
+                                        384,
+                                        616
+                                    ],
+                                    "score": 1.0,
+                                    "content": "International Conference on Computer Vision, pp. 609–617, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 26.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        621,
+                        504,
+                        644
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                620,
+                                505,
+                                635
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        620,
+                                        505,
+                                        635
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Relja Arandjelovic and Andrew Zisserman. Objects that sound. In Proceedings of the European",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                632,
+                                364,
+                                645
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        632,
+                                        364,
+                                        645
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Conference on Computer Vision (ECCV), pp. 435–451, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 28.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        650,
+                        504,
+                        673
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                649,
+                                505,
+                                664
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        649,
+                                        505,
+                                        664
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lei Jimmy Ba, Ryan Kiros, and Geoffrey E. Hinton. Layer normalization. CoRR, abs/1607.06450,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                659,
+                                144,
+                                675
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        659,
+                                        144,
+                                        675
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        }
+                    ],
+                    "index": 30.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        680,
+                        504,
+                        703
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                679,
+                                505,
+                                694
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        679,
+                                        505,
+                                        694
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Philip Bachman, R Devon Hjelm, and William Buchwalter. Learning representations by maximizing",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                691,
+                                415,
+                                704
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        691,
+                                        415,
+                                        704
+                                    ],
+                                    "score": 1.0,
+                                    "content": "mutual information across views. arXiv preprint arXiv:1906.00910, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 32.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        709,
+                        503,
+                        731
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                709,
+                                505,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        709,
+                                        505,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "H.B. Barlow. Unsupervised learning. Neural Computation, 1(3):295–311, 1989. doi: 10.1162/neco.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                720,
+                                173,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        720,
+                                        173,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1989.1.3.295.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        }
+                    ],
+                    "index": 34.5
+                }
+            ],
+            "page_idx": 9,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        301,
+                        751,
+                        311,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                313,
+                                765
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        313,
+                                        765
+                                    ],
+                                    "score": 1.0,
+                                    "content": "",
+                                    "type": "text",
+                                    "height": 15,
+                                    "width": 14
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        308,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                26,
+                                308,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        26,
+                                        308,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Under review as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "table",
+                    "bbox": [
+                        147,
+                        170,
+                        464,
+                        362
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                106,
+                                89,
+                                505,
+                                166
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        89,
+                                        505,
+                                        101
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                89,
+                                                202,
+                                                101
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 3: Faster-RCNN",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
+                                                203,
+                                                90,
+                                                216,
+                                                101
+                                            ],
+                                            "score": 0.88,
+                                            "content": "h _ { \\psi }",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
+                                                216,
+                                                89,
+                                                271,
+                                                101
+                                            ],
+                                            "score": 1.0,
+                                            "content": "trained with",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
+                                                271,
+                                                89,
+                                                297,
+                                                100
+                                            ],
+                                            "score": 0.86,
+                                            "content": "100 \\%",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
+                                                298,
+                                                89,
+                                                505,
+                                                101
+                                            ],
+                                            "score": 1.0,
+                                            "content": "of PASCAL labels. Comparison of PASCAL 2007",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        100,
+                                        505,
+                                        113
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                100,
+                                                505,
+                                                113
+                                            ],
+                                            "score": 1.0,
+                                            "content": "image detection accuracy to other transfer methods. The supervised baseline learns from the entire",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        111,
+                                        505,
+                                        123
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                111,
+                                                505,
+                                                123
+                                            ],
+                                            "score": 1.0,
+                                            "content": "labeled ImageNet dataset and fine-tunes for PASCAL detection. The second class of methods learns",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 2
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        123,
+                                        505,
+                                        134
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                123,
+                                                505,
+                                                134
+                                            ],
+                                            "score": 1.0,
+                                            "content": "from the same unlabeled images before transferring. All of these methods pre-train on the ImageNet",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        133,
+                                        505,
+                                        146
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                133,
+                                                505,
+                                                146
+                                            ],
+                                            "score": 1.0,
+                                            "content": "dataset, except for DeeperCluster which learns from the larger, but uncurated, YFCC100M dataset",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        144,
+                                        505,
+                                        157
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                144,
+                                                464,
+                                                157
+                                            ],
+                                            "score": 1.0,
+                                            "content": "(Thomee et al., 2015). All results are reported in terms of mean average precision (mAP).",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
+                                                465,
+                                                145,
+                                                471,
+                                                156
+                                            ],
+                                            "score": 0.73,
+                                            "content": "\\dagger",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
+                                                472,
+                                                144,
+                                                505,
+                                                157
+                                            ],
+                                            "score": 1.0,
+                                            "content": "denotes",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 5
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        156,
+                                        249,
+                                        167
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                156,
+                                                249,
+                                                167
+                                            ],
+                                            "score": 1.0,
+                                            "content": "methods implemented in this work.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 6
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                147,
+                                170,
+                                464,
+                                362
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        147,
+                                        170,
+                                        464,
+                                        362
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                147,
+                                                170,
+                                                464,
+                                                362
+                                            ],
+                                            "score": 0.527,
+                                            "html": "<table><tr><td>Method</td><td>mAP</td></tr><tr><td>Transfer from labeled data: Supervised - ResNet-152</td><td>74.7</td></tr><tr><td>Transfer from unlabeled data: Exemplar (Ex) (Dosovitskiy et al., 2014) Motion Segmentation (MS) (Pathak et al.,2016)</td><td>60.9</td></tr><tr><td>Colorization (Col) (Zhang et al.,2016) Relative Position (RP) (Doersch et al.,2015)</td><td>61.1 65.5</td></tr><tr><td>Combination of Ex + MS + Col +RP (Doersch &amp; Zisserman,2017)</td><td>66.8 70.5</td></tr><tr><td>Instance Discrimination (Wu et al., 2018)</td><td>65.4</td></tr><tr><td>Deep Cluster (Caron et al., 2018) Deeper Cluster (Caron et al., 2019)</td><td>65.9</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "d005a0a972800a539ffdecef950a4659796c2a8300a3ab9b860336449e53c88e.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 8,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        147,
+                                        170,
+                                        464,
+                                        234.0
+                                    ],
+                                    "spans": [],
+                                    "index": 7
+                                },
+                                {
+                                    "bbox": [
+                                        147,
+                                        234.0,
+                                        464,
+                                        298.0
+                                    ],
+                                    "spans": [],
+                                    "index": 8
+                                },
+                                {
+                                    "bbox": [
+                                        147,
+                                        298.0,
+                                        464,
+                                        362.0
+                                    ],
+                                    "spans": [],
+                                    "index": 9
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        385,
+                        505,
+                        539
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                385,
+                                505,
+                                398
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        385,
+                                        505,
+                                        398
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Furthermore, images are far from the only domain where unsupervised representation learning is",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                397,
+                                505,
+                                409
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        397,
+                                        505,
+                                        409
+                                    ],
+                                    "score": 1.0,
+                                    "content": "important: for example, unsupervised learning is already a critical step in language (Mikolov et al.,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                407,
+                                505,
+                                420
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        407,
+                                        505,
+                                        420
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2013; Devlin et al., 2018), and shows promise in domains like audio (van den Oord et al., 2018;",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                419,
+                                505,
+                                430
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        419,
+                                        505,
+                                        430
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Arandjelovic & Zisserman, 2018; 2017), video (Jing & Tian, 2018; Misra et al., 2016), and robotic",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                430,
+                                505,
+                                442
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        430,
+                                        505,
+                                        442
+                                    ],
+                                    "score": 1.0,
+                                    "content": "manipulation (Pinto & Gupta, 2016; Pinto et al., 2016; Sermanet et al., 2018). Currently much",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                439,
+                                505,
+                                453
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        439,
+                                        505,
+                                        453
+                                    ],
+                                    "score": 1.0,
+                                    "content": "self-supervised work builds upon tasks tailored for a specific domain (often images), which may",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                450,
+                                506,
+                                465
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        450,
+                                        506,
+                                        465
+                                    ],
+                                    "score": 1.0,
+                                    "content": "not be easily adapted to other domains. Contrastive prediction methods, including the techniques",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                462,
+                                506,
+                                475
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        462,
+                                        506,
+                                        475
+                                    ],
+                                    "score": 1.0,
+                                    "content": "suggested in this paper, are task agnostic and could therefore serve as a unifying framework for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                474,
+                                505,
+                                486
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        474,
+                                        505,
+                                        486
+                                    ],
+                                    "score": 1.0,
+                                    "content": "integrating these tasks and modalities. This generality is particularly useful given that many real-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                484,
+                                505,
+                                497
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        484,
+                                        505,
+                                        497
+                                    ],
+                                    "score": 1.0,
+                                    "content": "world environments are inherently multimodal, e.g. robotic environments which can have vision,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                495,
+                                505,
+                                508
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        495,
+                                        505,
+                                        508
+                                    ],
+                                    "score": 1.0,
+                                    "content": "audio, touch, proprioception, action, and more over long temporal sequences. Given the importance",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                505,
+                                506,
+                                520
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        505,
+                                        506,
+                                        520
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of increasing the amounts of self-supervision (via additional directions of prediction), integrating",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                517,
+                                506,
+                                530
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        517,
+                                        506,
+                                        530
+                                    ],
+                                    "score": 1.0,
+                                    "content": "these modalities and tasks could lead to unsupervised representations which rival the efficiency and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                528,
+                                237,
+                                541
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        528,
+                                        237,
+                                        541
+                                    ],
+                                    "score": 1.0,
+                                    "content": "effectiveness of biological ones.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 16.5,
+                    "bbox_fs": [
+                        104,
+                        385,
+                        506,
+                        541
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        556,
+                        175,
+                        568
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                555,
+                                176,
+                                569
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        555,
+                                        176,
+                                        569
+                                    ],
+                                    "score": 1.0,
+                                    "content": "REFERENCES",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 24
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        574,
+                        486,
+                        586
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                572,
+                                487,
+                                588
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        572,
+                                        487,
+                                        588
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Pulkit Agrawal, Joao Carreira, and Jitendra Malik. Learning to see by moving. In ICCV, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 25,
+                    "bbox_fs": [
+                        105,
+                        572,
+                        487,
+                        588
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        592,
+                        504,
+                        615
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                592,
+                                505,
+                                605
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        592,
+                                        505,
+                                        605
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Relja Arandjelovic and Andrew Zisserman. Look, listen and learn. In Proceedings of the IEEE",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                603,
+                                384,
+                                616
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        603,
+                                        384,
+                                        616
+                                    ],
+                                    "score": 1.0,
+                                    "content": "International Conference on Computer Vision, pp. 609–617, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 26.5,
+                    "bbox_fs": [
+                        106,
+                        592,
+                        505,
+                        616
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        621,
+                        504,
+                        644
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                620,
+                                505,
+                                635
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        620,
+                                        505,
+                                        635
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Relja Arandjelovic and Andrew Zisserman. Objects that sound. In Proceedings of the European",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                632,
+                                364,
+                                645
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        632,
+                                        364,
+                                        645
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Conference on Computer Vision (ECCV), pp. 435–451, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 28.5,
+                    "bbox_fs": [
+                        105,
+                        620,
+                        505,
+                        645
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        650,
+                        504,
+                        673
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                649,
+                                505,
+                                664
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        649,
+                                        505,
+                                        664
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lei Jimmy Ba, Ryan Kiros, and Geoffrey E. Hinton. Layer normalization. CoRR, abs/1607.06450,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                659,
+                                144,
+                                675
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        659,
+                                        144,
+                                        675
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        }
+                    ],
+                    "index": 30.5,
+                    "bbox_fs": [
+                        105,
+                        649,
+                        505,
+                        675
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        680,
+                        504,
+                        703
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                679,
+                                505,
+                                694
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        679,
+                                        505,
+                                        694
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Philip Bachman, R Devon Hjelm, and William Buchwalter. Learning representations by maximizing",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                691,
+                                415,
+                                704
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        691,
+                                        415,
+                                        704
+                                    ],
+                                    "score": 1.0,
+                                    "content": "mutual information across views. arXiv preprint arXiv:1906.00910, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 32.5,
+                    "bbox_fs": [
+                        105,
+                        679,
+                        505,
+                        704
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        709,
+                        503,
+                        731
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                709,
+                                505,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        709,
+                                        505,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "H.B. Barlow. Unsupervised learning. Neural Computation, 1(3):295–311, 1989. doi: 10.1162/neco.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                720,
+                                173,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        720,
+                                        173,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1989.1.3.295.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        }
+                    ],
+                    "index": 34.5,
+                    "bbox_fs": [
+                        105,
+                        709,
+                        505,
+                        732
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        82,
+                        504,
+                        116
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                81,
+                                505,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        81,
+                                        505,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Mathilde Caron, Piotr Bojanowski, Armand Joulin, and Matthijs Douze. Deep clustering for unsu-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                93,
+                                505,
+                                107
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        93,
+                                        505,
+                                        107
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pervised learning of visual features. In The European Conference on Computer Vision (ECCV),",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                104,
+                                187,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        104,
+                                        187,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "September 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        124,
+                        502,
+                        147
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                123,
+                                503,
+                                138
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        123,
+                                        503,
+                                        138
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Mathilde Caron, Piotr Bojanowski, Julien Mairal, and Armand Joulin. Leveraging large-scale uncu-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                136,
+                                376,
+                                148
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        136,
+                                        376,
+                                        148
+                                    ],
+                                    "score": 1.0,
+                                    "content": "rated data for unsupervised pre-training of visual features. 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 3.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        155,
+                        503,
+                        178
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                155,
+                                505,
+                                169
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        155,
+                                        505,
+                                        169
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. BERT: pre-training of deep",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                166,
+                                459,
+                                179
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        166,
+                                        459,
+                                        179
+                                    ],
+                                    "score": 1.0,
+                                    "content": "bidirectional transformers for language understanding. CoRR, abs/1810.04805, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 5.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        186,
+                        504,
+                        210
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                186,
+                                505,
+                                200
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        186,
+                                        505,
+                                        200
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Carl Doersch and Andrew Zisserman. Multi-task self-supervised visual learning. In Proceedings of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                198,
+                                433,
+                                210
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        198,
+                                        433,
+                                        210
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the IEEE International Conference on Computer Vision, pp. 2051–2060, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 7.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        217,
+                        506,
+                        252
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                216,
+                                505,
+                                232
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        216,
+                                        505,
+                                        232
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Carl Doersch, Abhinav Gupta, and Alexei A Efros. Unsupervised visual representation learning by",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                228,
+                                505,
+                                243
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        228,
+                                        505,
+                                        243
+                                    ],
+                                    "score": 1.0,
+                                    "content": "context prediction. In Proceedings of the IEEE International Conference on Computer Vision, pp.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                240,
+                                192,
+                                251
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        240,
+                                        192,
+                                        251
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1422–1430, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        259,
+                        504,
+                        283
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                258,
+                                505,
+                                274
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        258,
+                                        505,
+                                        274
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Jeff Donahue and Karen Simonyan. Large scale adversarial representation learning. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                271,
+                                219,
+                                282
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        271,
+                                        219,
+                                        282
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1907.02544, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 12.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        291,
+                        504,
+                        314
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                289,
+                                505,
+                                305
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        289,
+                                        505,
+                                        305
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Jeff Donahue, Philipp Krahenb ¨ uhl, and Trevor Darrell. Adversarial feature learning. ¨ arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                302,
+                                219,
+                                315
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        302,
+                                        219,
+                                        315
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1605.09782, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 14.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        322,
+                        505,
+                        357
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                322,
+                                504,
+                                335
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        322,
+                                        504,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Alexey Dosovitskiy, Jost Tobias Springenberg, Martin Riedmiller, and Thomas Brox. Discrimina-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                334,
+                                505,
+                                346
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        334,
+                                        505,
+                                        346
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tive unsupervised feature learning with convolutional neural networks. In Advances in neural",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                344,
+                                326,
+                                357
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        344,
+                                        326,
+                                        357
+                                    ],
+                                    "score": 1.0,
+                                    "content": "information processing systems, pp. 766–774, 2014.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        109,
+                        364,
+                        504,
+                        388
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                364,
+                                505,
+                                377
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        364,
+                                        505,
+                                        377
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Mark Everingham, Luc Van Gool, Christopher KI Williams, John Winn, and Andrew Zisserman.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                375,
+                                408,
+                                388
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        375,
+                                        408,
+                                        388
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The pascal visual object classes challenge 2007 (voc2007) results. 2007.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 19.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        395,
+                        504,
+                        419
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                395,
+                                505,
+                                410
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        395,
+                                        505,
+                                        410
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Spyros Gidaris, Praveer Singh, and Nikos Komodakis. Unsupervised representation learning by",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                407,
+                                389,
+                                419
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        407,
+                                        389,
+                                        419
+                                    ],
+                                    "score": 1.0,
+                                    "content": "predicting image rotations. arXiv preprint arXiv:1803.07728, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 21.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        427,
+                        504,
+                        450
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                426,
+                                505,
+                                441
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        426,
+                                        505,
+                                        441
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Yves Grandvalet and Yoshua Bengio. Semi-supervised learning by entropy minimization. In Ad-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                438,
+                                394,
+                                451
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        438,
+                                        394,
+                                        451
+                                    ],
+                                    "score": 1.0,
+                                    "content": "vances in neural information processing systems, pp. 529–536, 2005.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 23.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        457,
+                        505,
+                        492
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                457,
+                                505,
+                                471
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        457,
+                                        505,
+                                        471
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Michael Gutmann and Aapo Hyvarinen. Noise-contrastive estimation: A new estimation principle ¨",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                469,
+                                505,
+                                482
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        469,
+                                        505,
+                                        482
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for unnormalized statistical models. In Proceedings of the Thirteenth International Conference",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                481,
+                                354,
+                                492
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        481,
+                                        354,
+                                        492
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on Artificial Intelligence and Statistics, pp. 297–304, 2010.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 26
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        500,
+                        505,
+                        534
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                499,
+                                505,
+                                514
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        499,
+                                        505,
+                                        514
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recog-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                510,
+                                505,
+                                525
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        510,
+                                        505,
+                                        525
+                                    ],
+                                    "score": 1.0,
+                                    "content": "nition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                520,
+                                186,
+                                535
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        520,
+                                        186,
+                                        535
+                                    ],
+                                    "score": 1.0,
+                                    "content": "770–778, 2016a.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 29
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        542,
+                        505,
+                        566
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                542,
+                                505,
+                                555
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        542,
+                                        505,
+                                        555
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Identity mappings in deep residual",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                553,
+                                462,
+                                567
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        553,
+                                        462,
+                                        567
+                                    ],
+                                    "score": 1.0,
+                                    "content": "networks. In European conference on computer vision, pp. 630–645. Springer, 2016b.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 31.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        573,
+                        505,
+                        607
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                573,
+                                505,
+                                586
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        573,
+                                        505,
+                                        586
+                                    ],
+                                    "score": 1.0,
+                                    "content": "G.E. Hinton, T.J. Sejnowski, H.H.M.I.C.N.L.T.J. Sejnowski, and T.A. Poggio. Unsupervised",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                585,
+                                505,
+                                596
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        585,
+                                        505,
+                                        596
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Learning: Foundations of Neural Computation. A Bradford Book. MIT Press, 1999. ISBN",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                596,
+                                186,
+                                607
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        596,
+                                        186,
+                                        607
+                                    ],
+                                    "score": 1.0,
+                                    "content": "9780262581684.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        }
+                    ],
+                    "index": 34
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        615,
+                        505,
+                        639
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                614,
+                                505,
+                                629
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        614,
+                                        505,
+                                        629
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Olivier J. Henaff, Robbe L. T. Goris, and Eero P. Simoncelli. Perceptual straightening of natural ´",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                627,
+                                280,
+                                640
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        627,
+                                        280,
+                                        640
+                                    ],
+                                    "score": 1.0,
+                                    "content": "videos. Nature Neuroscience, Apr 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 36.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        647,
+                        504,
+                        670
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                646,
+                                505,
+                                661
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        646,
+                                        505,
+                                        661
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sergey Ioffe and Christian Szegedy. Batch normalization: Accelerating deep network training by",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                658,
+                                412,
+                                670
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        658,
+                                        412,
+                                        670
+                                    ],
+                                    "score": 1.0,
+                                    "content": "reducing internal covariate shift. arXiv preprint arXiv:1502.03167, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 38.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        678,
+                        504,
+                        701
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                677,
+                                505,
+                                691
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        677,
+                                        505,
+                                        691
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Dinesh Jayaraman and Kristen Grauman. Learning image representations tied to ego-motion. In",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                689,
+                                169,
+                                701
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        689,
+                                        169,
+                                        701
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ICCV, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        }
+                    ],
+                    "index": 40.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        709,
+                        503,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                708,
+                                505,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        708,
+                                        505,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Longlong Jing and Yingli Tian. Self-supervised spatiotemporal feature learning by video geometric",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                720,
+                                347,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        720,
+                                        347,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "transformations. arXiv preprint arXiv:1811.11387, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        }
+                    ],
+                    "index": 42.5
+                }
+            ],
+            "page_idx": 10,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        308,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                26,
+                                308,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        26,
+                                        308,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Under review as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        310,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                312,
+                                765
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        312,
+                                        765
+                                    ],
+                                    "score": 1.0,
+                                    "content": "",
+                                    "type": "text",
+                                    "height": 15,
+                                    "width": 13
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        82,
+                        504,
+                        116
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                81,
+                                505,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        81,
+                                        505,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Mathilde Caron, Piotr Bojanowski, Armand Joulin, and Matthijs Douze. Deep clustering for unsu-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                93,
+                                505,
+                                107
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        93,
+                                        505,
+                                        107
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pervised learning of visual features. In The European Conference on Computer Vision (ECCV),",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                104,
+                                187,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        104,
+                                        187,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "September 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1,
+                    "bbox_fs": [
+                        105,
+                        81,
+                        505,
+                        117
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        124,
+                        502,
+                        147
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                123,
+                                503,
+                                138
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        123,
+                                        503,
+                                        138
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Mathilde Caron, Piotr Bojanowski, Julien Mairal, and Armand Joulin. Leveraging large-scale uncu-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                136,
+                                376,
+                                148
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        136,
+                                        376,
+                                        148
+                                    ],
+                                    "score": 1.0,
+                                    "content": "rated data for unsupervised pre-training of visual features. 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 3.5,
+                    "bbox_fs": [
+                        105,
+                        123,
+                        503,
+                        148
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        155,
+                        503,
+                        178
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                155,
+                                505,
+                                169
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        155,
+                                        505,
+                                        169
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. BERT: pre-training of deep",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                166,
+                                459,
+                                179
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        166,
+                                        459,
+                                        179
+                                    ],
+                                    "score": 1.0,
+                                    "content": "bidirectional transformers for language understanding. CoRR, abs/1810.04805, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 5.5,
+                    "bbox_fs": [
+                        105,
+                        155,
+                        505,
+                        179
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        186,
+                        504,
+                        210
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                186,
+                                505,
+                                200
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        186,
+                                        505,
+                                        200
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Carl Doersch and Andrew Zisserman. Multi-task self-supervised visual learning. In Proceedings of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                198,
+                                433,
+                                210
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        198,
+                                        433,
+                                        210
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the IEEE International Conference on Computer Vision, pp. 2051–2060, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 7.5,
+                    "bbox_fs": [
+                        105,
+                        186,
+                        505,
+                        210
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        217,
+                        506,
+                        252
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                216,
+                                505,
+                                232
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        216,
+                                        505,
+                                        232
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Carl Doersch, Abhinav Gupta, and Alexei A Efros. Unsupervised visual representation learning by",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                228,
+                                505,
+                                243
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        228,
+                                        505,
+                                        243
+                                    ],
+                                    "score": 1.0,
+                                    "content": "context prediction. In Proceedings of the IEEE International Conference on Computer Vision, pp.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                240,
+                                192,
+                                251
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        240,
+                                        192,
+                                        251
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1422–1430, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 10,
+                    "bbox_fs": [
+                        105,
+                        216,
+                        505,
+                        251
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        259,
+                        504,
+                        283
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                258,
+                                505,
+                                274
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        258,
+                                        505,
+                                        274
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Jeff Donahue and Karen Simonyan. Large scale adversarial representation learning. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                271,
+                                219,
+                                282
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        271,
+                                        219,
+                                        282
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1907.02544, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 12.5,
+                    "bbox_fs": [
+                        105,
+                        258,
+                        505,
+                        282
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        291,
+                        504,
+                        314
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                289,
+                                505,
+                                305
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        289,
+                                        505,
+                                        305
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Jeff Donahue, Philipp Krahenb ¨ uhl, and Trevor Darrell. Adversarial feature learning. ¨ arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                302,
+                                219,
+                                315
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        302,
+                                        219,
+                                        315
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1605.09782, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 14.5,
+                    "bbox_fs": [
+                        105,
+                        289,
+                        505,
+                        315
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        322,
+                        505,
+                        357
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                322,
+                                504,
+                                335
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        322,
+                                        504,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Alexey Dosovitskiy, Jost Tobias Springenberg, Martin Riedmiller, and Thomas Brox. Discrimina-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                334,
+                                505,
+                                346
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        334,
+                                        505,
+                                        346
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tive unsupervised feature learning with convolutional neural networks. In Advances in neural",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                344,
+                                326,
+                                357
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        344,
+                                        326,
+                                        357
+                                    ],
+                                    "score": 1.0,
+                                    "content": "information processing systems, pp. 766–774, 2014.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 17,
+                    "bbox_fs": [
+                        106,
+                        322,
+                        505,
+                        357
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        109,
+                        364,
+                        504,
+                        388
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                364,
+                                505,
+                                377
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        364,
+                                        505,
+                                        377
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Mark Everingham, Luc Van Gool, Christopher KI Williams, John Winn, and Andrew Zisserman.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                375,
+                                408,
+                                388
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        375,
+                                        408,
+                                        388
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The pascal visual object classes challenge 2007 (voc2007) results. 2007.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 19.5,
+                    "bbox_fs": [
+                        106,
+                        364,
+                        505,
+                        388
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        395,
+                        504,
+                        419
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                395,
+                                505,
+                                410
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        395,
+                                        505,
+                                        410
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Spyros Gidaris, Praveer Singh, and Nikos Komodakis. Unsupervised representation learning by",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                407,
+                                389,
+                                419
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        407,
+                                        389,
+                                        419
+                                    ],
+                                    "score": 1.0,
+                                    "content": "predicting image rotations. arXiv preprint arXiv:1803.07728, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 21.5,
+                    "bbox_fs": [
+                        105,
+                        395,
+                        505,
+                        419
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        427,
+                        504,
+                        450
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                426,
+                                505,
+                                441
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        426,
+                                        505,
+                                        441
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Yves Grandvalet and Yoshua Bengio. Semi-supervised learning by entropy minimization. In Ad-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                438,
+                                394,
+                                451
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        438,
+                                        394,
+                                        451
+                                    ],
+                                    "score": 1.0,
+                                    "content": "vances in neural information processing systems, pp. 529–536, 2005.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 23.5,
+                    "bbox_fs": [
+                        106,
+                        426,
+                        505,
+                        451
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        457,
+                        505,
+                        492
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                457,
+                                505,
+                                471
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        457,
+                                        505,
+                                        471
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Michael Gutmann and Aapo Hyvarinen. Noise-contrastive estimation: A new estimation principle ¨",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                469,
+                                505,
+                                482
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        469,
+                                        505,
+                                        482
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for unnormalized statistical models. In Proceedings of the Thirteenth International Conference",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                481,
+                                354,
+                                492
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        481,
+                                        354,
+                                        492
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on Artificial Intelligence and Statistics, pp. 297–304, 2010.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 26,
+                    "bbox_fs": [
+                        105,
+                        457,
+                        505,
+                        492
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        500,
+                        505,
+                        534
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                499,
+                                505,
+                                514
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        499,
+                                        505,
+                                        514
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recog-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                510,
+                                505,
+                                525
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        510,
+                                        505,
+                                        525
+                                    ],
+                                    "score": 1.0,
+                                    "content": "nition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                520,
+                                186,
+                                535
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        520,
+                                        186,
+                                        535
+                                    ],
+                                    "score": 1.0,
+                                    "content": "770–778, 2016a.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 29,
+                    "bbox_fs": [
+                        106,
+                        499,
+                        505,
+                        535
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        542,
+                        505,
+                        566
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                542,
+                                505,
+                                555
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        542,
+                                        505,
+                                        555
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Identity mappings in deep residual",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                553,
+                                462,
+                                567
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        553,
+                                        462,
+                                        567
+                                    ],
+                                    "score": 1.0,
+                                    "content": "networks. In European conference on computer vision, pp. 630–645. Springer, 2016b.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 31.5,
+                    "bbox_fs": [
+                        106,
+                        542,
+                        505,
+                        567
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        573,
+                        505,
+                        607
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                573,
+                                505,
+                                586
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        573,
+                                        505,
+                                        586
+                                    ],
+                                    "score": 1.0,
+                                    "content": "G.E. Hinton, T.J. Sejnowski, H.H.M.I.C.N.L.T.J. Sejnowski, and T.A. Poggio. Unsupervised",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                585,
+                                505,
+                                596
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        585,
+                                        505,
+                                        596
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Learning: Foundations of Neural Computation. A Bradford Book. MIT Press, 1999. ISBN",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                596,
+                                186,
+                                607
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        596,
+                                        186,
+                                        607
+                                    ],
+                                    "score": 1.0,
+                                    "content": "9780262581684.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        }
+                    ],
+                    "index": 34,
+                    "bbox_fs": [
+                        106,
+                        573,
+                        505,
+                        607
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        615,
+                        505,
+                        639
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                614,
+                                505,
+                                629
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        614,
+                                        505,
+                                        629
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Olivier J. Henaff, Robbe L. T. Goris, and Eero P. Simoncelli. Perceptual straightening of natural ´",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                627,
+                                280,
+                                640
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        627,
+                                        280,
+                                        640
+                                    ],
+                                    "score": 1.0,
+                                    "content": "videos. Nature Neuroscience, Apr 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 36.5,
+                    "bbox_fs": [
+                        106,
+                        614,
+                        505,
+                        640
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        647,
+                        504,
+                        670
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                646,
+                                505,
+                                661
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        646,
+                                        505,
+                                        661
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sergey Ioffe and Christian Szegedy. Batch normalization: Accelerating deep network training by",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                658,
+                                412,
+                                670
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        658,
+                                        412,
+                                        670
+                                    ],
+                                    "score": 1.0,
+                                    "content": "reducing internal covariate shift. arXiv preprint arXiv:1502.03167, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 38.5,
+                    "bbox_fs": [
+                        105,
+                        646,
+                        505,
+                        670
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        678,
+                        504,
+                        701
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                677,
+                                505,
+                                691
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        677,
+                                        505,
+                                        691
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Dinesh Jayaraman and Kristen Grauman. Learning image representations tied to ego-motion. In",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                689,
+                                169,
+                                701
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        689,
+                                        169,
+                                        701
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ICCV, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        }
+                    ],
+                    "index": 40.5,
+                    "bbox_fs": [
+                        105,
+                        677,
+                        505,
+                        701
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        709,
+                        503,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                708,
+                                505,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        708,
+                                        505,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Longlong Jing and Yingli Tian. Self-supervised spatiotemporal feature learning by video geometric",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                720,
+                                347,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        720,
+                                        347,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "transformations. arXiv preprint arXiv:1811.11387, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        }
+                    ],
+                    "index": 42.5,
+                    "bbox_fs": [
+                        105,
+                        708,
+                        505,
+                        732
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        82,
+                        504,
+                        116
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                82,
+                                505,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        82,
+                                        505,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Durk P Kingma, Shakir Mohamed, Danilo Jimenez Rezende, and Max Welling. Semi-supervised",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                92,
+                                505,
+                                108
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        92,
+                                        505,
+                                        108
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning with deep generative models. In Advances in neural information processing systems, pp.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                105,
+                                191,
+                                115
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        105,
+                                        191,
+                                        115
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3581–3589, 2014.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        123,
+                        504,
+                        146
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                123,
+                                505,
+                                136
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        123,
+                                        505,
+                                        136
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Alexander Kolesnikov, Xiaohua Zhai, and Lucas Beyer. Revisiting self-supervised visual representa-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                134,
+                                505,
+                                147
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        134,
+                                        505,
+                                        147
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tion learning. CoRR, abs/1901.09005, 2019. URL http://arxiv.org/abs/1901.09005.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 3.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        153,
+                        504,
+                        176
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                151,
+                                506,
+                                168
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        151,
+                                        506,
+                                        168
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Brenden M Lake, Ruslan Salakhutdinov, and Joshua B Tenenbaum. Human-level concept learning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                165,
+                                437,
+                                177
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        165,
+                                        437,
+                                        177
+                                    ],
+                                    "score": 1.0,
+                                    "content": "through probabilistic program induction. Science, 350(6266):1332–1338, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 5.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        183,
+                        504,
+                        207
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                182,
+                                505,
+                                197
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        182,
+                                        505,
+                                        197
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Barbara Landau, Linda B Smith, and Susan S Jones. The importance of shape in early lexical",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                195,
+                                335,
+                                207
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        195,
+                                        335,
+                                        207
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning. Cognitive development, 3(3):299–321, 1988.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 7.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        213,
+                        502,
+                        237
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                213,
+                                504,
+                                226
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        213,
+                                        504,
+                                        226
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Gustav Larsson, Michael Maire, and Gregory Shakhnarovich. Colorization as a proxy task for visual",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                225,
+                                309,
+                                237
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        225,
+                                        309,
+                                        237
+                                    ],
+                                    "score": 1.0,
+                                    "content": "understanding. In CVPR, pp. 6874–6883, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 9.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        243,
+                        496,
+                        256
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                242,
+                                498,
+                                258
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        242,
+                                        498,
+                                        258
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Yann LeCun, Yoshua Bengio, and Geoffrey Hinton. Deep learning. nature, 521(7553):436, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        263,
+                        505,
+                        297
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                262,
+                                505,
+                                277
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        262,
+                                        505,
+                                        277
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Dong-Hyun Lee. Pseudo-label: The simple and efficient semi-supervised learning method for deep",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                273,
+                                505,
+                                288
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        273,
+                                        505,
+                                        288
+                                    ],
+                                    "score": 1.0,
+                                    "content": "neural networks. In Workshop on Challenges in Representation Learning, ICML, volume 3, pp.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                284,
+                                152,
+                                297
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        284,
+                                        152,
+                                        297
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2, 2013.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        303,
+                        503,
+                        327
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                302,
+                                505,
+                                318
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        302,
+                                        505,
+                                        318
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Yin Li, Manohar Paluri, James M Rehg, and Piotr Dollar. Unsupervised learning of edges. In ´ CVPR,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                314,
+                                143,
+                                328
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        314,
+                                        143,
+                                        328
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 15.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        334,
+                        503,
+                        347
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                334,
+                                505,
+                                348
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        334,
+                                        505,
+                                        348
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Ellen M Markman. Categorization and naming in children: Problems of induction. mit Press, 1989.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        352,
+                        505,
+                        398
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                353,
+                                505,
+                                367
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        353,
+                                        505,
+                                        367
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg S Corrado, and Jeff Dean. Distributed representa-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                363,
+                                505,
+                                379
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        363,
+                                        505,
+                                        379
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tions of words and phrases and their compositionality. In C. J. C. Burges, L. Bottou, M. Welling,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                375,
+                                505,
+                                389
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        375,
+                                        505,
+                                        389
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Z. Ghahramani, and K. Q. Weinberger (eds.), Advances in Neural Information Processing Systems",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                386,
+                                319,
+                                399
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        386,
+                                        319,
+                                        399
+                                    ],
+                                    "score": 1.0,
+                                    "content": "26, pp. 3111–3119. Curran Associates, Inc., 2013.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 19.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        405,
+                        504,
+                        428
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                403,
+                                506,
+                                420
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        403,
+                                        506,
+                                        420
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Ishan Misra, C Lawrence Zitnick, and Martial Hebert. Shuffle and learn: unsupervised learning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                417,
+                                319,
+                                428
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        417,
+                                        319,
+                                        428
+                                    ],
+                                    "score": 1.0,
+                                    "content": "using temporal order verification. In ECCV, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 22.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        435,
+                        505,
+                        469
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                434,
+                                506,
+                                449
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        434,
+                                        506,
+                                        449
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Takeru Miyato, Shin-ichi Maeda, Shin Ishii, and Masanori Koyama. Virtual adversarial training: a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                446,
+                                505,
+                                460
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        446,
+                                        505,
+                                        460
+                                    ],
+                                    "score": 1.0,
+                                    "content": "regularization method for supervised and semi-supervised learning. IEEE transactions on pattern",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                457,
+                                281,
+                                470
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        457,
+                                        281,
+                                        470
+                                    ],
+                                    "score": 1.0,
+                                    "content": "analysis and machine intelligence, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        476,
+                        503,
+                        500
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                476,
+                                505,
+                                489
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        476,
+                                        505,
+                                        489
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Andriy Mnih and Koray Kavukcuoglu. Learning word embeddings efficiently with noise-contrastive",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                487,
+                                474,
+                                501
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        487,
+                                        474,
+                                        501
+                                    ],
+                                    "score": 1.0,
+                                    "content": "estimation. In Advances in neural information processing systems, pp. 2265–2273, 2013.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 27.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        506,
+                        503,
+                        530
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                505,
+                                505,
+                                520
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        505,
+                                        505,
+                                        520
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Mehdi Noroozi and Paolo Favaro. Unsupervised learning of visual representations by solving jigsaw",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                518,
+                                447,
+                                531
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        518,
+                                        447,
+                                        531
+                                    ],
+                                    "score": 1.0,
+                                    "content": "puzzles. In European Conference on Computer Vision, pp. 69–84. Springer, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 29.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        109,
+                        536,
+                        504,
+                        570
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                536,
+                                505,
+                                550
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        536,
+                                        505,
+                                        550
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Stephanie E Palmer, Olivier Marre, Michael J Berry, and William Bialek. Predictive information",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                548,
+                                505,
+                                560
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        548,
+                                        505,
+                                        560
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in a sensory population. Proceedings of the National Academy of Sciences, 112(22):6908–6913,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                558,
+                                143,
+                                571
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        558,
+                                        143,
+                                        571
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 32
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        577,
+                        504,
+                        601
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                578,
+                                504,
+                                591
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        578,
+                                        504,
+                                        591
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Deepak Pathak, Ross Girshick, Piotr Dollar, Trevor Darrell, and Bharath Hariharan. Learning fea-´",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                589,
+                                410,
+                                601
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        589,
+                                        410,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tures by watching objects move. arXiv preprint arXiv:1612.06370, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        }
+                    ],
+                    "index": 34.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        608,
+                        505,
+                        631
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                607,
+                                506,
+                                622
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        607,
+                                        506,
+                                        622
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lerrel Pinto and Abhinav Gupta. Supersizing self-supervision: Learning to grasp from 50k tries and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                619,
+                                248,
+                                631
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        619,
+                                        248,
+                                        631
+                                    ],
+                                    "score": 1.0,
+                                    "content": "700 robot hours. In ICRA, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 36.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        638,
+                        504,
+                        661
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                636,
+                                505,
+                                652
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        636,
+                                        505,
+                                        652
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lerrel Pinto, James Davidson, and Abhinav Gupta. Supervision via competition: Robot adversaries",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                649,
+                                354,
+                                662
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        649,
+                                        354,
+                                        662
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for learning tasks. arXiv preprint arXiv:1610.01685, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 38.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        668,
+                        504,
+                        691
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                668,
+                                504,
+                                681
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        668,
+                                        504,
+                                        681
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Rajesh PN Rao and Dana H Ballard. Predictive coding in the visual cortex: a functional interpreta-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                680,
+                                466,
+                                691
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        680,
+                                        466,
+                                        691
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tion of some extra-classical receptive-field effects. Nature neuroscience, 2(1):79, 1999.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        }
+                    ],
+                    "index": 40.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        698,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                698,
+                                506,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        698,
+                                        506,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Shaoqing Ren, Kaiming He, Ross Girshick, and Jian Sun. Faster r-cnn: Towards real-time object",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                709,
+                                505,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        709,
+                                        505,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "detection with region proposal networks. In Advances in neural information processing systems,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                720,
+                                187,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        720,
+                                        187,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pp. 91–99, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        }
+                    ],
+                    "index": 43
+                }
+            ],
+            "page_idx": 11,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        308,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                26,
+                                308,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        26,
+                                        308,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Under review as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        311,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                313,
+                                764
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        313,
+                                        764
+                                    ],
+                                    "score": 1.0,
+                                    "content": "12",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        82,
+                        504,
+                        116
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                82,
+                                505,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        82,
+                                        505,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Durk P Kingma, Shakir Mohamed, Danilo Jimenez Rezende, and Max Welling. Semi-supervised",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                92,
+                                505,
+                                108
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        92,
+                                        505,
+                                        108
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning with deep generative models. In Advances in neural information processing systems, pp.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                105,
+                                191,
+                                115
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        105,
+                                        191,
+                                        115
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3581–3589, 2014.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1,
+                    "bbox_fs": [
+                        106,
+                        82,
+                        505,
+                        115
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        123,
+                        504,
+                        146
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                123,
+                                505,
+                                136
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        123,
+                                        505,
+                                        136
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Alexander Kolesnikov, Xiaohua Zhai, and Lucas Beyer. Revisiting self-supervised visual representa-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                134,
+                                505,
+                                147
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        134,
+                                        505,
+                                        147
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tion learning. CoRR, abs/1901.09005, 2019. URL http://arxiv.org/abs/1901.09005.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 3.5,
+                    "bbox_fs": [
+                        106,
+                        123,
+                        505,
+                        147
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        153,
+                        504,
+                        176
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                151,
+                                506,
+                                168
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        151,
+                                        506,
+                                        168
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Brenden M Lake, Ruslan Salakhutdinov, and Joshua B Tenenbaum. Human-level concept learning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                165,
+                                437,
+                                177
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        165,
+                                        437,
+                                        177
+                                    ],
+                                    "score": 1.0,
+                                    "content": "through probabilistic program induction. Science, 350(6266):1332–1338, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 5.5,
+                    "bbox_fs": [
+                        105,
+                        151,
+                        506,
+                        177
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        183,
+                        504,
+                        207
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                182,
+                                505,
+                                197
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        182,
+                                        505,
+                                        197
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Barbara Landau, Linda B Smith, and Susan S Jones. The importance of shape in early lexical",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                195,
+                                335,
+                                207
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        195,
+                                        335,
+                                        207
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning. Cognitive development, 3(3):299–321, 1988.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 7.5,
+                    "bbox_fs": [
+                        105,
+                        182,
+                        505,
+                        207
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        213,
+                        502,
+                        237
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                213,
+                                504,
+                                226
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        213,
+                                        504,
+                                        226
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Gustav Larsson, Michael Maire, and Gregory Shakhnarovich. Colorization as a proxy task for visual",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                225,
+                                309,
+                                237
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        225,
+                                        309,
+                                        237
+                                    ],
+                                    "score": 1.0,
+                                    "content": "understanding. In CVPR, pp. 6874–6883, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 9.5,
+                    "bbox_fs": [
+                        106,
+                        213,
+                        504,
+                        237
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        243,
+                        496,
+                        256
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                242,
+                                498,
+                                258
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        242,
+                                        498,
+                                        258
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Yann LeCun, Yoshua Bengio, and Geoffrey Hinton. Deep learning. nature, 521(7553):436, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 11,
+                    "bbox_fs": [
+                        106,
+                        242,
+                        498,
+                        258
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        263,
+                        505,
+                        297
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                262,
+                                505,
+                                277
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        262,
+                                        505,
+                                        277
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Dong-Hyun Lee. Pseudo-label: The simple and efficient semi-supervised learning method for deep",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                273,
+                                505,
+                                288
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        273,
+                                        505,
+                                        288
+                                    ],
+                                    "score": 1.0,
+                                    "content": "neural networks. In Workshop on Challenges in Representation Learning, ICML, volume 3, pp.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                284,
+                                152,
+                                297
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        284,
+                                        152,
+                                        297
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2, 2013.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 13,
+                    "bbox_fs": [
+                        105,
+                        262,
+                        505,
+                        297
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        303,
+                        503,
+                        327
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                302,
+                                505,
+                                318
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        302,
+                                        505,
+                                        318
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Yin Li, Manohar Paluri, James M Rehg, and Piotr Dollar. Unsupervised learning of edges. In ´ CVPR,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                314,
+                                143,
+                                328
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        314,
+                                        143,
+                                        328
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 15.5,
+                    "bbox_fs": [
+                        105,
+                        302,
+                        505,
+                        328
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        334,
+                        503,
+                        347
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                334,
+                                505,
+                                348
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        334,
+                                        505,
+                                        348
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Ellen M Markman. Categorization and naming in children: Problems of induction. mit Press, 1989.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 17,
+                    "bbox_fs": [
+                        106,
+                        334,
+                        505,
+                        348
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        352,
+                        505,
+                        398
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                353,
+                                505,
+                                367
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        353,
+                                        505,
+                                        367
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg S Corrado, and Jeff Dean. Distributed representa-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                363,
+                                505,
+                                379
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        363,
+                                        505,
+                                        379
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tions of words and phrases and their compositionality. In C. J. C. Burges, L. Bottou, M. Welling,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                375,
+                                505,
+                                389
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        375,
+                                        505,
+                                        389
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Z. Ghahramani, and K. Q. Weinberger (eds.), Advances in Neural Information Processing Systems",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                386,
+                                319,
+                                399
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        386,
+                                        319,
+                                        399
+                                    ],
+                                    "score": 1.0,
+                                    "content": "26, pp. 3111–3119. Curran Associates, Inc., 2013.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 19.5,
+                    "bbox_fs": [
+                        105,
+                        353,
+                        505,
+                        399
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        405,
+                        504,
+                        428
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                403,
+                                506,
+                                420
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        403,
+                                        506,
+                                        420
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Ishan Misra, C Lawrence Zitnick, and Martial Hebert. Shuffle and learn: unsupervised learning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                417,
+                                319,
+                                428
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        417,
+                                        319,
+                                        428
+                                    ],
+                                    "score": 1.0,
+                                    "content": "using temporal order verification. In ECCV, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 22.5,
+                    "bbox_fs": [
+                        104,
+                        403,
+                        506,
+                        428
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        435,
+                        505,
+                        469
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                434,
+                                506,
+                                449
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        434,
+                                        506,
+                                        449
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Takeru Miyato, Shin-ichi Maeda, Shin Ishii, and Masanori Koyama. Virtual adversarial training: a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                446,
+                                505,
+                                460
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        446,
+                                        505,
+                                        460
+                                    ],
+                                    "score": 1.0,
+                                    "content": "regularization method for supervised and semi-supervised learning. IEEE transactions on pattern",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                457,
+                                281,
+                                470
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        457,
+                                        281,
+                                        470
+                                    ],
+                                    "score": 1.0,
+                                    "content": "analysis and machine intelligence, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 25,
+                    "bbox_fs": [
+                        105,
+                        434,
+                        506,
+                        470
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        476,
+                        503,
+                        500
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                476,
+                                505,
+                                489
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        476,
+                                        505,
+                                        489
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Andriy Mnih and Koray Kavukcuoglu. Learning word embeddings efficiently with noise-contrastive",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                487,
+                                474,
+                                501
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        487,
+                                        474,
+                                        501
+                                    ],
+                                    "score": 1.0,
+                                    "content": "estimation. In Advances in neural information processing systems, pp. 2265–2273, 2013.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 27.5,
+                    "bbox_fs": [
+                        106,
+                        476,
+                        505,
+                        501
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        506,
+                        503,
+                        530
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                505,
+                                505,
+                                520
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        505,
+                                        505,
+                                        520
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Mehdi Noroozi and Paolo Favaro. Unsupervised learning of visual representations by solving jigsaw",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                518,
+                                447,
+                                531
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        518,
+                                        447,
+                                        531
+                                    ],
+                                    "score": 1.0,
+                                    "content": "puzzles. In European Conference on Computer Vision, pp. 69–84. Springer, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 29.5,
+                    "bbox_fs": [
+                        105,
+                        505,
+                        505,
+                        531
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        109,
+                        536,
+                        504,
+                        570
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                536,
+                                505,
+                                550
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        536,
+                                        505,
+                                        550
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Stephanie E Palmer, Olivier Marre, Michael J Berry, and William Bialek. Predictive information",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                548,
+                                505,
+                                560
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        548,
+                                        505,
+                                        560
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in a sensory population. Proceedings of the National Academy of Sciences, 112(22):6908–6913,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                558,
+                                143,
+                                571
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        558,
+                                        143,
+                                        571
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 32,
+                    "bbox_fs": [
+                        106,
+                        536,
+                        505,
+                        571
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        577,
+                        504,
+                        601
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                578,
+                                504,
+                                591
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        578,
+                                        504,
+                                        591
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Deepak Pathak, Ross Girshick, Piotr Dollar, Trevor Darrell, and Bharath Hariharan. Learning fea-´",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                589,
+                                410,
+                                601
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        589,
+                                        410,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tures by watching objects move. arXiv preprint arXiv:1612.06370, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        }
+                    ],
+                    "index": 34.5,
+                    "bbox_fs": [
+                        106,
+                        578,
+                        504,
+                        601
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        608,
+                        505,
+                        631
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                607,
+                                506,
+                                622
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        607,
+                                        506,
+                                        622
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lerrel Pinto and Abhinav Gupta. Supersizing self-supervision: Learning to grasp from 50k tries and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                619,
+                                248,
+                                631
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        619,
+                                        248,
+                                        631
+                                    ],
+                                    "score": 1.0,
+                                    "content": "700 robot hours. In ICRA, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 36.5,
+                    "bbox_fs": [
+                        104,
+                        607,
+                        506,
+                        631
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        638,
+                        504,
+                        661
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                636,
+                                505,
+                                652
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        636,
+                                        505,
+                                        652
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lerrel Pinto, James Davidson, and Abhinav Gupta. Supervision via competition: Robot adversaries",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                649,
+                                354,
+                                662
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        649,
+                                        354,
+                                        662
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for learning tasks. arXiv preprint arXiv:1610.01685, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 38.5,
+                    "bbox_fs": [
+                        105,
+                        636,
+                        505,
+                        662
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        668,
+                        504,
+                        691
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                668,
+                                504,
+                                681
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        668,
+                                        504,
+                                        681
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Rajesh PN Rao and Dana H Ballard. Predictive coding in the visual cortex: a functional interpreta-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                680,
+                                466,
+                                691
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        680,
+                                        466,
+                                        691
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tion of some extra-classical receptive-field effects. Nature neuroscience, 2(1):79, 1999.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        }
+                    ],
+                    "index": 40.5,
+                    "bbox_fs": [
+                        106,
+                        668,
+                        504,
+                        691
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        698,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                698,
+                                506,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        698,
+                                        506,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Shaoqing Ren, Kaiming He, Ross Girshick, and Jian Sun. Faster r-cnn: Towards real-time object",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                709,
+                                505,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        709,
+                                        505,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "detection with region proposal networks. In Advances in neural information processing systems,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                720,
+                                187,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        720,
+                                        187,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pp. 91–99, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        }
+                    ],
+                    "index": 43,
+                    "bbox_fs": [
+                        105,
+                        698,
+                        506,
+                        732
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        109,
+                        82,
+                        503,
+                        116
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                81,
+                                505,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        81,
+                                        505,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                94,
+                                505,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        94,
+                                        505,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Huang, Andrej Karpathy, Aditya Khosla, Michael Bernstein, et al. Imagenet large scale visual",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                104,
+                                469,
+                                118
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        104,
+                                        469,
+                                        118
+                                    ],
+                                    "score": 1.0,
+                                    "content": "recognition challenge. International journal of computer vision, 115(3):211–252, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        123,
+                        505,
+                        167
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                122,
+                                505,
+                                137
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        122,
+                                        505,
+                                        137
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Pierre Sermanet, Corey Lynch, Yevgen Chebotar, Jasmine Hsu, Eric Jang, Stefan Schaal, Sergey",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                135,
+                                505,
+                                146
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        135,
+                                        505,
+                                        146
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Levine, and Google Brain. Time-contrastive networks: Self-supervised learning from video. In",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                144,
+                                506,
+                                158
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        144,
+                                        506,
+                                        158
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2018 IEEE International Conference on Robotics and Automation (ICRA), pp. 1134–1141. IEEE,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                155,
+                                143,
+                                169
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        155,
+                                        143,
+                                        169
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 4.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        174,
+                        504,
+                        209
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                174,
+                                505,
+                                188
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        174,
+                                        505,
+                                        188
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                187,
+                                504,
+                                198
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        187,
+                                        504,
+                                        198
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Dropout: a simple way to prevent neural networks from overfitting. The journal of machine",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                197,
+                                291,
+                                209
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        197,
+                                        291,
+                                        209
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning research, 15(1):1929–1958, 2014.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        215,
+                        505,
+                        250
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                214,
+                                505,
+                                229
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        214,
+                                        505,
+                                        229
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Christian Szegedy, Wei Liu, Yangqing Jia, Pierre Sermanet, Scott E. Reed, Dragomir Anguelov,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                227,
+                                504,
+                                239
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        227,
+                                        504,
+                                        239
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Dumitru Erhan, Vincent Vanhoucke, and Andrew Rabinovich. Going deeper with convolutions.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                237,
+                                442,
+                                250
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        237,
+                                        442,
+                                        250
+                                    ],
+                                    "score": 1.0,
+                                    "content": "CoRR, abs/1409.4842, 2014. URL http://arxiv.org/abs/1409.4842.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        256,
+                        504,
+                        290
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                257,
+                                505,
+                                269
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        257,
+                                        505,
+                                        269
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Bart Thomee, David A Shamma, Gerald Friedland, Benjamin Elizalde, Karl Ni, Douglas Poland,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                267,
+                                505,
+                                280
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        267,
+                                        505,
+                                        280
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Damian Borth, and Li-Jia Li. Yfcc100m: The new data in multimedia research. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                278,
+                                220,
+                                290
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        278,
+                                        220,
+                                        290
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1503.01817, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        297,
+                        504,
+                        320
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                296,
+                                505,
+                                311
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        296,
+                                        505,
+                                        311
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Yonglong Tian, Dilip Krishnan, and Phillip Isola. Contrastive multiview coding. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                309,
+                                219,
+                                320
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        309,
+                                        219,
+                                        320
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1906.05849, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 16.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        327,
+                        504,
+                        350
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                327,
+                                504,
+                                340
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        327,
+                                        504,
+                                        340
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Aaron van den Oord, Yazhe Li, and Oriol Vinyals. Representation learning with contrastive predic-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                338,
+                                329,
+                                351
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        338,
+                                        329,
+                                        351
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tive coding. arXiv preprint arXiv:1807.03748, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 18.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        357,
+                        504,
+                        380
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                356,
+                                505,
+                                370
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        356,
+                                        505,
+                                        370
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Xiaolong Wang and Abhinav Gupta. Unsupervised learning of visual representations using videos.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                368,
+                                180,
+                                380
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        368,
+                                        180,
+                                        380
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In ICCV, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 20.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        387,
+                        504,
+                        421
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                386,
+                                505,
+                                401
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        386,
+                                        505,
+                                        401
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Zhirong Wu, Yuanjun Xiong, Stella X Yu, and Dahua Lin. Unsupervised feature learning via non-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                398,
+                                506,
+                                411
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        398,
+                                        506,
+                                        411
+                                    ],
+                                    "score": 1.0,
+                                    "content": "parametric instance discrimination. In Proceedings of the IEEE Conference on Computer Vision",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                410,
+                                308,
+                                421
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        410,
+                                        308,
+                                        421
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and Pattern Recognition, pp. 3733–3742, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 23
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        428,
+                        504,
+                        451
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                428,
+                                505,
+                                441
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        428,
+                                        505,
+                                        441
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Qizhe Xie, Zihang Dai, Eduard Hovy, Minh-Thang Luong, and Quoc V. Le. Unsupervised Data",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                439,
+                                376,
+                                451
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        439,
+                                        376,
+                                        451
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Augmentation. arXiv e-prints, art. arXiv:1904.12848, Apr 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 25.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        457,
+                        503,
+                        481
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                457,
+                                504,
+                                471
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        457,
+                                        504,
+                                        471
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Amir R Zamir, Tilman Wekel, Pulkit Agrawal, Colin Wei, Jitendra Malik, and Silvio Savarese.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                469,
+                                430,
+                                481
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        469,
+                                        430,
+                                        481
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Generic 3D representation via pose estimation and matching. In ECCV, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 27.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        487,
+                        503,
+                        511
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                486,
+                                505,
+                                501
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        486,
+                                        391,
+                                        501
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Xiaohua Zhai, Avital Oliver, Alexander Kolesnikov, and Lucas Beyer.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        391,
+                                        487,
+                                        411,
+                                        498
+                                    ],
+                                    "score": 0.87,
+                                    "content": "S ^ { 4 } L",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        411,
+                                        486,
+                                        505,
+                                        501
+                                    ],
+                                    "score": 1.0,
+                                    "content": ": Self-supervised semi-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                499,
+                                362,
+                                511
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        499,
+                                        362,
+                                        511
+                                    ],
+                                    "score": 1.0,
+                                    "content": "supervised learning. arXiv preprint arXiv:1905.03670, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 29.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        517,
+                        503,
+                        541
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                516,
+                                505,
+                                532
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        516,
+                                        505,
+                                        532
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Richard Zhang, Phillip Isola, and Alexei A Efros. Colorful image colorization. In European confer-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                529,
+                                337,
+                                541
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        529,
+                                        337,
+                                        541
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ence on computer vision, pp. 649–666. Springer, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 31.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        547,
+                        503,
+                        571
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                547,
+                                504,
+                                560
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        547,
+                                        504,
+                                        560
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Xiaojin Zhu and Zoubin Ghahramani. Learning from labeled and unlabeled data with label propa-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                559,
+                                457,
+                                572
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        559,
+                                        457,
+                                        572
+                                    ],
+                                    "score": 1.0,
+                                    "content": "gation. In Technical Report CMU-CALD-02-107, Carnegie Mellon University, 2002.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        }
+                    ],
+                    "index": 33.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        577,
+                        504,
+                        601
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                575,
+                                505,
+                                592
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        575,
+                                        505,
+                                        592
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Chengxu Zhuang, Alex Lin Zhai, and Daniel Yamins. Local aggregation for unsupervised learning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                588,
+                                370,
+                                600
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        588,
+                                        370,
+                                        600
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of visual embeddings. arXiv preprint arXiv:1903.12355, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 35.5
+                }
+            ],
+            "page_idx": 12,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        308,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                26,
+                                308,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        26,
+                                        308,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Under review as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        311,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                313,
+                                764
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        313,
+                                        764
+                                    ],
+                                    "score": 1.0,
+                                    "content": "13",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        109,
+                        82,
+                        503,
+                        116
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                81,
+                                505,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        81,
+                                        505,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                94,
+                                505,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        94,
+                                        505,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Huang, Andrej Karpathy, Aditya Khosla, Michael Bernstein, et al. Imagenet large scale visual",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                104,
+                                469,
+                                118
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        104,
+                                        469,
+                                        118
+                                    ],
+                                    "score": 1.0,
+                                    "content": "recognition challenge. International journal of computer vision, 115(3):211–252, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1,
+                    "bbox_fs": [
+                        106,
+                        81,
+                        505,
+                        118
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        123,
+                        505,
+                        167
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                122,
+                                505,
+                                137
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        122,
+                                        505,
+                                        137
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Pierre Sermanet, Corey Lynch, Yevgen Chebotar, Jasmine Hsu, Eric Jang, Stefan Schaal, Sergey",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                135,
+                                505,
+                                146
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        135,
+                                        505,
+                                        146
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Levine, and Google Brain. Time-contrastive networks: Self-supervised learning from video. In",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                144,
+                                506,
+                                158
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        144,
+                                        506,
+                                        158
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2018 IEEE International Conference on Robotics and Automation (ICRA), pp. 1134–1141. IEEE,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                155,
+                                143,
+                                169
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        155,
+                                        143,
+                                        169
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 4.5,
+                    "bbox_fs": [
+                        105,
+                        122,
+                        506,
+                        169
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        174,
+                        504,
+                        209
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                174,
+                                505,
+                                188
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        174,
+                                        505,
+                                        188
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                187,
+                                504,
+                                198
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        187,
+                                        504,
+                                        198
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Dropout: a simple way to prevent neural networks from overfitting. The journal of machine",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                197,
+                                291,
+                                209
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        197,
+                                        291,
+                                        209
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning research, 15(1):1929–1958, 2014.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 8,
+                    "bbox_fs": [
+                        106,
+                        174,
+                        505,
+                        209
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        215,
+                        505,
+                        250
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                214,
+                                505,
+                                229
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        214,
+                                        505,
+                                        229
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Christian Szegedy, Wei Liu, Yangqing Jia, Pierre Sermanet, Scott E. Reed, Dragomir Anguelov,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                227,
+                                504,
+                                239
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        227,
+                                        504,
+                                        239
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Dumitru Erhan, Vincent Vanhoucke, and Andrew Rabinovich. Going deeper with convolutions.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                237,
+                                442,
+                                250
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        237,
+                                        442,
+                                        250
+                                    ],
+                                    "score": 1.0,
+                                    "content": "CoRR, abs/1409.4842, 2014. URL http://arxiv.org/abs/1409.4842.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "index": 11,
+                    "bbox_fs": [
+                        106,
+                        214,
+                        505,
+                        250
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        256,
+                        504,
+                        290
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                257,
+                                505,
+                                269
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        257,
+                                        505,
+                                        269
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Bart Thomee, David A Shamma, Gerald Friedland, Benjamin Elizalde, Karl Ni, Douglas Poland,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                267,
+                                505,
+                                280
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        267,
+                                        505,
+                                        280
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Damian Borth, and Li-Jia Li. Yfcc100m: The new data in multimedia research. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                278,
+                                220,
+                                290
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        278,
+                                        220,
+                                        290
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1503.01817, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 14,
+                    "bbox_fs": [
+                        106,
+                        257,
+                        505,
+                        290
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        297,
+                        504,
+                        320
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                296,
+                                505,
+                                311
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        296,
+                                        505,
+                                        311
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Yonglong Tian, Dilip Krishnan, and Phillip Isola. Contrastive multiview coding. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                309,
+                                219,
+                                320
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        309,
+                                        219,
+                                        320
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1906.05849, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 16.5,
+                    "bbox_fs": [
+                        105,
+                        296,
+                        505,
+                        320
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        327,
+                        504,
+                        350
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                327,
+                                504,
+                                340
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        327,
+                                        504,
+                                        340
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Aaron van den Oord, Yazhe Li, and Oriol Vinyals. Representation learning with contrastive predic-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                338,
+                                329,
+                                351
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        338,
+                                        329,
+                                        351
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tive coding. arXiv preprint arXiv:1807.03748, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 18.5,
+                    "bbox_fs": [
+                        106,
+                        327,
+                        504,
+                        351
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        357,
+                        504,
+                        380
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                356,
+                                505,
+                                370
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        356,
+                                        505,
+                                        370
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Xiaolong Wang and Abhinav Gupta. Unsupervised learning of visual representations using videos.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                368,
+                                180,
+                                380
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        368,
+                                        180,
+                                        380
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In ICCV, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 20.5,
+                    "bbox_fs": [
+                        105,
+                        356,
+                        505,
+                        380
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        387,
+                        504,
+                        421
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                386,
+                                505,
+                                401
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        386,
+                                        505,
+                                        401
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Zhirong Wu, Yuanjun Xiong, Stella X Yu, and Dahua Lin. Unsupervised feature learning via non-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                398,
+                                506,
+                                411
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        398,
+                                        506,
+                                        411
+                                    ],
+                                    "score": 1.0,
+                                    "content": "parametric instance discrimination. In Proceedings of the IEEE Conference on Computer Vision",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                410,
+                                308,
+                                421
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        410,
+                                        308,
+                                        421
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and Pattern Recognition, pp. 3733–3742, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 23,
+                    "bbox_fs": [
+                        105,
+                        386,
+                        506,
+                        421
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        428,
+                        504,
+                        451
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                428,
+                                505,
+                                441
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        428,
+                                        505,
+                                        441
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Qizhe Xie, Zihang Dai, Eduard Hovy, Minh-Thang Luong, and Quoc V. Le. Unsupervised Data",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                439,
+                                376,
+                                451
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        439,
+                                        376,
+                                        451
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Augmentation. arXiv e-prints, art. arXiv:1904.12848, Apr 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 25.5,
+                    "bbox_fs": [
+                        107,
+                        428,
+                        505,
+                        451
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        457,
+                        503,
+                        481
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                457,
+                                504,
+                                471
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        457,
+                                        504,
+                                        471
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Amir R Zamir, Tilman Wekel, Pulkit Agrawal, Colin Wei, Jitendra Malik, and Silvio Savarese.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                469,
+                                430,
+                                481
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        469,
+                                        430,
+                                        481
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Generic 3D representation via pose estimation and matching. In ECCV, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 27.5,
+                    "bbox_fs": [
+                        105,
+                        457,
+                        504,
+                        481
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        487,
+                        503,
+                        511
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                486,
+                                505,
+                                501
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        486,
+                                        391,
+                                        501
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Xiaohua Zhai, Avital Oliver, Alexander Kolesnikov, and Lucas Beyer.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        391,
+                                        487,
+                                        411,
+                                        498
+                                    ],
+                                    "score": 0.87,
+                                    "content": "S ^ { 4 } L",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        411,
+                                        486,
+                                        505,
+                                        501
+                                    ],
+                                    "score": 1.0,
+                                    "content": ": Self-supervised semi-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                499,
+                                362,
+                                511
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        499,
+                                        362,
+                                        511
+                                    ],
+                                    "score": 1.0,
+                                    "content": "supervised learning. arXiv preprint arXiv:1905.03670, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 29.5,
+                    "bbox_fs": [
+                        105,
+                        486,
+                        505,
+                        511
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        517,
+                        503,
+                        541
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                516,
+                                505,
+                                532
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        516,
+                                        505,
+                                        532
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Richard Zhang, Phillip Isola, and Alexei A Efros. Colorful image colorization. In European confer-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                529,
+                                337,
+                                541
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        529,
+                                        337,
+                                        541
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ence on computer vision, pp. 649–666. Springer, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 31.5,
+                    "bbox_fs": [
+                        105,
+                        516,
+                        505,
+                        541
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        547,
+                        503,
+                        571
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                547,
+                                504,
+                                560
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        547,
+                                        504,
+                                        560
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Xiaojin Zhu and Zoubin Ghahramani. Learning from labeled and unlabeled data with label propa-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                559,
+                                457,
+                                572
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        559,
+                                        457,
+                                        572
+                                    ],
+                                    "score": 1.0,
+                                    "content": "gation. In Technical Report CMU-CALD-02-107, Carnegie Mellon University, 2002.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        }
+                    ],
+                    "index": 33.5,
+                    "bbox_fs": [
+                        106,
+                        547,
+                        504,
+                        572
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        577,
+                        504,
+                        601
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                575,
+                                505,
+                                592
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        575,
+                                        505,
+                                        592
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Chengxu Zhuang, Alex Lin Zhai, and Daniel Yamins. Local aggregation for unsupervised learning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                588,
+                                370,
+                                600
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        588,
+                                        370,
+                                        600
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of visual embeddings. arXiv preprint arXiv:1903.12355, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 35.5,
+                    "bbox_fs": [
+                        106,
+                        575,
+                        505,
+                        600
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        82,
+                        183,
+                        93
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                79,
+                                185,
+                                97
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        79,
+                                        185,
+                                        97
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A APPENDIX",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        106,
+                        231,
+                        118
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                106,
+                                231,
+                                119
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        106,
+                                        231,
+                                        119
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.1 ADDITIONAL RESULTS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        113,
+                        153,
+                        499,
+                        212
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                174,
+                                138,
+                                435,
+                                150
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        174,
+                                        136,
+                                        437,
+                                        153
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                174,
+                                                136,
+                                                437,
+                                                153
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 4: Data efficient classification results with Top-1 accuracy.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 2
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                113,
+                                153,
+                                499,
+                                212
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        153,
+                                        499,
+                                        212
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                113,
+                                                153,
+                                                499,
+                                                212
+                                            ],
+                                            "score": 0.947,
+                                            "html": "<table><tr><td>Labeled data Method</td><td>1%</td><td>2%</td><td>5%</td><td>10% Top-1 accuracy</td><td>20%</td><td>50%</td><td>100%</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Supervised trained on pixels</td><td>23.1</td><td>34.8</td><td>50.2</td><td>60.0</td><td>67.6</td><td>74.4</td><td>78.0</td></tr><tr><td>ReseNet trained on CPC v2 (fine-tuned)</td><td>46.3</td><td>54.7</td><td>64.1</td><td>69.7</td><td>73.0</td><td>77.3</td><td>80.6</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "cd16abc0799fc70d1a375836e8cc04ff4651be0d7ba68507f20886a5866fd0b3.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 4,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        153,
+                                        499,
+                                        172.66666666666666
+                                    ],
+                                    "spans": [],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        113,
+                                        172.66666666666666,
+                                        499,
+                                        192.33333333333331
+                                    ],
+                                    "spans": [],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        113,
+                                        192.33333333333331,
+                                        499,
+                                        211.99999999999997
+                                    ],
+                                    "spans": [],
+                                    "index": 5
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3.0
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        113,
+                        255,
+                        499,
+                        315
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                144,
+                                241,
+                                466,
+                                254
+                            ],
+                            "group_id": 1,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        239,
+                                        467,
+                                        255
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                142,
+                                                239,
+                                                467,
+                                                255
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 5: Data efficient classification results with Top-5 accuracy (data in Fig. 1).",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 6
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                113,
+                                255,
+                                499,
+                                315
+                            ],
+                            "group_id": 1,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        255,
+                                        499,
+                                        315
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                113,
+                                                255,
+                                                499,
+                                                315
+                                            ],
+                                            "score": 0.956,
+                                            "html": "<table><tr><td>Labeled data Method</td><td>1%</td><td>2%</td><td>5%</td><td>10% Top-5 accuracy</td><td>20%</td><td>50%</td><td>100%</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Supervised trained on pixels</td><td>44.1</td><td>59.9</td><td>75.2</td><td>82.1</td><td>87.9</td><td>91.8</td><td>93.8</td></tr><tr><td>ReseNet trained on CPC v2 (fine-tuned)</td><td>72.9</td><td>79.6</td><td>86.1</td><td>89.5</td><td>91.4</td><td>93.6</td><td>95.2</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "ef57c53b71083a6069724c7b7ef7e00273991c3de17438cac7824c7e459eff57.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 8,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        255,
+                                        499,
+                                        275.0
+                                    ],
+                                    "spans": [],
+                                    "index": 7
+                                },
+                                {
+                                    "bbox": [
+                                        113,
+                                        275.0,
+                                        499,
+                                        295.0
+                                    ],
+                                    "spans": [],
+                                    "index": 8
+                                },
+                                {
+                                    "bbox": [
+                                        113,
+                                        295.0,
+                                        499,
+                                        315.0
+                                    ],
+                                    "spans": [],
+                                    "index": 9
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7.0
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        340,
+                        256,
+                        352
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                340,
+                                257,
+                                353
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        340,
+                                        257,
+                                        353
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.2 INFONCE IMPLEMENTATION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        361,
+                        505,
+                        406
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                361,
+                                505,
+                                373
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        361,
+                                        505,
+                                        373
+                                    ],
+                                    "score": 1.0,
+                                    "content": "For completeness, we provide pseudo-code for the main calculations involved in the InfoNCE ob-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                372,
+                                506,
+                                384
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        372,
+                                        506,
+                                        384
+                                    ],
+                                    "score": 1.0,
+                                    "content": "jective, loosely modeled after Tensorflow operations. We suppose we have just calculated a set of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                383,
+                                505,
+                                396
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        383,
+                                        136,
+                                        396
+                                    ],
+                                    "score": 1.0,
+                                    "content": "latents",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        136,
+                                        383,
+                                        200,
+                                        396
+                                    ],
+                                    "score": 0.94,
+                                    "content": "z _ { i , j } = f _ { \\theta } ( \\pmb { x } _ { i , j } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        201,
+                                        383,
+                                        217,
+                                        396
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        218,
+                                        383,
+                                        287,
+                                        395
+                                    ],
+                                    "score": 0.92,
+                                    "content": "i , j \\in \\{ 1 , . . . , 7 \\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        288,
+                                        383,
+                                        505,
+                                        396
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", each one being e.g. a 4096-dimensional vector. As-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                394,
+                                505,
+                                406
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        394,
+                                        231,
+                                        406
+                                    ],
+                                    "score": 1.0,
+                                    "content": "suming we do so for a batch of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        231,
+                                        395,
+                                        240,
+                                        404
+                                    ],
+                                    "score": 0.8,
+                                    "content": "B",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        240,
+                                        394,
+                                        271,
+                                        406
+                                    ],
+                                    "score": 1.0,
+                                    "content": "images",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        272,
+                                        395,
+                                        289,
+                                        406
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\{ { \\pmb x } \\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        394,
+                                        430,
+                                        406
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the set of latents is a tensor of size",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        430,
+                                        394,
+                                        501,
+                                        405
+                                    ],
+                                    "score": 0.91,
+                                    "content": "B \\times 7 \\times 7 \\times 4 0 9 6",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        502,
+                                        394,
+                                        505,
+                                        406
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 12.5
+                }
+            ],
+            "page_idx": 13,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        308,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                26,
+                                308,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        26,
+                                        308,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Under review as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        311,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                313,
+                                764
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        313,
+                                        764
+                                    ],
+                                    "score": 1.0,
+                                    "content": "14",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        105,
+                        425,
+                        492,
+                        715
+                    ],
+                    "lines": []
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        82,
+                        183,
+                        93
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                79,
+                                185,
+                                97
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        79,
+                                        185,
+                                        97
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A APPENDIX",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        106,
+                        231,
+                        118
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                106,
+                                231,
+                                119
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        106,
+                                        231,
+                                        119
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.1 ADDITIONAL RESULTS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        113,
+                        153,
+                        499,
+                        212
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                174,
+                                138,
+                                435,
+                                150
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        174,
+                                        136,
+                                        437,
+                                        153
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                174,
+                                                136,
+                                                437,
+                                                153
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 4: Data efficient classification results with Top-1 accuracy.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 2
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                113,
+                                153,
+                                499,
+                                212
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        153,
+                                        499,
+                                        212
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                113,
+                                                153,
+                                                499,
+                                                212
+                                            ],
+                                            "score": 0.947,
+                                            "html": "<table><tr><td>Labeled data Method</td><td>1%</td><td>2%</td><td>5%</td><td>10% Top-1 accuracy</td><td>20%</td><td>50%</td><td>100%</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Supervised trained on pixels</td><td>23.1</td><td>34.8</td><td>50.2</td><td>60.0</td><td>67.6</td><td>74.4</td><td>78.0</td></tr><tr><td>ReseNet trained on CPC v2 (fine-tuned)</td><td>46.3</td><td>54.7</td><td>64.1</td><td>69.7</td><td>73.0</td><td>77.3</td><td>80.6</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "cd16abc0799fc70d1a375836e8cc04ff4651be0d7ba68507f20886a5866fd0b3.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 4,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        153,
+                                        499,
+                                        172.66666666666666
+                                    ],
+                                    "spans": [],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        113,
+                                        172.66666666666666,
+                                        499,
+                                        192.33333333333331
+                                    ],
+                                    "spans": [],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        113,
+                                        192.33333333333331,
+                                        499,
+                                        211.99999999999997
+                                    ],
+                                    "spans": [],
+                                    "index": 5
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3.0
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        113,
+                        255,
+                        499,
+                        315
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                144,
+                                241,
+                                466,
+                                254
+                            ],
+                            "group_id": 1,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        239,
+                                        467,
+                                        255
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                142,
+                                                239,
+                                                467,
+                                                255
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 5: Data efficient classification results with Top-5 accuracy (data in Fig. 1).",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 6
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                113,
+                                255,
+                                499,
+                                315
+                            ],
+                            "group_id": 1,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        255,
+                                        499,
+                                        315
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                113,
+                                                255,
+                                                499,
+                                                315
+                                            ],
+                                            "score": 0.956,
+                                            "html": "<table><tr><td>Labeled data Method</td><td>1%</td><td>2%</td><td>5%</td><td>10% Top-5 accuracy</td><td>20%</td><td>50%</td><td>100%</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Supervised trained on pixels</td><td>44.1</td><td>59.9</td><td>75.2</td><td>82.1</td><td>87.9</td><td>91.8</td><td>93.8</td></tr><tr><td>ReseNet trained on CPC v2 (fine-tuned)</td><td>72.9</td><td>79.6</td><td>86.1</td><td>89.5</td><td>91.4</td><td>93.6</td><td>95.2</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "ef57c53b71083a6069724c7b7ef7e00273991c3de17438cac7824c7e459eff57.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 8,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        255,
+                                        499,
+                                        275.0
+                                    ],
+                                    "spans": [],
+                                    "index": 7
+                                },
+                                {
+                                    "bbox": [
+                                        113,
+                                        275.0,
+                                        499,
+                                        295.0
+                                    ],
+                                    "spans": [],
+                                    "index": 8
+                                },
+                                {
+                                    "bbox": [
+                                        113,
+                                        295.0,
+                                        499,
+                                        315.0
+                                    ],
+                                    "spans": [],
+                                    "index": 9
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7.0
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        340,
+                        256,
+                        352
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                340,
+                                257,
+                                353
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        340,
+                                        257,
+                                        353
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.2 INFONCE IMPLEMENTATION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        361,
+                        505,
+                        406
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                361,
+                                505,
+                                373
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        361,
+                                        505,
+                                        373
+                                    ],
+                                    "score": 1.0,
+                                    "content": "For completeness, we provide pseudo-code for the main calculations involved in the InfoNCE ob-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                372,
+                                506,
+                                384
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        372,
+                                        506,
+                                        384
+                                    ],
+                                    "score": 1.0,
+                                    "content": "jective, loosely modeled after Tensorflow operations. We suppose we have just calculated a set of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                383,
+                                505,
+                                396
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        383,
+                                        136,
+                                        396
+                                    ],
+                                    "score": 1.0,
+                                    "content": "latents",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        136,
+                                        383,
+                                        200,
+                                        396
+                                    ],
+                                    "score": 0.94,
+                                    "content": "z _ { i , j } = f _ { \\theta } ( \\pmb { x } _ { i , j } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        201,
+                                        383,
+                                        217,
+                                        396
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        218,
+                                        383,
+                                        287,
+                                        395
+                                    ],
+                                    "score": 0.92,
+                                    "content": "i , j \\in \\{ 1 , . . . , 7 \\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        288,
+                                        383,
+                                        505,
+                                        396
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", each one being e.g. a 4096-dimensional vector. As-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                394,
+                                505,
+                                406
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        394,
+                                        231,
+                                        406
+                                    ],
+                                    "score": 1.0,
+                                    "content": "suming we do so for a batch of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        231,
+                                        395,
+                                        240,
+                                        404
+                                    ],
+                                    "score": 0.8,
+                                    "content": "B",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        240,
+                                        394,
+                                        271,
+                                        406
+                                    ],
+                                    "score": 1.0,
+                                    "content": "images",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        272,
+                                        395,
+                                        289,
+                                        406
+                                    ],
+                                    "score": 0.9,
+                                    "content": "\\{ { \\pmb x } \\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        394,
+                                        430,
+                                        406
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the set of latents is a tensor of size",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        430,
+                                        394,
+                                        501,
+                                        405
+                                    ],
+                                    "score": 0.91,
+                                    "content": "B \\times 7 \\times 7 \\times 4 0 9 6",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        502,
+                                        394,
+                                        505,
+                                        406
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 12.5,
+                    "bbox_fs": [
+                        105,
+                        361,
+                        506,
+                        406
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        95,
+                        406,
+                        316
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                94,
+                                240,
+                                105
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        94,
+                                        240,
+                                        105
+                                    ],
+                                    "score": 1.0,
+                                    "content": "def pixelCNN(latents):",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                129,
+                                105,
+                                269,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        129,
+                                        105,
+                                        269,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "# latents: [B, H, W, D]",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                131,
+                                117,
+                                217,
+                                127
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        131,
+                                        117,
+                                        158,
+                                        127
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cres",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        159,
+                                        117,
+                                        170,
+                                        126
+                                    ],
+                                    "score": 0.71,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        170,
+                                        117,
+                                        217,
+                                        127
+                                    ],
+                                    "score": 1.0,
+                                    "content": "latents",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                130,
+                                127,
+                                281,
+                                138
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        130,
+                                        127,
+                                        182,
+                                        138
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cres_dim",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        182,
+                                        128,
+                                        194,
+                                        137
+                                    ],
+                                    "score": 0.74,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        194,
+                                        127,
+                                        281,
+                                        138
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cres.shape[-1]",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                131,
+                                137,
+                                240,
+                                150
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        131,
+                                        138,
+                                        152,
+                                        149
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        164,
+                                        137,
+                                        240,
+                                        150
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in range(5):",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                149,
+                                329,
+                                160
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        149,
+                                        152,
+                                        160
+                                    ],
+                                    "score": 1.0,
+                                    "content": "c",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        152,
+                                        150,
+                                        164,
+                                        159
+                                    ],
+                                    "score": 0.63,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        164,
+                                        149,
+                                        298,
+                                        160
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Conv2D(output_channels",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        298,
+                                        149,
+                                        323,
+                                        159
+                                    ],
+                                    "score": 0.4,
+                                    "content": "= 2 5 6",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        323,
+                                        149,
+                                        329,
+                                        160
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                207,
+                                159,
+                                364,
+                                172
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        207,
+                                        159,
+                                        280,
+                                        172
+                                    ],
+                                    "score": 1.0,
+                                    "content": "kernel_shape",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        280,
+                                        162,
+                                        288,
+                                        169
+                                    ],
+                                    "score": 0.66,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        159,
+                                        364,
+                                        172
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(1, 1))(cres)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                171,
+                                209,
+                                182
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        171,
+                                        209,
+                                        182
+                                    ],
+                                    "score": 1.0,
+                                    "content": "c = ReLU(c)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                182,
+                                329,
+                                193
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        182,
+                                        297,
+                                        193
+                                    ],
+                                    "score": 1.0,
+                                    "content": "c = Conv2D(output_channels",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        298,
+                                        182,
+                                        323,
+                                        192
+                                    ],
+                                    "score": 0.42,
+                                    "content": "= 2 5 6",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        324,
+                                        182,
+                                        329,
+                                        193
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                207,
+                                193,
+                                347,
+                                204
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        207,
+                                        193,
+                                        280,
+                                        204
+                                    ],
+                                    "score": 1.0,
+                                    "content": "kernel_shape",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        280,
+                                        194,
+                                        288,
+                                        202
+                                    ],
+                                    "score": 0.74,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        193,
+                                        347,
+                                        204
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(1, 3))(c)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                203,
+                                406,
+                                216
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        203,
+                                        406,
+                                        216
+                                    ],
+                                    "score": 1.0,
+                                    "content": "c = Pad(c, [[0, 0], [1, 0], [0, 0], [0, 0]])",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                214,
+                                329,
+                                227
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        214,
+                                        297,
+                                        227
+                                    ],
+                                    "score": 1.0,
+                                    "content": "c = Conv2D(output_channels",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        298,
+                                        215,
+                                        323,
+                                        225
+                                    ],
+                                    "score": 0.29,
+                                    "content": "= 2 5 6",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        323,
+                                        214,
+                                        329,
+                                        227
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                207,
+                                225,
+                                329,
+                                237
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        207,
+                                        225,
+                                        280,
+                                        237
+                                    ],
+                                    "score": 1.0,
+                                    "content": "kernel_shape",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        280,
+                                        227,
+                                        288,
+                                        235
+                                    ],
+                                    "score": 0.77,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        225,
+                                        329,
+                                        237
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(2, 1),",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                208,
+                                236,
+                                304,
+                                248
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        208,
+                                        236,
+                                        232,
+                                        248
+                                    ],
+                                    "score": 1.0,
+                                    "content": "type",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        232,
+                                        238,
+                                        244,
+                                        246
+                                    ],
+                                    "score": 0.65,
+                                    "content": "= ^ { \\parallel }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        244,
+                                        236,
+                                        304,
+                                        248
+                                    ],
+                                    "score": 1.0,
+                                    "content": "VALID')(c)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                248,
+                                208,
+                                258
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        248,
+                                        153,
+                                        258
+                                    ],
+                                    "score": 1.0,
+                                    "content": "c",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        249,
+                                        164,
+                                        257
+                                    ],
+                                    "score": 0.31,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        164,
+                                        248,
+                                        208,
+                                        258
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ReLU(c)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                258,
+                                358,
+                                271
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        258,
+                                        153,
+                                        271
+                                    ],
+                                    "score": 1.0,
+                                    "content": "c",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        259,
+                                        164,
+                                        268
+                                    ],
+                                    "score": 0.28,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        164,
+                                        258,
+                                        298,
+                                        271
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Conv2D(output_channels",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        298,
+                                        261,
+                                        305,
+                                        268
+                                    ],
+                                    "score": 0.69,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        258,
+                                        358,
+                                        271
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cres_dim,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                207,
+                                269,
+                                346,
+                                281
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        207,
+                                        269,
+                                        280,
+                                        281
+                                    ],
+                                    "score": 1.0,
+                                    "content": "kernel_shape",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        280,
+                                        271,
+                                        288,
+                                        279
+                                    ],
+                                    "score": 0.7,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        269,
+                                        346,
+                                        281
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(1, 1))(c)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                281,
+                                235,
+                                291
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        281,
+                                        171,
+                                        291
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cres",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        171,
+                                        282,
+                                        182,
+                                        290
+                                    ],
+                                    "score": 0.38,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        182,
+                                        281,
+                                        235,
+                                        291
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cres + c",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                130,
+                                291,
+                                233,
+                                303
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        130,
+                                        291,
+                                        159,
+                                        303
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cres",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        159,
+                                        293,
+                                        169,
+                                        301
+                                    ],
+                                    "score": 0.59,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        169,
+                                        291,
+                                        233,
+                                        303
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ReLU(cres)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                130,
+                                302,
+                                199,
+                                313
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        130,
+                                        302,
+                                        199,
+                                        313
+                                    ],
+                                    "score": 1.0,
+                                    "content": "return cres",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 9.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        334,
+                        240,
+                        345
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                333,
+                                241,
+                                347
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        333,
+                                        241,
+                                        347
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.3 LINEAR CLASSIFICATION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 20
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        133,
+                        351,
+                        506,
+                        491
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                135,
+                                351,
+                                504,
+                                363
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        135,
+                                        351,
+                                        293,
+                                        363
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• Model architecture: Having extracted",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        293,
+                                        351,
+                                        320,
+                                        362
+                                    ],
+                                    "score": 0.64,
+                                    "content": "8 0 \\mathrm { x } 8 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        320,
+                                        351,
+                                        412,
+                                        363
+                                    ],
+                                    "score": 1.0,
+                                    "content": "patches with a stride of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        413,
+                                        351,
+                                        439,
+                                        361
+                                    ],
+                                    "score": 0.33,
+                                    "content": "3 2 \\mathrm { x } 3 2 ",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        439,
+                                        351,
+                                        467,
+                                        363
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from a",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        468,
+                                        351,
+                                        504,
+                                        362
+                                    ],
+                                    "score": 0.68,
+                                    "content": "2 4 0 \\times 2 4 0",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                361,
+                                506,
+                                375
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        361,
+                                        506,
+                                        375
+                                    ],
+                                    "score": 1.0,
+                                    "content": "shaped input image, we end up with a grid of 6x6 features (each of which is obtained",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                373,
+                                506,
+                                386
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        373,
+                                        506,
+                                        386
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from our ResNet-161 architecture). This gives us a [6,6,4096] tensor for the image. We",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                384,
+                                505,
+                                396
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        384,
+                                        505,
+                                        396
+                                    ],
+                                    "score": 1.0,
+                                    "content": "then use a Batch-Normalization layer to normalize the features (without scale parameter)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                394,
+                                506,
+                                408
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        394,
+                                        506,
+                                        408
+                                    ],
+                                    "score": 1.0,
+                                    "content": "followed by a 1x1 convolution mapping each feature in the grid to the 1000 logits for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                406,
+                                505,
+                                419
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        406,
+                                        505,
+                                        419
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ImageNet classification. We then spatially-mean-pool these logits to end up with the final",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                417,
+                                321,
+                                429
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        417,
+                                        321,
+                                        429
+                                    ],
+                                    "score": 1.0,
+                                    "content": "log probabilities for the linear classification.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                134,
+                                430,
+                                506,
+                                446
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        134,
+                                        430,
+                                        420,
+                                        446
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• We use the Inception preprocessing (Szegedy et al., 2014) to extract",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        421,
+                                        432,
+                                        457,
+                                        442
+                                    ],
+                                    "score": 0.62,
+                                    "content": "2 4 0 \\times 2 4 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        457,
+                                        430,
+                                        506,
+                                        446
+                                    ],
+                                    "score": 1.0,
+                                    "content": "crops from",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                443,
+                                505,
+                                456
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        443,
+                                        505,
+                                        456
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the raw image. The image is divided into subcrops as per CPC data-preprocessing used for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                453,
+                                216,
+                                468
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        453,
+                                        216,
+                                        468
+                                    ],
+                                    "score": 1.0,
+                                    "content": "CPC pre-training.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                133,
+                                468,
+                                505,
+                                482
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        133,
+                                        468,
+                                        505,
+                                        482
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• Optimization details: We use Adam Optimizer with a learning rate of 5e-4. We train the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                479,
+                                486,
+                                492
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        479,
+                                        486,
+                                        492
+                                    ],
+                                    "score": 1.0,
+                                    "content": "model on a batch size of 512 images with 32 images per core spread over 16 workers.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 26.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        505,
+                        346,
+                        515
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                504,
+                                347,
+                                516
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        504,
+                                        347,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.4 EFFICIENT CLASSIFICATION: PURELY SUPERVISED",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 33
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        524,
+                        459,
+                        536
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                523,
+                                461,
+                                538
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        523,
+                                        461,
+                                        538
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In order to find the best model within this class, we vary the following hyperparameters:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        }
+                    ],
+                    "index": 34
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        133,
+                        546,
+                        504,
+                        643
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                133,
+                                546,
+                                506,
+                                558
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        133,
+                                        546,
+                                        506,
+                                        558
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• Model architecture: We investigate using ResNet-50, ResNet-101, and ResNet-152 model",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                557,
+                                505,
+                                569
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        557,
+                                        288,
+                                        569
+                                    ],
+                                    "score": 1.0,
+                                    "content": "architectures, all of them using the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        288,
+                                        558,
+                                        306,
+                                        568
+                                    ],
+                                    "score": 0.42,
+                                    "content": "\\mathbf { \\hat { v } } _ { \\mathbf { \\Delta } } 2 \\mathbf { \\hat { \\mu } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        557,
+                                        505,
+                                        569
+                                    ],
+                                    "score": 1.0,
+                                    "content": "variant (He et al., 2016b), and find larger archi-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                568,
+                                505,
+                                580
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        568,
+                                        505,
+                                        580
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tecture to perform better, even when given smaller amounts of data. We insert a DropOut",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                579,
+                                428,
+                                591
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        579,
+                                        428,
+                                        591
+                                    ],
+                                    "score": 1.0,
+                                    "content": "layer before the final linear classification layer (Srivastava et al., 2014).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                133,
+                                593,
+                                502,
+                                607
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        133,
+                                        593,
+                                        502,
+                                        607
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• Data pre-processing: We use the Inception pre-processing pipeline (Szegedy et al., 2014).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                133,
+                                608,
+                                505,
+                                622
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        133,
+                                        608,
+                                        346,
+                                        622
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• Optimization details: We vary the learning rate in",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        347,
+                                        608,
+                                        411,
+                                        621
+                                    ],
+                                    "score": 0.7,
+                                    "content": "\\{ 0 . 0 5 , 0 . 1 , 0 . 2 \\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        411,
+                                        608,
+                                        505,
+                                        622
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the weight decay log-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                618,
+                                506,
+                                633
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        618,
+                                        216,
+                                        633
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arithmically from",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        216,
+                                        619,
+                                        237,
+                                        630
+                                    ],
+                                    "score": 0.9,
+                                    "content": "1 0 ^ { - 5 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        238,
+                                        618,
+                                        250,
+                                        633
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        250,
+                                        619,
+                                        272,
+                                        630
+                                    ],
+                                    "score": 0.89,
+                                    "content": "1 0 ^ { - 2 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        272,
+                                        618,
+                                        506,
+                                        633
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the DropOut linearly from 0 to 1, and the batch size per",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                630,
+                                224,
+                                644
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        630,
+                                        183,
+                                        644
+                                    ],
+                                    "score": 1.0,
+                                    "content": "worker in",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        183,
+                                        631,
+                                        219,
+                                        643
+                                    ],
+                                    "score": 0.77,
+                                    "content": "\\{ 1 6 , 3 2 \\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        219,
+                                        630,
+                                        224,
+                                        644
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        }
+                    ],
+                    "index": 38.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        109,
+                        651,
+                        505,
+                        685
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                650,
+                                505,
+                                666
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        650,
+                                        350,
+                                        666
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We chose the best performing model for each training subset",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        351,
+                                        652,
+                                        362,
+                                        663
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\mathbb { D } _ { l }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        362,
+                                        650,
+                                        505,
+                                        666
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of labeled ImageNet (using a sepa-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                662,
+                                505,
+                                675
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        662,
+                                        505,
+                                        675
+                                    ],
+                                    "score": 1.0,
+                                    "content": "rate validation set), and report its accuracy on the test set (i.e. the publicly available ILSVRC-2012",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                674,
+                                167,
+                                685
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        674,
+                                        167,
+                                        685
+                                    ],
+                                    "score": 1.0,
+                                    "content": "validation set).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        }
+                    ],
+                    "index": 44
+                }
+            ],
+            "page_idx": 14,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        308,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                26,
+                                308,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        26,
+                                        308,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Under review as a conference paper at ICLR 2020",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        311,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                313,
+                                764
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        313,
+                                        764
+                                    ],
+                                    "score": 1.0,
+                                    "content": "15",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        95,
+                        406,
+                        316
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                94,
+                                240,
+                                105
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        94,
+                                        240,
+                                        105
+                                    ],
+                                    "score": 1.0,
+                                    "content": "def pixelCNN(latents):",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                129,
+                                105,
+                                269,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        129,
+                                        105,
+                                        269,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "# latents: [B, H, W, D]",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                131,
+                                117,
+                                217,
+                                127
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        131,
+                                        117,
+                                        158,
+                                        127
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cres",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        159,
+                                        117,
+                                        170,
+                                        126
+                                    ],
+                                    "score": 0.71,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        170,
+                                        117,
+                                        217,
+                                        127
+                                    ],
+                                    "score": 1.0,
+                                    "content": "latents",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                130,
+                                127,
+                                281,
+                                138
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        130,
+                                        127,
+                                        182,
+                                        138
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cres_dim",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        182,
+                                        128,
+                                        194,
+                                        137
+                                    ],
+                                    "score": 0.74,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        194,
+                                        127,
+                                        281,
+                                        138
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cres.shape[-1]",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                131,
+                                137,
+                                240,
+                                150
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        131,
+                                        138,
+                                        152,
+                                        149
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        164,
+                                        137,
+                                        240,
+                                        150
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in range(5):",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                149,
+                                329,
+                                160
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        149,
+                                        152,
+                                        160
+                                    ],
+                                    "score": 1.0,
+                                    "content": "c",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        152,
+                                        150,
+                                        164,
+                                        159
+                                    ],
+                                    "score": 0.63,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        164,
+                                        149,
+                                        298,
+                                        160
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Conv2D(output_channels",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        298,
+                                        149,
+                                        323,
+                                        159
+                                    ],
+                                    "score": 0.4,
+                                    "content": "= 2 5 6",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        323,
+                                        149,
+                                        329,
+                                        160
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                207,
+                                159,
+                                364,
+                                172
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        207,
+                                        159,
+                                        280,
+                                        172
+                                    ],
+                                    "score": 1.0,
+                                    "content": "kernel_shape",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        280,
+                                        162,
+                                        288,
+                                        169
+                                    ],
+                                    "score": 0.66,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        159,
+                                        364,
+                                        172
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(1, 1))(cres)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                171,
+                                209,
+                                182
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        171,
+                                        209,
+                                        182
+                                    ],
+                                    "score": 1.0,
+                                    "content": "c = ReLU(c)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                182,
+                                329,
+                                193
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        182,
+                                        297,
+                                        193
+                                    ],
+                                    "score": 1.0,
+                                    "content": "c = Conv2D(output_channels",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        298,
+                                        182,
+                                        323,
+                                        192
+                                    ],
+                                    "score": 0.42,
+                                    "content": "= 2 5 6",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        324,
+                                        182,
+                                        329,
+                                        193
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                207,
+                                193,
+                                347,
+                                204
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        207,
+                                        193,
+                                        280,
+                                        204
+                                    ],
+                                    "score": 1.0,
+                                    "content": "kernel_shape",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        280,
+                                        194,
+                                        288,
+                                        202
+                                    ],
+                                    "score": 0.74,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        193,
+                                        347,
+                                        204
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(1, 3))(c)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                203,
+                                406,
+                                216
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        203,
+                                        406,
+                                        216
+                                    ],
+                                    "score": 1.0,
+                                    "content": "c = Pad(c, [[0, 0], [1, 0], [0, 0], [0, 0]])",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                214,
+                                329,
+                                227
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        214,
+                                        297,
+                                        227
+                                    ],
+                                    "score": 1.0,
+                                    "content": "c = Conv2D(output_channels",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        298,
+                                        215,
+                                        323,
+                                        225
+                                    ],
+                                    "score": 0.29,
+                                    "content": "= 2 5 6",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        323,
+                                        214,
+                                        329,
+                                        227
+                                    ],
+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                207,
+                                225,
+                                329,
+                                237
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        207,
+                                        225,
+                                        280,
+                                        237
+                                    ],
+                                    "score": 1.0,
+                                    "content": "kernel_shape",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        280,
+                                        227,
+                                        288,
+                                        235
+                                    ],
+                                    "score": 0.77,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        225,
+                                        329,
+                                        237
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(2, 1),",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                208,
+                                236,
+                                304,
+                                248
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        208,
+                                        236,
+                                        232,
+                                        248
+                                    ],
+                                    "score": 1.0,
+                                    "content": "type",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        232,
+                                        238,
+                                        244,
+                                        246
+                                    ],
+                                    "score": 0.65,
+                                    "content": "= ^ { \\parallel }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        244,
+                                        236,
+                                        304,
+                                        248
+                                    ],
+                                    "score": 1.0,
+                                    "content": "VALID')(c)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                248,
+                                208,
+                                258
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        248,
+                                        153,
+                                        258
+                                    ],
+                                    "score": 1.0,
+                                    "content": "c",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        249,
+                                        164,
+                                        257
+                                    ],
+                                    "score": 0.31,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        164,
+                                        248,
+                                        208,
+                                        258
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ReLU(c)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                258,
+                                358,
+                                271
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        258,
+                                        153,
+                                        271
+                                    ],
+                                    "score": 1.0,
+                                    "content": "c",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        153,
+                                        259,
+                                        164,
+                                        268
+                                    ],
+                                    "score": 0.28,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        164,
+                                        258,
+                                        298,
+                                        271
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Conv2D(output_channels",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        298,
+                                        261,
+                                        305,
+                                        268
+                                    ],
+                                    "score": 0.69,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        258,
+                                        358,
+                                        271
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cres_dim,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                207,
+                                269,
+                                346,
+                                281
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        207,
+                                        269,
+                                        280,
+                                        281
+                                    ],
+                                    "score": 1.0,
+                                    "content": "kernel_shape",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        280,
+                                        271,
+                                        288,
+                                        279
+                                    ],
+                                    "score": 0.7,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        289,
+                                        269,
+                                        346,
+                                        281
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(1, 1))(c)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                281,
+                                235,
+                                291
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        281,
+                                        171,
+                                        291
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cres",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        171,
+                                        282,
+                                        182,
+                                        290
+                                    ],
+                                    "score": 0.38,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        182,
+                                        281,
+                                        235,
+                                        291
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cres + c",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                130,
+                                291,
+                                233,
+                                303
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        130,
+                                        291,
+                                        159,
+                                        303
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cres",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        159,
+                                        293,
+                                        169,
+                                        301
+                                    ],
+                                    "score": 0.59,
+                                    "content": "=",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        169,
+                                        291,
+                                        233,
+                                        303
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ReLU(cres)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                130,
+                                302,
+                                199,
+                                313
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        130,
+                                        302,
+                                        199,
+                                        313
+                                    ],
+                                    "score": 1.0,
+                                    "content": "return cres",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 9.5,
+                    "bbox_fs": [
+                        106,
+                        94,
+                        406,
+                        313
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        334,
+                        240,
+                        345
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                333,
+                                241,
+                                347
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        333,
+                                        241,
+                                        347
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.3 LINEAR CLASSIFICATION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 20
+                },
+                {
+                    "type": "list",
+                    "bbox": [
+                        133,
+                        351,
+                        506,
+                        491
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                135,
+                                351,
+                                504,
+                                363
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        135,
+                                        351,
+                                        293,
+                                        363
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• Model architecture: Having extracted",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        293,
+                                        351,
+                                        320,
+                                        362
+                                    ],
+                                    "score": 0.64,
+                                    "content": "8 0 \\mathrm { x } 8 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        320,
+                                        351,
+                                        412,
+                                        363
+                                    ],
+                                    "score": 1.0,
+                                    "content": "patches with a stride of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        413,
+                                        351,
+                                        439,
+                                        361
+                                    ],
+                                    "score": 0.33,
+                                    "content": "3 2 \\mathrm { x } 3 2 ",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        439,
+                                        351,
+                                        467,
+                                        363
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from a",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        468,
+                                        351,
+                                        504,
+                                        362
+                                    ],
+                                    "score": 0.68,
+                                    "content": "2 4 0 \\times 2 4 0",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 21,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                361,
+                                506,
+                                375
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        361,
+                                        506,
+                                        375
+                                    ],
+                                    "score": 1.0,
+                                    "content": "shaped input image, we end up with a grid of 6x6 features (each of which is obtained",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                373,
+                                506,
+                                386
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        373,
+                                        506,
+                                        386
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from our ResNet-161 architecture). This gives us a [6,6,4096] tensor for the image. We",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                384,
+                                505,
+                                396
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        384,
+                                        505,
+                                        396
+                                    ],
+                                    "score": 1.0,
+                                    "content": "then use a Batch-Normalization layer to normalize the features (without scale parameter)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                394,
+                                506,
+                                408
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        394,
+                                        506,
+                                        408
+                                    ],
+                                    "score": 1.0,
+                                    "content": "followed by a 1x1 convolution mapping each feature in the grid to the 1000 logits for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                406,
+                                505,
+                                419
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        406,
+                                        505,
+                                        419
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ImageNet classification. We then spatially-mean-pool these logits to end up with the final",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                417,
+                                321,
+                                429
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        417,
+                                        321,
+                                        429
+                                    ],
+                                    "score": 1.0,
+                                    "content": "log probabilities for the linear classification.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                134,
+                                430,
+                                506,
+                                446
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        134,
+                                        430,
+                                        420,
+                                        446
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• We use the Inception preprocessing (Szegedy et al., 2014) to extract",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        421,
+                                        432,
+                                        457,
+                                        442
+                                    ],
+                                    "score": 0.62,
+                                    "content": "2 4 0 \\times 2 4 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        457,
+                                        430,
+                                        506,
+                                        446
+                                    ],
+                                    "score": 1.0,
+                                    "content": "crops from",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                443,
+                                505,
+                                456
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        443,
+                                        505,
+                                        456
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the raw image. The image is divided into subcrops as per CPC data-preprocessing used for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                453,
+                                216,
+                                468
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        453,
+                                        216,
+                                        468
+                                    ],
+                                    "score": 1.0,
+                                    "content": "CPC pre-training.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                133,
+                                468,
+                                505,
+                                482
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        133,
+                                        468,
+                                        505,
+                                        482
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• Optimization details: We use Adam Optimizer with a learning rate of 5e-4. We train the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                479,
+                                486,
+                                492
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        479,
+                                        486,
+                                        492
+                                    ],
+                                    "score": 1.0,
+                                    "content": "model on a batch size of 512 images with 32 images per core spread over 16 workers.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32,
+                            "is_list_end_line": true
+                        }
+                    ],
+                    "index": 26.5,
+                    "bbox_fs": [
+                        133,
+                        351,
+                        506,
+                        492
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        505,
+                        346,
+                        515
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                504,
+                                347,
+                                516
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        504,
+                                        347,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.4 EFFICIENT CLASSIFICATION: PURELY SUPERVISED",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 33,
+                    "bbox_fs": [
+                        106,
+                        504,
+                        347,
+                        516
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        524,
+                        459,
+                        536
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                523,
+                                461,
+                                538
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        523,
+                                        461,
+                                        538
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In order to find the best model within this class, we vary the following hyperparameters:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        }
+                    ],
+                    "index": 34,
+                    "bbox_fs": [
+                        105,
+                        523,
+                        461,
+                        538
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        133,
+                        546,
+                        504,
+                        643
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                133,
+                                546,
+                                506,
+                                558
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        133,
+                                        546,
+                                        506,
+                                        558
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• Model architecture: We investigate using ResNet-50, ResNet-101, and ResNet-152 model",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                557,
+                                505,
+                                569
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        557,
+                                        288,
+                                        569
+                                    ],
+                                    "score": 1.0,
+                                    "content": "architectures, all of them using the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        288,
+                                        558,
+                                        306,
+                                        568
+                                    ],
+                                    "score": 0.42,
+                                    "content": "\\mathbf { \\hat { v } } _ { \\mathbf { \\Delta } } 2 \\mathbf { \\hat { \\mu } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        557,
+                                        505,
+                                        569
+                                    ],
+                                    "score": 1.0,
+                                    "content": "variant (He et al., 2016b), and find larger archi-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                568,
+                                505,
+                                580
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        568,
+                                        505,
+                                        580
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tecture to perform better, even when given smaller amounts of data. We insert a DropOut",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                579,
+                                428,
+                                591
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        579,
+                                        428,
+                                        591
+                                    ],
+                                    "score": 1.0,
+                                    "content": "layer before the final linear classification layer (Srivastava et al., 2014).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                133,
+                                593,
+                                502,
+                                607
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        133,
+                                        593,
+                                        502,
+                                        607
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• Data pre-processing: We use the Inception pre-processing pipeline (Szegedy et al., 2014).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                133,
+                                608,
+                                505,
+                                622
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        133,
+                                        608,
+                                        346,
+                                        622
+                                    ],
+                                    "score": 1.0,
+                                    "content": "• Optimization details: We vary the learning rate in",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        347,
+                                        608,
+                                        411,
+                                        621
+                                    ],
+                                    "score": 0.7,
+                                    "content": "\\{ 0 . 0 5 , 0 . 1 , 0 . 2 \\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        411,
+                                        608,
+                                        505,
+                                        622
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the weight decay log-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                618,
+                                506,
+                                633
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        618,
+                                        216,
+                                        633
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arithmically from",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        216,
+                                        619,
+                                        237,
+                                        630
+                                    ],
+                                    "score": 0.9,
+                                    "content": "1 0 ^ { - 5 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        238,
+                                        618,
+                                        250,
+                                        633
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        250,
+                                        619,
+                                        272,
+                                        630
+                                    ],
+                                    "score": 0.89,
+                                    "content": "1 0 ^ { - 2 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        272,
+                                        618,
+                                        506,
+                                        633
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the DropOut linearly from 0 to 1, and the batch size per",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                630,
+                                224,
+                                644
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        630,
+                                        183,
+                                        644
+                                    ],
+                                    "score": 1.0,
+                                    "content": "worker in",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        183,
+                                        631,
+                                        219,
+                                        643
+                                    ],
+                                    "score": 0.77,
+                                    "content": "\\{ 1 6 , 3 2 \\}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        219,
+                                        630,
+                                        224,
+                                        644
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        }
+                    ],
+                    "index": 38.5,
+                    "bbox_fs": [
+                        133,
+                        546,
+                        506,
+                        644
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        109,
+                        651,
+                        505,
+                        685
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                650,
+                                505,
+                                666
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        650,
+                                        350,
+                                        666
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We chose the best performing model for each training subset",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        351,
+                                        652,
+                                        362,
+                                        663
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\mathbb { D } _ { l }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        362,
+                                        650,
+                                        505,
+                                        666
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of labeled ImageNet (using a sepa-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                662,
+                                505,
+                                675
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        662,
+                                        505,
+                                        675
+                                    ],
+                                    "score": 1.0,
+                                    "content": "rate validation set), and report its accuracy on the test set (i.e. the publicly available ILSVRC-2012",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                674,
+                                167,
+                                685
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        674,
+                                        167,
+                                        685
+                                    ],
+                                    "score": 1.0,
+                                    "content": "validation set).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        }
+                    ],
+                    "index": 44,
+                    "bbox_fs": [
+                        105,
+                        650,
+                        505,
+                        685
+                    ]
+                }
+            ]
+        }
+    ],
+    "_backend": "pipeline",
+    "_version_name": "2.2.2"
+}
\ No newline at end of file
diff --git a/parse/train/rJerHlrYwH/rJerHlrYwH_model.json b/parse/train/rJerHlrYwH/rJerHlrYwH_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..9198570e889173181978158a20fdf40a0e195ad6
--- /dev/null
+++ b/parse/train/rJerHlrYwH/rJerHlrYwH_model.json
@@ -0,0 +1,22521 @@
+[
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    398,
+                    591,
+                    1302,
+                    591,
+                    1302,
+                    986,
+                    398,
+                    986
+                ],
+                "score": 0.983
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1123,
+                    824,
+                    1123,
+                    824,
+                    1941,
+                    298,
+                    1941
+                ],
+                "score": 0.979
+            },
+            {
+                "category_id": 3,
+                "poly": [
+                    852,
+                    1129,
+                    1395,
+                    1129,
+                    1395,
+                    1614,
+                    852,
+                    1614
+                ],
+                "score": 0.973
+            },
+            {
+                "category_id": 4,
+                "poly": [
+                    847,
+                    1628,
+                    1401,
+                    1628,
+                    1401,
+                    1902,
+                    847,
+                    1902
+                ],
+                "score": 0.97
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    299,
+                    218,
+                    1166,
+                    218,
+                    1166,
+                    324,
+                    299,
+                    324
+                ],
+                "score": 0.963
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    300,
+                    1944,
+                    1401,
+                    1944,
+                    1401,
+                    2034,
+                    300,
+                    2034
+                ],
+                "score": 0.959
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    313,
+                    377,
+                    680,
+                    377,
+                    680,
+                    437,
+                    313,
+                    437
+                ],
+                "score": 0.937
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    75,
+                    858,
+                    75,
+                    858,
+                    105,
+                    298,
+                    105
+                ],
+                "score": 0.897
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    303,
+                    1049,
+                    572,
+                    1049,
+                    572,
+                    1084,
+                    303,
+                    1084
+                ],
+                "score": 0.89
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    773,
+                    518,
+                    926,
+                    518,
+                    926,
+                    553,
+                    773,
+                    553
+                ],
+                "score": 0.86
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2089,
+                    857,
+                    2089,
+                    857,
+                    2112,
+                    841,
+                    2112
+                ],
+                "score": 0.666
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    699,
+                    864,
+                    754,
+                    864,
+                    754,
+                    893,
+                    699,
+                    893
+                ],
+                "score": 0.87,
+                "latex": "65 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    609,
+                    864,
+                    665,
+                    864,
+                    665,
+                    893,
+                    609,
+                    893
+                ],
+                "score": 0.87,
+                "latex": "28 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    660,
+                    895,
+                    712,
+                    895,
+                    712,
+                    924,
+                    660,
+                    924
+                ],
+                "score": 0.87,
+                "latex": "14 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    809,
+                    834,
+                    865,
+                    834,
+                    865,
+                    863,
+                    809,
+                    863
+                ],
+                "score": 0.86,
+                "latex": "73 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    619,
+                    804,
+                    660,
+                    804,
+                    660,
+                    833,
+                    619,
+                    833
+                ],
+                "score": 0.86,
+                "latex": "1 \\%"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    869.0,
+                    1175.0,
+                    919.0,
+                    1175.0,
+                    919.0,
+                    1210.0,
+                    869.0,
+                    1210.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1290.0,
+                    1175.0,
+                    1302.0,
+                    1175.0,
+                    1302.0,
+                    1184.0,
+                    1290.0,
+                    1184.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1143.0,
+                    1189.0,
+                    1161.0,
+                    1189.0,
+                    1161.0,
+                    1206.0,
+                    1143.0,
+                    1206.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1206.0,
+                    1204.0,
+                    1221.0,
+                    1204.0,
+                    1221.0,
+                    1216.0,
+                    1206.0,
+                    1216.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1281.0,
+                    1194.0,
+                    1373.0,
+                    1194.0,
+                    1373.0,
+                    1223.0,
+                    1281.0,
+                    1223.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    848.0,
+                    1212.0,
+                    890.0,
+                    1212.0,
+                    890.0,
+                    1480.0,
+                    848.0,
+                    1480.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1297.0,
+                    1212.0,
+                    1356.0,
+                    1212.0,
+                    1356.0,
+                    1244.0,
+                    1297.0,
+                    1244.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1081.0,
+                    1215.0,
+                    1099.0,
+                    1215.0,
+                    1099.0,
+                    1230.0,
+                    1081.0,
+                    1230.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1145.0,
+                    1246.0,
+                    1160.0,
+                    1246.0,
+                    1160.0,
+                    1258.0,
+                    1145.0,
+                    1258.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    872.0,
+                    1251.0,
+                    915.0,
+                    1251.0,
+                    915.0,
+                    1281.0,
+                    872.0,
+                    1281.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1082.0,
+                    1293.0,
+                    1100.0,
+                    1293.0,
+                    1100.0,
+                    1311.0,
+                    1082.0,
+                    1311.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    939.0,
+                    1310.0,
+                    956.0,
+                    1310.0,
+                    956.0,
+                    1327.0,
+                    939.0,
+                    1327.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    870.0,
+                    1324.0,
+                    915.0,
+                    1324.0,
+                    915.0,
+                    1353.0,
+                    870.0,
+                    1353.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    969.0,
+                    1319.0,
+                    1060.0,
+                    1319.0,
+                    1060.0,
+                    1348.0,
+                    969.0,
+                    1348.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    986.0,
+                    1339.0,
+                    1042.0,
+                    1339.0,
+                    1042.0,
+                    1367.0,
+                    986.0,
+                    1367.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    871.0,
+                    1397.0,
+                    916.0,
+                    1397.0,
+                    916.0,
+                    1427.0,
+                    871.0,
+                    1427.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    868.0,
+                    1466.0,
+                    922.0,
+                    1466.0,
+                    922.0,
+                    1503.0,
+                    868.0,
+                    1503.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1134.0,
+                    1484.0,
+                    1375.0,
+                    1484.0,
+                    1375.0,
+                    1516.0,
+                    1134.0,
+                    1516.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    939.0,
+                    1520.0,
+                    956.0,
+                    1520.0,
+                    956.0,
+                    1535.0,
+                    939.0,
+                    1535.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1137.0,
+                    1514.0,
+                    1383.0,
+                    1514.0,
+                    1383.0,
+                    1543.0,
+                    1137.0,
+                    1543.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    870.0,
+                    1539.0,
+                    916.0,
+                    1539.0,
+                    916.0,
+                    1573.0,
+                    870.0,
+                    1573.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    940.0,
+                    1564.0,
+                    955.0,
+                    1564.0,
+                    955.0,
+                    1585.0,
+                    940.0,
+                    1585.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    997.0,
+                    1560.0,
+                    1021.0,
+                    1560.0,
+                    1021.0,
+                    1589.0,
+                    997.0,
+                    1589.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1079.0,
+                    1560.0,
+                    1102.0,
+                    1560.0,
+                    1102.0,
+                    1589.0,
+                    1079.0,
+                    1589.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1135.0,
+                    1558.0,
+                    1173.0,
+                    1558.0,
+                    1173.0,
+                    1590.0,
+                    1135.0,
+                    1590.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1194.0,
+                    1559.0,
+                    1232.0,
+                    1559.0,
+                    1232.0,
+                    1590.0,
+                    1194.0,
+                    1590.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1274.0,
+                    1556.0,
+                    1383.0,
+                    1556.0,
+                    1383.0,
+                    1594.0,
+                    1274.0,
+                    1594.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1034.0,
+                    1588.0,
+                    1278.0,
+                    1588.0,
+                    1278.0,
+                    1617.0,
+                    1034.0,
+                    1617.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    988.75,
+                    1264.5,
+                    1025.75,
+                    1264.5,
+                    1025.75,
+                    1279.0,
+                    988.75,
+                    1279.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    947.75,
+                    1307.5,
+                    964.75,
+                    1307.5,
+                    964.75,
+                    1315.5,
+                    947.75,
+                    1315.5
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    984.75,
+                    1413.5,
+                    1022.75,
+                    1413.5,
+                    1022.75,
+                    1425.0,
+                    984.75,
+                    1425.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    845.0,
+                    1628.0,
+                    1403.0,
+                    1628.0,
+                    1403.0,
+                    1661.0,
+                    845.0,
+                    1661.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    845.0,
+                    1657.0,
+                    1404.0,
+                    1657.0,
+                    1404.0,
+                    1691.0,
+                    845.0,
+                    1691.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    844.0,
+                    1689.0,
+                    1403.0,
+                    1689.0,
+                    1403.0,
+                    1721.0,
+                    844.0,
+                    1721.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    844.0,
+                    1718.0,
+                    1405.0,
+                    1718.0,
+                    1405.0,
+                    1751.0,
+                    844.0,
+                    1751.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    845.0,
+                    1748.0,
+                    1405.0,
+                    1748.0,
+                    1405.0,
+                    1782.0,
+                    845.0,
+                    1782.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    845.0,
+                    1780.0,
+                    1406.0,
+                    1780.0,
+                    1406.0,
+                    1813.0,
+                    845.0,
+                    1813.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    845.0,
+                    1811.0,
+                    1404.0,
+                    1811.0,
+                    1404.0,
+                    1844.0,
+                    845.0,
+                    1844.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    845.0,
+                    1841.0,
+                    1405.0,
+                    1841.0,
+                    1405.0,
+                    1874.0,
+                    845.0,
+                    1874.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    844.0,
+                    1871.0,
+                    1296.0,
+                    1871.0,
+                    1296.0,
+                    1904.0,
+                    844.0,
+                    1904.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    216.0,
+                    1106.0,
+                    216.0,
+                    1106.0,
+                    270.0,
+                    294.0,
+                    270.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    274.0,
+                    1168.0,
+                    274.0,
+                    1168.0,
+                    325.0,
+                    297.0,
+                    325.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    298.0,
+                    73.0,
+                    858.0,
+                    73.0,
+                    858.0,
+                    108.0,
+                    298.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1045.0,
+                    578.0,
+                    1045.0,
+                    578.0,
+                    1092.0,
+                    294.0,
+                    1092.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    769.0,
+                    518.0,
+                    932.0,
+                    518.0,
+                    932.0,
+                    556.0,
+                    769.0,
+                    556.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    840.0,
+                    2088.0,
+                    861.0,
+                    2088.0,
+                    861.0,
+                    2118.0,
+                    840.0,
+                    2118.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    591.0,
+                    1303.0,
+                    591.0,
+                    1303.0,
+                    626.0,
+                    394.0,
+                    626.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    618.0,
+                    1304.0,
+                    618.0,
+                    1304.0,
+                    657.0,
+                    393.0,
+                    657.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    648.0,
+                    1306.0,
+                    648.0,
+                    1306.0,
+                    686.0,
+                    393.0,
+                    686.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    681.0,
+                    1306.0,
+                    681.0,
+                    1306.0,
+                    715.0,
+                    394.0,
+                    715.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    712.0,
+                    1306.0,
+                    712.0,
+                    1306.0,
+                    745.0,
+                    392.0,
+                    745.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    744.0,
+                    1305.0,
+                    744.0,
+                    1305.0,
+                    776.0,
+                    393.0,
+                    776.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    773.0,
+                    1305.0,
+                    773.0,
+                    1305.0,
+                    805.0,
+                    393.0,
+                    805.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    804.0,
+                    618.0,
+                    804.0,
+                    618.0,
+                    839.0,
+                    394.0,
+                    839.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    661.0,
+                    804.0,
+                    1306.0,
+                    804.0,
+                    1306.0,
+                    839.0,
+                    661.0,
+                    839.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    836.0,
+                    808.0,
+                    836.0,
+                    808.0,
+                    868.0,
+                    394.0,
+                    868.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    866.0,
+                    836.0,
+                    1303.0,
+                    836.0,
+                    1303.0,
+                    868.0,
+                    866.0,
+                    868.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    395.0,
+                    865.0,
+                    608.0,
+                    865.0,
+                    608.0,
+                    897.0,
+                    395.0,
+                    897.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    666.0,
+                    865.0,
+                    698.0,
+                    865.0,
+                    698.0,
+                    897.0,
+                    666.0,
+                    897.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    755.0,
+                    865.0,
+                    1305.0,
+                    865.0,
+                    1305.0,
+                    897.0,
+                    755.0,
+                    897.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    895.0,
+                    659.0,
+                    895.0,
+                    659.0,
+                    929.0,
+                    393.0,
+                    929.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    713.0,
+                    895.0,
+                    1306.0,
+                    895.0,
+                    1306.0,
+                    929.0,
+                    713.0,
+                    929.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    925.0,
+                    1305.0,
+                    925.0,
+                    1305.0,
+                    960.0,
+                    394.0,
+                    960.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    956.0,
+                    1288.0,
+                    956.0,
+                    1288.0,
+                    993.0,
+                    392.0,
+                    993.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1120.0,
+                    824.0,
+                    1120.0,
+                    824.0,
+                    1154.0,
+                    296.0,
+                    1154.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1148.0,
+                    827.0,
+                    1148.0,
+                    827.0,
+                    1185.0,
+                    295.0,
+                    1185.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1180.0,
+                    826.0,
+                    1180.0,
+                    826.0,
+                    1214.0,
+                    296.0,
+                    1214.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1211.0,
+                    827.0,
+                    1211.0,
+                    827.0,
+                    1246.0,
+                    296.0,
+                    1246.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1240.0,
+                    825.0,
+                    1240.0,
+                    825.0,
+                    1276.0,
+                    294.0,
+                    1276.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1272.0,
+                    825.0,
+                    1272.0,
+                    825.0,
+                    1304.0,
+                    296.0,
+                    1304.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1302.0,
+                    827.0,
+                    1302.0,
+                    827.0,
+                    1336.0,
+                    295.0,
+                    1336.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1332.0,
+                    826.0,
+                    1332.0,
+                    826.0,
+                    1366.0,
+                    295.0,
+                    1366.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1362.0,
+                    827.0,
+                    1362.0,
+                    827.0,
+                    1397.0,
+                    294.0,
+                    1397.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1392.0,
+                    825.0,
+                    1392.0,
+                    825.0,
+                    1428.0,
+                    295.0,
+                    1428.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1424.0,
+                    825.0,
+                    1424.0,
+                    825.0,
+                    1458.0,
+                    294.0,
+                    1458.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1453.0,
+                    827.0,
+                    1453.0,
+                    827.0,
+                    1488.0,
+                    294.0,
+                    1488.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1486.0,
+                    828.0,
+                    1486.0,
+                    828.0,
+                    1518.0,
+                    294.0,
+                    1518.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1516.0,
+                    827.0,
+                    1516.0,
+                    827.0,
+                    1548.0,
+                    294.0,
+                    1548.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1547.0,
+                    826.0,
+                    1547.0,
+                    826.0,
+                    1580.0,
+                    294.0,
+                    1580.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1574.0,
+                    828.0,
+                    1574.0,
+                    828.0,
+                    1610.0,
+                    293.0,
+                    1610.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1608.0,
+                    828.0,
+                    1608.0,
+                    828.0,
+                    1640.0,
+                    293.0,
+                    1640.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1639.0,
+                    827.0,
+                    1639.0,
+                    827.0,
+                    1668.0,
+                    294.0,
+                    1668.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1670.0,
+                    827.0,
+                    1670.0,
+                    827.0,
+                    1700.0,
+                    296.0,
+                    1700.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1698.0,
+                    826.0,
+                    1698.0,
+                    826.0,
+                    1731.0,
+                    295.0,
+                    1731.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1726.0,
+                    827.0,
+                    1726.0,
+                    827.0,
+                    1764.0,
+                    295.0,
+                    1764.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1761.0,
+                    828.0,
+                    1761.0,
+                    828.0,
+                    1794.0,
+                    295.0,
+                    1794.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1790.0,
+                    827.0,
+                    1790.0,
+                    827.0,
+                    1824.0,
+                    294.0,
+                    1824.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1822.0,
+                    827.0,
+                    1822.0,
+                    827.0,
+                    1852.0,
+                    294.0,
+                    1852.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1851.0,
+                    827.0,
+                    1851.0,
+                    827.0,
+                    1884.0,
+                    294.0,
+                    1884.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1881.0,
+                    827.0,
+                    1881.0,
+                    827.0,
+                    1916.0,
+                    295.0,
+                    1916.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1912.0,
+                    827.0,
+                    1912.0,
+                    827.0,
+                    1943.0,
+                    294.0,
+                    1943.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1942.0,
+                    1402.0,
+                    1942.0,
+                    1402.0,
+                    1978.0,
+                    295.0,
+                    1978.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1974.0,
+                    1403.0,
+                    1974.0,
+                    1403.0,
+                    2007.0,
+                    294.0,
+                    2007.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    2003.0,
+                    1405.0,
+                    2003.0,
+                    1405.0,
+                    2038.0,
+                    294.0,
+                    2038.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    315.0,
+                    378.0,
+                    560.0,
+                    378.0,
+                    560.0,
+                    410.0,
+                    315.0,
+                    410.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    312.0,
+                    406.0,
+                    681.0,
+                    406.0,
+                    681.0,
+                    441.0,
+                    312.0,
+                    441.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 0,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    307,
+                    1403,
+                    307,
+                    1403,
+                    522,
+                    299,
+                    522
+                ],
+                "score": 0.978
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1420,
+                    1403,
+                    1420,
+                    1403,
+                    1636,
+                    298,
+                    1636
+                ],
+                "score": 0.976
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1650,
+                    1403,
+                    1650,
+                    1403,
+                    1899,
+                    298,
+                    1899
+                ],
+                "score": 0.975
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1911,
+                    1401,
+                    1911,
+                    1401,
+                    2034,
+                    299,
+                    2034
+                ],
+                "score": 0.972
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    370,
+                    595,
+                    1403,
+                    595,
+                    1403,
+                    1150,
+                    370,
+                    1150
+                ],
+                "score": 0.959
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    294,
+                    229,
+                    1400,
+                    229,
+                    1400,
+                    292,
+                    294,
+                    292
+                ],
+                "score": 0.952
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    300,
+                    1264,
+                    1403,
+                    1264,
+                    1403,
+                    1326,
+                    300,
+                    1326
+                ],
+                "score": 0.951
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    537,
+                    798,
+                    537,
+                    798,
+                    568,
+                    299,
+                    568
+                ],
+                "score": 0.928
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    299,
+                    1194,
+                    679,
+                    1194,
+                    679,
+                    1230,
+                    299,
+                    1230
+                ],
+                "score": 0.895
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    300,
+                    1363,
+                    796,
+                    1363,
+                    796,
+                    1395,
+                    300,
+                    1395
+                ],
+                "score": 0.872
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    76,
+                    858,
+                    76,
+                    858,
+                    104,
+                    298,
+                    104
+                ],
+                "score": 0.727
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2088,
+                    858,
+                    2088,
+                    858,
+                    2112,
+                    841,
+                    2112
+                ],
+                "score": 0.703
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    75,
+                    858,
+                    75,
+                    858,
+                    104,
+                    298,
+                    104
+                ],
+                "score": 0.176
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2088,
+                    859,
+                    2088,
+                    859,
+                    2112,
+                    841,
+                    2112
+                ],
+                "score": 0.173
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1105,
+                    1682,
+                    1283,
+                    1682,
+                    1283,
+                    1717,
+                    1105,
+                    1717
+                ],
+                "score": 0.93,
+                "latex": "z _ { i , j } = f _ { \\theta } ( \\pmb { x } _ { i , j } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    746,
+                    1773,
+                    890,
+                    1773,
+                    890,
+                    1808,
+                    746,
+                    1808
+                ],
+                "score": 0.92,
+                "latex": "\\{ z _ { u , v } \\} _ { u \\leq i , v } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1286,
+                    1943,
+                    1338,
+                    1943,
+                    1338,
+                    1976,
+                    1286,
+                    1976
+                ],
+                "score": 0.92,
+                "latex": "\\{ z _ { l } \\}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    634,
+                    1868,
+                    826,
+                    1868,
+                    826,
+                    1899,
+                    634,
+                    1899
+                ],
+                "score": 0.91,
+                "latex": "\\hat { \\boldsymbol { z } } _ { i + k , j } = \\boldsymbol { W } _ { k } \\boldsymbol { c } _ { i , j }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1092,
+                    1804,
+                    1166,
+                    1804,
+                    1166,
+                    1832,
+                    1092,
+                    1832
+                ],
+                "score": 0.9,
+                "latex": "k > 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    996,
+                    1836,
+                    1069,
+                    1836,
+                    1069,
+                    1863,
+                    996,
+                    1863
+                ],
+                "score": 0.9,
+                "latex": "k > 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    562,
+                    1808,
+                    633,
+                    1808,
+                    633,
+                    1838,
+                    562,
+                    1838
+                ],
+                "score": 0.9,
+                "latex": "z _ { i + k , j }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    847,
+                    1683,
+                    876,
+                    1683,
+                    876,
+                    1713,
+                    847,
+                    1713
+                ],
+                "score": 0.88,
+                "latex": "f _ { \\theta }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1112,
+                    1747,
+                    1153,
+                    1747,
+                    1153,
+                    1776,
+                    1112,
+                    1776
+                ],
+                "score": 0.88,
+                "latex": "c _ { i , j }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1351,
+                    1835,
+                    1392,
+                    1835,
+                    1392,
+                    1865,
+                    1351,
+                    1865
+                ],
+                "score": 0.88,
+                "latex": "W _ { k }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    963,
+                    1808,
+                    1004,
+                    1808,
+                    1004,
+                    1837,
+                    963,
+                    1837
+                ],
+                "score": 0.88,
+                "latex": "c _ { i , j }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1202,
+                    760,
+                    1257,
+                    760,
+                    1257,
+                    789,
+                    1202,
+                    789
+                ],
+                "score": 0.88,
+                "latex": "28 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1346,
+                    1658,
+                    1393,
+                    1658,
+                    1393,
+                    1685,
+                    1346,
+                    1685
+                ],
+                "score": 0.88,
+                "latex": "\\mathbf { \\delta } _ { \\mathbf { x } _ { i , j } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1327,
+                    791,
+                    1401,
+                    791,
+                    1401,
+                    821,
+                    1327,
+                    821
+                ],
+                "score": 0.87,
+                "latex": "( + 1 5 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    534,
+                    657,
+                    605,
+                    657,
+                    605,
+                    687,
+                    534,
+                    687
+                ],
+                "score": 0.87,
+                "latex": "+ 1 7 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    806,
+                    1717,
+                    838,
+                    1717,
+                    838,
+                    1746,
+                    806,
+                    1746
+                ],
+                "score": 0.87,
+                "latex": "g _ { \\phi }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    724,
+                    1840,
+                    765,
+                    1840,
+                    765,
+                    1868,
+                    724,
+                    1868
+                ],
+                "score": 0.86,
+                "latex": "c _ { i , j }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    405,
+                    882,
+                    462,
+                    882,
+                    462,
+                    912,
+                    405,
+                    912
+                ],
+                "score": 0.85,
+                "latex": "+ 1 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    943,
+                    760,
+                    997,
+                    760,
+                    997,
+                    790,
+                    943,
+                    790
+                ],
+                "score": 0.85,
+                "latex": "73 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    602,
+                    730,
+                    641,
+                    730,
+                    641,
+                    759,
+                    602,
+                    759
+                ],
+                "score": 0.85,
+                "latex": "1 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    637,
+                    1947,
+                    707,
+                    1947,
+                    707,
+                    1977,
+                    637,
+                    1977
+                ],
+                "score": 0.82,
+                "latex": "z _ { i + k , j }"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1191.0,
+                    683.0,
+                    1191.0,
+                    683.0,
+                    1234.0,
+                    292.0,
+                    1234.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1363.0,
+                    799.0,
+                    1363.0,
+                    799.0,
+                    1399.0,
+                    295.0,
+                    1399.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    70.0,
+                    859.0,
+                    70.0,
+                    859.0,
+                    109.0,
+                    296.0,
+                    109.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    839.0,
+                    2085.0,
+                    862.0,
+                    2085.0,
+                    862.0,
+                    2120.0,
+                    839.0,
+                    2120.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    72.0,
+                    858.0,
+                    72.0,
+                    858.0,
+                    108.0,
+                    297.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    838.0,
+                    2085.0,
+                    862.0,
+                    2085.0,
+                    862.0,
+                    2120.0,
+                    838.0,
+                    2120.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    305.0,
+                    1407.0,
+                    305.0,
+                    1407.0,
+                    346.0,
+                    293.0,
+                    346.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    341.0,
+                    1404.0,
+                    341.0,
+                    1404.0,
+                    371.0,
+                    295.0,
+                    371.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    369.0,
+                    1404.0,
+                    369.0,
+                    1404.0,
+                    403.0,
+                    294.0,
+                    403.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    398.0,
+                    1404.0,
+                    398.0,
+                    1404.0,
+                    435.0,
+                    293.0,
+                    435.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    429.0,
+                    1404.0,
+                    429.0,
+                    1404.0,
+                    464.0,
+                    295.0,
+                    464.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    460.0,
+                    1407.0,
+                    460.0,
+                    1407.0,
+                    498.0,
+                    294.0,
+                    498.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    490.0,
+                    703.0,
+                    490.0,
+                    703.0,
+                    527.0,
+                    294.0,
+                    527.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1419.0,
+                    1405.0,
+                    1419.0,
+                    1405.0,
+                    1456.0,
+                    294.0,
+                    1456.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1453.0,
+                    1405.0,
+                    1453.0,
+                    1405.0,
+                    1487.0,
+                    294.0,
+                    1487.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1484.0,
+                    1403.0,
+                    1484.0,
+                    1403.0,
+                    1518.0,
+                    294.0,
+                    1518.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1516.0,
+                    1404.0,
+                    1516.0,
+                    1404.0,
+                    1547.0,
+                    296.0,
+                    1547.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1542.0,
+                    1407.0,
+                    1542.0,
+                    1407.0,
+                    1581.0,
+                    292.0,
+                    1581.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1574.0,
+                    1405.0,
+                    1574.0,
+                    1405.0,
+                    1607.0,
+                    293.0,
+                    1607.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1605.0,
+                    1407.0,
+                    1605.0,
+                    1407.0,
+                    1642.0,
+                    292.0,
+                    1642.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1644.0,
+                    1345.0,
+                    1644.0,
+                    1345.0,
+                    1692.0,
+                    291.0,
+                    1692.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1394.0,
+                    1644.0,
+                    1409.0,
+                    1644.0,
+                    1409.0,
+                    1692.0,
+                    1394.0,
+                    1692.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1679.0,
+                    846.0,
+                    1679.0,
+                    846.0,
+                    1719.0,
+                    292.0,
+                    1719.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    877.0,
+                    1679.0,
+                    1104.0,
+                    1679.0,
+                    1104.0,
+                    1719.0,
+                    877.0,
+                    1719.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1284.0,
+                    1679.0,
+                    1407.0,
+                    1679.0,
+                    1407.0,
+                    1719.0,
+                    1284.0,
+                    1719.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1711.0,
+                    805.0,
+                    1711.0,
+                    805.0,
+                    1749.0,
+                    293.0,
+                    1749.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    839.0,
+                    1711.0,
+                    1407.0,
+                    1711.0,
+                    1407.0,
+                    1749.0,
+                    839.0,
+                    1749.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1742.0,
+                    1111.0,
+                    1742.0,
+                    1111.0,
+                    1779.0,
+                    292.0,
+                    1779.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1154.0,
+                    1742.0,
+                    1407.0,
+                    1742.0,
+                    1407.0,
+                    1779.0,
+                    1154.0,
+                    1779.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1771.0,
+                    745.0,
+                    1771.0,
+                    745.0,
+                    1812.0,
+                    292.0,
+                    1812.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    891.0,
+                    1771.0,
+                    1407.0,
+                    1771.0,
+                    1407.0,
+                    1812.0,
+                    891.0,
+                    1812.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1800.0,
+                    561.0,
+                    1800.0,
+                    561.0,
+                    1841.0,
+                    296.0,
+                    1841.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    634.0,
+                    1800.0,
+                    962.0,
+                    1800.0,
+                    962.0,
+                    1841.0,
+                    634.0,
+                    1841.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1005.0,
+                    1800.0,
+                    1091.0,
+                    1800.0,
+                    1091.0,
+                    1841.0,
+                    1005.0,
+                    1841.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1167.0,
+                    1800.0,
+                    1407.0,
+                    1800.0,
+                    1407.0,
+                    1841.0,
+                    1167.0,
+                    1841.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1834.0,
+                    723.0,
+                    1834.0,
+                    723.0,
+                    1871.0,
+                    293.0,
+                    1871.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    766.0,
+                    1834.0,
+                    995.0,
+                    1834.0,
+                    995.0,
+                    1871.0,
+                    766.0,
+                    1871.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1070.0,
+                    1834.0,
+                    1350.0,
+                    1834.0,
+                    1350.0,
+                    1871.0,
+                    1070.0,
+                    1871.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1393.0,
+                    1834.0,
+                    1407.0,
+                    1834.0,
+                    1407.0,
+                    1871.0,
+                    1393.0,
+                    1871.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1864.0,
+                    633.0,
+                    1864.0,
+                    633.0,
+                    1903.0,
+                    294.0,
+                    1903.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    827.0,
+                    1864.0,
+                    838.0,
+                    1864.0,
+                    838.0,
+                    1903.0,
+                    827.0,
+                    1903.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    1912.0,
+                    1403.0,
+                    1912.0,
+                    1403.0,
+                    1945.0,
+                    297.0,
+                    1945.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1942.0,
+                    636.0,
+                    1942.0,
+                    636.0,
+                    1977.0,
+                    293.0,
+                    1977.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    708.0,
+                    1942.0,
+                    1285.0,
+                    1942.0,
+                    1285.0,
+                    1977.0,
+                    708.0,
+                    1977.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1339.0,
+                    1942.0,
+                    1406.0,
+                    1942.0,
+                    1406.0,
+                    1977.0,
+                    1339.0,
+                    1977.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1971.0,
+                    1406.0,
+                    1971.0,
+                    1406.0,
+                    2011.0,
+                    293.0,
+                    2011.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    2003.0,
+                    1405.0,
+                    2003.0,
+                    1405.0,
+                    2039.0,
+                    294.0,
+                    2039.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    370.0,
+                    594.0,
+                    1405.0,
+                    594.0,
+                    1405.0,
+                    632.0,
+                    370.0,
+                    632.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    627.0,
+                    1403.0,
+                    627.0,
+                    1403.0,
+                    661.0,
+                    393.0,
+                    661.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    658.0,
+                    533.0,
+                    658.0,
+                    533.0,
+                    692.0,
+                    392.0,
+                    692.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    606.0,
+                    658.0,
+                    1069.0,
+                    658.0,
+                    1069.0,
+                    692.0,
+                    606.0,
+                    692.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    384.0,
+                    699.0,
+                    1403.0,
+                    699.0,
+                    1403.0,
+                    733.0,
+                    384.0,
+                    733.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    727.0,
+                    601.0,
+                    727.0,
+                    601.0,
+                    767.0,
+                    392.0,
+                    767.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    642.0,
+                    727.0,
+                    1405.0,
+                    727.0,
+                    1405.0,
+                    767.0,
+                    642.0,
+                    767.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    759.0,
+                    942.0,
+                    759.0,
+                    942.0,
+                    794.0,
+                    392.0,
+                    794.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    998.0,
+                    759.0,
+                    1201.0,
+                    759.0,
+                    1201.0,
+                    794.0,
+                    998.0,
+                    794.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1258.0,
+                    759.0,
+                    1405.0,
+                    759.0,
+                    1405.0,
+                    794.0,
+                    1258.0,
+                    794.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    789.0,
+                    1326.0,
+                    789.0,
+                    1326.0,
+                    826.0,
+                    392.0,
+                    826.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1402.0,
+                    789.0,
+                    1405.0,
+                    789.0,
+                    1405.0,
+                    826.0,
+                    1402.0,
+                    826.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    820.0,
+                    1406.0,
+                    820.0,
+                    1406.0,
+                    857.0,
+                    393.0,
+                    857.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    853.0,
+                    1405.0,
+                    853.0,
+                    1405.0,
+                    887.0,
+                    393.0,
+                    887.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    882.0,
+                    404.0,
+                    882.0,
+                    404.0,
+                    916.0,
+                    393.0,
+                    916.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    463.0,
+                    882.0,
+                    658.0,
+                    882.0,
+                    658.0,
+                    916.0,
+                    463.0,
+                    916.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    386.0,
+                    919.0,
+                    1405.0,
+                    919.0,
+                    1405.0,
+                    959.0,
+                    386.0,
+                    959.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    954.0,
+                    1405.0,
+                    954.0,
+                    1405.0,
+                    988.0,
+                    394.0,
+                    988.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    983.0,
+                    1405.0,
+                    983.0,
+                    1405.0,
+                    1021.0,
+                    393.0,
+                    1021.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    1010.0,
+                    823.0,
+                    1010.0,
+                    823.0,
+                    1053.0,
+                    392.0,
+                    1053.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    377.0,
+                    1053.0,
+                    1406.0,
+                    1053.0,
+                    1406.0,
+                    1093.0,
+                    377.0,
+                    1093.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    396.0,
+                    1088.0,
+                    1405.0,
+                    1088.0,
+                    1405.0,
+                    1122.0,
+                    396.0,
+                    1122.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    396.0,
+                    1119.0,
+                    1301.0,
+                    1119.0,
+                    1301.0,
+                    1153.0,
+                    396.0,
+                    1153.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    227.0,
+                    1404.0,
+                    227.0,
+                    1404.0,
+                    266.0,
+                    296.0,
+                    266.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    257.0,
+                    1093.0,
+                    257.0,
+                    1093.0,
+                    300.0,
+                    293.0,
+                    300.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1260.0,
+                    1405.0,
+                    1260.0,
+                    1405.0,
+                    1301.0,
+                    294.0,
+                    1301.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1295.0,
+                    1125.0,
+                    1295.0,
+                    1125.0,
+                    1328.0,
+                    294.0,
+                    1328.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    532.0,
+                    803.0,
+                    532.0,
+                    803.0,
+                    574.0,
+                    294.0,
+                    574.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 1,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1849,
+                    1404,
+                    1849,
+                    1404,
+                    2035,
+                    296,
+                    2035
+                ],
+                "score": 0.98
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1424,
+                    1405,
+                    1424,
+                    1405,
+                    1580,
+                    298,
+                    1580
+                ],
+                "score": 0.979
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1682,
+                    1404,
+                    1682,
+                    1404,
+                    1837,
+                    296,
+                    1837
+                ],
+                "score": 0.978
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1208,
+                    1403,
+                    1208,
+                    1403,
+                    1335,
+                    298,
+                    1335
+                ],
+                "score": 0.975
+            },
+            {
+                "category_id": 4,
+                "poly": [
+                    296,
+                    659,
+                    1406,
+                    659,
+                    1406,
+                    1027,
+                    296,
+                    1027
+                ],
+                "score": 0.972
+            },
+            {
+                "category_id": 3,
+                "poly": [
+                    299,
+                    232,
+                    1400,
+                    232,
+                    1400,
+                    648,
+                    299,
+                    648
+                ],
+                "score": 0.97
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    367,
+                    1587,
+                    1326,
+                    1587,
+                    1326,
+                    1677,
+                    367,
+                    1677
+                ],
+                "score": 0.95
+            },
+            {
+                "category_id": 8,
+                "poly": [
+                    317,
+                    1114,
+                    1380,
+                    1114,
+                    1380,
+                    1202,
+                    317,
+                    1202
+                ],
+                "score": 0.928
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1072,
+                    1184,
+                    1072,
+                    1184,
+                    1106,
+                    297,
+                    1106
+                ],
+                "score": 0.909
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    299,
+                    1368,
+                    654,
+                    1368,
+                    654,
+                    1399,
+                    299,
+                    1399
+                ],
+                "score": 0.904
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    76,
+                    858,
+                    76,
+                    858,
+                    104,
+                    298,
+                    104
+                ],
+                "score": 0.767
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2088,
+                    858,
+                    2088,
+                    858,
+                    2112,
+                    841,
+                    2112
+                ],
+                "score": 0.659
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    300,
+                    77,
+                    856,
+                    77,
+                    856,
+                    103,
+                    300,
+                    103
+                ],
+                "score": 0.437
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2088,
+                    859,
+                    2088,
+                    859,
+                    2112,
+                    841,
+                    2112
+                ],
+                "score": 0.343
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    370,
+                    1583,
+                    1329,
+                    1583,
+                    1329,
+                    1679,
+                    370,
+                    1679
+                ],
+                "score": 0.94,
+                "latex": "\\theta ^ { * } = \\arg \\operatorname* { m i n } _ { \\theta } \\frac { 1 } { N } \\sum _ { n = 1 } ^ { N } \\mathcal { L } _ { \\mathrm { C P C } } [ f _ { \\theta } ( x _ { n } ) ] , \\quad \\psi ^ { * } = \\arg \\operatorname* { m i n } _ { \\psi } \\frac { 1 } { M } \\sum _ { m = 1 } ^ { M } \\mathcal { L } _ { \\mathrm { S u p } } [ h _ { \\psi } \\circ f _ { \\theta ^ { * } } ( x _ { m } ) , y _ { m } ]"
+            },
+            {
+                "category_id": 14,
+                "poly": [
+                    319,
+                    1111,
+                    1377,
+                    1111,
+                    1377,
+                    1205,
+                    319,
+                    1205
+                ],
+                "score": 0.94,
+                "latex": "\\mathcal { L } _ { \\mathrm { C P C } } = - \\sum _ { i , j , k } \\log p ( z _ { i + k , j } | \\hat { z } _ { i + k , j } , \\{ z _ { l } \\} ) = - \\sum _ { i , j , k } \\log \\frac { \\exp ( \\hat { z } _ { i + k , j } ^ { T } z _ { i + k , j } ) } { \\exp ( \\hat { z } _ { i + k , j } ^ { T } z _ { i + k , j } ) + \\sum _ { l } \\exp ( \\hat { z } _ { i + k , j } ^ { T } z _ { l } ) }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    777,
+                    1456,
+                    898,
+                    1456,
+                    898,
+                    1490,
+                    777,
+                    1490
+                ],
+                "score": 0.93,
+                "latex": "z = f _ { \\boldsymbol { \\theta } } ( \\pmb { x } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1059,
+                    1547,
+                    1239,
+                    1547,
+                    1239,
+                    1581,
+                    1059,
+                    1581
+                ],
+                "score": 0.92,
+                "latex": "\\mathbb { D } _ { l } = \\{ x _ { m } , y _ { m } \\}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    542,
+                    1210,
+                    595,
+                    1210,
+                    595,
+                    1243,
+                    542,
+                    1243
+                ],
+                "score": 0.92,
+                "latex": "\\left\\{ z _ { l } \\right\\}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    1547,
+                    358,
+                    1547,
+                    358,
+                    1581,
+                    298,
+                    1581
+                ],
+                "score": 0.91,
+                "latex": "\\left\\{ x _ { n } \\right\\}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1327,
+                    1425,
+                    1400,
+                    1425,
+                    1400,
+                    1459,
+                    1327,
+                    1459
+                ],
+                "score": 0.91,
+                "latex": "\\{ W _ { k } \\}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    774,
+                    1306,
+                    818,
+                    1306,
+                    818,
+                    1335,
+                    774,
+                    1335
+                ],
+                "score": 0.91,
+                "latex": "\\mathbf { } _ { c _ { i , j } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    868,
+                    1305,
+                    943,
+                    1305,
+                    943,
+                    1336,
+                    868,
+                    1336
+                ],
+                "score": 0.9,
+                "latex": "z _ { i + k , j }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    781,
+                    1945,
+                    835,
+                    1945,
+                    835,
+                    1976,
+                    781,
+                    1976
+                ],
+                "score": 0.9,
+                "latex": "\\mathcal { L } _ { \\mathrm { { S u p } } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    965,
+                    1743,
+                    1020,
+                    1743,
+                    1020,
+                    1776,
+                    965,
+                    1776
+                ],
+                "score": 0.9,
+                "latex": "\\mathcal { L } _ { \\mathrm { { S u p } } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1002,
+                    1488,
+                    1038,
+                    1488,
+                    1038,
+                    1520,
+                    1002,
+                    1520
+                ],
+                "score": 0.9,
+                "latex": "h _ { \\psi }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    681,
+                    1744,
+                    717,
+                    1744,
+                    717,
+                    1776,
+                    681,
+                    1776
+                ],
+                "score": 0.9,
+                "latex": "h _ { \\psi }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    821,
+                    1683,
+                    859,
+                    1683,
+                    859,
+                    1713,
+                    821,
+                    1713
+                ],
+                "score": 0.89,
+                "latex": "\\mathbb { D } _ { u }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1328,
+                    1518,
+                    1403,
+                    1518,
+                    1403,
+                    1549,
+                    1328,
+                    1549
+                ],
+                "score": 0.89,
+                "latex": "\\mathbb { D } _ { u } ="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    937,
+                    1883,
+                    973,
+                    1883,
+                    973,
+                    1915,
+                    937,
+                    1915
+                ],
+                "score": 0.89,
+                "latex": "h _ { \\psi }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1231,
+                    1913,
+                    1264,
+                    1913,
+                    1264,
+                    1942,
+                    1231,
+                    1942
+                ],
+                "score": 0.88,
+                "latex": "\\mathbb { D } _ { l }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    811,
+                    1913,
+                    839,
+                    1913,
+                    839,
+                    1943,
+                    811,
+                    1943
+                ],
+                "score": 0.88,
+                "latex": "f _ { \\theta }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1199,
+                    1713,
+                    1232,
+                    1713,
+                    1232,
+                    1743,
+                    1199,
+                    1743
+                ],
+                "score": 0.87,
+                "latex": "\\mathbb { D } _ { l }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    881,
+                    1805,
+                    908,
+                    1805,
+                    908,
+                    1836,
+                    881,
+                    1836
+                ],
+                "score": 0.87,
+                "latex": "f _ { \\theta }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    701,
+                    1427,
+                    730,
+                    1427,
+                    730,
+                    1458,
+                    701,
+                    1458
+                ],
+                "score": 0.87,
+                "latex": "f _ { \\theta }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    952,
+                    1431,
+                    982,
+                    1431,
+                    982,
+                    1459,
+                    952,
+                    1459
+                ],
+                "score": 0.86,
+                "latex": "g _ { \\phi }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    851,
+                    1549,
+                    883,
+                    1549,
+                    883,
+                    1575,
+                    851,
+                    1575
+                ],
+                "score": 0.85,
+                "latex": "M"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1089,
+                    1519,
+                    1118,
+                    1519,
+                    1118,
+                    1545,
+                    1089,
+                    1545
+                ],
+                "score": 0.82,
+                "latex": "N"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1343,
+                    1464,
+                    1362,
+                    1464,
+                    1362,
+                    1484,
+                    1343,
+                    1484
+                ],
+                "score": 0.78,
+                "latex": "x"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    550,
+                    1272,
+                    577,
+                    1272,
+                    577,
+                    1299,
+                    550,
+                    1299
+                ],
+                "score": 0.43,
+                "latex": "\\&"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    660.0,
+                    1406.0,
+                    660.0,
+                    1406.0,
+                    694.0,
+                    295.0,
+                    694.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    691.0,
+                    1404.0,
+                    691.0,
+                    1404.0,
+                    725.0,
+                    295.0,
+                    725.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    720.0,
+                    1406.0,
+                    720.0,
+                    1406.0,
+                    758.0,
+                    293.0,
+                    758.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    748.0,
+                    1406.0,
+                    748.0,
+                    1406.0,
+                    787.0,
+                    294.0,
+                    787.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    781.0,
+                    1407.0,
+                    781.0,
+                    1407.0,
+                    819.0,
+                    293.0,
+                    819.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    813.0,
+                    1404.0,
+                    813.0,
+                    1404.0,
+                    847.0,
+                    295.0,
+                    847.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    843.0,
+                    1406.0,
+                    843.0,
+                    1406.0,
+                    876.0,
+                    293.0,
+                    876.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    871.0,
+                    1407.0,
+                    871.0,
+                    1407.0,
+                    908.0,
+                    291.0,
+                    908.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    900.0,
+                    1407.0,
+                    900.0,
+                    1407.0,
+                    941.0,
+                    293.0,
+                    941.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    932.0,
+                    1406.0,
+                    932.0,
+                    1406.0,
+                    970.0,
+                    293.0,
+                    970.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    966.0,
+                    1404.0,
+                    966.0,
+                    1404.0,
+                    997.0,
+                    295.0,
+                    997.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    995.0,
+                    1348.0,
+                    995.0,
+                    1348.0,
+                    1029.0,
+                    295.0,
+                    1029.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    464.0,
+                    255.0,
+                    572.0,
+                    255.0,
+                    572.0,
+                    296.0,
+                    464.0,
+                    296.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    756.0,
+                    242.0,
+                    892.0,
+                    242.0,
+                    892.0,
+                    302.0,
+                    756.0,
+                    302.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    913.0,
+                    249.0,
+                    975.0,
+                    249.0,
+                    975.0,
+                    295.0,
+                    913.0,
+                    295.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    992.0,
+                    239.0,
+                    1048.0,
+                    239.0,
+                    1048.0,
+                    297.0,
+                    992.0,
+                    297.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1066.0,
+                    249.0,
+                    1123.0,
+                    249.0,
+                    1123.0,
+                    296.0,
+                    1066.0,
+                    296.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1142.0,
+                    234.0,
+                    1196.0,
+                    234.0,
+                    1196.0,
+                    299.0,
+                    1142.0,
+                    299.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1214.0,
+                    248.0,
+                    1271.0,
+                    248.0,
+                    1271.0,
+                    294.0,
+                    1214.0,
+                    294.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1290.0,
+                    261.0,
+                    1341.0,
+                    261.0,
+                    1341.0,
+                    282.0,
+                    1290.0,
+                    282.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1373.0,
+                    224.0,
+                    1398.0,
+                    224.0,
+                    1398.0,
+                    324.0,
+                    1373.0,
+                    324.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    970.0,
+                    319.0,
+                    1071.0,
+                    319.0,
+                    1071.0,
+                    342.0,
+                    970.0,
+                    342.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    310.0,
+                    330.0,
+                    355.0,
+                    330.0,
+                    355.0,
+                    351.0,
+                    310.0,
+                    351.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    372.0,
+                    407.0,
+                    372.0,
+                    407.0,
+                    388.0,
+                    393.0,
+                    388.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    577.0,
+                    379.0,
+                    589.0,
+                    379.0,
+                    589.0,
+                    389.0,
+                    577.0,
+                    389.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    604.0,
+                    338.0,
+                    613.0,
+                    338.0,
+                    613.0,
+                    348.0,
+                    604.0,
+                    348.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    618.0,
+                    369.0,
+                    714.0,
+                    369.0,
+                    714.0,
+                    389.0,
+                    618.0,
+                    389.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    749.0,
+                    342.0,
+                    912.0,
+                    342.0,
+                    912.0,
+                    386.0,
+                    749.0,
+                    386.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    913.0,
+                    335.0,
+                    1123.0,
+                    335.0,
+                    1123.0,
+                    383.0,
+                    913.0,
+                    383.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1150.0,
+                    333.0,
+                    1189.0,
+                    333.0,
+                    1189.0,
+                    354.0,
+                    1150.0,
+                    354.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1217.0,
+                    333.0,
+                    1267.0,
+                    333.0,
+                    1267.0,
+                    383.0,
+                    1217.0,
+                    383.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1277.0,
+                    354.0,
+                    1290.0,
+                    354.0,
+                    1290.0,
+                    363.0,
+                    1277.0,
+                    363.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1298.0,
+                    339.0,
+                    1337.0,
+                    339.0,
+                    1337.0,
+                    377.0,
+                    1298.0,
+                    377.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    981.0,
+                    397.0,
+                    1061.0,
+                    397.0,
+                    1061.0,
+                    429.0,
+                    981.0,
+                    429.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1367.0,
+                    400.0,
+                    1396.0,
+                    400.0,
+                    1396.0,
+                    492.0,
+                    1367.0,
+                    492.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    644.0,
+                    423.0,
+                    654.0,
+                    423.0,
+                    654.0,
+                    433.0,
+                    644.0,
+                    433.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    913.0,
+                    421.0,
+                    973.0,
+                    421.0,
+                    973.0,
+                    441.0,
+                    913.0,
+                    441.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    991.0,
+                    423.0,
+                    1048.0,
+                    423.0,
+                    1048.0,
+                    439.0,
+                    991.0,
+                    439.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1061.0,
+                    421.0,
+                    1128.0,
+                    421.0,
+                    1128.0,
+                    441.0,
+                    1061.0,
+                    441.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1141.0,
+                    421.0,
+                    1197.0,
+                    421.0,
+                    1197.0,
+                    441.0,
+                    1141.0,
+                    441.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1220.0,
+                    423.0,
+                    1266.0,
+                    423.0,
+                    1266.0,
+                    440.0,
+                    1220.0,
+                    440.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    742.0,
+                    431.0,
+                    917.0,
+                    431.0,
+                    917.0,
+                    455.0,
+                    742.0,
+                    455.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1297.0,
+                    431.0,
+                    1335.0,
+                    431.0,
+                    1335.0,
+                    449.0,
+                    1297.0,
+                    449.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    746.0,
+                    450.0,
+                    915.0,
+                    450.0,
+                    915.0,
+                    470.0,
+                    746.0,
+                    470.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    938.0,
+                    452.0,
+                    960.0,
+                    452.0,
+                    960.0,
+                    467.0,
+                    938.0,
+                    467.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1008.0,
+                    449.0,
+                    1031.0,
+                    449.0,
+                    1031.0,
+                    470.0,
+                    1008.0,
+                    470.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1067.0,
+                    449.0,
+                    1106.0,
+                    449.0,
+                    1106.0,
+                    470.0,
+                    1067.0,
+                    470.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1217.0,
+                    449.0,
+                    1256.0,
+                    449.0,
+                    1256.0,
+                    470.0,
+                    1217.0,
+                    470.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1302.0,
+                    442.0,
+                    1331.0,
+                    442.0,
+                    1331.0,
+                    461.0,
+                    1302.0,
+                    461.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    986.0,
+                    483.0,
+                    1055.0,
+                    483.0,
+                    1055.0,
+                    503.0,
+                    986.0,
+                    503.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    980.0,
+                    496.0,
+                    1061.0,
+                    496.0,
+                    1061.0,
+                    516.0,
+                    980.0,
+                    516.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    921.0,
+                    508.0,
+                    967.0,
+                    508.0,
+                    967.0,
+                    529.0,
+                    921.0,
+                    529.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    991.0,
+                    509.0,
+                    1050.0,
+                    509.0,
+                    1050.0,
+                    526.0,
+                    991.0,
+                    526.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1051.0,
+                    508.0,
+                    1201.0,
+                    508.0,
+                    1201.0,
+                    528.0,
+                    1051.0,
+                    528.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1225.0,
+                    508.0,
+                    1261.0,
+                    508.0,
+                    1261.0,
+                    529.0,
+                    1225.0,
+                    529.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    761.0,
+                    517.0,
+                    898.0,
+                    517.0,
+                    898.0,
+                    544.0,
+                    761.0,
+                    544.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1299.0,
+                    517.0,
+                    1334.0,
+                    517.0,
+                    1334.0,
+                    538.0,
+                    1299.0,
+                    538.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    762.0,
+                    537.0,
+                    898.0,
+                    537.0,
+                    898.0,
+                    557.0,
+                    762.0,
+                    557.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    936.0,
+                    538.0,
+                    958.0,
+                    538.0,
+                    958.0,
+                    557.0,
+                    936.0,
+                    557.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1006.0,
+                    534.0,
+                    1033.0,
+                    534.0,
+                    1033.0,
+                    559.0,
+                    1006.0,
+                    559.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1068.0,
+                    536.0,
+                    1106.0,
+                    536.0,
+                    1106.0,
+                    557.0,
+                    1068.0,
+                    557.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1155.0,
+                    533.0,
+                    1184.0,
+                    533.0,
+                    1184.0,
+                    559.0,
+                    1155.0,
+                    559.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1216.0,
+                    536.0,
+                    1256.0,
+                    536.0,
+                    1256.0,
+                    557.0,
+                    1216.0,
+                    557.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1299.0,
+                    528.0,
+                    1334.0,
+                    528.0,
+                    1334.0,
+                    549.0,
+                    1299.0,
+                    549.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    747.0,
+                    599.0,
+                    911.0,
+                    599.0,
+                    911.0,
+                    631.0,
+                    747.0,
+                    631.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    913.0,
+                    595.0,
+                    975.0,
+                    595.0,
+                    975.0,
+                    615.0,
+                    913.0,
+                    615.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1140.0,
+                    593.0,
+                    1199.0,
+                    593.0,
+                    1199.0,
+                    612.0,
+                    1140.0,
+                    612.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1219.0,
+                    594.0,
+                    1267.0,
+                    594.0,
+                    1267.0,
+                    615.0,
+                    1219.0,
+                    615.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1297.0,
+                    602.0,
+                    1336.0,
+                    602.0,
+                    1336.0,
+                    624.0,
+                    1297.0,
+                    624.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1367.0,
+                    574.0,
+                    1396.0,
+                    574.0,
+                    1396.0,
+                    652.0,
+                    1367.0,
+                    652.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    744.0,
+                    620.0,
+                    916.0,
+                    620.0,
+                    916.0,
+                    640.0,
+                    744.0,
+                    640.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    938.0,
+                    625.0,
+                    956.0,
+                    625.0,
+                    956.0,
+                    641.0,
+                    938.0,
+                    641.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1155.0,
+                    620.0,
+                    1184.0,
+                    620.0,
+                    1184.0,
+                    646.0,
+                    1155.0,
+                    646.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1217.0,
+                    622.0,
+                    1256.0,
+                    622.0,
+                    1256.0,
+                    643.0,
+                    1217.0,
+                    643.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1300.0,
+                    615.0,
+                    1331.0,
+                    615.0,
+                    1331.0,
+                    637.0,
+                    1300.0,
+                    637.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    610.0,
+                    348.5,
+                    720.0,
+                    348.5,
+                    720.0,
+                    376.5,
+                    610.0,
+                    376.5
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1156.0,
+                    360.0,
+                    1181.0,
+                    360.0,
+                    1181.0,
+                    385.0,
+                    1156.0,
+                    385.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1157.0,
+                    448.0,
+                    1181.0,
+                    448.0,
+                    1181.0,
+                    471.5,
+                    1157.0,
+                    471.5
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    358.0,
+                    519.5,
+                    440.0,
+                    519.5,
+                    440.0,
+                    553.0,
+                    358.0,
+                    553.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1367.0,
+                    657.0,
+                    1367.0,
+                    657.0,
+                    1403.0,
+                    295.0,
+                    1403.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    70.0,
+                    859.0,
+                    70.0,
+                    859.0,
+                    109.0,
+                    296.0,
+                    109.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    839.0,
+                    2085.0,
+                    860.0,
+                    2085.0,
+                    860.0,
+                    2116.0,
+                    839.0,
+                    2116.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    73.0,
+                    859.0,
+                    73.0,
+                    859.0,
+                    108.0,
+                    297.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    838.0,
+                    2085.0,
+                    862.0,
+                    2085.0,
+                    862.0,
+                    2118.0,
+                    838.0,
+                    2118.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1845.0,
+                    1405.0,
+                    1845.0,
+                    1405.0,
+                    1888.0,
+                    291.0,
+                    1888.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1882.0,
+                    936.0,
+                    1882.0,
+                    936.0,
+                    1916.0,
+                    291.0,
+                    1916.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    974.0,
+                    1882.0,
+                    1405.0,
+                    1882.0,
+                    1405.0,
+                    1916.0,
+                    974.0,
+                    1916.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1909.0,
+                    810.0,
+                    1909.0,
+                    810.0,
+                    1948.0,
+                    293.0,
+                    1948.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    840.0,
+                    1909.0,
+                    1230.0,
+                    1909.0,
+                    1230.0,
+                    1948.0,
+                    840.0,
+                    1948.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1265.0,
+                    1909.0,
+                    1406.0,
+                    1909.0,
+                    1406.0,
+                    1948.0,
+                    1265.0,
+                    1948.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1941.0,
+                    780.0,
+                    1941.0,
+                    780.0,
+                    1980.0,
+                    293.0,
+                    1980.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    836.0,
+                    1941.0,
+                    1405.0,
+                    1941.0,
+                    1405.0,
+                    1980.0,
+                    836.0,
+                    1980.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1973.0,
+                    1406.0,
+                    1973.0,
+                    1406.0,
+                    2008.0,
+                    294.0,
+                    2008.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    2001.0,
+                    509.0,
+                    2001.0,
+                    509.0,
+                    2039.0,
+                    294.0,
+                    2039.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1423.0,
+                    700.0,
+                    1423.0,
+                    700.0,
+                    1461.0,
+                    295.0,
+                    1461.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    731.0,
+                    1423.0,
+                    951.0,
+                    1423.0,
+                    951.0,
+                    1461.0,
+                    731.0,
+                    1461.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    983.0,
+                    1423.0,
+                    1326.0,
+                    1423.0,
+                    1326.0,
+                    1461.0,
+                    983.0,
+                    1461.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1457.0,
+                    776.0,
+                    1457.0,
+                    776.0,
+                    1490.0,
+                    296.0,
+                    1490.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    899.0,
+                    1457.0,
+                    1342.0,
+                    1457.0,
+                    1342.0,
+                    1490.0,
+                    899.0,
+                    1490.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1363.0,
+                    1457.0,
+                    1403.0,
+                    1457.0,
+                    1403.0,
+                    1490.0,
+                    1363.0,
+                    1490.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1483.0,
+                    1001.0,
+                    1483.0,
+                    1001.0,
+                    1522.0,
+                    295.0,
+                    1522.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1039.0,
+                    1483.0,
+                    1403.0,
+                    1483.0,
+                    1403.0,
+                    1522.0,
+                    1039.0,
+                    1522.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1514.0,
+                    1088.0,
+                    1514.0,
+                    1088.0,
+                    1555.0,
+                    293.0,
+                    1555.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1119.0,
+                    1514.0,
+                    1327.0,
+                    1514.0,
+                    1327.0,
+                    1555.0,
+                    1119.0,
+                    1555.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    359.0,
+                    1543.0,
+                    850.0,
+                    1543.0,
+                    850.0,
+                    1587.0,
+                    359.0,
+                    1587.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    884.0,
+                    1543.0,
+                    1058.0,
+                    1543.0,
+                    1058.0,
+                    1587.0,
+                    884.0,
+                    1587.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1240.0,
+                    1543.0,
+                    1251.0,
+                    1543.0,
+                    1251.0,
+                    1587.0,
+                    1240.0,
+                    1587.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1680.0,
+                    820.0,
+                    1680.0,
+                    820.0,
+                    1717.0,
+                    294.0,
+                    1717.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    860.0,
+                    1680.0,
+                    1406.0,
+                    1680.0,
+                    1406.0,
+                    1717.0,
+                    860.0,
+                    1717.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1710.0,
+                    1198.0,
+                    1710.0,
+                    1198.0,
+                    1746.0,
+                    295.0,
+                    1746.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1233.0,
+                    1710.0,
+                    1404.0,
+                    1710.0,
+                    1404.0,
+                    1746.0,
+                    1233.0,
+                    1746.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1742.0,
+                    680.0,
+                    1742.0,
+                    680.0,
+                    1779.0,
+                    294.0,
+                    1779.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    718.0,
+                    1742.0,
+                    964.0,
+                    1742.0,
+                    964.0,
+                    1779.0,
+                    718.0,
+                    1779.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1021.0,
+                    1742.0,
+                    1406.0,
+                    1742.0,
+                    1406.0,
+                    1779.0,
+                    1021.0,
+                    1779.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1771.0,
+                    1406.0,
+                    1771.0,
+                    1406.0,
+                    1807.0,
+                    291.0,
+                    1807.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1801.0,
+                    880.0,
+                    1801.0,
+                    880.0,
+                    1841.0,
+                    293.0,
+                    1841.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    909.0,
+                    1801.0,
+                    919.0,
+                    1801.0,
+                    919.0,
+                    1841.0,
+                    909.0,
+                    1841.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1208.0,
+                    541.0,
+                    1208.0,
+                    541.0,
+                    1244.0,
+                    293.0,
+                    1244.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    596.0,
+                    1208.0,
+                    1403.0,
+                    1208.0,
+                    1403.0,
+                    1244.0,
+                    596.0,
+                    1244.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1240.0,
+                    1407.0,
+                    1240.0,
+                    1407.0,
+                    1276.0,
+                    293.0,
+                    1276.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1271.0,
+                    549.0,
+                    1271.0,
+                    549.0,
+                    1305.0,
+                    294.0,
+                    1305.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    578.0,
+                    1271.0,
+                    1405.0,
+                    1271.0,
+                    1405.0,
+                    1305.0,
+                    578.0,
+                    1305.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1301.0,
+                    773.0,
+                    1301.0,
+                    773.0,
+                    1338.0,
+                    293.0,
+                    1338.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    819.0,
+                    1301.0,
+                    867.0,
+                    1301.0,
+                    867.0,
+                    1338.0,
+                    819.0,
+                    1338.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    944.0,
+                    1301.0,
+                    1258.0,
+                    1301.0,
+                    1258.0,
+                    1338.0,
+                    944.0,
+                    1338.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1071.0,
+                    1188.0,
+                    1071.0,
+                    1188.0,
+                    1110.0,
+                    295.0,
+                    1110.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 2,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1668,
+                    1403,
+                    1668,
+                    1403,
+                    2034,
+                    298,
+                    2034
+                ],
+                "score": 0.983
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1286,
+                    1404,
+                    1286,
+                    1404,
+                    1651,
+                    298,
+                    1651
+                ],
+                "score": 0.983
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    629,
+                    1403,
+                    629,
+                    1403,
+                    813,
+                    299,
+                    813
+                ],
+                "score": 0.979
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    229,
+                    1403,
+                    229,
+                    1403,
+                    445,
+                    298,
+                    445
+                ],
+                "score": 0.979
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    460,
+                    1403,
+                    460,
+                    1403,
+                    614,
+                    299,
+                    614
+                ],
+                "score": 0.976
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    978,
+                    1402,
+                    978,
+                    1402,
+                    1101,
+                    299,
+                    1101
+                ],
+                "score": 0.975
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1117,
+                    1402,
+                    1117,
+                    1402,
+                    1270,
+                    299,
+                    1270
+                ],
+                "score": 0.974
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    301,
+                    888,
+                    586,
+                    888,
+                    586,
+                    924,
+                    301,
+                    924
+                ],
+                "score": 0.9
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    76,
+                    857,
+                    76,
+                    857,
+                    104,
+                    298,
+                    104
+                ],
+                "score": 0.89
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2089,
+                    858,
+                    2089,
+                    858,
+                    2111,
+                    841,
+                    2111
+                ],
+                "score": 0.754
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    635,
+                    553,
+                    689,
+                    553,
+                    689,
+                    585,
+                    635,
+                    585
+                ],
+                "score": 0.91,
+                "latex": "\\mathcal { L } _ { \\mathrm { { S u p } } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1055,
+                    353,
+                    1110,
+                    353,
+                    1110,
+                    385,
+                    1055,
+                    385
+                ],
+                "score": 0.9,
+                "latex": "\\mathcal { L } _ { \\mathrm { { S u p } } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    730,
+                    262,
+                    766,
+                    262,
+                    766,
+                    295,
+                    730,
+                    295
+                ],
+                "score": 0.89,
+                "latex": "h _ { \\psi }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1077,
+                    1071,
+                    1113,
+                    1071,
+                    1113,
+                    1105,
+                    1077,
+                    1105
+                ],
+                "score": 0.89,
+                "latex": "h _ { \\psi }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    548,
+                    552,
+                    583,
+                    552,
+                    583,
+                    585,
+                    548,
+                    585
+                ],
+                "score": 0.88,
+                "latex": "h _ { \\psi }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    792,
+                    522,
+                    824,
+                    522,
+                    824,
+                    552,
+                    792,
+                    552
+                ],
+                "score": 0.88,
+                "latex": "\\mathbb { D } _ { l }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    516,
+                    323,
+                    547,
+                    323,
+                    547,
+                    352,
+                    516,
+                    352
+                ],
+                "score": 0.87,
+                "latex": "\\mathbb { D } _ { l }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1259,
+                    1041,
+                    1288,
+                    1041,
+                    1288,
+                    1072,
+                    1259,
+                    1072
+                ],
+                "score": 0.87,
+                "latex": "f _ { \\theta }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    471,
+                    353,
+                    538,
+                    353,
+                    538,
+                    382,
+                    471,
+                    382
+                ],
+                "score": 0.87,
+                "latex": "100 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    362,
+                    352,
+                    418,
+                    352,
+                    418,
+                    382,
+                    362,
+                    382
+                ],
+                "score": 0.86,
+                "latex": "50 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    296,
+                    352,
+                    351,
+                    352,
+                    351,
+                    382,
+                    296,
+                    382
+                ],
+                "score": 0.84,
+                "latex": "20 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1340,
+                    322,
+                    1393,
+                    322,
+                    1393,
+                    352,
+                    1340,
+                    352
+                ],
+                "score": 0.83,
+                "latex": "10 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1288,
+                    322,
+                    1329,
+                    322,
+                    1329,
+                    352,
+                    1288,
+                    352
+                ],
+                "score": 0.78,
+                "latex": "5 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1238,
+                    322,
+                    1279,
+                    322,
+                    1279,
+                    351,
+                    1238,
+                    351
+                ],
+                "score": 0.77,
+                "latex": "2 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1190,
+                    322,
+                    1229,
+                    322,
+                    1229,
+                    351,
+                    1190,
+                    351
+                ],
+                "score": 0.76,
+                "latex": "1 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    651,
+                    721,
+                    681,
+                    721,
+                    681,
+                    750,
+                    651,
+                    750
+                ],
+                "score": 0.61,
+                "latex": "\\theta ^ { * }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    690,
+                    721,
+                    725,
+                    721,
+                    725,
+                    752,
+                    690,
+                    752
+                ],
+                "score": 0.55,
+                "latex": "\\psi ^ { * }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    651,
+                    721,
+                    723,
+                    721,
+                    723,
+                    752,
+                    651,
+                    752
+                ],
+                "score": 0.4,
+                "latex": "\\theta ^ { * } , \\psi ^ { * }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    923,
+                    630,
+                    951,
+                    630,
+                    951,
+                    662,
+                    923,
+                    662
+                ],
+                "score": 0.34,
+                "latex": "f _ { \\theta }"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    886.0,
+                    592.0,
+                    886.0,
+                    592.0,
+                    929.0,
+                    292.0,
+                    929.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    298.0,
+                    73.0,
+                    858.0,
+                    73.0,
+                    858.0,
+                    108.0,
+                    298.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    838.0,
+                    2086.0,
+                    862.0,
+                    2086.0,
+                    862.0,
+                    2118.0,
+                    838.0,
+                    2118.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1665.0,
+                    1407.0,
+                    1665.0,
+                    1407.0,
+                    1705.0,
+                    293.0,
+                    1705.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1699.0,
+                    1404.0,
+                    1699.0,
+                    1404.0,
+                    1730.0,
+                    296.0,
+                    1730.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1730.0,
+                    1405.0,
+                    1730.0,
+                    1405.0,
+                    1764.0,
+                    292.0,
+                    1764.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1760.0,
+                    1405.0,
+                    1760.0,
+                    1405.0,
+                    1793.0,
+                    293.0,
+                    1793.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1792.0,
+                    1404.0,
+                    1792.0,
+                    1404.0,
+                    1822.0,
+                    296.0,
+                    1822.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1821.0,
+                    1404.0,
+                    1821.0,
+                    1404.0,
+                    1855.0,
+                    293.0,
+                    1855.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1851.0,
+                    1403.0,
+                    1851.0,
+                    1403.0,
+                    1884.0,
+                    293.0,
+                    1884.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1881.0,
+                    1404.0,
+                    1881.0,
+                    1404.0,
+                    1914.0,
+                    293.0,
+                    1914.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1910.0,
+                    1404.0,
+                    1910.0,
+                    1404.0,
+                    1948.0,
+                    293.0,
+                    1948.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1943.0,
+                    1405.0,
+                    1943.0,
+                    1405.0,
+                    1977.0,
+                    294.0,
+                    1977.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1970.0,
+                    1407.0,
+                    1970.0,
+                    1407.0,
+                    2009.0,
+                    292.0,
+                    2009.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    2003.0,
+                    1315.0,
+                    2003.0,
+                    1315.0,
+                    2037.0,
+                    294.0,
+                    2037.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1286.0,
+                    1405.0,
+                    1286.0,
+                    1405.0,
+                    1323.0,
+                    293.0,
+                    1323.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1316.0,
+                    1405.0,
+                    1316.0,
+                    1405.0,
+                    1353.0,
+                    293.0,
+                    1353.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1349.0,
+                    1405.0,
+                    1349.0,
+                    1405.0,
+                    1383.0,
+                    294.0,
+                    1383.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1376.0,
+                    1406.0,
+                    1376.0,
+                    1406.0,
+                    1414.0,
+                    291.0,
+                    1414.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1408.0,
+                    1405.0,
+                    1408.0,
+                    1405.0,
+                    1442.0,
+                    293.0,
+                    1442.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1439.0,
+                    1405.0,
+                    1439.0,
+                    1405.0,
+                    1473.0,
+                    293.0,
+                    1473.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1467.0,
+                    1405.0,
+                    1467.0,
+                    1405.0,
+                    1504.0,
+                    293.0,
+                    1504.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1500.0,
+                    1405.0,
+                    1500.0,
+                    1405.0,
+                    1534.0,
+                    294.0,
+                    1534.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1528.0,
+                    1405.0,
+                    1528.0,
+                    1405.0,
+                    1567.0,
+                    292.0,
+                    1567.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1557.0,
+                    1405.0,
+                    1557.0,
+                    1405.0,
+                    1597.0,
+                    291.0,
+                    1597.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1591.0,
+                    1406.0,
+                    1591.0,
+                    1406.0,
+                    1626.0,
+                    292.0,
+                    1626.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1623.0,
+                    640.0,
+                    1623.0,
+                    640.0,
+                    1654.0,
+                    294.0,
+                    1654.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    628.0,
+                    922.0,
+                    628.0,
+                    922.0,
+                    664.0,
+                    294.0,
+                    664.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    952.0,
+                    628.0,
+                    1404.0,
+                    628.0,
+                    1404.0,
+                    664.0,
+                    952.0,
+                    664.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    654.0,
+                    1407.0,
+                    654.0,
+                    1407.0,
+                    698.0,
+                    292.0,
+                    698.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    691.0,
+                    1405.0,
+                    691.0,
+                    1405.0,
+                    722.0,
+                    295.0,
+                    722.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    720.0,
+                    650.0,
+                    720.0,
+                    650.0,
+                    755.0,
+                    294.0,
+                    755.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    726.0,
+                    720.0,
+                    1407.0,
+                    720.0,
+                    1407.0,
+                    755.0,
+                    726.0,
+                    755.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    751.0,
+                    1404.0,
+                    751.0,
+                    1404.0,
+                    783.0,
+                    295.0,
+                    783.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    779.0,
+                    1294.0,
+                    779.0,
+                    1294.0,
+                    819.0,
+                    293.0,
+                    819.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    230.0,
+                    1405.0,
+                    230.0,
+                    1405.0,
+                    264.0,
+                    294.0,
+                    264.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    258.0,
+                    729.0,
+                    258.0,
+                    729.0,
+                    296.0,
+                    293.0,
+                    296.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    767.0,
+                    258.0,
+                    1405.0,
+                    258.0,
+                    1405.0,
+                    296.0,
+                    767.0,
+                    296.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    289.0,
+                    1403.0,
+                    289.0,
+                    1403.0,
+                    326.0,
+                    292.0,
+                    326.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    320.0,
+                    515.0,
+                    320.0,
+                    515.0,
+                    356.0,
+                    294.0,
+                    356.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    548.0,
+                    320.0,
+                    1189.0,
+                    320.0,
+                    1189.0,
+                    356.0,
+                    548.0,
+                    356.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1230.0,
+                    320.0,
+                    1237.0,
+                    320.0,
+                    1237.0,
+                    356.0,
+                    1230.0,
+                    356.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1280.0,
+                    320.0,
+                    1287.0,
+                    320.0,
+                    1287.0,
+                    356.0,
+                    1280.0,
+                    356.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1330.0,
+                    320.0,
+                    1339.0,
+                    320.0,
+                    1339.0,
+                    356.0,
+                    1330.0,
+                    356.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1394.0,
+                    320.0,
+                    1404.0,
+                    320.0,
+                    1404.0,
+                    356.0,
+                    1394.0,
+                    356.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    349.0,
+                    295.0,
+                    349.0,
+                    295.0,
+                    390.0,
+                    292.0,
+                    390.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    352.0,
+                    349.0,
+                    361.0,
+                    349.0,
+                    361.0,
+                    390.0,
+                    352.0,
+                    390.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    419.0,
+                    349.0,
+                    470.0,
+                    349.0,
+                    470.0,
+                    390.0,
+                    419.0,
+                    390.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    539.0,
+                    349.0,
+                    1054.0,
+                    349.0,
+                    1054.0,
+                    390.0,
+                    539.0,
+                    390.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1111.0,
+                    349.0,
+                    1407.0,
+                    349.0,
+                    1407.0,
+                    390.0,
+                    1111.0,
+                    390.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    380.0,
+                    1405.0,
+                    380.0,
+                    1405.0,
+                    420.0,
+                    293.0,
+                    420.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    412.0,
+                    1186.0,
+                    412.0,
+                    1186.0,
+                    451.0,
+                    295.0,
+                    451.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    459.0,
+                    1405.0,
+                    459.0,
+                    1405.0,
+                    496.0,
+                    297.0,
+                    496.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    491.0,
+                    1405.0,
+                    491.0,
+                    1405.0,
+                    524.0,
+                    297.0,
+                    524.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    520.0,
+                    791.0,
+                    520.0,
+                    791.0,
+                    557.0,
+                    294.0,
+                    557.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    825.0,
+                    520.0,
+                    1407.0,
+                    520.0,
+                    1407.0,
+                    557.0,
+                    825.0,
+                    557.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    549.0,
+                    547.0,
+                    549.0,
+                    547.0,
+                    590.0,
+                    293.0,
+                    590.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    584.0,
+                    549.0,
+                    634.0,
+                    549.0,
+                    634.0,
+                    590.0,
+                    584.0,
+                    590.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    690.0,
+                    549.0,
+                    1407.0,
+                    549.0,
+                    1407.0,
+                    590.0,
+                    690.0,
+                    590.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    578.0,
+                    1295.0,
+                    578.0,
+                    1295.0,
+                    622.0,
+                    292.0,
+                    622.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    978.0,
+                    1407.0,
+                    978.0,
+                    1407.0,
+                    1014.0,
+                    294.0,
+                    1014.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1010.0,
+                    1404.0,
+                    1010.0,
+                    1404.0,
+                    1043.0,
+                    295.0,
+                    1043.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1042.0,
+                    1258.0,
+                    1042.0,
+                    1258.0,
+                    1073.0,
+                    294.0,
+                    1073.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1289.0,
+                    1042.0,
+                    1404.0,
+                    1042.0,
+                    1404.0,
+                    1073.0,
+                    1289.0,
+                    1073.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1071.0,
+                    1076.0,
+                    1071.0,
+                    1076.0,
+                    1106.0,
+                    293.0,
+                    1106.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1114.0,
+                    1071.0,
+                    1401.0,
+                    1071.0,
+                    1401.0,
+                    1106.0,
+                    1114.0,
+                    1106.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1117.0,
+                    1406.0,
+                    1117.0,
+                    1406.0,
+                    1154.0,
+                    294.0,
+                    1154.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1146.0,
+                    1404.0,
+                    1146.0,
+                    1404.0,
+                    1183.0,
+                    294.0,
+                    1183.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1179.0,
+                    1404.0,
+                    1179.0,
+                    1404.0,
+                    1212.0,
+                    295.0,
+                    1212.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1207.0,
+                    1406.0,
+                    1207.0,
+                    1406.0,
+                    1245.0,
+                    293.0,
+                    1245.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1240.0,
+                    725.0,
+                    1240.0,
+                    725.0,
+                    1275.0,
+                    294.0,
+                    1275.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 3,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    625,
+                    1404,
+                    625,
+                    1404,
+                    932,
+                    298,
+                    932
+                ],
+                "score": 0.983
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    229,
+                    1404,
+                    229,
+                    1404,
+                    507,
+                    298,
+                    507
+                ],
+                "score": 0.982
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1576,
+                    823,
+                    1576,
+                    823,
+                    2033,
+                    299,
+                    2033
+                ],
+                "score": 0.981
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1233,
+                    825,
+                    1233,
+                    825,
+                    1537,
+                    298,
+                    1537
+                ],
+                "score": 0.98
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1032,
+                    1404,
+                    1032,
+                    1404,
+                    1217,
+                    298,
+                    1217
+                ],
+                "score": 0.979
+            },
+            {
+                "category_id": 3,
+                "poly": [
+                    854,
+                    1248,
+                    1393,
+                    1248,
+                    1393,
+                    1713,
+                    854,
+                    1713
+                ],
+                "score": 0.97
+            },
+            {
+                "category_id": 4,
+                "poly": [
+                    847,
+                    1724,
+                    1402,
+                    1724,
+                    1402,
+                    1999,
+                    847,
+                    1999
+                ],
+                "score": 0.952
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    300,
+                    973,
+                    682,
+                    973,
+                    682,
+                    1004,
+                    300,
+                    1004
+                ],
+                "score": 0.892
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    300,
+                    554,
+                    480,
+                    554,
+                    480,
+                    589,
+                    300,
+                    589
+                ],
+                "score": 0.887
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    76,
+                    857,
+                    76,
+                    857,
+                    104,
+                    298,
+                    104
+                ],
+                "score": 0.884
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2088,
+                    858,
+                    2088,
+                    858,
+                    2112,
+                    841,
+                    2112
+                ],
+                "score": 0.732
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    867.0,
+                    1248.0,
+                    1063.0,
+                    1248.0,
+                    1063.0,
+                    1297.0,
+                    867.0,
+                    1297.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1341.0,
+                    1258.0,
+                    1370.0,
+                    1258.0,
+                    1370.0,
+                    1285.0,
+                    1341.0,
+                    1285.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    938.0,
+                    1299.0,
+                    1070.0,
+                    1299.0,
+                    1070.0,
+                    1331.0,
+                    938.0,
+                    1331.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1208.0,
+                    1318.0,
+                    1235.0,
+                    1318.0,
+                    1235.0,
+                    1342.0,
+                    1208.0,
+                    1342.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    869.0,
+                    1353.0,
+                    930.0,
+                    1353.0,
+                    930.0,
+                    1387.0,
+                    869.0,
+                    1387.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    824.0,
+                    1363.0,
+                    956.0,
+                    1363.0,
+                    956.0,
+                    1613.0,
+                    824.0,
+                    1613.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1018.0,
+                    1440.0,
+                    1026.0,
+                    1440.0,
+                    1026.0,
+                    1447.0,
+                    1018.0,
+                    1447.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    869.0,
+                    1451.0,
+                    928.0,
+                    1451.0,
+                    928.0,
+                    1488.0,
+                    869.0,
+                    1488.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    941.0,
+                    1477.0,
+                    969.0,
+                    1477.0,
+                    969.0,
+                    1501.0,
+                    941.0,
+                    1501.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    868.0,
+                    1501.0,
+                    929.0,
+                    1501.0,
+                    929.0,
+                    1534.0,
+                    868.0,
+                    1534.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1139.0,
+                    1509.0,
+                    1170.0,
+                    1509.0,
+                    1170.0,
+                    1535.0,
+                    1139.0,
+                    1535.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1345.0,
+                    1507.0,
+                    1364.0,
+                    1507.0,
+                    1364.0,
+                    1522.0,
+                    1345.0,
+                    1522.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1004.0,
+                    1557.0,
+                    1039.0,
+                    1557.0,
+                    1039.0,
+                    1587.0,
+                    1004.0,
+                    1587.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    869.0,
+                    1598.0,
+                    935.0,
+                    1598.0,
+                    935.0,
+                    1640.0,
+                    869.0,
+                    1640.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    937.0,
+                    1604.0,
+                    972.0,
+                    1604.0,
+                    972.0,
+                    1636.0,
+                    937.0,
+                    1636.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    911.0,
+                    1640.0,
+                    996.0,
+                    1640.0,
+                    996.0,
+                    1677.0,
+                    911.0,
+                    1677.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1312.0,
+                    1641.0,
+                    1396.0,
+                    1641.0,
+                    1396.0,
+                    1675.0,
+                    1312.0,
+                    1675.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1004.0,
+                    1674.0,
+                    1014.0,
+                    1674.0,
+                    1014.0,
+                    1683.0,
+                    1004.0,
+                    1683.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1267.0,
+                    1671.0,
+                    1287.0,
+                    1671.0,
+                    1287.0,
+                    1686.0,
+                    1267.0,
+                    1686.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1329.0,
+                    1668.0,
+                    1360.0,
+                    1668.0,
+                    1360.0,
+                    1690.0,
+                    1329.0,
+                    1690.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    956.0,
+                    1684.0,
+                    1347.0,
+                    1684.0,
+                    1347.0,
+                    1718.0,
+                    956.0,
+                    1718.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    878.25,
+                    1279.5,
+                    882.25,
+                    1279.5,
+                    882.25,
+                    1409.5,
+                    878.25,
+                    1409.5
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1076.0,
+                    1533.0,
+                    1101.0,
+                    1533.0,
+                    1101.0,
+                    1548.0,
+                    1076.0,
+                    1548.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    846.0,
+                    1724.0,
+                    1406.0,
+                    1724.0,
+                    1406.0,
+                    1758.0,
+                    846.0,
+                    1758.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    844.0,
+                    1754.0,
+                    1406.0,
+                    1754.0,
+                    1406.0,
+                    1787.0,
+                    844.0,
+                    1787.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    845.0,
+                    1785.0,
+                    1403.0,
+                    1785.0,
+                    1403.0,
+                    1819.0,
+                    845.0,
+                    1819.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    844.0,
+                    1816.0,
+                    1404.0,
+                    1816.0,
+                    1404.0,
+                    1848.0,
+                    844.0,
+                    1848.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    845.0,
+                    1846.0,
+                    1403.0,
+                    1846.0,
+                    1403.0,
+                    1876.0,
+                    845.0,
+                    1876.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    844.0,
+                    1877.0,
+                    1403.0,
+                    1877.0,
+                    1403.0,
+                    1908.0,
+                    844.0,
+                    1908.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    845.0,
+                    1907.0,
+                    1403.0,
+                    1907.0,
+                    1403.0,
+                    1938.0,
+                    845.0,
+                    1938.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    845.0,
+                    1937.0,
+                    1405.0,
+                    1937.0,
+                    1405.0,
+                    1970.0,
+                    845.0,
+                    1970.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    844.0,
+                    1969.0,
+                    1330.0,
+                    1969.0,
+                    1330.0,
+                    1999.0,
+                    844.0,
+                    1999.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    969.0,
+                    687.0,
+                    969.0,
+                    687.0,
+                    1009.0,
+                    292.0,
+                    1009.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    549.0,
+                    486.0,
+                    549.0,
+                    486.0,
+                    597.0,
+                    291.0,
+                    597.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    298.0,
+                    73.0,
+                    858.0,
+                    73.0,
+                    858.0,
+                    108.0,
+                    298.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    839.0,
+                    2085.0,
+                    861.0,
+                    2085.0,
+                    861.0,
+                    2120.0,
+                    839.0,
+                    2120.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    625.0,
+                    1404.0,
+                    625.0,
+                    1404.0,
+                    662.0,
+                    295.0,
+                    662.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    658.0,
+                    1405.0,
+                    658.0,
+                    1405.0,
+                    693.0,
+                    294.0,
+                    693.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    687.0,
+                    1404.0,
+                    687.0,
+                    1404.0,
+                    721.0,
+                    293.0,
+                    721.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    719.0,
+                    1404.0,
+                    719.0,
+                    1404.0,
+                    754.0,
+                    294.0,
+                    754.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    749.0,
+                    1405.0,
+                    749.0,
+                    1405.0,
+                    782.0,
+                    292.0,
+                    782.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    780.0,
+                    1405.0,
+                    780.0,
+                    1405.0,
+                    814.0,
+                    293.0,
+                    814.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    808.0,
+                    1407.0,
+                    808.0,
+                    1407.0,
+                    845.0,
+                    291.0,
+                    845.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    841.0,
+                    1406.0,
+                    841.0,
+                    1406.0,
+                    876.0,
+                    293.0,
+                    876.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    873.0,
+                    1404.0,
+                    873.0,
+                    1404.0,
+                    904.0,
+                    294.0,
+                    904.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    901.0,
+                    1405.0,
+                    901.0,
+                    1405.0,
+                    935.0,
+                    293.0,
+                    935.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    230.0,
+                    1401.0,
+                    230.0,
+                    1401.0,
+                    263.0,
+                    296.0,
+                    263.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    262.0,
+                    1404.0,
+                    262.0,
+                    1404.0,
+                    294.0,
+                    294.0,
+                    294.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    291.0,
+                    1405.0,
+                    291.0,
+                    1405.0,
+                    326.0,
+                    295.0,
+                    326.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    318.0,
+                    1405.0,
+                    318.0,
+                    1405.0,
+                    360.0,
+                    292.0,
+                    360.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    351.0,
+                    1405.0,
+                    351.0,
+                    1405.0,
+                    388.0,
+                    294.0,
+                    388.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    384.0,
+                    1402.0,
+                    384.0,
+                    1402.0,
+                    417.0,
+                    296.0,
+                    417.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    413.0,
+                    1404.0,
+                    413.0,
+                    1404.0,
+                    449.0,
+                    293.0,
+                    449.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    441.0,
+                    1405.0,
+                    441.0,
+                    1405.0,
+                    480.0,
+                    292.0,
+                    480.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    477.0,
+                    705.0,
+                    477.0,
+                    705.0,
+                    510.0,
+                    296.0,
+                    510.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    1576.0,
+                    826.0,
+                    1576.0,
+                    826.0,
+                    1608.0,
+                    297.0,
+                    1608.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1605.0,
+                    826.0,
+                    1605.0,
+                    826.0,
+                    1643.0,
+                    294.0,
+                    1643.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1637.0,
+                    826.0,
+                    1637.0,
+                    826.0,
+                    1671.0,
+                    296.0,
+                    1671.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1668.0,
+                    825.0,
+                    1668.0,
+                    825.0,
+                    1700.0,
+                    295.0,
+                    1700.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1698.0,
+                    825.0,
+                    1698.0,
+                    825.0,
+                    1730.0,
+                    295.0,
+                    1730.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1729.0,
+                    826.0,
+                    1729.0,
+                    826.0,
+                    1760.0,
+                    296.0,
+                    1760.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1759.0,
+                    826.0,
+                    1759.0,
+                    826.0,
+                    1791.0,
+                    296.0,
+                    1791.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1788.0,
+                    826.0,
+                    1788.0,
+                    826.0,
+                    1822.0,
+                    295.0,
+                    1822.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1821.0,
+                    827.0,
+                    1821.0,
+                    827.0,
+                    1853.0,
+                    296.0,
+                    1853.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1850.0,
+                    827.0,
+                    1850.0,
+                    827.0,
+                    1884.0,
+                    294.0,
+                    1884.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1881.0,
+                    825.0,
+                    1881.0,
+                    825.0,
+                    1913.0,
+                    296.0,
+                    1913.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1911.0,
+                    825.0,
+                    1911.0,
+                    825.0,
+                    1945.0,
+                    295.0,
+                    1945.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1943.0,
+                    825.0,
+                    1943.0,
+                    825.0,
+                    1974.0,
+                    296.0,
+                    1974.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1972.0,
+                    825.0,
+                    1972.0,
+                    825.0,
+                    2004.0,
+                    296.0,
+                    2004.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    2002.0,
+                    828.0,
+                    2002.0,
+                    828.0,
+                    2037.0,
+                    296.0,
+                    2037.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    1230.0,
+                    827.0,
+                    1230.0,
+                    827.0,
+                    1267.0,
+                    297.0,
+                    1267.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1264.0,
+                    826.0,
+                    1264.0,
+                    826.0,
+                    1297.0,
+                    296.0,
+                    1297.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1292.0,
+                    825.0,
+                    1292.0,
+                    825.0,
+                    1328.0,
+                    294.0,
+                    1328.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1324.0,
+                    826.0,
+                    1324.0,
+                    826.0,
+                    1357.0,
+                    295.0,
+                    1357.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1357.0,
+                    824.0,
+                    1357.0,
+                    824.0,
+                    1387.0,
+                    296.0,
+                    1387.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1384.0,
+                    825.0,
+                    1384.0,
+                    825.0,
+                    1417.0,
+                    294.0,
+                    1417.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1416.0,
+                    826.0,
+                    1416.0,
+                    826.0,
+                    1449.0,
+                    295.0,
+                    1449.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1443.0,
+                    825.0,
+                    1443.0,
+                    825.0,
+                    1479.0,
+                    294.0,
+                    1479.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1475.0,
+                    827.0,
+                    1475.0,
+                    827.0,
+                    1513.0,
+                    292.0,
+                    1513.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1507.0,
+                    430.0,
+                    1507.0,
+                    430.0,
+                    1538.0,
+                    295.0,
+                    1538.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    1034.0,
+                    1404.0,
+                    1034.0,
+                    1404.0,
+                    1066.0,
+                    297.0,
+                    1066.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1065.0,
+                    1405.0,
+                    1065.0,
+                    1405.0,
+                    1097.0,
+                    296.0,
+                    1097.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1095.0,
+                    1405.0,
+                    1095.0,
+                    1405.0,
+                    1127.0,
+                    296.0,
+                    1127.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1124.0,
+                    1404.0,
+                    1124.0,
+                    1404.0,
+                    1160.0,
+                    294.0,
+                    1160.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1156.0,
+                    1405.0,
+                    1156.0,
+                    1405.0,
+                    1192.0,
+                    294.0,
+                    1192.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1179.0,
+                    811.0,
+                    1179.0,
+                    811.0,
+                    1225.0,
+                    292.0,
+                    1225.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 4,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1372,
+                    1404,
+                    1372,
+                    1404,
+                    1739,
+                    297,
+                    1739
+                ],
+                "score": 0.982
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1045,
+                    1404,
+                    1045,
+                    1404,
+                    1322,
+                    298,
+                    1322
+                ],
+                "score": 0.982
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1788,
+                    1403,
+                    1788,
+                    1403,
+                    2034,
+                    298,
+                    2034
+                ],
+                "score": 0.978
+            },
+            {
+                "category_id": 5,
+                "poly": [
+                    348,
+                    350,
+                    1351,
+                    350,
+                    1351,
+                    819,
+                    348,
+                    819
+                ],
+                "score": 0.974,
+                "html": "<table><tr><td>Method</td><td>Top-1</td><td>Top-5</td></tr><tr><td>Motion Segmentation (MS) (Pathak et al., 2016) Exemplar (Ex) (Dosovitskiy et al.,2014) Relative Position (RP) (Doersch et al.,2015) Colorization (Col) (Zhang et al., 2016) Combination of MS + Ex + RP+ Col (Doersch &amp; Zisserman,2017) CPC v1 (van den Oord et al., 2018) Rotation (Kolesnikov et al., 2019)</td><td>27.6 31.5 36.2 39.6 1 48.7 55.4</td><td>48.3 53.1 59.2 62.5 69.3 73.6</td></tr><tr><td>CMC (Tian et al., 2019) Local Aggregation (Zhuang et al., 2019)</td><td>60.1 60.2</td><td>82.8 1 =</td></tr><tr><td>BigBiGAN (Donahue &amp; Simonyan,2019) AMDIM (Bachman et al., 2019) CPC v2 (ours) 65.9</td><td>61.3 68.1</td><td>81.9</td></tr></table>"
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    300,
+                    903,
+                    1402,
+                    903,
+                    1402,
+                    996,
+                    300,
+                    996
+                ],
+                "score": 0.97
+            },
+            {
+                "category_id": 6,
+                "poly": [
+                    299,
+                    248,
+                    1402,
+                    248,
+                    1402,
+                    343,
+                    299,
+                    343
+                ],
+                "score": 0.936
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    75,
+                    858,
+                    75,
+                    858,
+                    104,
+                    298,
+                    104
+                ],
+                "score": 0.896
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    840,
+                    2089,
+                    858,
+                    2089,
+                    858,
+                    2112,
+                    840,
+                    2112
+                ],
+                "score": 0.772
+            },
+            {
+                "category_id": 7,
+                "poly": [
+                    369,
+                    782,
+                    534,
+                    782,
+                    534,
+                    814,
+                    369,
+                    814
+                ],
+                "score": 0.463
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1023,
+                    1677,
+                    1142,
+                    1677,
+                    1142,
+                    1711,
+                    1023,
+                    1711
+                ],
+                "score": 0.93,
+                "latex": "\\{ 2 , \\ldots , 5 \\}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    695,
+                    1677,
+                    765,
+                    1677,
+                    765,
+                    1711,
+                    695,
+                    1711
+                ],
+                "score": 0.93,
+                "latex": "\\{ 2 , 3 \\}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    463,
+                    2003,
+                    539,
+                    2003,
+                    539,
+                    2034,
+                    463,
+                    2034
+                ],
+                "score": 0.9,
+                "latex": "( + 1 \\% )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1279,
+                    1525,
+                    1360,
+                    1525,
+                    1360,
+                    1554,
+                    1279,
+                    1554
+                ],
+                "score": 0.9,
+                "latex": "+ 1 . 5 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    608,
+                    251,
+                    644,
+                    251,
+                    644,
+                    283,
+                    608,
+                    283
+                ],
+                "score": 0.89,
+                "latex": "h _ { \\psi }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    813,
+                    965,
+                    886,
+                    965,
+                    886,
+                    994,
+                    813,
+                    994
+                ],
+                "score": 0.88,
+                "latex": "+ 1 0 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    296,
+                    1973,
+                    357,
+                    1973,
+                    357,
+                    2002,
+                    296,
+                    2002
+                ],
+                "score": 0.87,
+                "latex": "+3 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    913,
+                    1260,
+                    972,
+                    1260,
+                    972,
+                    1289,
+                    913,
+                    1289
+                ],
+                "score": 0.87,
+                "latex": "+ 1 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1233,
+                    1495,
+                    1294,
+                    1495,
+                    1294,
+                    1524,
+                    1233,
+                    1524
+                ],
+                "score": 0.87,
+                "latex": "42 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1129,
+                    1291,
+                    1212,
+                    1291,
+                    1212,
+                    1321,
+                    1129,
+                    1321
+                ],
+                "score": 0.87,
+                "latex": "( + 2 . 5 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    811,
+                    249,
+                    883,
+                    249,
+                    883,
+                    279,
+                    811,
+                    279
+                ],
+                "score": 0.86,
+                "latex": "100 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1112,
+                    1943,
+                    1173,
+                    1943,
+                    1173,
+                    1972,
+                    1112,
+                    1972
+                ],
+                "score": 0.86,
+                "latex": "( + 1 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    306,
+                    1708,
+                    366,
+                    1708,
+                    366,
+                    1737,
+                    306,
+                    1737
+                ],
+                "score": 0.86,
+                "latex": "+ 1 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    493,
+                    1556,
+                    547,
+                    1556,
+                    547,
+                    1585,
+                    493,
+                    1585
+                ],
+                "score": 0.85,
+                "latex": "{ \\bf - 1 \\% }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    551,
+                    539,
+                    790,
+                    539,
+                    790,
+                    568,
+                    551,
+                    568
+                ],
+                "score": 0.84,
+                "latex": "\\mathrm { M S } + \\mathrm { E x } + \\mathrm { R P } + \\mathrm { C o l }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1339,
+                    934,
+                    1399,
+                    934,
+                    1399,
+                    965,
+                    1339,
+                    965
+                ],
+                "score": 0.84,
+                "latex": "+5 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    640,
+                    1678,
+                    659,
+                    1678,
+                    659,
+                    1705,
+                    640,
+                    1705
+                ],
+                "score": 0.8,
+                "latex": "k"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    517,
+                    509,
+                    577,
+                    509,
+                    577,
+                    538,
+                    517,
+                    538
+                ],
+                "score": 0.26,
+                "latex": "\\mathbf { \\tau } ( \\mathbf { C o l } )"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    246.0,
+                    607.0,
+                    246.0,
+                    607.0,
+                    286.0,
+                    293.0,
+                    286.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    645.0,
+                    246.0,
+                    810.0,
+                    246.0,
+                    810.0,
+                    286.0,
+                    645.0,
+                    286.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    884.0,
+                    246.0,
+                    1404.0,
+                    246.0,
+                    1404.0,
+                    286.0,
+                    884.0,
+                    286.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    281.0,
+                    1406.0,
+                    281.0,
+                    1406.0,
+                    315.0,
+                    295.0,
+                    315.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    311.0,
+                    1269.0,
+                    311.0,
+                    1269.0,
+                    345.0,
+                    295.0,
+                    345.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    72.0,
+                    858.0,
+                    72.0,
+                    858.0,
+                    108.0,
+                    297.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    840.0,
+                    2087.0,
+                    861.0,
+                    2087.0,
+                    861.0,
+                    2118.0,
+                    840.0,
+                    2118.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    368.0,
+                    779.0,
+                    538.0,
+                    779.0,
+                    538.0,
+                    820.0,
+                    368.0,
+                    820.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1371.0,
+                    1405.0,
+                    1371.0,
+                    1405.0,
+                    1408.0,
+                    294.0,
+                    1408.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1403.0,
+                    1404.0,
+                    1403.0,
+                    1404.0,
+                    1438.0,
+                    295.0,
+                    1438.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1430.0,
+                    1405.0,
+                    1430.0,
+                    1405.0,
+                    1472.0,
+                    292.0,
+                    1472.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1464.0,
+                    1405.0,
+                    1464.0,
+                    1405.0,
+                    1498.0,
+                    294.0,
+                    1498.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1491.0,
+                    1232.0,
+                    1491.0,
+                    1232.0,
+                    1531.0,
+                    291.0,
+                    1531.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1295.0,
+                    1491.0,
+                    1405.0,
+                    1491.0,
+                    1405.0,
+                    1531.0,
+                    1295.0,
+                    1531.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1524.0,
+                    1278.0,
+                    1524.0,
+                    1278.0,
+                    1558.0,
+                    294.0,
+                    1558.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1361.0,
+                    1524.0,
+                    1405.0,
+                    1524.0,
+                    1405.0,
+                    1558.0,
+                    1361.0,
+                    1558.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1556.0,
+                    492.0,
+                    1556.0,
+                    492.0,
+                    1590.0,
+                    295.0,
+                    1590.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    548.0,
+                    1556.0,
+                    1406.0,
+                    1556.0,
+                    1406.0,
+                    1590.0,
+                    548.0,
+                    1590.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1586.0,
+                    1404.0,
+                    1586.0,
+                    1404.0,
+                    1619.0,
+                    292.0,
+                    1619.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1618.0,
+                    1404.0,
+                    1618.0,
+                    1404.0,
+                    1652.0,
+                    295.0,
+                    1652.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1645.0,
+                    1405.0,
+                    1645.0,
+                    1405.0,
+                    1683.0,
+                    292.0,
+                    1683.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1677.0,
+                    639.0,
+                    1677.0,
+                    639.0,
+                    1715.0,
+                    292.0,
+                    1715.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    660.0,
+                    1677.0,
+                    694.0,
+                    1677.0,
+                    694.0,
+                    1715.0,
+                    660.0,
+                    1715.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    766.0,
+                    1677.0,
+                    1022.0,
+                    1677.0,
+                    1022.0,
+                    1715.0,
+                    766.0,
+                    1715.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1143.0,
+                    1677.0,
+                    1404.0,
+                    1677.0,
+                    1404.0,
+                    1715.0,
+                    1143.0,
+                    1715.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1708.0,
+                    305.0,
+                    1708.0,
+                    305.0,
+                    1742.0,
+                    295.0,
+                    1742.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    367.0,
+                    1708.0,
+                    613.0,
+                    1708.0,
+                    613.0,
+                    1742.0,
+                    367.0,
+                    1742.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1047.0,
+                    1404.0,
+                    1047.0,
+                    1404.0,
+                    1080.0,
+                    296.0,
+                    1080.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1076.0,
+                    1406.0,
+                    1076.0,
+                    1406.0,
+                    1113.0,
+                    293.0,
+                    1113.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1105.0,
+                    1402.0,
+                    1105.0,
+                    1402.0,
+                    1142.0,
+                    294.0,
+                    1142.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1138.0,
+                    1405.0,
+                    1138.0,
+                    1405.0,
+                    1173.0,
+                    293.0,
+                    1173.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1169.0,
+                    1405.0,
+                    1169.0,
+                    1405.0,
+                    1202.0,
+                    294.0,
+                    1202.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1198.0,
+                    1405.0,
+                    1198.0,
+                    1405.0,
+                    1236.0,
+                    293.0,
+                    1236.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1229.0,
+                    1404.0,
+                    1229.0,
+                    1404.0,
+                    1266.0,
+                    294.0,
+                    1266.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1257.0,
+                    912.0,
+                    1257.0,
+                    912.0,
+                    1296.0,
+                    293.0,
+                    1296.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    973.0,
+                    1257.0,
+                    1405.0,
+                    1257.0,
+                    1405.0,
+                    1296.0,
+                    973.0,
+                    1296.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1286.0,
+                    1128.0,
+                    1286.0,
+                    1128.0,
+                    1329.0,
+                    292.0,
+                    1329.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1213.0,
+                    1286.0,
+                    1338.0,
+                    1286.0,
+                    1338.0,
+                    1329.0,
+                    1213.0,
+                    1329.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1787.0,
+                    1404.0,
+                    1787.0,
+                    1404.0,
+                    1825.0,
+                    293.0,
+                    1825.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1820.0,
+                    1403.0,
+                    1820.0,
+                    1403.0,
+                    1856.0,
+                    293.0,
+                    1856.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1850.0,
+                    1407.0,
+                    1850.0,
+                    1407.0,
+                    1887.0,
+                    293.0,
+                    1887.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1879.0,
+                    1404.0,
+                    1879.0,
+                    1404.0,
+                    1918.0,
+                    292.0,
+                    1918.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1912.0,
+                    1405.0,
+                    1912.0,
+                    1405.0,
+                    1946.0,
+                    294.0,
+                    1946.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1941.0,
+                    1111.0,
+                    1941.0,
+                    1111.0,
+                    1977.0,
+                    293.0,
+                    1977.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1174.0,
+                    1941.0,
+                    1404.0,
+                    1941.0,
+                    1404.0,
+                    1977.0,
+                    1174.0,
+                    1977.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1970.0,
+                    295.0,
+                    1970.0,
+                    295.0,
+                    2010.0,
+                    292.0,
+                    2010.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    358.0,
+                    1970.0,
+                    1407.0,
+                    1970.0,
+                    1407.0,
+                    2010.0,
+                    358.0,
+                    2010.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    2000.0,
+                    462.0,
+                    2000.0,
+                    462.0,
+                    2037.0,
+                    293.0,
+                    2037.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    540.0,
+                    2000.0,
+                    553.0,
+                    2000.0,
+                    553.0,
+                    2037.0,
+                    540.0,
+                    2037.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    902.0,
+                    1406.0,
+                    902.0,
+                    1406.0,
+                    940.0,
+                    295.0,
+                    940.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    933.0,
+                    1338.0,
+                    933.0,
+                    1338.0,
+                    970.0,
+                    294.0,
+                    970.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    964.0,
+                    812.0,
+                    964.0,
+                    812.0,
+                    1001.0,
+                    295.0,
+                    1001.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    887.0,
+                    964.0,
+                    1168.0,
+                    964.0,
+                    1168.0,
+                    1001.0,
+                    887.0,
+                    1001.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 5,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    230,
+                    1404,
+                    230,
+                    1404,
+                    535,
+                    297,
+                    535
+                ],
+                "score": 0.982
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    636,
+                    1404,
+                    636,
+                    1404,
+                    852,
+                    298,
+                    852
+                ],
+                "score": 0.98
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    891,
+                    824,
+                    891,
+                    824,
+                    1651,
+                    298,
+                    1651
+                ],
+                "score": 0.979
+            },
+            {
+                "category_id": 3,
+                "poly": [
+                    856,
+                    900,
+                    1380,
+                    900,
+                    1380,
+                    1448,
+                    856,
+                    1448
+                ],
+                "score": 0.97
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1790,
+                    1403,
+                    1790,
+                    1403,
+                    2034,
+                    298,
+                    2034
+                ],
+                "score": 0.968
+            },
+            {
+                "category_id": 4,
+                "poly": [
+                    847,
+                    1462,
+                    1401,
+                    1462,
+                    1401,
+                    1767,
+                    847,
+                    1767
+                ],
+                "score": 0.967
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1669,
+                    821,
+                    1669,
+                    821,
+                    1789,
+                    298,
+                    1789
+                ],
+                "score": 0.945
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    303,
+                    579,
+                    776,
+                    579,
+                    776,
+                    609,
+                    303,
+                    609
+                ],
+                "score": 0.877
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    299,
+                    76,
+                    857,
+                    76,
+                    857,
+                    104,
+                    299,
+                    104
+                ],
+                "score": 0.862
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    842,
+                    2088,
+                    858,
+                    2088,
+                    858,
+                    2111,
+                    842,
+                    2111
+                ],
+                "score": 0.635
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    842,
+                    2088,
+                    859,
+                    2088,
+                    859,
+                    2111,
+                    842,
+                    2111
+                ],
+                "score": 0.253
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    300,
+                    76,
+                    856,
+                    76,
+                    856,
+                    104,
+                    300,
+                    104
+                ],
+                "score": 0.155
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    364,
+                    1103,
+                    519,
+                    1103,
+                    519,
+                    1136,
+                    364,
+                    1136
+                ],
+                "score": 0.92,
+                "latex": "\\begin{array} { r l r } { z } & { { } = } & { f _ { \\theta } ( { \\pmb x } ) } \\end{array}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    388,
+                    1469,
+                    540,
+                    1469,
+                    540,
+                    1499,
+                    388,
+                    1499
+                ],
+                "score": 0.9,
+                "latex": "8 0 . 6 \\% / 9 5 . 2 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    297,
+                    1530,
+                    452,
+                    1530,
+                    452,
+                    1559,
+                    297,
+                    1559
+                ],
+                "score": 0.89,
+                "latex": "7 8 . 0 \\% / 9 3 . 9 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    382,
+                    699,
+                    415,
+                    699,
+                    415,
+                    729,
+                    382,
+                    729
+                ],
+                "score": 0.88,
+                "latex": "\\mathbb { D } _ { l }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1086,
+                    262,
+                    1140,
+                    262,
+                    1140,
+                    291,
+                    1086,
+                    291
+                ],
+                "score": 0.87,
+                "latex": "17 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    634,
+                    699,
+                    701,
+                    699,
+                    701,
+                    728,
+                    634,
+                    728
+                ],
+                "score": 0.87,
+                "latex": "100 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    322,
+                    1378,
+                    379,
+                    1378,
+                    379,
+                    1407,
+                    322,
+                    1407
+                ],
+                "score": 0.87,
+                "latex": "2 9 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    904,
+                    352,
+                    979,
+                    352,
+                    979,
+                    382,
+                    904,
+                    382
+                ],
+                "score": 0.87,
+                "latex": "6 2 . 5 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1081,
+                    790,
+                    1156,
+                    790,
+                    1156,
+                    819,
+                    1081,
+                    819
+                ],
+                "score": 0.86,
+                "latex": "4 4 . 1 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    764,
+                    821,
+                    839,
+                    821,
+                    839,
+                    850,
+                    764,
+                    850
+                ],
+                "score": 0.86,
+                "latex": "9 3 . 9 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    346,
+                    352,
+                    422,
+                    352,
+                    422,
+                    382,
+                    346,
+                    382
+                ],
+                "score": 0.86,
+                "latex": "6 6 . 4 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    454,
+                    1561,
+                    608,
+                    1561,
+                    608,
+                    1590,
+                    454,
+                    1590
+                ],
+                "score": 0.86,
+                "latex": "7 9 . 9 \\% / 9 5 . 2 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    747,
+                    1317,
+                    824,
+                    1317,
+                    824,
+                    1346,
+                    747,
+                    1346
+                ],
+                "score": 0.85,
+                "latex": "7 2 . 9 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    613,
+                    1348,
+                    655,
+                    1348,
+                    655,
+                    1377,
+                    613,
+                    1377
+                ],
+                "score": 0.85,
+                "latex": "1 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1249,
+                    475,
+                    1302,
+                    475,
+                    1302,
+                    504,
+                    1249,
+                    504
+                ],
+                "score": 0.85,
+                "latex": "10 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    415,
+                    822,
+                    455,
+                    822,
+                    455,
+                    849,
+                    415,
+                    849
+                ],
+                "score": 0.84,
+                "latex": "1 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    557,
+                    699,
+                    597,
+                    699,
+                    597,
+                    727,
+                    557,
+                    727
+                ],
+                "score": 0.84,
+                "latex": "1 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    803,
+                    262,
+                    879,
+                    262,
+                    879,
+                    292,
+                    803,
+                    292
+                ],
+                "score": 0.83,
+                "latex": "6 5 . 9 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    664,
+                    1378,
+                    719,
+                    1378,
+                    719,
+                    1407,
+                    664,
+                    1407
+                ],
+                "score": 0.83,
+                "latex": "65 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1194,
+                    1420,
+                    1257,
+                    1420,
+                    1257,
+                    1448,
+                    1194,
+                    1448
+                ],
+                "score": 0.78,
+                "latex": "100 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    428,
+                    1139,
+                    451,
+                    1139,
+                    451,
+                    1162,
+                    428,
+                    1162
+                ],
+                "score": 0.74,
+                "latex": "_ { \\textbf { \\em x } }"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    871.0,
+                    896.0,
+                    952.0,
+                    896.0,
+                    952.0,
+                    951.0,
+                    871.0,
+                    951.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1222.0,
+                    925.0,
+                    1249.0,
+                    925.0,
+                    1249.0,
+                    948.0,
+                    1222.0,
+                    948.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1341.0,
+                    949.0,
+                    1362.0,
+                    949.0,
+                    1362.0,
+                    964.0,
+                    1341.0,
+                    964.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    876.0,
+                    1004.0,
+                    943.0,
+                    1004.0,
+                    943.0,
+                    1048.0,
+                    876.0,
+                    1048.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1206.0,
+                    995.0,
+                    1232.0,
+                    995.0,
+                    1232.0,
+                    1019.0,
+                    1206.0,
+                    1019.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1033.0,
+                    1046.0,
+                    1060.0,
+                    1046.0,
+                    1060.0,
+                    1071.0,
+                    1033.0,
+                    1071.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1111.0,
+                    1067.0,
+                    1137.0,
+                    1067.0,
+                    1137.0,
+                    1090.0,
+                    1111.0,
+                    1090.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1134.0,
+                    1081.0,
+                    1157.0,
+                    1081.0,
+                    1157.0,
+                    1101.0,
+                    1134.0,
+                    1101.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    876.0,
+                    1104.0,
+                    941.0,
+                    1104.0,
+                    941.0,
+                    1145.0,
+                    876.0,
+                    1145.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1288.0,
+                    1157.0,
+                    1310.0,
+                    1157.0,
+                    1310.0,
+                    1178.0,
+                    1288.0,
+                    1178.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1031.0,
+                    1180.0,
+                    1056.0,
+                    1180.0,
+                    1056.0,
+                    1205.0,
+                    1031.0,
+                    1205.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    887.0,
+                    1201.0,
+                    946.0,
+                    1201.0,
+                    946.0,
+                    1247.0,
+                    887.0,
+                    1247.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1122.0,
+                    1223.0,
+                    1147.0,
+                    1223.0,
+                    1147.0,
+                    1247.0,
+                    1122.0,
+                    1247.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1241.0,
+                    1245.0,
+                    1257.0,
+                    1245.0,
+                    1257.0,
+                    1260.0,
+                    1241.0,
+                    1260.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1154.0,
+                    1284.0,
+                    1366.0,
+                    1284.0,
+                    1366.0,
+                    1329.0,
+                    1154.0,
+                    1329.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1155.0,
+                    1313.0,
+                    1374.0,
+                    1313.0,
+                    1374.0,
+                    1354.0,
+                    1155.0,
+                    1354.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    953.0,
+                    1347.0,
+                    981.0,
+                    1347.0,
+                    981.0,
+                    1372.0,
+                    953.0,
+                    1372.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1154.0,
+                    1337.0,
+                    1376.0,
+                    1337.0,
+                    1376.0,
+                    1382.0,
+                    1154.0,
+                    1382.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    923.0,
+                    1381.0,
+                    990.0,
+                    1381.0,
+                    990.0,
+                    1423.0,
+                    923.0,
+                    1423.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1016.0,
+                    1382.0,
+                    1072.0,
+                    1382.0,
+                    1072.0,
+                    1422.0,
+                    1016.0,
+                    1422.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1098.0,
+                    1383.0,
+                    1165.0,
+                    1383.0,
+                    1165.0,
+                    1421.0,
+                    1098.0,
+                    1421.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1187.0,
+                    1382.0,
+                    1252.0,
+                    1382.0,
+                    1252.0,
+                    1421.0,
+                    1187.0,
+                    1421.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1272.0,
+                    1378.0,
+                    1343.0,
+                    1378.0,
+                    1343.0,
+                    1424.0,
+                    1272.0,
+                    1424.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    955.0,
+                    1411.0,
+                    1193.0,
+                    1411.0,
+                    1193.0,
+                    1455.0,
+                    955.0,
+                    1455.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1258.0,
+                    1411.0,
+                    1359.0,
+                    1411.0,
+                    1359.0,
+                    1455.0,
+                    1258.0,
+                    1455.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    845.0,
+                    1462.0,
+                    1404.0,
+                    1462.0,
+                    1404.0,
+                    1494.0,
+                    845.0,
+                    1494.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    844.0,
+                    1492.0,
+                    1404.0,
+                    1492.0,
+                    1404.0,
+                    1524.0,
+                    844.0,
+                    1524.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    845.0,
+                    1523.0,
+                    1403.0,
+                    1523.0,
+                    1403.0,
+                    1553.0,
+                    845.0,
+                    1553.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    845.0,
+                    1554.0,
+                    1403.0,
+                    1554.0,
+                    1403.0,
+                    1584.0,
+                    845.0,
+                    1584.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    844.0,
+                    1585.0,
+                    1405.0,
+                    1585.0,
+                    1405.0,
+                    1616.0,
+                    844.0,
+                    1616.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    844.0,
+                    1614.0,
+                    1405.0,
+                    1614.0,
+                    1405.0,
+                    1648.0,
+                    844.0,
+                    1648.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    844.0,
+                    1645.0,
+                    1406.0,
+                    1645.0,
+                    1406.0,
+                    1679.0,
+                    844.0,
+                    1679.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    843.0,
+                    1675.0,
+                    1405.0,
+                    1675.0,
+                    1405.0,
+                    1708.0,
+                    843.0,
+                    1708.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    843.0,
+                    1704.0,
+                    1406.0,
+                    1704.0,
+                    1406.0,
+                    1739.0,
+                    843.0,
+                    1739.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    844.0,
+                    1737.0,
+                    1316.0,
+                    1737.0,
+                    1316.0,
+                    1769.0,
+                    844.0,
+                    1769.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    578.0,
+                    782.0,
+                    578.0,
+                    782.0,
+                    612.0,
+                    297.0,
+                    612.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    298.0,
+                    73.0,
+                    858.0,
+                    73.0,
+                    858.0,
+                    108.0,
+                    298.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    840.0,
+                    2086.0,
+                    860.0,
+                    2086.0,
+                    860.0,
+                    2119.0,
+                    840.0,
+                    2119.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    840.0,
+                    2087.0,
+                    861.0,
+                    2087.0,
+                    861.0,
+                    2119.0,
+                    840.0,
+                    2119.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    73.0,
+                    859.0,
+                    73.0,
+                    859.0,
+                    108.0,
+                    297.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    229.0,
+                    1405.0,
+                    229.0,
+                    1405.0,
+                    265.0,
+                    296.0,
+                    265.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    260.0,
+                    802.0,
+                    260.0,
+                    802.0,
+                    298.0,
+                    294.0,
+                    298.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    880.0,
+                    260.0,
+                    1085.0,
+                    260.0,
+                    1085.0,
+                    298.0,
+                    880.0,
+                    298.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1141.0,
+                    260.0,
+                    1404.0,
+                    260.0,
+                    1404.0,
+                    298.0,
+                    1141.0,
+                    298.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    288.0,
+                    1405.0,
+                    288.0,
+                    1405.0,
+                    329.0,
+                    291.0,
+                    329.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    319.0,
+                    1404.0,
+                    319.0,
+                    1404.0,
+                    356.0,
+                    292.0,
+                    356.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    352.0,
+                    345.0,
+                    352.0,
+                    345.0,
+                    388.0,
+                    295.0,
+                    388.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    423.0,
+                    352.0,
+                    903.0,
+                    352.0,
+                    903.0,
+                    388.0,
+                    423.0,
+                    388.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    980.0,
+                    352.0,
+                    1405.0,
+                    352.0,
+                    1405.0,
+                    388.0,
+                    980.0,
+                    388.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    382.0,
+                    1404.0,
+                    382.0,
+                    1404.0,
+                    418.0,
+                    295.0,
+                    418.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    412.0,
+                    1405.0,
+                    412.0,
+                    1405.0,
+                    450.0,
+                    294.0,
+                    450.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    443.0,
+                    1404.0,
+                    443.0,
+                    1404.0,
+                    479.0,
+                    295.0,
+                    479.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    472.0,
+                    1248.0,
+                    472.0,
+                    1248.0,
+                    510.0,
+                    292.0,
+                    510.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1303.0,
+                    472.0,
+                    1407.0,
+                    472.0,
+                    1407.0,
+                    510.0,
+                    1303.0,
+                    510.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    503.0,
+                    947.0,
+                    503.0,
+                    947.0,
+                    538.0,
+                    295.0,
+                    538.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    638.0,
+                    1404.0,
+                    638.0,
+                    1404.0,
+                    672.0,
+                    294.0,
+                    672.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    666.0,
+                    1406.0,
+                    666.0,
+                    1406.0,
+                    704.0,
+                    294.0,
+                    704.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    698.0,
+                    381.0,
+                    698.0,
+                    381.0,
+                    733.0,
+                    294.0,
+                    733.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    416.0,
+                    698.0,
+                    556.0,
+                    698.0,
+                    556.0,
+                    733.0,
+                    416.0,
+                    733.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    598.0,
+                    698.0,
+                    633.0,
+                    698.0,
+                    633.0,
+                    733.0,
+                    598.0,
+                    733.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    702.0,
+                    698.0,
+                    1405.0,
+                    698.0,
+                    1405.0,
+                    733.0,
+                    702.0,
+                    733.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    727.0,
+                    1406.0,
+                    727.0,
+                    1406.0,
+                    764.0,
+                    293.0,
+                    764.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    758.0,
+                    1405.0,
+                    758.0,
+                    1405.0,
+                    795.0,
+                    293.0,
+                    795.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    790.0,
+                    1080.0,
+                    790.0,
+                    1080.0,
+                    824.0,
+                    296.0,
+                    824.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1157.0,
+                    790.0,
+                    1405.0,
+                    790.0,
+                    1405.0,
+                    824.0,
+                    1157.0,
+                    824.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    821.0,
+                    414.0,
+                    821.0,
+                    414.0,
+                    855.0,
+                    294.0,
+                    855.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    456.0,
+                    821.0,
+                    763.0,
+                    821.0,
+                    763.0,
+                    855.0,
+                    456.0,
+                    855.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    840.0,
+                    821.0,
+                    1404.0,
+                    821.0,
+                    1404.0,
+                    855.0,
+                    840.0,
+                    855.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    298.0,
+                    889.0,
+                    825.0,
+                    889.0,
+                    825.0,
+                    924.0,
+                    298.0,
+                    924.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    920.0,
+                    826.0,
+                    920.0,
+                    826.0,
+                    953.0,
+                    296.0,
+                    953.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    950.0,
+                    826.0,
+                    950.0,
+                    826.0,
+                    984.0,
+                    296.0,
+                    984.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    981.0,
+                    827.0,
+                    981.0,
+                    827.0,
+                    1016.0,
+                    295.0,
+                    1016.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1009.0,
+                    827.0,
+                    1009.0,
+                    827.0,
+                    1048.0,
+                    293.0,
+                    1048.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1040.0,
+                    827.0,
+                    1040.0,
+                    827.0,
+                    1077.0,
+                    294.0,
+                    1077.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1073.0,
+                    826.0,
+                    1073.0,
+                    826.0,
+                    1107.0,
+                    295.0,
+                    1107.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1103.0,
+                    363.0,
+                    1103.0,
+                    363.0,
+                    1138.0,
+                    295.0,
+                    1138.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    520.0,
+                    1103.0,
+                    826.0,
+                    1103.0,
+                    826.0,
+                    1138.0,
+                    520.0,
+                    1138.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1134.0,
+                    427.0,
+                    1134.0,
+                    427.0,
+                    1167.0,
+                    293.0,
+                    1167.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    452.0,
+                    1134.0,
+                    828.0,
+                    1134.0,
+                    828.0,
+                    1167.0,
+                    452.0,
+                    1167.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1163.0,
+                    827.0,
+                    1163.0,
+                    827.0,
+                    1198.0,
+                    295.0,
+                    1198.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1193.0,
+                    827.0,
+                    1193.0,
+                    827.0,
+                    1226.0,
+                    295.0,
+                    1226.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1225.0,
+                    827.0,
+                    1225.0,
+                    827.0,
+                    1259.0,
+                    295.0,
+                    1259.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1255.0,
+                    826.0,
+                    1255.0,
+                    826.0,
+                    1289.0,
+                    294.0,
+                    1289.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1287.0,
+                    827.0,
+                    1287.0,
+                    827.0,
+                    1321.0,
+                    294.0,
+                    1321.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1315.0,
+                    746.0,
+                    1315.0,
+                    746.0,
+                    1350.0,
+                    295.0,
+                    1350.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1347.0,
+                    612.0,
+                    1347.0,
+                    612.0,
+                    1380.0,
+                    294.0,
+                    1380.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    656.0,
+                    1347.0,
+                    826.0,
+                    1347.0,
+                    826.0,
+                    1380.0,
+                    656.0,
+                    1380.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1376.0,
+                    321.0,
+                    1376.0,
+                    321.0,
+                    1409.0,
+                    294.0,
+                    1409.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    380.0,
+                    1376.0,
+                    663.0,
+                    1376.0,
+                    663.0,
+                    1409.0,
+                    380.0,
+                    1409.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    720.0,
+                    1376.0,
+                    825.0,
+                    1376.0,
+                    825.0,
+                    1409.0,
+                    720.0,
+                    1409.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1408.0,
+                    826.0,
+                    1408.0,
+                    826.0,
+                    1442.0,
+                    294.0,
+                    1442.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1438.0,
+                    826.0,
+                    1438.0,
+                    826.0,
+                    1469.0,
+                    296.0,
+                    1469.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1467.0,
+                    387.0,
+                    1467.0,
+                    387.0,
+                    1502.0,
+                    294.0,
+                    1502.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    541.0,
+                    1467.0,
+                    826.0,
+                    1467.0,
+                    826.0,
+                    1502.0,
+                    541.0,
+                    1502.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1501.0,
+                    826.0,
+                    1501.0,
+                    826.0,
+                    1530.0,
+                    293.0,
+                    1530.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    453.0,
+                    1527.0,
+                    826.0,
+                    1527.0,
+                    826.0,
+                    1563.0,
+                    453.0,
+                    1563.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1558.0,
+                    453.0,
+                    1558.0,
+                    453.0,
+                    1595.0,
+                    295.0,
+                    1595.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    609.0,
+                    1558.0,
+                    826.0,
+                    1558.0,
+                    826.0,
+                    1595.0,
+                    609.0,
+                    1595.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1587.0,
+                    826.0,
+                    1587.0,
+                    826.0,
+                    1624.0,
+                    295.0,
+                    1624.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1618.0,
+                    603.0,
+                    1618.0,
+                    603.0,
+                    1655.0,
+                    294.0,
+                    1655.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1790.0,
+                    1405.0,
+                    1790.0,
+                    1405.0,
+                    1824.0,
+                    294.0,
+                    1824.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1822.0,
+                    1404.0,
+                    1822.0,
+                    1404.0,
+                    1852.0,
+                    296.0,
+                    1852.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1851.0,
+                    1405.0,
+                    1851.0,
+                    1405.0,
+                    1885.0,
+                    294.0,
+                    1885.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1882.0,
+                    1405.0,
+                    1882.0,
+                    1405.0,
+                    1916.0,
+                    294.0,
+                    1916.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1911.0,
+                    1406.0,
+                    1911.0,
+                    1406.0,
+                    1945.0,
+                    292.0,
+                    1945.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1942.0,
+                    1405.0,
+                    1942.0,
+                    1405.0,
+                    1975.0,
+                    293.0,
+                    1975.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1973.0,
+                    1404.0,
+                    1973.0,
+                    1404.0,
+                    2006.0,
+                    294.0,
+                    2006.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    2003.0,
+                    1404.0,
+                    2003.0,
+                    1404.0,
+                    2036.0,
+                    294.0,
+                    2036.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1669.0,
+                    824.0,
+                    1669.0,
+                    824.0,
+                    1700.0,
+                    296.0,
+                    1700.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1698.0,
+                    826.0,
+                    1698.0,
+                    826.0,
+                    1731.0,
+                    294.0,
+                    1731.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1728.0,
+                    825.0,
+                    1728.0,
+                    825.0,
+                    1761.0,
+                    294.0,
+                    1761.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1759.0,
+                    826.0,
+                    1759.0,
+                    826.0,
+                    1791.0,
+                    293.0,
+                    1791.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 6,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1389,
+                    1404,
+                    1389,
+                    1404,
+                    1754,
+                    297,
+                    1754
+                ],
+                "score": 0.982
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1769,
+                    1403,
+                    1769,
+                    1403,
+                    1956,
+                    297,
+                    1956
+                ],
+                "score": 0.973
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1170,
+                    1404,
+                    1170,
+                    1404,
+                    1355,
+                    298,
+                    1355
+                ],
+                "score": 0.967
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    1978,
+                    1404,
+                    1978,
+                    1404,
+                    2034,
+                    298,
+                    2034
+                ],
+                "score": 0.937
+            },
+            {
+                "category_id": 5,
+                "poly": [
+                    427,
+                    504,
+                    1268,
+                    504,
+                    1268,
+                    1073,
+                    427,
+                    1073
+                ],
+                "score": 0.91,
+                "html": "<table><tr><td>Labeled data 1% 10% 100% Method Top-5 accuracy</td></tr><tr><td></td></tr><tr><td>Supervised baseline 44.1 82.1 93.9 Methods using label-propagation:</td></tr><tr><td>Pseudolabeling (Zhai et al., 2019) 51.6 82.4 VAT + Entropy Minimization (Zhai et al., 2019) 47.0 83.4 Unsup. Data Augmentation (Xie et al., 2019) 88.5</td></tr><tr><td>Rotation+ VAT+Ent.Min. (Zhai et al.,2019) 91.2 95.0 =</td></tr><tr><td>Methods using representation learning only:</td></tr><tr><td>Instance Discrimination (Wu et al., 2018) 39.2 77.4</td></tr><tr><td>Rotation (Zhai et al., 2019) 57.5 86.4</td></tr><tr><td>+ResNet trained on BigBiGAN (fixed) 55.2 78.8 87.0</td></tr><tr><td>+ResNet trained on AMDIM (fixed) 67.4 85.8 92.2</td></tr><tr><td>+ResNet trained on CPC v2 (fixed) 72.3 89.1 94.4 +ResNet trained on CPC v2 (fine-tuned) 72.9 89.5 95.2</td></tr></table>"
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    75,
+                    858,
+                    75,
+                    858,
+                    104,
+                    298,
+                    104
+                ],
+                "score": 0.89
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    840,
+                    2089,
+                    858,
+                    2089,
+                    858,
+                    2112,
+                    840,
+                    2112
+                ],
+                "score": 0.8
+            },
+            {
+                "category_id": 6,
+                "poly": [
+                    297,
+                    247,
+                    1404,
+                    247,
+                    1404,
+                    494,
+                    297,
+                    494
+                ],
+                "score": 0.62
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    247,
+                    1404,
+                    247,
+                    1404,
+                    494,
+                    297,
+                    494
+                ],
+                "score": 0.578
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1140,
+                    1893,
+                    1271,
+                    1893,
+                    1271,
+                    1923,
+                    1140,
+                    1923
+                ],
+                "score": 0.9,
+                "latex": "7 \\times 7 \\times 2 5 6 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    637,
+                    1893,
+                    767,
+                    1893,
+                    767,
+                    1922,
+                    637,
+                    1922
+                ],
+                "score": 0.9,
+                "latex": "7 \\times 7 \\times 8 1 9 2"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    603,
+                    251,
+                    638,
+                    251,
+                    638,
+                    283,
+                    603,
+                    283
+                ],
+                "score": 0.89,
+                "latex": "h _ { \\psi }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    776,
+                    281,
+                    830,
+                    281,
+                    830,
+                    310,
+                    776,
+                    310
+                ],
+                "score": 0.88,
+                "latex": "10 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    523,
+                    1802,
+                    599,
+                    1802,
+                    599,
+                    1831,
+                    523,
+                    1831
+                ],
+                "score": 0.86,
+                "latex": "6 8 . 1 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1326,
+                    1693,
+                    1401,
+                    1693,
+                    1401,
+                    1723,
+                    1326,
+                    1723
+                ],
+                "score": 0.85,
+                "latex": "6 5 . 9 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    297,
+                    1694,
+                    372,
+                    1694,
+                    372,
+                    1723,
+                    297,
+                    1723
+                ],
+                "score": 0.85,
+                "latex": "5 7 . 5 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    798,
+                    250,
+                    843,
+                    250,
+                    843,
+                    278,
+                    798,
+                    278
+                ],
+                "score": 0.85,
+                "latex": "1 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    957,
+                    1663,
+                    998,
+                    1663,
+                    998,
+                    1692,
+                    957,
+                    1692
+                ],
+                "score": 0.85,
+                "latex": "1 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    883,
+                    250,
+                    941,
+                    250,
+                    941,
+                    279,
+                    883,
+                    279
+                ],
+                "score": 0.85,
+                "latex": "10 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    697,
+                    281,
+                    738,
+                    281,
+                    738,
+                    310,
+                    697,
+                    310
+                ],
+                "score": 0.84,
+                "latex": "1 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    392,
+                    1802,
+                    468,
+                    1802,
+                    468,
+                    1832,
+                    392,
+                    1832
+                ],
+                "score": 0.83,
+                "latex": "6 1 . 3 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1218,
+                    1694,
+                    1292,
+                    1694,
+                    1292,
+                    1723,
+                    1218,
+                    1723
+                ],
+                "score": 0.82,
+                "latex": "5 5 . 4 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1145,
+                    1200,
+                    1386,
+                    1200,
+                    1386,
+                    1234,
+                    1145,
+                    1234
+                ],
+                "score": 0.78,
+                "latex": "R ^ { 2 } = 0 . 1 7 , p = 0 . 3 6"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1042,
+                    403,
+                    1060,
+                    403,
+                    1060,
+                    435,
+                    1042,
+                    435
+                ],
+                "score": 0.76,
+                "latex": "\\dagger"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    505,
+                    725,
+                    528,
+                    725,
+                    528,
+                    750,
+                    505,
+                    750
+                ],
+                "score": 0.71,
+                "latex": "^ +"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    550,
+                    785,
+                    573,
+                    785,
+                    573,
+                    810,
+                    550,
+                    810
+                ],
+                "score": 0.36,
+                "latex": "^ +"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    550,
+                    783,
+                    689,
+                    783,
+                    689,
+                    812,
+                    550,
+                    812
+                ],
+                "score": 0.34,
+                "latex": "+ \\mathrm { V A T } + \\mathrm { E n }"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    330.0,
+                    1973.0,
+                    1405.0,
+                    1973.0,
+                    1405.0,
+                    2011.0,
+                    330.0,
+                    2011.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    2005.0,
+                    884.0,
+                    2005.0,
+                    884.0,
+                    2035.0,
+                    296.0,
+                    2035.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    72.0,
+                    858.0,
+                    72.0,
+                    858.0,
+                    108.0,
+                    297.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    838.0,
+                    2085.0,
+                    862.0,
+                    2085.0,
+                    862.0,
+                    2117.0,
+                    838.0,
+                    2117.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    249.0,
+                    602.0,
+                    249.0,
+                    602.0,
+                    283.0,
+                    295.0,
+                    283.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    639.0,
+                    249.0,
+                    797.0,
+                    249.0,
+                    797.0,
+                    283.0,
+                    639.0,
+                    283.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    844.0,
+                    249.0,
+                    882.0,
+                    249.0,
+                    882.0,
+                    283.0,
+                    844.0,
+                    283.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    942.0,
+                    249.0,
+                    1404.0,
+                    249.0,
+                    1404.0,
+                    283.0,
+                    942.0,
+                    283.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    281.0,
+                    696.0,
+                    281.0,
+                    696.0,
+                    315.0,
+                    295.0,
+                    315.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    739.0,
+                    281.0,
+                    775.0,
+                    281.0,
+                    775.0,
+                    315.0,
+                    739.0,
+                    315.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    831.0,
+                    281.0,
+                    1404.0,
+                    281.0,
+                    1404.0,
+                    315.0,
+                    831.0,
+                    315.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    308.0,
+                    1404.0,
+                    308.0,
+                    1404.0,
+                    348.0,
+                    294.0,
+                    348.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    342.0,
+                    1405.0,
+                    342.0,
+                    1405.0,
+                    375.0,
+                    296.0,
+                    375.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    372.0,
+                    1404.0,
+                    372.0,
+                    1404.0,
+                    405.0,
+                    295.0,
+                    405.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    402.0,
+                    1041.0,
+                    402.0,
+                    1041.0,
+                    436.0,
+                    295.0,
+                    436.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1061.0,
+                    402.0,
+                    1405.0,
+                    402.0,
+                    1405.0,
+                    436.0,
+                    1061.0,
+                    436.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    433.0,
+                    1405.0,
+                    433.0,
+                    1405.0,
+                    467.0,
+                    294.0,
+                    467.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    461.0,
+                    578.0,
+                    461.0,
+                    578.0,
+                    498.0,
+                    294.0,
+                    498.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1390.0,
+                    1405.0,
+                    1390.0,
+                    1405.0,
+                    1424.0,
+                    296.0,
+                    1424.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1419.0,
+                    1406.0,
+                    1419.0,
+                    1406.0,
+                    1455.0,
+                    291.0,
+                    1455.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1450.0,
+                    1402.0,
+                    1450.0,
+                    1402.0,
+                    1484.0,
+                    294.0,
+                    1484.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1481.0,
+                    1404.0,
+                    1481.0,
+                    1404.0,
+                    1515.0,
+                    295.0,
+                    1515.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1511.0,
+                    1405.0,
+                    1511.0,
+                    1405.0,
+                    1545.0,
+                    295.0,
+                    1545.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1539.0,
+                    1405.0,
+                    1539.0,
+                    1405.0,
+                    1578.0,
+                    292.0,
+                    1578.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1570.0,
+                    1405.0,
+                    1570.0,
+                    1405.0,
+                    1607.0,
+                    292.0,
+                    1607.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1601.0,
+                    1405.0,
+                    1601.0,
+                    1405.0,
+                    1638.0,
+                    294.0,
+                    1638.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1633.0,
+                    1404.0,
+                    1633.0,
+                    1404.0,
+                    1667.0,
+                    294.0,
+                    1667.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1661.0,
+                    956.0,
+                    1661.0,
+                    956.0,
+                    1695.0,
+                    295.0,
+                    1695.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    999.0,
+                    1661.0,
+                    1402.0,
+                    1661.0,
+                    1402.0,
+                    1695.0,
+                    999.0,
+                    1695.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1690.0,
+                    296.0,
+                    1690.0,
+                    296.0,
+                    1730.0,
+                    291.0,
+                    1730.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    373.0,
+                    1690.0,
+                    1217.0,
+                    1690.0,
+                    1217.0,
+                    1730.0,
+                    373.0,
+                    1730.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1293.0,
+                    1690.0,
+                    1325.0,
+                    1690.0,
+                    1325.0,
+                    1730.0,
+                    1293.0,
+                    1730.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1402.0,
+                    1690.0,
+                    1405.0,
+                    1690.0,
+                    1405.0,
+                    1730.0,
+                    1402.0,
+                    1730.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1722.0,
+                    423.0,
+                    1722.0,
+                    423.0,
+                    1758.0,
+                    294.0,
+                    1758.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1768.0,
+                    1405.0,
+                    1768.0,
+                    1405.0,
+                    1806.0,
+                    294.0,
+                    1806.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1800.0,
+                    391.0,
+                    1800.0,
+                    391.0,
+                    1837.0,
+                    292.0,
+                    1837.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    469.0,
+                    1800.0,
+                    522.0,
+                    1800.0,
+                    522.0,
+                    1837.0,
+                    469.0,
+                    1837.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    600.0,
+                    1800.0,
+                    1407.0,
+                    1800.0,
+                    1407.0,
+                    1837.0,
+                    600.0,
+                    1837.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1829.0,
+                    1407.0,
+                    1829.0,
+                    1407.0,
+                    1868.0,
+                    294.0,
+                    1868.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1863.0,
+                    1408.0,
+                    1863.0,
+                    1408.0,
+                    1898.0,
+                    295.0,
+                    1898.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1889.0,
+                    636.0,
+                    1889.0,
+                    636.0,
+                    1928.0,
+                    292.0,
+                    1928.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    768.0,
+                    1889.0,
+                    1139.0,
+                    1889.0,
+                    1139.0,
+                    1928.0,
+                    768.0,
+                    1928.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1272.0,
+                    1889.0,
+                    1405.0,
+                    1889.0,
+                    1405.0,
+                    1928.0,
+                    1272.0,
+                    1928.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1923.0,
+                    1405.0,
+                    1923.0,
+                    1405.0,
+                    1959.0,
+                    293.0,
+                    1959.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1171.0,
+                    1406.0,
+                    1171.0,
+                    1406.0,
+                    1206.0,
+                    292.0,
+                    1206.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1200.0,
+                    1144.0,
+                    1200.0,
+                    1144.0,
+                    1237.0,
+                    292.0,
+                    1237.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1387.0,
+                    1200.0,
+                    1405.0,
+                    1200.0,
+                    1405.0,
+                    1237.0,
+                    1387.0,
+                    1237.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1232.0,
+                    1402.0,
+                    1232.0,
+                    1402.0,
+                    1268.0,
+                    294.0,
+                    1268.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1260.0,
+                    1404.0,
+                    1260.0,
+                    1404.0,
+                    1298.0,
+                    293.0,
+                    1298.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1290.0,
+                    1406.0,
+                    1290.0,
+                    1406.0,
+                    1331.0,
+                    291.0,
+                    1331.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1321.0,
+                    628.0,
+                    1321.0,
+                    628.0,
+                    1359.0,
+                    295.0,
+                    1359.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    249.0,
+                    602.0,
+                    249.0,
+                    602.0,
+                    283.0,
+                    295.0,
+                    283.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    639.0,
+                    249.0,
+                    797.0,
+                    249.0,
+                    797.0,
+                    283.0,
+                    639.0,
+                    283.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    844.0,
+                    249.0,
+                    882.0,
+                    249.0,
+                    882.0,
+                    283.0,
+                    844.0,
+                    283.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    942.0,
+                    249.0,
+                    1404.0,
+                    249.0,
+                    1404.0,
+                    283.0,
+                    942.0,
+                    283.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    281.0,
+                    696.0,
+                    281.0,
+                    696.0,
+                    315.0,
+                    295.0,
+                    315.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    739.0,
+                    281.0,
+                    775.0,
+                    281.0,
+                    775.0,
+                    315.0,
+                    739.0,
+                    315.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    831.0,
+                    281.0,
+                    1404.0,
+                    281.0,
+                    1404.0,
+                    315.0,
+                    831.0,
+                    315.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    308.0,
+                    1404.0,
+                    308.0,
+                    1404.0,
+                    348.0,
+                    294.0,
+                    348.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    342.0,
+                    1405.0,
+                    342.0,
+                    1405.0,
+                    375.0,
+                    296.0,
+                    375.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    372.0,
+                    1404.0,
+                    372.0,
+                    1404.0,
+                    405.0,
+                    295.0,
+                    405.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    402.0,
+                    1041.0,
+                    402.0,
+                    1041.0,
+                    436.0,
+                    295.0,
+                    436.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1061.0,
+                    402.0,
+                    1405.0,
+                    402.0,
+                    1405.0,
+                    436.0,
+                    1061.0,
+                    436.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    433.0,
+                    1405.0,
+                    433.0,
+                    1405.0,
+                    467.0,
+                    294.0,
+                    467.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    461.0,
+                    578.0,
+                    461.0,
+                    578.0,
+                    498.0,
+                    294.0,
+                    498.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 7,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    639,
+                    1402,
+                    639,
+                    1402,
+                    1004,
+                    299,
+                    1004
+                ],
+                "score": 0.985
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1113,
+                    1404,
+                    1113,
+                    1404,
+                    1631,
+                    298,
+                    1631
+                ],
+                "score": 0.984
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1759,
+                    1403,
+                    1759,
+                    1403,
+                    2034,
+                    297,
+                    2034
+                ],
+                "score": 0.982
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    230,
+                    1403,
+                    230,
+                    1403,
+                    596,
+                    298,
+                    596
+                ],
+                "score": 0.982
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    300,
+                    1684,
+                    529,
+                    1684,
+                    529,
+                    1719,
+                    300,
+                    1719
+                ],
+                "score": 0.888
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    300,
+                    1052,
+                    1159,
+                    1052,
+                    1159,
+                    1083,
+                    300,
+                    1083
+                ],
+                "score": 0.821
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    299,
+                    76,
+                    857,
+                    76,
+                    857,
+                    104,
+                    299,
+                    104
+                ],
+                "score": 0.819
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2089,
+                    858,
+                    2089,
+                    858,
+                    2111,
+                    841,
+                    2111
+                ],
+                "score": 0.79
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    300,
+                    76,
+                    856,
+                    76,
+                    856,
+                    104,
+                    300,
+                    104
+                ],
+                "score": 0.316
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    404,
+                    1235,
+                    439,
+                    1235,
+                    439,
+                    1268,
+                    404,
+                    1268
+                ],
+                "score": 0.9,
+                "latex": "h _ { \\psi }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    584,
+                    231,
+                    660,
+                    231,
+                    660,
+                    260,
+                    584,
+                    260
+                ],
+                "score": 0.89,
+                "latex": "7 2 . 3 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1144,
+                    1540,
+                    1172,
+                    1540,
+                    1172,
+                    1570,
+                    1144,
+                    1570
+                ],
+                "score": 0.89,
+                "latex": "f _ { \\theta }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    791,
+                    383,
+                    867,
+                    383,
+                    867,
+                    412,
+                    791,
+                    412
+                ],
+                "score": 0.88,
+                "latex": "5 5 . 2 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    297,
+                    475,
+                    373,
+                    475,
+                    373,
+                    504,
+                    297,
+                    504
+                ],
+                "score": 0.88,
+                "latex": "6 7 . 4 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    905,
+                    853,
+                    982,
+                    853,
+                    982,
+                    883,
+                    905,
+                    883
+                ],
+                "score": 0.88,
+                "latex": "8 9 . 4 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    986,
+                    414,
+                    1044,
+                    414,
+                    1044,
+                    444,
+                    986,
+                    444
+                ],
+                "score": 0.87,
+                "latex": "( + 6 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    414,
+                    389,
+                    414,
+                    389,
+                    445,
+                    298,
+                    445
+                ],
+                "score": 0.87,
+                "latex": "( 5 7 . 5 \\% )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    538,
+                    853,
+                    592,
+                    853,
+                    592,
+                    882,
+                    538,
+                    882
+                ],
+                "score": 0.87,
+                "latex": "10 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    833,
+                    1479,
+                    909,
+                    1479,
+                    909,
+                    1508,
+                    833,
+                    1508
+                ],
+                "score": 0.87,
+                "latex": "7 0 . 6 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    296,
+                    1570,
+                    372,
+                    1570,
+                    372,
+                    1599,
+                    296,
+                    1599
+                ],
+                "score": 0.87,
+                "latex": "7 2 . 7 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    297,
+                    1448,
+                    373,
+                    1448,
+                    373,
+                    1478,
+                    297,
+                    1478
+                ],
+                "score": 0.86,
+                "latex": "7 0 . 5 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    403,
+                    1510,
+                    431,
+                    1510,
+                    431,
+                    1540,
+                    403,
+                    1540
+                ],
+                "score": 0.86,
+                "latex": "f _ { \\theta }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    296,
+                    1387,
+                    352,
+                    1387,
+                    352,
+                    1416,
+                    296,
+                    1416
+                ],
+                "score": 0.86,
+                "latex": "65 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1326,
+                    822,
+                    1401,
+                    822,
+                    1401,
+                    852,
+                    1326,
+                    852
+                ],
+                "score": 0.86,
+                "latex": "8 2 . 4 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    905,
+                    231,
+                    945,
+                    231,
+                    945,
+                    259,
+                    905,
+                    259
+                ],
+                "score": 0.86,
+                "latex": "1 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    326,
+                    1418,
+                    401,
+                    1418,
+                    401,
+                    1447,
+                    326,
+                    1447
+                ],
+                "score": 0.86,
+                "latex": "6 7 . 8 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1105,
+                    823,
+                    1179,
+                    823,
+                    1179,
+                    852,
+                    1105,
+                    852
+                ],
+                "score": 0.86,
+                "latex": "8 5 . 8 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    736,
+                    1570,
+                    777,
+                    1570,
+                    777,
+                    1599,
+                    736,
+                    1599
+                ],
+                "score": 0.84,
+                "latex": "2 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    364,
+                    231,
+                    439,
+                    231,
+                    439,
+                    261,
+                    364,
+                    261
+                ],
+                "score": 0.84,
+                "latex": "7 2 . 9 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1143,
+                    353,
+                    1184,
+                    353,
+                    1184,
+                    382,
+                    1143,
+                    382
+                ],
+                "score": 0.84,
+                "latex": "1 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1191,
+                    823,
+                    1265,
+                    823,
+                    1265,
+                    852,
+                    1191,
+                    852
+                ],
+                "score": 0.83,
+                "latex": "8 3 . 4 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1266,
+                    884,
+                    1343,
+                    884,
+                    1343,
+                    914,
+                    1266,
+                    914
+                ],
+                "score": 0.8,
+                "latex": "9 1 . 2 \\%"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1683.0,
+                    535.0,
+                    1683.0,
+                    535.0,
+                    1726.0,
+                    292.0,
+                    1726.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1050.0,
+                    1165.0,
+                    1050.0,
+                    1165.0,
+                    1088.0,
+                    294.0,
+                    1088.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    298.0,
+                    73.0,
+                    858.0,
+                    73.0,
+                    858.0,
+                    108.0,
+                    298.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    839.0,
+                    2087.0,
+                    860.0,
+                    2087.0,
+                    860.0,
+                    2117.0,
+                    839.0,
+                    2117.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    73.0,
+                    859.0,
+                    73.0,
+                    859.0,
+                    108.0,
+                    297.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    639.0,
+                    1407.0,
+                    639.0,
+                    1407.0,
+                    676.0,
+                    294.0,
+                    676.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    671.0,
+                    1406.0,
+                    671.0,
+                    1406.0,
+                    704.0,
+                    293.0,
+                    704.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    702.0,
+                    1402.0,
+                    702.0,
+                    1402.0,
+                    736.0,
+                    295.0,
+                    736.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    731.0,
+                    1402.0,
+                    731.0,
+                    1402.0,
+                    765.0,
+                    295.0,
+                    765.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    759.0,
+                    1404.0,
+                    759.0,
+                    1404.0,
+                    799.0,
+                    294.0,
+                    799.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    790.0,
+                    1406.0,
+                    790.0,
+                    1406.0,
+                    826.0,
+                    294.0,
+                    826.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    823.0,
+                    1104.0,
+                    823.0,
+                    1104.0,
+                    857.0,
+                    295.0,
+                    857.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1180.0,
+                    823.0,
+                    1190.0,
+                    823.0,
+                    1190.0,
+                    857.0,
+                    1180.0,
+                    857.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1266.0,
+                    823.0,
+                    1325.0,
+                    823.0,
+                    1325.0,
+                    857.0,
+                    1266.0,
+                    857.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    851.0,
+                    537.0,
+                    851.0,
+                    537.0,
+                    889.0,
+                    293.0,
+                    889.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    593.0,
+                    851.0,
+                    904.0,
+                    851.0,
+                    904.0,
+                    889.0,
+                    593.0,
+                    889.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    983.0,
+                    851.0,
+                    1406.0,
+                    851.0,
+                    1406.0,
+                    889.0,
+                    983.0,
+                    889.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    883.0,
+                    1265.0,
+                    883.0,
+                    1265.0,
+                    921.0,
+                    293.0,
+                    921.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1344.0,
+                    883.0,
+                    1406.0,
+                    883.0,
+                    1406.0,
+                    921.0,
+                    1344.0,
+                    921.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    915.0,
+                    1406.0,
+                    915.0,
+                    1406.0,
+                    949.0,
+                    294.0,
+                    949.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    944.0,
+                    1407.0,
+                    944.0,
+                    1407.0,
+                    981.0,
+                    293.0,
+                    981.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    976.0,
+                    721.0,
+                    976.0,
+                    721.0,
+                    1007.0,
+                    297.0,
+                    1007.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1112.0,
+                    1405.0,
+                    1112.0,
+                    1405.0,
+                    1148.0,
+                    296.0,
+                    1148.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1143.0,
+                    1406.0,
+                    1143.0,
+                    1406.0,
+                    1179.0,
+                    293.0,
+                    1179.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1171.0,
+                    1406.0,
+                    1171.0,
+                    1406.0,
+                    1210.0,
+                    292.0,
+                    1210.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1206.0,
+                    1402.0,
+                    1206.0,
+                    1402.0,
+                    1238.0,
+                    294.0,
+                    1238.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1233.0,
+                    403.0,
+                    1233.0,
+                    403.0,
+                    1269.0,
+                    294.0,
+                    1269.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    440.0,
+                    1233.0,
+                    1405.0,
+                    1233.0,
+                    1405.0,
+                    1269.0,
+                    440.0,
+                    1269.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1264.0,
+                    1405.0,
+                    1264.0,
+                    1405.0,
+                    1299.0,
+                    293.0,
+                    1299.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1295.0,
+                    1406.0,
+                    1295.0,
+                    1406.0,
+                    1331.0,
+                    292.0,
+                    1331.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1324.0,
+                    1406.0,
+                    1324.0,
+                    1406.0,
+                    1360.0,
+                    293.0,
+                    1360.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1355.0,
+                    1408.0,
+                    1355.0,
+                    1408.0,
+                    1395.0,
+                    291.0,
+                    1395.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1384.0,
+                    295.0,
+                    1384.0,
+                    295.0,
+                    1426.0,
+                    291.0,
+                    1426.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    1384.0,
+                    1406.0,
+                    1384.0,
+                    1406.0,
+                    1426.0,
+                    353.0,
+                    1426.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1416.0,
+                    325.0,
+                    1416.0,
+                    325.0,
+                    1452.0,
+                    293.0,
+                    1452.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    402.0,
+                    1416.0,
+                    1405.0,
+                    1416.0,
+                    1405.0,
+                    1452.0,
+                    402.0,
+                    1452.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1444.0,
+                    296.0,
+                    1444.0,
+                    296.0,
+                    1485.0,
+                    293.0,
+                    1485.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    374.0,
+                    1444.0,
+                    1406.0,
+                    1444.0,
+                    1406.0,
+                    1485.0,
+                    374.0,
+                    1485.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1479.0,
+                    832.0,
+                    1479.0,
+                    832.0,
+                    1514.0,
+                    293.0,
+                    1514.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    910.0,
+                    1479.0,
+                    1406.0,
+                    1479.0,
+                    1406.0,
+                    1514.0,
+                    910.0,
+                    1514.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1507.0,
+                    402.0,
+                    1507.0,
+                    402.0,
+                    1543.0,
+                    293.0,
+                    1543.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    432.0,
+                    1507.0,
+                    1405.0,
+                    1507.0,
+                    1405.0,
+                    1543.0,
+                    432.0,
+                    1543.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1538.0,
+                    1143.0,
+                    1538.0,
+                    1143.0,
+                    1574.0,
+                    294.0,
+                    1574.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1173.0,
+                    1538.0,
+                    1405.0,
+                    1538.0,
+                    1405.0,
+                    1574.0,
+                    1173.0,
+                    1574.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    373.0,
+                    1566.0,
+                    735.0,
+                    1566.0,
+                    735.0,
+                    1605.0,
+                    373.0,
+                    1605.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    778.0,
+                    1566.0,
+                    1405.0,
+                    1566.0,
+                    1405.0,
+                    1605.0,
+                    778.0,
+                    1605.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1600.0,
+                    1365.0,
+                    1600.0,
+                    1365.0,
+                    1636.0,
+                    294.0,
+                    1636.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1757.0,
+                    1405.0,
+                    1757.0,
+                    1405.0,
+                    1795.0,
+                    295.0,
+                    1795.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1790.0,
+                    1405.0,
+                    1790.0,
+                    1405.0,
+                    1824.0,
+                    293.0,
+                    1824.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1818.0,
+                    1405.0,
+                    1818.0,
+                    1405.0,
+                    1856.0,
+                    292.0,
+                    1856.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1850.0,
+                    1405.0,
+                    1850.0,
+                    1405.0,
+                    1886.0,
+                    293.0,
+                    1886.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1881.0,
+                    1405.0,
+                    1881.0,
+                    1405.0,
+                    1916.0,
+                    292.0,
+                    1916.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1911.0,
+                    1403.0,
+                    1911.0,
+                    1403.0,
+                    1947.0,
+                    292.0,
+                    1947.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1942.0,
+                    1404.0,
+                    1942.0,
+                    1404.0,
+                    1979.0,
+                    292.0,
+                    1979.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1969.0,
+                    1407.0,
+                    1969.0,
+                    1407.0,
+                    2010.0,
+                    292.0,
+                    2010.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    2001.0,
+                    947.0,
+                    2001.0,
+                    947.0,
+                    2038.0,
+                    292.0,
+                    2038.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    231.0,
+                    363.0,
+                    231.0,
+                    363.0,
+                    265.0,
+                    296.0,
+                    265.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    440.0,
+                    231.0,
+                    583.0,
+                    231.0,
+                    583.0,
+                    265.0,
+                    440.0,
+                    265.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    661.0,
+                    231.0,
+                    904.0,
+                    231.0,
+                    904.0,
+                    265.0,
+                    661.0,
+                    265.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    946.0,
+                    231.0,
+                    1403.0,
+                    231.0,
+                    1403.0,
+                    265.0,
+                    946.0,
+                    265.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    261.0,
+                    1404.0,
+                    261.0,
+                    1404.0,
+                    295.0,
+                    294.0,
+                    295.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    289.0,
+                    1403.0,
+                    289.0,
+                    1403.0,
+                    328.0,
+                    293.0,
+                    328.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    320.0,
+                    1407.0,
+                    320.0,
+                    1407.0,
+                    358.0,
+                    292.0,
+                    358.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    351.0,
+                    1142.0,
+                    351.0,
+                    1142.0,
+                    388.0,
+                    293.0,
+                    388.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1185.0,
+                    351.0,
+                    1405.0,
+                    351.0,
+                    1405.0,
+                    388.0,
+                    1185.0,
+                    388.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    381.0,
+                    790.0,
+                    381.0,
+                    790.0,
+                    418.0,
+                    293.0,
+                    418.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    868.0,
+                    381.0,
+                    1405.0,
+                    381.0,
+                    1405.0,
+                    418.0,
+                    868.0,
+                    418.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    390.0,
+                    414.0,
+                    985.0,
+                    414.0,
+                    985.0,
+                    448.0,
+                    390.0,
+                    448.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1045.0,
+                    414.0,
+                    1403.0,
+                    414.0,
+                    1403.0,
+                    448.0,
+                    1045.0,
+                    448.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    443.0,
+                    1405.0,
+                    443.0,
+                    1405.0,
+                    477.0,
+                    294.0,
+                    477.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    474.0,
+                    296.0,
+                    474.0,
+                    296.0,
+                    509.0,
+                    293.0,
+                    509.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    374.0,
+                    474.0,
+                    1405.0,
+                    474.0,
+                    1405.0,
+                    509.0,
+                    374.0,
+                    509.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    505.0,
+                    1405.0,
+                    505.0,
+                    1405.0,
+                    539.0,
+                    294.0,
+                    539.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    536.0,
+                    1405.0,
+                    536.0,
+                    1405.0,
+                    570.0,
+                    294.0,
+                    570.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    566.0,
+                    1211.0,
+                    566.0,
+                    1211.0,
+                    600.0,
+                    294.0,
+                    600.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 8,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1072,
+                    1405,
+                    1072,
+                    1405,
+                    1498,
+                    297,
+                    1498
+                ],
+                "score": 0.982
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    299,
+                    1546,
+                    488,
+                    1546,
+                    488,
+                    1578,
+                    299,
+                    1578
+                ],
+                "score": 0.863
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    837,
+                    2088,
+                    865,
+                    2088,
+                    865,
+                    2112,
+                    837,
+                    2112
+                ],
+                "score": 0.839
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    293,
+                    1596,
+                    1352,
+                    1596,
+                    1352,
+                    1628,
+                    293,
+                    1628
+                ],
+                "score": 0.734
+            },
+            {
+                "category_id": 6,
+                "poly": [
+                    296,
+                    248,
+                    1405,
+                    248,
+                    1405,
+                    463,
+                    296,
+                    463
+                ],
+                "score": 0.606
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    248,
+                    1405,
+                    248,
+                    1405,
+                    463,
+                    296,
+                    463
+                ],
+                "score": 0.584
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1646,
+                    1401,
+                    1646,
+                    1401,
+                    1710,
+                    296,
+                    1710
+                ],
+                "score": 0.564
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1971,
+                    1399,
+                    1971,
+                    1399,
+                    2033,
+                    299,
+                    2033
+                ],
+                "score": 0.561
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    75,
+                    858,
+                    75,
+                    858,
+                    105,
+                    298,
+                    105
+                ],
+                "score": 0.56
+            },
+            {
+                "category_id": 5,
+                "poly": [
+                    409,
+                    474,
+                    1289,
+                    474,
+                    1289,
+                    1006,
+                    409,
+                    1006
+                ],
+                "score": 0.527,
+                "html": "<table><tr><td>Method</td><td>mAP</td></tr><tr><td>Transfer from labeled data: Supervised - ResNet-152</td><td>74.7</td></tr><tr><td>Transfer from unlabeled data: Exemplar (Ex) (Dosovitskiy et al., 2014) Motion Segmentation (MS) (Pathak et al.,2016)</td><td>60.9</td></tr><tr><td>Colorization (Col) (Zhang et al.,2016) Relative Position (RP) (Doersch et al.,2015)</td><td>61.1 65.5</td></tr><tr><td>Combination of Ex + MS + Col +RP (Doersch &amp; Zisserman,2017)</td><td>66.8 70.5</td></tr><tr><td>Instance Discrimination (Wu et al., 2018)</td><td>65.4</td></tr><tr><td>Deep Cluster (Caron et al., 2018) Deeper Cluster (Caron et al., 2019)</td><td>65.9</td></tr></table>"
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1890,
+                    1400,
+                    1890,
+                    1400,
+                    1953,
+                    297,
+                    1953
+                ],
+                "score": 0.497
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1727,
+                    1401,
+                    1727,
+                    1401,
+                    1791,
+                    297,
+                    1791
+                ],
+                "score": 0.493
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1808,
+                    1400,
+                    1808,
+                    1400,
+                    1872,
+                    296,
+                    1872
+                ],
+                "score": 0.489
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    75,
+                    858,
+                    75,
+                    858,
+                    104,
+                    298,
+                    104
+                ],
+                "score": 0.345
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    607,
+                    783,
+                    843,
+                    783,
+                    843,
+                    812,
+                    607,
+                    812
+                ],
+                "score": 0.9,
+                "latex": "\\operatorname { E x } + \\mathbf { M S } + \\mathbf { C o l } + \\mathbf { R P }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    564,
+                    250,
+                    600,
+                    250,
+                    600,
+                    283,
+                    564,
+                    283
+                ],
+                "score": 0.88,
+                "latex": "h _ { \\psi }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    755,
+                    249,
+                    827,
+                    249,
+                    827,
+                    279,
+                    755,
+                    279
+                ],
+                "score": 0.86,
+                "latex": "100 \\%"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1292,
+                    403,
+                    1311,
+                    403,
+                    1311,
+                    435,
+                    1292,
+                    435
+                ],
+                "score": 0.73,
+                "latex": "\\dagger"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1543.0,
+                    491.0,
+                    1543.0,
+                    491.0,
+                    1583.0,
+                    296.0,
+                    1583.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    831.0,
+                    2084.0,
+                    871.0,
+                    2084.0,
+                    871.0,
+                    2125.0,
+                    831.0,
+                    2125.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    248.0,
+                    563.0,
+                    248.0,
+                    563.0,
+                    283.0,
+                    295.0,
+                    283.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    601.0,
+                    248.0,
+                    754.0,
+                    248.0,
+                    754.0,
+                    283.0,
+                    601.0,
+                    283.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    828.0,
+                    248.0,
+                    1403.0,
+                    248.0,
+                    1403.0,
+                    283.0,
+                    828.0,
+                    283.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    280.0,
+                    1405.0,
+                    280.0,
+                    1405.0,
+                    314.0,
+                    293.0,
+                    314.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    310.0,
+                    1405.0,
+                    310.0,
+                    1405.0,
+                    344.0,
+                    294.0,
+                    344.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    343.0,
+                    1403.0,
+                    343.0,
+                    1403.0,
+                    374.0,
+                    295.0,
+                    374.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    371.0,
+                    1405.0,
+                    371.0,
+                    1405.0,
+                    406.0,
+                    294.0,
+                    406.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    400.0,
+                    1291.0,
+                    400.0,
+                    1291.0,
+                    437.0,
+                    294.0,
+                    437.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1312.0,
+                    400.0,
+                    1405.0,
+                    400.0,
+                    1405.0,
+                    437.0,
+                    1312.0,
+                    437.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    434.0,
+                    694.0,
+                    434.0,
+                    694.0,
+                    465.0,
+                    296.0,
+                    465.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    298.0,
+                    73.0,
+                    858.0,
+                    73.0,
+                    858.0,
+                    108.0,
+                    298.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    72.0,
+                    858.0,
+                    72.0,
+                    858.0,
+                    108.0,
+                    297.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1070.0,
+                    1405.0,
+                    1070.0,
+                    1405.0,
+                    1108.0,
+                    294.0,
+                    1108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1105.0,
+                    1403.0,
+                    1105.0,
+                    1403.0,
+                    1137.0,
+                    295.0,
+                    1137.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1131.0,
+                    1405.0,
+                    1131.0,
+                    1405.0,
+                    1169.0,
+                    294.0,
+                    1169.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1165.0,
+                    1403.0,
+                    1165.0,
+                    1403.0,
+                    1196.0,
+                    296.0,
+                    1196.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1196.0,
+                    1403.0,
+                    1196.0,
+                    1403.0,
+                    1228.0,
+                    295.0,
+                    1228.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1222.0,
+                    1403.0,
+                    1222.0,
+                    1403.0,
+                    1261.0,
+                    294.0,
+                    1261.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1252.0,
+                    1406.0,
+                    1252.0,
+                    1406.0,
+                    1293.0,
+                    291.0,
+                    1293.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1285.0,
+                    1406.0,
+                    1285.0,
+                    1406.0,
+                    1320.0,
+                    291.0,
+                    1320.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1317.0,
+                    1405.0,
+                    1317.0,
+                    1405.0,
+                    1352.0,
+                    295.0,
+                    1352.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1347.0,
+                    1405.0,
+                    1347.0,
+                    1405.0,
+                    1382.0,
+                    295.0,
+                    1382.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1377.0,
+                    1405.0,
+                    1377.0,
+                    1405.0,
+                    1413.0,
+                    295.0,
+                    1413.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1404.0,
+                    1406.0,
+                    1404.0,
+                    1406.0,
+                    1446.0,
+                    292.0,
+                    1446.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1438.0,
+                    1406.0,
+                    1438.0,
+                    1406.0,
+                    1473.0,
+                    295.0,
+                    1473.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1467.0,
+                    659.0,
+                    1467.0,
+                    659.0,
+                    1504.0,
+                    294.0,
+                    1504.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1591.0,
+                    1355.0,
+                    1591.0,
+                    1355.0,
+                    1634.0,
+                    294.0,
+                    1634.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    248.0,
+                    563.0,
+                    248.0,
+                    563.0,
+                    283.0,
+                    295.0,
+                    283.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    601.0,
+                    248.0,
+                    754.0,
+                    248.0,
+                    754.0,
+                    283.0,
+                    601.0,
+                    283.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    828.0,
+                    248.0,
+                    1403.0,
+                    248.0,
+                    1403.0,
+                    283.0,
+                    828.0,
+                    283.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    280.0,
+                    1405.0,
+                    280.0,
+                    1405.0,
+                    314.0,
+                    293.0,
+                    314.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    310.0,
+                    1405.0,
+                    310.0,
+                    1405.0,
+                    344.0,
+                    294.0,
+                    344.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    343.0,
+                    1403.0,
+                    343.0,
+                    1403.0,
+                    374.0,
+                    295.0,
+                    374.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    371.0,
+                    1405.0,
+                    371.0,
+                    1405.0,
+                    406.0,
+                    294.0,
+                    406.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    400.0,
+                    1291.0,
+                    400.0,
+                    1291.0,
+                    437.0,
+                    294.0,
+                    437.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1312.0,
+                    400.0,
+                    1405.0,
+                    400.0,
+                    1405.0,
+                    437.0,
+                    1312.0,
+                    437.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    434.0,
+                    694.0,
+                    434.0,
+                    694.0,
+                    465.0,
+                    296.0,
+                    465.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1646.0,
+                    1405.0,
+                    1646.0,
+                    1405.0,
+                    1682.0,
+                    295.0,
+                    1682.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    1677.0,
+                    1069.0,
+                    1677.0,
+                    1069.0,
+                    1713.0,
+                    323.0,
+                    1713.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1972.0,
+                    1403.0,
+                    1972.0,
+                    1403.0,
+                    2007.0,
+                    294.0,
+                    2007.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    2002.0,
+                    483.0,
+                    2002.0,
+                    483.0,
+                    2035.0,
+                    324.0,
+                    2035.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1888.0,
+                    1404.0,
+                    1888.0,
+                    1404.0,
+                    1928.0,
+                    293.0,
+                    1928.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    1920.0,
+                    1153.0,
+                    1920.0,
+                    1153.0,
+                    1956.0,
+                    323.0,
+                    1956.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1724.0,
+                    1405.0,
+                    1724.0,
+                    1405.0,
+                    1765.0,
+                    292.0,
+                    1765.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    1758.0,
+                    1013.0,
+                    1758.0,
+                    1013.0,
+                    1792.0,
+                    323.0,
+                    1792.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1805.0,
+                    1405.0,
+                    1805.0,
+                    1405.0,
+                    1845.0,
+                    292.0,
+                    1845.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    319.0,
+                    1833.0,
+                    400.0,
+                    1833.0,
+                    400.0,
+                    1876.0,
+                    319.0,
+                    1876.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 9,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    1506,
+                    1403,
+                    1506,
+                    1403,
+                    1573,
+                    295,
+                    1573
+                ],
+                "score": 0.886
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    228,
+                    1400,
+                    228,
+                    1400,
+                    323,
+                    296,
+                    323
+                ],
+                "score": 0.877
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    75,
+                    858,
+                    75,
+                    858,
+                    105,
+                    298,
+                    105
+                ],
+                "score": 0.875
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    293,
+                    809,
+                    1402,
+                    809,
+                    1402,
+                    873,
+                    293,
+                    873
+                ],
+                "score": 0.861
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    300,
+                    1272,
+                    1403,
+                    1272,
+                    1403,
+                    1369,
+                    300,
+                    1369
+                ],
+                "score": 0.851
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    291,
+                    722,
+                    1402,
+                    722,
+                    1402,
+                    788,
+                    291,
+                    788
+                ],
+                "score": 0.85
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1389,
+                    1403,
+                    1389,
+                    1403,
+                    1484,
+                    298,
+                    1484
+                ],
+                "score": 0.848
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    518,
+                    1401,
+                    518,
+                    1401,
+                    584,
+                    298,
+                    584
+                ],
+                "score": 0.847
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    432,
+                    1399,
+                    432,
+                    1399,
+                    497,
+                    296,
+                    497
+                ],
+                "score": 0.844
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    346,
+                    1397,
+                    346,
+                    1397,
+                    411,
+                    296,
+                    411
+                ],
+                "score": 0.842
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    293,
+                    1710,
+                    1404,
+                    1710,
+                    1404,
+                    1776,
+                    293,
+                    1776
+                ],
+                "score": 0.839
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    294,
+                    1187,
+                    1402,
+                    1187,
+                    1402,
+                    1252,
+                    294,
+                    1252
+                ],
+                "score": 0.836
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1592,
+                    1405,
+                    1592,
+                    1405,
+                    1687,
+                    297,
+                    1687
+                ],
+                "score": 0.832
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    605,
+                    1407,
+                    605,
+                    1407,
+                    700,
+                    296,
+                    700
+                ],
+                "score": 0.831
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    303,
+                    1012,
+                    1400,
+                    1012,
+                    1400,
+                    1078,
+                    303,
+                    1078
+                ],
+                "score": 0.829
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    836,
+                    2088,
+                    863,
+                    2088,
+                    863,
+                    2113,
+                    836,
+                    2113
+                ],
+                "score": 0.825
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1099,
+                    1402,
+                    1099,
+                    1402,
+                    1164,
+                    299,
+                    1164
+                ],
+                "score": 0.809
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1972,
+                    1398,
+                    1972,
+                    1398,
+                    2035,
+                    297,
+                    2035
+                ],
+                "score": 0.799
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    293,
+                    1798,
+                    1402,
+                    1798,
+                    1402,
+                    1863,
+                    293,
+                    1863
+                ],
+                "score": 0.795
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    895,
+                    1405,
+                    895,
+                    1405,
+                    992,
+                    298,
+                    992
+                ],
+                "score": 0.795
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    294,
+                    1884,
+                    1402,
+                    1884,
+                    1402,
+                    1948,
+                    294,
+                    1948
+                ],
+                "score": 0.762
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    298.0,
+                    73.0,
+                    858.0,
+                    73.0,
+                    858.0,
+                    108.0,
+                    298.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    832.0,
+                    2085.0,
+                    868.0,
+                    2085.0,
+                    868.0,
+                    2125.0,
+                    832.0,
+                    2125.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    1506.0,
+                    1403.0,
+                    1506.0,
+                    1403.0,
+                    1542.0,
+                    297.0,
+                    1542.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1538.0,
+                    1286.0,
+                    1538.0,
+                    1286.0,
+                    1575.0,
+                    322.0,
+                    1575.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    227.0,
+                    1404.0,
+                    227.0,
+                    1404.0,
+                    267.0,
+                    292.0,
+                    267.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    261.0,
+                    1405.0,
+                    261.0,
+                    1405.0,
+                    299.0,
+                    323.0,
+                    299.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    290.0,
+                    520.0,
+                    290.0,
+                    520.0,
+                    325.0,
+                    322.0,
+                    325.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    805.0,
+                    1405.0,
+                    805.0,
+                    1405.0,
+                    849.0,
+                    292.0,
+                    849.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    840.0,
+                    611.0,
+                    840.0,
+                    611.0,
+                    876.0,
+                    322.0,
+                    876.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1270.0,
+                    1404.0,
+                    1270.0,
+                    1404.0,
+                    1311.0,
+                    293.0,
+                    1311.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1304.0,
+                    1404.0,
+                    1304.0,
+                    1404.0,
+                    1340.0,
+                    321.0,
+                    1340.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    1337.0,
+                    984.0,
+                    1337.0,
+                    984.0,
+                    1368.0,
+                    323.0,
+                    1368.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    719.0,
+                    1405.0,
+                    719.0,
+                    1405.0,
+                    762.0,
+                    292.0,
+                    762.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    755.0,
+                    610.0,
+                    755.0,
+                    610.0,
+                    786.0,
+                    323.0,
+                    786.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1388.0,
+                    1403.0,
+                    1388.0,
+                    1403.0,
+                    1429.0,
+                    295.0,
+                    1429.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1418.0,
+                    1404.0,
+                    1418.0,
+                    1404.0,
+                    1461.0,
+                    321.0,
+                    1461.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    1447.0,
+                    518.0,
+                    1447.0,
+                    518.0,
+                    1487.0,
+                    323.0,
+                    1487.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    517.0,
+                    1405.0,
+                    517.0,
+                    1405.0,
+                    556.0,
+                    294.0,
+                    556.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    550.0,
+                    1204.0,
+                    550.0,
+                    1204.0,
+                    585.0,
+                    323.0,
+                    585.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    431.0,
+                    1404.0,
+                    431.0,
+                    1404.0,
+                    471.0,
+                    292.0,
+                    471.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    463.0,
+                    1277.0,
+                    463.0,
+                    1277.0,
+                    499.0,
+                    322.0,
+                    499.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    344.0,
+                    1399.0,
+                    344.0,
+                    1399.0,
+                    384.0,
+                    294.0,
+                    384.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    379.0,
+                    1047.0,
+                    379.0,
+                    1047.0,
+                    412.0,
+                    321.0,
+                    412.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1708.0,
+                    1404.0,
+                    1708.0,
+                    1404.0,
+                    1748.0,
+                    295.0,
+                    1748.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    1742.0,
+                    780.0,
+                    1742.0,
+                    780.0,
+                    1778.0,
+                    324.0,
+                    1778.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1186.0,
+                    1405.0,
+                    1186.0,
+                    1405.0,
+                    1226.0,
+                    296.0,
+                    1226.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1218.0,
+                    1096.0,
+                    1218.0,
+                    1096.0,
+                    1253.0,
+                    322.0,
+                    1253.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1594.0,
+                    1405.0,
+                    1594.0,
+                    1405.0,
+                    1629.0,
+                    296.0,
+                    1629.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1626.0,
+                    1405.0,
+                    1626.0,
+                    1405.0,
+                    1658.0,
+                    321.0,
+                    1658.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    1657.0,
+                    519.0,
+                    1657.0,
+                    519.0,
+                    1687.0,
+                    324.0,
+                    1687.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    602.0,
+                    1403.0,
+                    602.0,
+                    1403.0,
+                    645.0,
+                    294.0,
+                    645.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    634.0,
+                    1405.0,
+                    634.0,
+                    1405.0,
+                    676.0,
+                    320.0,
+                    676.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    668.0,
+                    534.0,
+                    668.0,
+                    534.0,
+                    699.0,
+                    324.0,
+                    699.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    1013.0,
+                    1403.0,
+                    1013.0,
+                    1403.0,
+                    1049.0,
+                    297.0,
+                    1049.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    1044.0,
+                    1136.0,
+                    1044.0,
+                    1136.0,
+                    1079.0,
+                    323.0,
+                    1079.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1098.0,
+                    1403.0,
+                    1098.0,
+                    1403.0,
+                    1139.0,
+                    294.0,
+                    1139.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1132.0,
+                    1083.0,
+                    1132.0,
+                    1083.0,
+                    1165.0,
+                    322.0,
+                    1165.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1969.0,
+                    1403.0,
+                    1969.0,
+                    1403.0,
+                    2010.0,
+                    292.0,
+                    2010.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    2002.0,
+                    966.0,
+                    2002.0,
+                    966.0,
+                    2035.0,
+                    322.0,
+                    2035.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1796.0,
+                    1404.0,
+                    1796.0,
+                    1404.0,
+                    1838.0,
+                    293.0,
+                    1838.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1829.0,
+                    1145.0,
+                    1829.0,
+                    1145.0,
+                    1863.0,
+                    321.0,
+                    1863.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    897.0,
+                    1401.0,
+                    897.0,
+                    1401.0,
+                    931.0,
+                    296.0,
+                    931.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    929.0,
+                    1405.0,
+                    929.0,
+                    1405.0,
+                    963.0,
+                    322.0,
+                    963.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    957.0,
+                    908.0,
+                    957.0,
+                    908.0,
+                    994.0,
+                    323.0,
+                    994.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1881.0,
+                    1404.0,
+                    1881.0,
+                    1404.0,
+                    1920.0,
+                    294.0,
+                    1920.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    1915.0,
+                    472.0,
+                    1915.0,
+                    472.0,
+                    1948.0,
+                    323.0,
+                    1948.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 10,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    75,
+                    858,
+                    75,
+                    858,
+                    105,
+                    298,
+                    105
+                ],
+                "score": 0.886
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    836,
+                    2088,
+                    865,
+                    2088,
+                    865,
+                    2113,
+                    836,
+                    2113
+                ],
+                "score": 0.826
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    677,
+                    1379,
+                    677,
+                    1379,
+                    713,
+                    296,
+                    713
+                ],
+                "score": 0.817
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    844,
+                    1399,
+                    844,
+                    1399,
+                    910,
+                    299,
+                    910
+                ],
+                "score": 0.816
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    731,
+                    1405,
+                    731,
+                    1405,
+                    825,
+                    297,
+                    825
+                ],
+                "score": 0.809
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1127,
+                    1401,
+                    1127,
+                    1401,
+                    1191,
+                    298,
+                    1191
+                ],
+                "score": 0.804
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    292,
+                    1689,
+                    1403,
+                    1689,
+                    1403,
+                    1754,
+                    292,
+                    1754
+                ],
+                "score": 0.773
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    594,
+                    1395,
+                    594,
+                    1395,
+                    659,
+                    298,
+                    659
+                ],
+                "score": 0.771
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    303,
+                    1491,
+                    1401,
+                    1491,
+                    1401,
+                    1586,
+                    303,
+                    1586
+                ],
+                "score": 0.764
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    293,
+                    928,
+                    1399,
+                    928,
+                    1399,
+                    964,
+                    293,
+                    964
+                ],
+                "score": 0.76
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    980,
+                    1404,
+                    980,
+                    1404,
+                    1107,
+                    297,
+                    1107
+                ],
+                "score": 0.744
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    293,
+                    1605,
+                    1400,
+                    1605,
+                    1400,
+                    1670,
+                    293,
+                    1670
+                ],
+                "score": 0.743
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1407,
+                    1399,
+                    1407,
+                    1399,
+                    1474,
+                    296,
+                    1474
+                ],
+                "score": 0.742
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1941,
+                    1403,
+                    1941,
+                    1403,
+                    2034,
+                    299,
+                    2034
+                ],
+                "score": 0.735
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1323,
+                    1399,
+                    1323,
+                    1399,
+                    1390,
+                    297,
+                    1390
+                ],
+                "score": 0.732
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    292,
+                    1773,
+                    1400,
+                    1773,
+                    1400,
+                    1838,
+                    292,
+                    1838
+                ],
+                "score": 0.73
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    294,
+                    1857,
+                    1401,
+                    1857,
+                    1401,
+                    1921,
+                    294,
+                    1921
+                ],
+                "score": 0.71
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    229,
+                    1400,
+                    229,
+                    1400,
+                    323,
+                    296,
+                    323
+                ],
+                "score": 0.709
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    294,
+                    510,
+                    1401,
+                    510,
+                    1401,
+                    575,
+                    294,
+                    575
+                ],
+                "score": 0.69
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    426,
+                    1401,
+                    426,
+                    1401,
+                    491,
+                    297,
+                    491
+                ],
+                "score": 0.682
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1209,
+                    1405,
+                    1209,
+                    1405,
+                    1304,
+                    297,
+                    1304
+                ],
+                "score": 0.674
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    343,
+                    1401,
+                    343,
+                    1401,
+                    408,
+                    296,
+                    408
+                ],
+                "score": 0.67
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    298.0,
+                    73.0,
+                    858.0,
+                    73.0,
+                    858.0,
+                    108.0,
+                    298.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    832.0,
+                    2085.0,
+                    870.0,
+                    2085.0,
+                    870.0,
+                    2124.0,
+                    832.0,
+                    2124.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    674.0,
+                    1385.0,
+                    674.0,
+                    1385.0,
+                    718.0,
+                    295.0,
+                    718.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    841.0,
+                    1404.0,
+                    841.0,
+                    1404.0,
+                    884.0,
+                    294.0,
+                    884.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    319.0,
+                    873.0,
+                    398.0,
+                    873.0,
+                    398.0,
+                    912.0,
+                    319.0,
+                    912.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    728.0,
+                    1405.0,
+                    728.0,
+                    1405.0,
+                    770.0,
+                    294.0,
+                    770.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    319.0,
+                    760.0,
+                    1405.0,
+                    760.0,
+                    1405.0,
+                    801.0,
+                    319.0,
+                    801.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    319.0,
+                    790.0,
+                    423.0,
+                    790.0,
+                    423.0,
+                    827.0,
+                    319.0,
+                    827.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1120.0,
+                    1407.0,
+                    1120.0,
+                    1407.0,
+                    1169.0,
+                    291.0,
+                    1169.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    1159.0,
+                    887.0,
+                    1159.0,
+                    887.0,
+                    1190.0,
+                    324.0,
+                    1190.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1687.0,
+                    1406.0,
+                    1687.0,
+                    1406.0,
+                    1728.0,
+                    291.0,
+                    1728.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    325.0,
+                    1721.0,
+                    690.0,
+                    1721.0,
+                    690.0,
+                    1754.0,
+                    325.0,
+                    1754.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    594.0,
+                    1400.0,
+                    594.0,
+                    1400.0,
+                    630.0,
+                    295.0,
+                    630.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    627.0,
+                    860.0,
+                    627.0,
+                    860.0,
+                    660.0,
+                    323.0,
+                    660.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1491.0,
+                    1405.0,
+                    1491.0,
+                    1405.0,
+                    1528.0,
+                    295.0,
+                    1528.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1524.0,
+                    1405.0,
+                    1524.0,
+                    1405.0,
+                    1558.0,
+                    322.0,
+                    1558.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    1551.0,
+                    399.0,
+                    1551.0,
+                    399.0,
+                    1587.0,
+                    320.0,
+                    1587.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    928.0,
+                    1403.0,
+                    928.0,
+                    1403.0,
+                    967.0,
+                    295.0,
+                    967.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    981.0,
+                    1405.0,
+                    981.0,
+                    1405.0,
+                    1020.0,
+                    294.0,
+                    1020.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    1009.0,
+                    1405.0,
+                    1009.0,
+                    1405.0,
+                    1053.0,
+                    320.0,
+                    1053.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    1042.0,
+                    1405.0,
+                    1042.0,
+                    1405.0,
+                    1083.0,
+                    320.0,
+                    1083.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1074.0,
+                    888.0,
+                    1074.0,
+                    888.0,
+                    1111.0,
+                    322.0,
+                    1111.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1607.0,
+                    1402.0,
+                    1607.0,
+                    1402.0,
+                    1643.0,
+                    295.0,
+                    1643.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1638.0,
+                    1141.0,
+                    1638.0,
+                    1141.0,
+                    1671.0,
+                    322.0,
+                    1671.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1404.0,
+                    1404.0,
+                    1404.0,
+                    1404.0,
+                    1447.0,
+                    292.0,
+                    1447.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    1439.0,
+                    1242.0,
+                    1439.0,
+                    1242.0,
+                    1476.0,
+                    320.0,
+                    1476.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1939.0,
+                    1407.0,
+                    1939.0,
+                    1407.0,
+                    1978.0,
+                    293.0,
+                    1978.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1972.0,
+                    1405.0,
+                    1972.0,
+                    1405.0,
+                    2008.0,
+                    322.0,
+                    2008.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    319.0,
+                    2002.0,
+                    520.0,
+                    2002.0,
+                    520.0,
+                    2035.0,
+                    319.0,
+                    2035.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1324.0,
+                    1404.0,
+                    1324.0,
+                    1404.0,
+                    1360.0,
+                    296.0,
+                    1360.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1355.0,
+                    1318.0,
+                    1355.0,
+                    1318.0,
+                    1392.0,
+                    322.0,
+                    1392.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1769.0,
+                    1403.0,
+                    1769.0,
+                    1403.0,
+                    1812.0,
+                    294.0,
+                    1812.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    1804.0,
+                    984.0,
+                    1804.0,
+                    984.0,
+                    1839.0,
+                    323.0,
+                    1839.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1857.0,
+                    1402.0,
+                    1857.0,
+                    1402.0,
+                    1892.0,
+                    296.0,
+                    1892.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    1889.0,
+                    1295.0,
+                    1889.0,
+                    1295.0,
+                    1921.0,
+                    323.0,
+                    1921.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    230.0,
+                    1404.0,
+                    230.0,
+                    1404.0,
+                    264.0,
+                    296.0,
+                    264.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    258.0,
+                    1404.0,
+                    258.0,
+                    1404.0,
+                    300.0,
+                    320.0,
+                    300.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    292.0,
+                    533.0,
+                    292.0,
+                    533.0,
+                    322.0,
+                    324.0,
+                    322.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    508.0,
+                    1403.0,
+                    508.0,
+                    1403.0,
+                    548.0,
+                    293.0,
+                    548.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    543.0,
+                    933.0,
+                    543.0,
+                    933.0,
+                    576.0,
+                    321.0,
+                    576.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    422.0,
+                    1406.0,
+                    422.0,
+                    1406.0,
+                    468.0,
+                    292.0,
+                    468.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    459.0,
+                    1215.0,
+                    459.0,
+                    1215.0,
+                    492.0,
+                    322.0,
+                    492.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1208.0,
+                    1406.0,
+                    1208.0,
+                    1406.0,
+                    1248.0,
+                    292.0,
+                    1248.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    1241.0,
+                    1405.0,
+                    1241.0,
+                    1405.0,
+                    1280.0,
+                    323.0,
+                    1280.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    1272.0,
+                    783.0,
+                    1272.0,
+                    783.0,
+                    1306.0,
+                    324.0,
+                    1306.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    343.0,
+                    1403.0,
+                    343.0,
+                    1403.0,
+                    379.0,
+                    296.0,
+                    379.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    374.0,
+                    1405.0,
+                    374.0,
+                    1405.0,
+                    410.0,
+                    323.0,
+                    410.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 11,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    75,
+                    858,
+                    75,
+                    858,
+                    105,
+                    298,
+                    105
+                ],
+                "score": 0.887
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    836,
+                    2088,
+                    865,
+                    2088,
+                    865,
+                    2113,
+                    836,
+                    2113
+                ],
+                "score": 0.84
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    303,
+                    229,
+                    1399,
+                    229,
+                    1399,
+                    324,
+                    303,
+                    324
+                ],
+                "score": 0.77
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    1355,
+                    1398,
+                    1355,
+                    1398,
+                    1421,
+                    295,
+                    1421
+                ],
+                "score": 0.722
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    291,
+                    1271,
+                    1399,
+                    1271,
+                    1399,
+                    1337,
+                    291,
+                    1337
+                ],
+                "score": 0.687
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    827,
+                    1400,
+                    827,
+                    1400,
+                    890,
+                    295,
+                    890
+                ],
+                "score": 0.679
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    343,
+                    1404,
+                    343,
+                    1404,
+                    465,
+                    298,
+                    465
+                ],
+                "score": 0.674
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    992,
+                    1400,
+                    992,
+                    1400,
+                    1056,
+                    295,
+                    1056
+                ],
+                "score": 0.663
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    291,
+                    1189,
+                    1402,
+                    1189,
+                    1402,
+                    1255,
+                    291,
+                    1255
+                ],
+                "score": 0.663
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1438,
+                    1399,
+                    1438,
+                    1399,
+                    1504,
+                    297,
+                    1504
+                ],
+                "score": 0.657
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    1075,
+                    1400,
+                    1075,
+                    1400,
+                    1171,
+                    295,
+                    1171
+                ],
+                "score": 0.656
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    909,
+                    1400,
+                    909,
+                    1400,
+                    974,
+                    295,
+                    974
+                ],
+                "score": 0.651
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    294,
+                    1521,
+                    1399,
+                    1521,
+                    1399,
+                    1587,
+                    294,
+                    1587
+                ],
+                "score": 0.601
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1604,
+                    1401,
+                    1604,
+                    1401,
+                    1670,
+                    296,
+                    1670
+                ],
+                "score": 0.558
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    599,
+                    1403,
+                    599,
+                    1403,
+                    695,
+                    297,
+                    695
+                ],
+                "score": 0.554
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    301,
+                    486,
+                    1401,
+                    486,
+                    1401,
+                    581,
+                    301,
+                    581
+                ],
+                "score": 0.388
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    713,
+                    1400,
+                    713,
+                    1400,
+                    808,
+                    299,
+                    808
+                ],
+                "score": 0.159
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1088,
+                    1354,
+                    1142,
+                    1354,
+                    1142,
+                    1385,
+                    1088,
+                    1385
+                ],
+                "score": 0.87,
+                "latex": "S ^ { 4 } L"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    298.0,
+                    73.0,
+                    858.0,
+                    73.0,
+                    858.0,
+                    108.0,
+                    298.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    832.0,
+                    2085.0,
+                    870.0,
+                    2085.0,
+                    870.0,
+                    2123.0,
+                    832.0,
+                    2123.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    227.0,
+                    1404.0,
+                    227.0,
+                    1404.0,
+                    268.0,
+                    297.0,
+                    268.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    262.0,
+                    1404.0,
+                    262.0,
+                    1404.0,
+                    296.0,
+                    324.0,
+                    296.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    291.0,
+                    1303.0,
+                    291.0,
+                    1303.0,
+                    329.0,
+                    323.0,
+                    329.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1350.0,
+                    1087.0,
+                    1350.0,
+                    1087.0,
+                    1393.0,
+                    293.0,
+                    1393.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1143.0,
+                    1350.0,
+                    1403.0,
+                    1350.0,
+                    1403.0,
+                    1393.0,
+                    1143.0,
+                    1393.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1388.0,
+                    1008.0,
+                    1388.0,
+                    1008.0,
+                    1420.0,
+                    321.0,
+                    1420.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1270.0,
+                    1402.0,
+                    1270.0,
+                    1402.0,
+                    1309.0,
+                    294.0,
+                    1309.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    1303.0,
+                    1195.0,
+                    1303.0,
+                    1195.0,
+                    1338.0,
+                    323.0,
+                    1338.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    824.0,
+                    1405.0,
+                    824.0,
+                    1405.0,
+                    865.0,
+                    294.0,
+                    865.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    859.0,
+                    609.0,
+                    859.0,
+                    609.0,
+                    889.0,
+                    321.0,
+                    889.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    339.0,
+                    1404.0,
+                    339.0,
+                    1404.0,
+                    382.0,
+                    292.0,
+                    382.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    375.0,
+                    1404.0,
+                    375.0,
+                    1404.0,
+                    407.0,
+                    321.0,
+                    407.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    402.0,
+                    1406.0,
+                    402.0,
+                    1406.0,
+                    440.0,
+                    320.0,
+                    440.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    431.0,
+                    398.0,
+                    431.0,
+                    398.0,
+                    470.0,
+                    320.0,
+                    470.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    991.0,
+                    1404.0,
+                    991.0,
+                    1404.0,
+                    1030.0,
+                    294.0,
+                    1030.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    1024.0,
+                    500.0,
+                    1024.0,
+                    500.0,
+                    1056.0,
+                    323.0,
+                    1056.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    298.0,
+                    1190.0,
+                    1405.0,
+                    1190.0,
+                    1405.0,
+                    1226.0,
+                    298.0,
+                    1226.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    1222.0,
+                    1046.0,
+                    1222.0,
+                    1046.0,
+                    1254.0,
+                    324.0,
+                    1254.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1435.0,
+                    1403.0,
+                    1435.0,
+                    1403.0,
+                    1478.0,
+                    292.0,
+                    1478.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1471.0,
+                    938.0,
+                    1471.0,
+                    938.0,
+                    1505.0,
+                    322.0,
+                    1505.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1073.0,
+                    1404.0,
+                    1073.0,
+                    1404.0,
+                    1114.0,
+                    293.0,
+                    1114.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    1107.0,
+                    1406.0,
+                    1107.0,
+                    1406.0,
+                    1144.0,
+                    320.0,
+                    1144.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1139.0,
+                    857.0,
+                    1139.0,
+                    857.0,
+                    1172.0,
+                    322.0,
+                    1172.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    911.0,
+                    1402.0,
+                    911.0,
+                    1402.0,
+                    947.0,
+                    296.0,
+                    947.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    940.0,
+                    915.0,
+                    940.0,
+                    915.0,
+                    975.0,
+                    322.0,
+                    975.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1520.0,
+                    1401.0,
+                    1520.0,
+                    1401.0,
+                    1557.0,
+                    295.0,
+                    1557.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1553.0,
+                    1271.0,
+                    1553.0,
+                    1271.0,
+                    1589.0,
+                    322.0,
+                    1589.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1599.0,
+                    1405.0,
+                    1599.0,
+                    1405.0,
+                    1645.0,
+                    295.0,
+                    1645.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1634.0,
+                    1029.0,
+                    1634.0,
+                    1029.0,
+                    1669.0,
+                    321.0,
+                    1669.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    597.0,
+                    1404.0,
+                    597.0,
+                    1404.0,
+                    638.0,
+                    295.0,
+                    638.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    631.0,
+                    1402.0,
+                    631.0,
+                    1402.0,
+                    664.0,
+                    324.0,
+                    664.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    660.0,
+                    1228.0,
+                    660.0,
+                    1228.0,
+                    696.0,
+                    324.0,
+                    696.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    486.0,
+                    1405.0,
+                    486.0,
+                    1405.0,
+                    524.0,
+                    295.0,
+                    524.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    521.0,
+                    1402.0,
+                    521.0,
+                    1402.0,
+                    552.0,
+                    323.0,
+                    552.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    548.0,
+                    810.0,
+                    548.0,
+                    810.0,
+                    582.0,
+                    322.0,
+                    582.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    714.0,
+                    1404.0,
+                    714.0,
+                    1404.0,
+                    748.0,
+                    295.0,
+                    748.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    743.0,
+                    1405.0,
+                    743.0,
+                    1405.0,
+                    780.0,
+                    322.0,
+                    780.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    774.0,
+                    612.0,
+                    774.0,
+                    612.0,
+                    807.0,
+                    321.0,
+                    807.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 12,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1004,
+                    1405,
+                    1004,
+                    1405,
+                    1129,
+                    297,
+                    1129
+                ],
+                "score": 0.967
+            },
+            {
+                "category_id": 5,
+                "poly": [
+                    315,
+                    710,
+                    1388,
+                    710,
+                    1388,
+                    875,
+                    315,
+                    875
+                ],
+                "score": 0.956,
+                "html": "<table><tr><td>Labeled data Method</td><td>1%</td><td>2%</td><td>5%</td><td>10% Top-5 accuracy</td><td>20%</td><td>50%</td><td>100%</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Supervised trained on pixels</td><td>44.1</td><td>59.9</td><td>75.2</td><td>82.1</td><td>87.9</td><td>91.8</td><td>93.8</td></tr><tr><td>ReseNet trained on CPC v2 (fine-tuned)</td><td>72.9</td><td>79.6</td><td>86.1</td><td>89.5</td><td>91.4</td><td>93.6</td><td>95.2</td></tr></table>"
+            },
+            {
+                "category_id": 5,
+                "poly": [
+                    315,
+                    425,
+                    1388,
+                    425,
+                    1388,
+                    589,
+                    315,
+                    589
+                ],
+                "score": 0.947,
+                "html": "<table><tr><td>Labeled data Method</td><td>1%</td><td>2%</td><td>5%</td><td>10% Top-1 accuracy</td><td>20%</td><td>50%</td><td>100%</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Supervised trained on pixels</td><td>23.1</td><td>34.8</td><td>50.2</td><td>60.0</td><td>67.6</td><td>74.4</td><td>78.0</td></tr><tr><td>ReseNet trained on CPC v2 (fine-tuned)</td><td>46.3</td><td>54.7</td><td>64.1</td><td>69.7</td><td>73.0</td><td>77.3</td><td>80.6</td></tr></table>"
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    75,
+                    858,
+                    75,
+                    858,
+                    105,
+                    298,
+                    105
+                ],
+                "score": 0.908
+            },
+            {
+                "category_id": 6,
+                "poly": [
+                    486,
+                    385,
+                    1211,
+                    385,
+                    1211,
+                    419,
+                    486,
+                    419
+                ],
+                "score": 0.901
+            },
+            {
+                "category_id": 6,
+                "poly": [
+                    400,
+                    671,
+                    1297,
+                    671,
+                    1297,
+                    706,
+                    400,
+                    706
+                ],
+                "score": 0.896
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    301,
+                    946,
+                    712,
+                    946,
+                    712,
+                    979,
+                    301,
+                    979
+                ],
+                "score": 0.889
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    836,
+                    2088,
+                    865,
+                    2088,
+                    865,
+                    2113,
+                    836,
+                    2113
+                ],
+                "score": 0.863
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    300,
+                    228,
+                    509,
+                    228,
+                    509,
+                    261,
+                    300,
+                    261
+                ],
+                "score": 0.704
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    294,
+                    1183,
+                    1367,
+                    1183,
+                    1367,
+                    1988,
+                    294,
+                    1988
+                ],
+                "score": 0.539
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    299,
+                    296,
+                    644,
+                    296,
+                    644,
+                    329,
+                    299,
+                    329
+                ],
+                "score": 0.532
+            },
+            {
+                "category_id": 5,
+                "poly": [
+                    294,
+                    1183,
+                    1367,
+                    1183,
+                    1367,
+                    1988,
+                    294,
+                    1988
+                ],
+                "score": 0.217,
+                "html": "<table><tr><td></td><td>def CPC(latents，target_dim=64，emb_scale=0.1, steps_to_ignore=2，steps_to_predict=3):</td><td></td><td></td><td></td></tr><tr><td></td><td># latents:[B，H，W，D] loss = 0.0</td><td></td><td></td><td></td></tr><tr><td></td><td>context = pixelCNN(latents)</td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td>targets = Conv2D(output_channels=target_dim,</td><td></td></tr><tr><td></td><td></td><td></td><td>kernel_shape=(l，1))(latents)</td><td></td></tr><tr><td></td><td></td><td></td><td>batch_dim， col_dim， row_dim = targets.shape[:-1]</td><td></td></tr><tr><td></td><td></td><td></td><td>targets = reshape(target，[-1，target_dim])</td><td></td></tr><tr><td></td><td>col_dim_i = col_dim - i - 1</td><td></td><td>for i in range(steps_to_ignore， steps_to_predict):</td><td></td></tr><tr><td></td><td>total_elements = batch_dim * col_dim_i * row_dim</td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>preds_i = Conv2D(output_channels=target_dim,</td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td>kernel_shape=(1，1))(context)</td><td></td></tr><tr><td></td><td></td><td></td><td>preds_i = preds_i[:，:-(i+l)，:，:] * emb_scale</td><td></td></tr><tr><td></td><td></td><td></td><td>preds_i = reshape(preds_i，[-1，target_dim])</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td>logits = matmul(preds_i，targets，transpose_b=True)</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td>b = range(total_elements)/ (col_dim_i * row_dim)</td><td></td></tr><tr><td></td><td>col = range(total_elements)</td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>labels = b * col_dim * im_row_dim + (i+l） * row_dim + col</td></tr><tr><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>loss += softmax_cross_entropy_with_logits(logits，labels)</td></tr><tr><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>return loss</td><td></td><td></td><td></td></tr></table>"
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    300,
+                    228,
+                    509,
+                    228,
+                    509,
+                    261,
+                    300,
+                    261
+                ],
+                "score": 0.193
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    379,
+                    1066,
+                    558,
+                    1066,
+                    558,
+                    1100,
+                    379,
+                    1100
+                ],
+                "score": 0.94,
+                "latex": "z _ { i , j } = f _ { \\theta } ( \\pmb { x } _ { i , j } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    606,
+                    1065,
+                    799,
+                    1065,
+                    799,
+                    1098,
+                    606,
+                    1098
+                ],
+                "score": 0.92,
+                "latex": "i , j \\in \\{ 1 , . . . , 7 \\}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1196,
+                    1097,
+                    1394,
+                    1097,
+                    1394,
+                    1126,
+                    1196,
+                    1126
+                ],
+                "score": 0.91,
+                "latex": "B \\times 7 \\times 7 \\times 4 0 9 6"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    756,
+                    1098,
+                    804,
+                    1098,
+                    804,
+                    1130,
+                    756,
+                    1130
+                ],
+                "score": 0.9,
+                "latex": "\\{ { \\pmb x } \\}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    491,
+                    1314,
+                    523,
+                    1314,
+                    523,
+                    1338,
+                    491,
+                    1338
+                ],
+                "score": 0.84,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    824,
+                    1407,
+                    854,
+                    1407,
+                    854,
+                    1429,
+                    824,
+                    1429
+                ],
+                "score": 0.81,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    643,
+                    1099,
+                    668,
+                    1099,
+                    668,
+                    1124,
+                    643,
+                    1124
+                ],
+                "score": 0.8,
+                "latex": "B"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    492,
+                    1345,
+                    522,
+                    1345,
+                    522,
+                    1368,
+                    492,
+                    1368
+                ],
+                "score": 0.8,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    640,
+                    1527,
+                    672,
+                    1527,
+                    672,
+                    1551,
+                    640,
+                    1551
+                ],
+                "score": 0.79,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    847,
+                    1376,
+                    868,
+                    1376,
+                    868,
+                    1398,
+                    847,
+                    1398
+                ],
+                "score": 0.78,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    491,
+                    1437,
+                    522,
+                    1437,
+                    522,
+                    1459,
+                    491,
+                    1459
+                ],
+                "score": 0.78,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    526,
+                    1649,
+                    556,
+                    1649,
+                    556,
+                    1672,
+                    526,
+                    1672
+                ],
+                "score": 0.77,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    525,
+                    1679,
+                    555,
+                    1679,
+                    555,
+                    1704,
+                    525,
+                    1704
+                ],
+                "score": 0.76,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    508,
+                    1741,
+                    538,
+                    1741,
+                    538,
+                    1765,
+                    508,
+                    1765
+                ],
+                "score": 0.74,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    879,
+                    1620,
+                    901,
+                    1620,
+                    901,
+                    1641,
+                    879,
+                    1641
+                ],
+                "score": 0.73,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    558,
+                    1496,
+                    589,
+                    1496,
+                    589,
+                    1521,
+                    558,
+                    1521
+                ],
+                "score": 0.73,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    747,
+                    1191,
+                    797,
+                    1191,
+                    797,
+                    1218,
+                    747,
+                    1218
+                ],
+                "score": 0.72,
+                "latex": "= 6 4"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    680,
+                    1222,
+                    715,
+                    1222,
+                    715,
+                    1248,
+                    680,
+                    1248
+                ],
+                "score": 0.72,
+                "latex": "= 2"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    507,
+                    1862,
+                    538,
+                    1862,
+                    538,
+                    1886,
+                    507,
+                    1886
+                ],
+                "score": 0.71,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    526,
+                    1587,
+                    556,
+                    1587,
+                    556,
+                    1611,
+                    526,
+                    1611
+                ],
+                "score": 0.7,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    458,
+                    1832,
+                    489,
+                    1832,
+                    489,
+                    1856,
+                    458,
+                    1856
+                ],
+                "score": 0.7,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    478,
+                    1921,
+                    522,
+                    1921,
+                    522,
+                    1947,
+                    478,
+                    1947
+                ],
+                "score": 0.69,
+                "latex": "+ ="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1012,
+                    1222,
+                    1048,
+                    1222,
+                    1048,
+                    1247,
+                    1012,
+                    1247
+                ],
+                "score": 0.67,
+                "latex": "= 3"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    845,
+                    1529,
+                    867,
+                    1529,
+                    867,
+                    1551,
+                    845,
+                    1551
+                ],
+                "score": 0.63,
+                "latex": "^ { \\star }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    994,
+                    1651,
+                    1016,
+                    1651,
+                    1016,
+                    1673,
+                    994,
+                    1673
+                ],
+                "score": 0.62,
+                "latex": "\\star"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    579,
+                    1863,
+                    601,
+                    1863,
+                    601,
+                    1886,
+                    579,
+                    1886
+                ],
+                "score": 0.6,
+                "latex": "\\star"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1044,
+                    1802,
+                    1066,
+                    1802,
+                    1066,
+                    1825,
+                    1044,
+                    1825
+                ],
+                "score": 0.6,
+                "latex": "\\star"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1093,
+                    1863,
+                    1117,
+                    1863,
+                    1117,
+                    1886,
+                    1093,
+                    1886
+                ],
+                "score": 0.58,
+                "latex": "\\star"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    745,
+                    1863,
+                    767,
+                    1863,
+                    767,
+                    1886,
+                    745,
+                    1886
+                ],
+                "score": 0.57,
+                "latex": "\\star"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    895,
+                    1346,
+                    914,
+                    1346,
+                    914,
+                    1367,
+                    895,
+                    1367
+                ],
+                "score": 0.56,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1145,
+                    1742,
+                    1163,
+                    1742,
+                    1163,
+                    1763,
+                    1145,
+                    1763
+                ],
+                "score": 0.55,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    930,
+                    1589,
+                    948,
+                    1589,
+                    948,
+                    1611,
+                    930,
+                    1611
+                ],
+                "score": 0.54,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1044,
+                    1528,
+                    1066,
+                    1528,
+                    1066,
+                    1551,
+                    1044,
+                    1551
+                ],
+                "score": 0.54,
+                "latex": "\\star"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    960,
+                    1861,
+                    985,
+                    1861,
+                    985,
+                    1886,
+                    960,
+                    1886
+                ],
+                "score": 0.5,
+                "latex": "^ +"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    443,
+                    1282,
+                    529,
+                    1282,
+                    529,
+                    1309,
+                    443,
+                    1309
+                ],
+                "score": 0.47,
+                "latex": "= ~ 0 . 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    426,
+                    1801,
+                    457,
+                    1801,
+                    457,
+                    1824,
+                    426,
+                    1824
+                ],
+                "score": 0.36,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    979,
+                    1191,
+                    1045,
+                    1191,
+                    1045,
+                    1217,
+                    979,
+                    1217
+                ],
+                "score": 0.33,
+                "latex": "= 0 \\mathrm { ~ . ~ } 1"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    298.0,
+                    73.0,
+                    858.0,
+                    73.0,
+                    858.0,
+                    108.0,
+                    298.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    486.0,
+                    378.0,
+                    1214.0,
+                    378.0,
+                    1214.0,
+                    427.0,
+                    486.0,
+                    427.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    397.0,
+                    666.0,
+                    1299.0,
+                    666.0,
+                    1299.0,
+                    711.0,
+                    397.0,
+                    711.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    946.0,
+                    715.0,
+                    946.0,
+                    715.0,
+                    982.0,
+                    296.0,
+                    982.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    832.0,
+                    2085.0,
+                    871.0,
+                    2085.0,
+                    871.0,
+                    2123.0,
+                    832.0,
+                    2123.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    221.0,
+                    514.0,
+                    221.0,
+                    514.0,
+                    271.0,
+                    294.0,
+                    271.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1186.0,
+                    746.0,
+                    1186.0,
+                    746.0,
+                    1223.0,
+                    295.0,
+                    1223.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    798.0,
+                    1186.0,
+                    978.0,
+                    1186.0,
+                    978.0,
+                    1223.0,
+                    798.0,
+                    1223.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1046.0,
+                    1186.0,
+                    1069.0,
+                    1186.0,
+                    1069.0,
+                    1223.0,
+                    1046.0,
+                    1223.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    430.0,
+                    1220.0,
+                    679.0,
+                    1220.0,
+                    679.0,
+                    1251.0,
+                    430.0,
+                    1251.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    716.0,
+                    1220.0,
+                    1011.0,
+                    1220.0,
+                    1011.0,
+                    1251.0,
+                    716.0,
+                    1251.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1049.0,
+                    1220.0,
+                    1082.0,
+                    1220.0,
+                    1082.0,
+                    1251.0,
+                    1049.0,
+                    1251.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    361.0,
+                    1247.0,
+                    751.0,
+                    1247.0,
+                    751.0,
+                    1284.0,
+                    361.0,
+                    1284.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    363.0,
+                    1279.0,
+                    442.0,
+                    1279.0,
+                    442.0,
+                    1311.0,
+                    363.0,
+                    1311.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    530.0,
+                    1279.0,
+                    537.0,
+                    1279.0,
+                    537.0,
+                    1311.0,
+                    530.0,
+                    1311.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    363.0,
+                    1309.0,
+                    490.0,
+                    1309.0,
+                    490.0,
+                    1343.0,
+                    363.0,
+                    1343.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    524.0,
+                    1309.0,
+                    815.0,
+                    1309.0,
+                    815.0,
+                    1343.0,
+                    524.0,
+                    1343.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    363.0,
+                    1341.0,
+                    491.0,
+                    1341.0,
+                    491.0,
+                    1375.0,
+                    363.0,
+                    1375.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    523.0,
+                    1341.0,
+                    894.0,
+                    1341.0,
+                    894.0,
+                    1375.0,
+                    523.0,
+                    1375.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    915.0,
+                    1341.0,
+                    1097.0,
+                    1341.0,
+                    1097.0,
+                    1375.0,
+                    915.0,
+                    1375.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    644.0,
+                    1370.0,
+                    846.0,
+                    1370.0,
+                    846.0,
+                    1404.0,
+                    644.0,
+                    1404.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    869.0,
+                    1370.0,
+                    1129.0,
+                    1370.0,
+                    1129.0,
+                    1404.0,
+                    869.0,
+                    1404.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    361.0,
+                    1400.0,
+                    823.0,
+                    1400.0,
+                    823.0,
+                    1437.0,
+                    361.0,
+                    1437.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    855.0,
+                    1400.0,
+                    1163.0,
+                    1400.0,
+                    1163.0,
+                    1437.0,
+                    855.0,
+                    1437.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    364.0,
+                    1434.0,
+                    490.0,
+                    1434.0,
+                    490.0,
+                    1465.0,
+                    364.0,
+                    1465.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    523.0,
+                    1434.0,
+                    1079.0,
+                    1434.0,
+                    1079.0,
+                    1465.0,
+                    523.0,
+                    1465.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    361.0,
+                    1463.0,
+                    1197.0,
+                    1463.0,
+                    1197.0,
+                    1497.0,
+                    361.0,
+                    1497.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    396.0,
+                    1493.0,
+                    557.0,
+                    1493.0,
+                    557.0,
+                    1524.0,
+                    396.0,
+                    1524.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    590.0,
+                    1493.0,
+                    854.0,
+                    1493.0,
+                    854.0,
+                    1524.0,
+                    590.0,
+                    1524.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    397.0,
+                    1523.0,
+                    639.0,
+                    1523.0,
+                    639.0,
+                    1557.0,
+                    397.0,
+                    1557.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    673.0,
+                    1523.0,
+                    844.0,
+                    1523.0,
+                    844.0,
+                    1557.0,
+                    673.0,
+                    1557.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    868.0,
+                    1523.0,
+                    1043.0,
+                    1523.0,
+                    1043.0,
+                    1557.0,
+                    868.0,
+                    1557.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1067.0,
+                    1523.0,
+                    1200.0,
+                    1523.0,
+                    1200.0,
+                    1557.0,
+                    1067.0,
+                    1557.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1584.0,
+                    525.0,
+                    1584.0,
+                    525.0,
+                    1619.0,
+                    394.0,
+                    1619.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    557.0,
+                    1584.0,
+                    929.0,
+                    1584.0,
+                    929.0,
+                    1619.0,
+                    557.0,
+                    1619.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    949.0,
+                    1584.0,
+                    1129.0,
+                    1584.0,
+                    1129.0,
+                    1619.0,
+                    949.0,
+                    1619.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    678.0,
+                    1616.0,
+                    878.0,
+                    1616.0,
+                    878.0,
+                    1647.0,
+                    678.0,
+                    1647.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    902.0,
+                    1616.0,
+                    1160.0,
+                    1616.0,
+                    1160.0,
+                    1647.0,
+                    902.0,
+                    1647.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    1646.0,
+                    525.0,
+                    1646.0,
+                    525.0,
+                    1678.0,
+                    392.0,
+                    1678.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    557.0,
+                    1646.0,
+                    993.0,
+                    1646.0,
+                    993.0,
+                    1678.0,
+                    557.0,
+                    1678.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1017.0,
+                    1646.0,
+                    1184.0,
+                    1646.0,
+                    1184.0,
+                    1678.0,
+                    1017.0,
+                    1678.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    1677.0,
+                    524.0,
+                    1677.0,
+                    524.0,
+                    1710.0,
+                    392.0,
+                    1710.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    556.0,
+                    1677.0,
+                    1129.0,
+                    1677.0,
+                    1129.0,
+                    1710.0,
+                    556.0,
+                    1710.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    397.0,
+                    1737.0,
+                    507.0,
+                    1737.0,
+                    507.0,
+                    1771.0,
+                    397.0,
+                    1771.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    539.0,
+                    1737.0,
+                    1144.0,
+                    1737.0,
+                    1144.0,
+                    1771.0,
+                    539.0,
+                    1771.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1164.0,
+                    1737.0,
+                    1243.0,
+                    1737.0,
+                    1243.0,
+                    1771.0,
+                    1164.0,
+                    1771.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    1795.0,
+                    425.0,
+                    1795.0,
+                    425.0,
+                    1829.0,
+                    393.0,
+                    1829.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    458.0,
+                    1795.0,
+                    1043.0,
+                    1795.0,
+                    1043.0,
+                    1829.0,
+                    458.0,
+                    1829.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1067.0,
+                    1795.0,
+                    1208.0,
+                    1795.0,
+                    1208.0,
+                    1829.0,
+                    1067.0,
+                    1829.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    396.0,
+                    1829.0,
+                    457.0,
+                    1829.0,
+                    457.0,
+                    1860.0,
+                    396.0,
+                    1860.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    490.0,
+                    1829.0,
+                    849.0,
+                    1829.0,
+                    849.0,
+                    1860.0,
+                    490.0,
+                    1860.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    396.0,
+                    1857.0,
+                    506.0,
+                    1857.0,
+                    506.0,
+                    1892.0,
+                    396.0,
+                    1892.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    539.0,
+                    1857.0,
+                    578.0,
+                    1857.0,
+                    578.0,
+                    1892.0,
+                    539.0,
+                    1892.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    602.0,
+                    1857.0,
+                    744.0,
+                    1857.0,
+                    744.0,
+                    1892.0,
+                    602.0,
+                    1892.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    768.0,
+                    1857.0,
+                    959.0,
+                    1857.0,
+                    959.0,
+                    1892.0,
+                    768.0,
+                    1892.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    986.0,
+                    1857.0,
+                    1092.0,
+                    1857.0,
+                    1092.0,
+                    1892.0,
+                    986.0,
+                    1892.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1118.0,
+                    1857.0,
+                    1347.0,
+                    1857.0,
+                    1347.0,
+                    1892.0,
+                    1118.0,
+                    1892.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    1916.0,
+                    477.0,
+                    1916.0,
+                    477.0,
+                    1953.0,
+                    393.0,
+                    1953.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    523.0,
+                    1916.0,
+                    1344.0,
+                    1916.0,
+                    1344.0,
+                    1953.0,
+                    523.0,
+                    1953.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    361.0,
+                    1951.0,
+                    554.0,
+                    1951.0,
+                    554.0,
+                    1983.0,
+                    361.0,
+                    1983.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    295.0,
+                    644.0,
+                    295.0,
+                    644.0,
+                    331.0,
+                    297.0,
+                    331.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1004.0,
+                    1403.0,
+                    1004.0,
+                    1403.0,
+                    1037.0,
+                    295.0,
+                    1037.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1036.0,
+                    1406.0,
+                    1036.0,
+                    1406.0,
+                    1069.0,
+                    295.0,
+                    1069.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1065.0,
+                    378.0,
+                    1065.0,
+                    378.0,
+                    1102.0,
+                    292.0,
+                    1102.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    559.0,
+                    1065.0,
+                    605.0,
+                    1065.0,
+                    605.0,
+                    1102.0,
+                    559.0,
+                    1102.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    800.0,
+                    1065.0,
+                    1405.0,
+                    1065.0,
+                    1405.0,
+                    1102.0,
+                    800.0,
+                    1102.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1096.0,
+                    642.0,
+                    1096.0,
+                    642.0,
+                    1129.0,
+                    294.0,
+                    1129.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    669.0,
+                    1096.0,
+                    755.0,
+                    1096.0,
+                    755.0,
+                    1129.0,
+                    669.0,
+                    1129.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    805.0,
+                    1096.0,
+                    1195.0,
+                    1096.0,
+                    1195.0,
+                    1129.0,
+                    805.0,
+                    1129.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1395.0,
+                    1096.0,
+                    1403.0,
+                    1096.0,
+                    1403.0,
+                    1129.0,
+                    1395.0,
+                    1129.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    221.0,
+                    514.0,
+                    221.0,
+                    514.0,
+                    271.0,
+                    294.0,
+                    271.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 13,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    303,
+                    1811,
+                    1404,
+                    1811,
+                    1404,
+                    1904,
+                    303,
+                    1904
+                ],
+                "score": 0.955
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    372,
+                    1517,
+                    1402,
+                    1517,
+                    1402,
+                    1787,
+                    372,
+                    1787
+                ],
+                "score": 0.946
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    300,
+                    264,
+                    1130,
+                    264,
+                    1130,
+                    878,
+                    300,
+                    878
+                ],
+                "score": 0.924
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    294,
+                    1458,
+                    1277,
+                    1458,
+                    1277,
+                    1491,
+                    294,
+                    1491
+                ],
+                "score": 0.906
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    75,
+                    858,
+                    75,
+                    858,
+                    105,
+                    298,
+                    105
+                ],
+                "score": 0.882
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    836,
+                    2088,
+                    865,
+                    2088,
+                    865,
+                    2112,
+                    836,
+                    2112
+                ],
+                "score": 0.85
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    300,
+                    930,
+                    669,
+                    930,
+                    669,
+                    960,
+                    300,
+                    960
+                ],
+                "score": 0.837
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    371,
+                    975,
+                    1406,
+                    975,
+                    1406,
+                    1366,
+                    371,
+                    1366
+                ],
+                "score": 0.78
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1403,
+                    962,
+                    1403,
+                    962,
+                    1433,
+                    298,
+                    1433
+                ],
+                "score": 0.509
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    298,
+                    1403,
+                    962,
+                    1403,
+                    962,
+                    1433,
+                    298,
+                    1433
+                ],
+                "score": 0.471
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    300,
+                    264,
+                    665,
+                    264,
+                    665,
+                    292,
+                    300,
+                    292
+                ],
+                "score": 0.254
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    601,
+                    1721,
+                    661,
+                    1721,
+                    661,
+                    1751,
+                    601,
+                    1751
+                ],
+                "score": 0.9,
+                "latex": "1 0 ^ { - 5 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    696,
+                    1721,
+                    756,
+                    1721,
+                    756,
+                    1751,
+                    696,
+                    1751
+                ],
+                "score": 0.89,
+                "latex": "1 0 ^ { - 2 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    975,
+                    1813,
+                    1007,
+                    1813,
+                    1007,
+                    1842,
+                    975,
+                    1842
+                ],
+                "score": 0.88,
+                "latex": "\\mathbb { D } _ { l }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    511,
+                    1753,
+                    610,
+                    1753,
+                    610,
+                    1787,
+                    511,
+                    1787
+                ],
+                "score": 0.77,
+                "latex": "\\{ 1 6 , 3 2 \\}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    780,
+                    632,
+                    802,
+                    632,
+                    802,
+                    653,
+                    780,
+                    653
+                ],
+                "score": 0.77,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    780,
+                    541,
+                    802,
+                    541,
+                    802,
+                    562,
+                    780,
+                    562
+                ],
+                "score": 0.74,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    507,
+                    357,
+                    539,
+                    357,
+                    539,
+                    381,
+                    507,
+                    381
+                ],
+                "score": 0.74,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    442,
+                    326,
+                    473,
+                    326,
+                    473,
+                    350,
+                    442,
+                    350
+                ],
+                "score": 0.71,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    964,
+                    1690,
+                    1143,
+                    1690,
+                    1143,
+                    1725,
+                    964,
+                    1725
+                ],
+                "score": 0.7,
+                "latex": "\\{ 0 . 0 5 , 0 . 1 , 0 . 2 \\}"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    780,
+                    754,
+                    802,
+                    754,
+                    802,
+                    775,
+                    780,
+                    775
+                ],
+                "score": 0.7,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    830,
+                    725,
+                    848,
+                    725,
+                    848,
+                    745,
+                    830,
+                    745
+                ],
+                "score": 0.69,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1300,
+                    976,
+                    1402,
+                    976,
+                    1402,
+                    1006,
+                    1300,
+                    1006
+                ],
+                "score": 0.68,
+                "latex": "2 4 0 \\times 2 4 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    780,
+                    450,
+                    802,
+                    450,
+                    802,
+                    472,
+                    780,
+                    472
+                ],
+                "score": 0.66,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    647,
+                    662,
+                    679,
+                    662,
+                    679,
+                    684,
+                    647,
+                    684
+                ],
+                "score": 0.65,
+                "latex": "= ^ { \\parallel }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    815,
+                    977,
+                    889,
+                    977,
+                    889,
+                    1006,
+                    815,
+                    1006
+                ],
+                "score": 0.64,
+                "latex": "8 0 \\mathrm { x } 8 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    424,
+                    418,
+                    456,
+                    418,
+                    456,
+                    442,
+                    424,
+                    442
+                ],
+                "score": 0.63,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1170,
+                    1201,
+                    1271,
+                    1201,
+                    1271,
+                    1230,
+                    1170,
+                    1230
+                ],
+                "score": 0.62,
+                "latex": "2 4 0 \\times 2 4 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    443,
+                    815,
+                    471,
+                    815,
+                    471,
+                    837,
+                    443,
+                    837
+                ],
+                "score": 0.59,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    802,
+                    1550,
+                    851,
+                    1550,
+                    851,
+                    1578,
+                    802,
+                    1578
+                ],
+                "score": 0.42,
+                "latex": "\\mathbf { \\hat { v } } _ { \\mathbf { \\Delta } } 2 \\mathbf { \\hat { \\mu } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    828,
+                    507,
+                    899,
+                    507,
+                    899,
+                    535,
+                    828,
+                    535
+                ],
+                "score": 0.42,
+                "latex": "= 2 5 6"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    829,
+                    415,
+                    898,
+                    415,
+                    898,
+                    443,
+                    829,
+                    443
+                ],
+                "score": 0.4,
+                "latex": "= 2 5 6"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    476,
+                    786,
+                    506,
+                    786,
+                    506,
+                    807,
+                    476,
+                    807
+                ],
+                "score": 0.38,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    829,
+                    601,
+                    850,
+                    601,
+                    850,
+                    624,
+                    829,
+                    624
+                ],
+                "score": 0.34,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1148,
+                    977,
+                    1221,
+                    977,
+                    1221,
+                    1005,
+                    1148,
+                    1005
+                ],
+                "score": 0.33,
+                "latex": "3 2 \\mathrm { x } 3 2 "
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    426,
+                    693,
+                    456,
+                    693,
+                    456,
+                    715,
+                    426,
+                    715
+                ],
+                "score": 0.31,
+                "latex": "="
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    828,
+                    599,
+                    898,
+                    599,
+                    898,
+                    626,
+                    828,
+                    626
+                ],
+                "score": 0.29,
+                "latex": "= 2 5 6"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    426,
+                    722,
+                    457,
+                    722,
+                    457,
+                    747,
+                    426,
+                    747
+                ],
+                "score": 0.28,
+                "latex": "="
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    298.0,
+                    73.0,
+                    858.0,
+                    73.0,
+                    858.0,
+                    108.0,
+                    298.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    832.0,
+                    2085.0,
+                    870.0,
+                    2085.0,
+                    870.0,
+                    2124.0,
+                    832.0,
+                    2124.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    927.0,
+                    672.0,
+                    927.0,
+                    672.0,
+                    964.0,
+                    295.0,
+                    964.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1402.0,
+                    964.0,
+                    1402.0,
+                    964.0,
+                    1436.0,
+                    296.0,
+                    1436.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    262.0,
+                    667.0,
+                    262.0,
+                    667.0,
+                    294.0,
+                    297.0,
+                    294.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1806.0,
+                    974.0,
+                    1806.0,
+                    974.0,
+                    1850.0,
+                    294.0,
+                    1850.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1008.0,
+                    1806.0,
+                    1405.0,
+                    1806.0,
+                    1405.0,
+                    1850.0,
+                    1008.0,
+                    1850.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1839.0,
+                    1405.0,
+                    1839.0,
+                    1405.0,
+                    1876.0,
+                    294.0,
+                    1876.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    1873.0,
+                    464.0,
+                    1873.0,
+                    464.0,
+                    1905.0,
+                    297.0,
+                    1905.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    370.0,
+                    1517.0,
+                    1406.0,
+                    1517.0,
+                    1406.0,
+                    1551.0,
+                    370.0,
+                    1551.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    395.0,
+                    1549.0,
+                    801.0,
+                    1549.0,
+                    801.0,
+                    1581.0,
+                    395.0,
+                    1581.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    852.0,
+                    1549.0,
+                    1403.0,
+                    1549.0,
+                    1403.0,
+                    1581.0,
+                    852.0,
+                    1581.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    1579.0,
+                    1404.0,
+                    1579.0,
+                    1404.0,
+                    1612.0,
+                    393.0,
+                    1612.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    395.0,
+                    1610.0,
+                    1191.0,
+                    1610.0,
+                    1191.0,
+                    1643.0,
+                    395.0,
+                    1643.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    370.0,
+                    1649.0,
+                    1396.0,
+                    1649.0,
+                    1396.0,
+                    1687.0,
+                    370.0,
+                    1687.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    370.0,
+                    1690.0,
+                    963.0,
+                    1690.0,
+                    963.0,
+                    1728.0,
+                    370.0,
+                    1728.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1144.0,
+                    1690.0,
+                    1404.0,
+                    1690.0,
+                    1404.0,
+                    1728.0,
+                    1144.0,
+                    1728.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    1718.0,
+                    600.0,
+                    1718.0,
+                    600.0,
+                    1761.0,
+                    392.0,
+                    1761.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    662.0,
+                    1718.0,
+                    695.0,
+                    1718.0,
+                    695.0,
+                    1761.0,
+                    662.0,
+                    1761.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    757.0,
+                    1718.0,
+                    1407.0,
+                    1718.0,
+                    1407.0,
+                    1761.0,
+                    757.0,
+                    1761.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1750.0,
+                    510.0,
+                    1750.0,
+                    510.0,
+                    1790.0,
+                    394.0,
+                    1790.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    611.0,
+                    1750.0,
+                    623.0,
+                    1750.0,
+                    623.0,
+                    1790.0,
+                    611.0,
+                    1790.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    262.0,
+                    668.0,
+                    262.0,
+                    668.0,
+                    293.0,
+                    297.0,
+                    293.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    361.0,
+                    292.0,
+                    749.0,
+                    292.0,
+                    749.0,
+                    325.0,
+                    361.0,
+                    325.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    364.0,
+                    325.0,
+                    441.0,
+                    325.0,
+                    441.0,
+                    354.0,
+                    364.0,
+                    354.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    474.0,
+                    325.0,
+                    605.0,
+                    325.0,
+                    605.0,
+                    354.0,
+                    474.0,
+                    354.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    362.0,
+                    354.0,
+                    506.0,
+                    354.0,
+                    506.0,
+                    385.0,
+                    362.0,
+                    385.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    540.0,
+                    354.0,
+                    781.0,
+                    354.0,
+                    781.0,
+                    385.0,
+                    540.0,
+                    385.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    364.0,
+                    384.0,
+                    424.0,
+                    384.0,
+                    424.0,
+                    415.0,
+                    364.0,
+                    415.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    458.0,
+                    382.0,
+                    668.0,
+                    382.0,
+                    668.0,
+                    417.0,
+                    458.0,
+                    417.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    415.0,
+                    423.0,
+                    415.0,
+                    423.0,
+                    445.0,
+                    393.0,
+                    445.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    457.0,
+                    415.0,
+                    828.0,
+                    415.0,
+                    828.0,
+                    445.0,
+                    457.0,
+                    445.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    899.0,
+                    415.0,
+                    914.0,
+                    415.0,
+                    914.0,
+                    445.0,
+                    899.0,
+                    445.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    576.0,
+                    444.0,
+                    779.0,
+                    444.0,
+                    779.0,
+                    478.0,
+                    576.0,
+                    478.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    803.0,
+                    444.0,
+                    1012.0,
+                    444.0,
+                    1012.0,
+                    478.0,
+                    803.0,
+                    478.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    395.0,
+                    476.0,
+                    583.0,
+                    476.0,
+                    583.0,
+                    508.0,
+                    395.0,
+                    508.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    507.0,
+                    827.0,
+                    507.0,
+                    827.0,
+                    538.0,
+                    394.0,
+                    538.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    900.0,
+                    507.0,
+                    914.0,
+                    507.0,
+                    914.0,
+                    538.0,
+                    900.0,
+                    538.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    577.0,
+                    537.0,
+                    779.0,
+                    537.0,
+                    779.0,
+                    568.0,
+                    577.0,
+                    568.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    803.0,
+                    537.0,
+                    964.0,
+                    537.0,
+                    964.0,
+                    568.0,
+                    803.0,
+                    568.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    566.0,
+                    1129.0,
+                    566.0,
+                    1129.0,
+                    600.0,
+                    394.0,
+                    600.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    395.0,
+                    596.0,
+                    827.0,
+                    596.0,
+                    827.0,
+                    631.0,
+                    395.0,
+                    631.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    899.0,
+                    596.0,
+                    916.0,
+                    596.0,
+                    916.0,
+                    631.0,
+                    899.0,
+                    631.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    576.0,
+                    625.0,
+                    779.0,
+                    625.0,
+                    779.0,
+                    661.0,
+                    576.0,
+                    661.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    803.0,
+                    625.0,
+                    914.0,
+                    625.0,
+                    914.0,
+                    661.0,
+                    803.0,
+                    661.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    579.0,
+                    658.0,
+                    646.0,
+                    658.0,
+                    646.0,
+                    691.0,
+                    579.0,
+                    691.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    680.0,
+                    658.0,
+                    847.0,
+                    658.0,
+                    847.0,
+                    691.0,
+                    680.0,
+                    691.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    689.0,
+                    425.0,
+                    689.0,
+                    425.0,
+                    719.0,
+                    394.0,
+                    719.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    457.0,
+                    689.0,
+                    580.0,
+                    689.0,
+                    580.0,
+                    719.0,
+                    457.0,
+                    719.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    395.0,
+                    719.0,
+                    425.0,
+                    719.0,
+                    425.0,
+                    753.0,
+                    395.0,
+                    753.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    458.0,
+                    719.0,
+                    829.0,
+                    719.0,
+                    829.0,
+                    753.0,
+                    458.0,
+                    753.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    849.0,
+                    719.0,
+                    996.0,
+                    719.0,
+                    996.0,
+                    753.0,
+                    849.0,
+                    753.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    577.0,
+                    748.0,
+                    779.0,
+                    748.0,
+                    779.0,
+                    782.0,
+                    577.0,
+                    782.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    803.0,
+                    748.0,
+                    963.0,
+                    748.0,
+                    963.0,
+                    782.0,
+                    803.0,
+                    782.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    395.0,
+                    782.0,
+                    475.0,
+                    782.0,
+                    475.0,
+                    810.0,
+                    395.0,
+                    810.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    507.0,
+                    782.0,
+                    653.0,
+                    782.0,
+                    653.0,
+                    810.0,
+                    507.0,
+                    810.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    362.0,
+                    810.0,
+                    442.0,
+                    810.0,
+                    442.0,
+                    842.0,
+                    362.0,
+                    842.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    472.0,
+                    810.0,
+                    648.0,
+                    810.0,
+                    648.0,
+                    842.0,
+                    472.0,
+                    842.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    363.0,
+                    840.0,
+                    554.0,
+                    840.0,
+                    554.0,
+                    872.0,
+                    363.0,
+                    872.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1454.0,
+                    1281.0,
+                    1454.0,
+                    1281.0,
+                    1497.0,
+                    293.0,
+                    1497.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    375.0,
+                    975.0,
+                    814.0,
+                    975.0,
+                    814.0,
+                    1011.0,
+                    375.0,
+                    1011.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    890.0,
+                    975.0,
+                    1147.0,
+                    975.0,
+                    1147.0,
+                    1011.0,
+                    890.0,
+                    1011.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1222.0,
+                    975.0,
+                    1299.0,
+                    975.0,
+                    1299.0,
+                    1011.0,
+                    1222.0,
+                    1011.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    1005.0,
+                    1406.0,
+                    1005.0,
+                    1406.0,
+                    1042.0,
+                    392.0,
+                    1042.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    1037.0,
+                    1406.0,
+                    1037.0,
+                    1406.0,
+                    1074.0,
+                    393.0,
+                    1074.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    1067.0,
+                    1404.0,
+                    1067.0,
+                    1404.0,
+                    1102.0,
+                    393.0,
+                    1102.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    1096.0,
+                    1406.0,
+                    1096.0,
+                    1406.0,
+                    1135.0,
+                    392.0,
+                    1135.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    1128.0,
+                    1405.0,
+                    1128.0,
+                    1405.0,
+                    1165.0,
+                    393.0,
+                    1165.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1161.0,
+                    892.0,
+                    1161.0,
+                    892.0,
+                    1194.0,
+                    394.0,
+                    1194.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    373.0,
+                    1196.0,
+                    1169.0,
+                    1196.0,
+                    1169.0,
+                    1239.0,
+                    373.0,
+                    1239.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1272.0,
+                    1196.0,
+                    1406.0,
+                    1196.0,
+                    1406.0,
+                    1239.0,
+                    1272.0,
+                    1239.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1232.0,
+                    1405.0,
+                    1232.0,
+                    1405.0,
+                    1268.0,
+                    394.0,
+                    1268.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    1260.0,
+                    600.0,
+                    1260.0,
+                    600.0,
+                    1301.0,
+                    392.0,
+                    1301.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    370.0,
+                    1301.0,
+                    1405.0,
+                    1301.0,
+                    1405.0,
+                    1339.0,
+                    370.0,
+                    1339.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    1333.0,
+                    1350.0,
+                    1333.0,
+                    1350.0,
+                    1369.0,
+                    393.0,
+                    1369.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1402.0,
+                    964.0,
+                    1402.0,
+                    964.0,
+                    1436.0,
+                    296.0,
+                    1436.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 14,
+            "width": 1700,
+            "height": 2200
+        }
+    }
+]
\ No newline at end of file
diff --git a/parse/train/tqc8n6oHCtZ/tqc8n6oHCtZ.md b/parse/train/tqc8n6oHCtZ/tqc8n6oHCtZ.md
new file mode 100644
index 0000000000000000000000000000000000000000..8a9552fa318e9287260436ce4695c37959ca364e
--- /dev/null
+++ b/parse/train/tqc8n6oHCtZ/tqc8n6oHCtZ.md
@@ -0,0 +1,232 @@
+# LENGTH-ADAPTIVE TRANSFORMER: TRAIN ONCE WITH LENGTH DROP, USE ANYTIME WITH SEARCH
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+Although transformers have achieved impressive accuracies in various tasks in natural language processing, they often come with a prohibitive computational cost, that prevents their use in scenarios with limited computational resources for inference. This need for computational efficiency in inference has been addressed by for instance PoWER-BERT (Goyal et al., 2020) which gradually decreases the length of a sequence as it is passed through layers. These approaches however often assume that the target computational complexity is known in advance at the time of training. This implies that a separate model must be trained for each inference scenario with its distinct computational budget. In this paper, we extend PoWER-BERT to address this issue of inefficiency and redundancy. The proposed extension enables us to train a large-scale transformer, called Length-Adaptive Transformer, once and uses it for various inference scenarios without re-training it. To do so, we train a transformer with LengthDrop, a structural variant of dropout, which stochastically determines the length of a sequence at each layer. We then use a multi-objective evolutionary search to find a length configuration that maximizes the accuracy and minimizes the computational complexity under any given computational budget. Additionally, we significantly extend the applicability of PoWER-BERT beyond sequence-level classification into token-level classification such as span-based question-answering, by introducing the idea of Drop-and-Restore. With Drop-and-Restore, word-vectors are dropped temporarily in intermediate layers and restored at the last layer if necessary. We empirically verify the utility of the proposed approach by demonstrating the superior accuracyefficiency trade-off under various setups, including SQuAD 1.1, MNLI-m, and SST-2. Upon publication, the code to reproduce our work will be open-sourced.
+
+# 1 INTRODUCTION
+
+Pretrained language models (Peters et al., 2018; Devlin et al., 2018; Radford et al., 2019; Yang et al., 2019) have achieved notable improvements in various natural language processing (NLP) tasks. Most of them rely on transformers (Vaswani et al., 2017), and the number of model parameters ranges from hundreds of millions to billions (Shoeybi et al., 2019; Raffel et al., 2019; Kaplan et al., 2020; Brown et al., 2020). Despite this high accuracy, excessive computational overhead during inference, both in terms of time and memory, has hindered its use in real applications. This level of excessive computation has further raised the concern over energy consumption as well (Schwartz et al., 2019; Strubell et al., 2019).
+
+Recent studies have attempted at addressing these concerns regarding large-scale transformers’ computational and energy efficiency (see $\ S 6$ for a more extensive discussion.) Among these, we focus on PoWER-BERT (Goyal et al., 2020) which progressively reduces sequence length by eliminating word-vectors based on the attention values as passing layers. PoWER-BERT establishes the superiority of accuracy-time trade-off over earlier approaches (Sanh et al., 2019; Sun et al., 2019; Michel et al., 2019). It however requires us to train a separate model for each efficiency constraint. In this paper, we thus develop a framework based on PoWER-BERT such that we can train a single model that can be adapted in the inference time to meet any given efficiency target.
+
+In order to train a transformer to cope with a diverse set of computational budgets in the inference time, we propose to train one while reducing the sequence length with a random proportion at each layer. We refer to this procedure as LengthDrop which was motivated by the nested dropout (Rippel et al., 2014). We can extract sub-models of shared weights with any length configuration without requiring extra post-processing nor additional finetuning.
+
+Once a transformer is trained with the proposed LengthDrop, we search for the length configuration that maximizes the accuracy given a computational budget. Because this search is combinatorial and has multiple objectives (accuracy and efficiency), we use an evolutionary search algorithm, which further allows us to obtain a full Pareto frontier of accuracy-efficiency trade-off of each model.
+
+It is not trivial to find an optimal length configuration given the inference-time computational budget, although it is extremely important in order to deploy these large-scale transformers in practice. In this work, we propose to use evolutionary search to find a length configuration that maximizes the accuracy within a given computational budget. We can further compute the Pareto frontier of accuracy-efficiency trade-off to obtain a sequence of length configurations with varying efficiency profiles.
+
+PoWER-BERT, which forms the foundation of the proposed two-stage procedure, is only applicable to sequence-level classification, because by design it eliminates some of the word vectors at each layer. In other words, it cannot be used for token-level tasks such as span-based question answering (Rajpurkar et al., 2016), because these tasks require hidden representations of the entire input sequence at the final layer. We thus propose to extend PoWER-BERT with a novel Drop-and-Restore process (§3.3), which eliminates this inherent limitation. Word vectors are dropped and set aside, rather than eliminated, in intermediate layers to maintain the saving of computational cost, as was with the original PoWER-BERT. These set-aside vectors are then restored at the final hidden layer and provided as an input to a subsequent task-specific layer, which is unlike the original PoWER-BERT.
+
+The main contributions of this work are two-fold. First, we introduce LengthDrop, a structured variant of dropout for training a single Length-Adaptive Transformer model that allows us to automatically derive multiple sub-models with different length configurations in the inference time using evolutionary search, without requiring any re-training. Second, we design Drop-and-Restore process that makes PoWER-BERT applicable beyond classification, which enables PoWER-BERT to be applicable to a wider range of NLP tasks such as span-based question answering. We empirically verify Length-Adaptive Transformer works quite well using the variants of BERT on a diverse set of NLP tasks, including SQuAD 1.1 (Rajpurkar et al., 2016) and two sequence-level classification tasks in GLUE benchmark (Wang et al., 2018). Our experiments reveal that the proposed approach grants us a fine-grained control of computational efficiency and a superior accuracy-efficiency trade-off in the inference time, compared to existing approaches.
+
+# 2 BACKGROUND: TRANSFORMERS AND POWER-BERT
+
+Before we describe our main approach, we review some of the building blocks in this section. In particular, we review transformers, which are a standard backbone used in natural language processing these days, and PoWER-BERT, which was recently proposed as an effective way to train a large-scale, but highly efficient transformer for sequence-level classification.
+
+# 2.1 TRANSFORMERS AND BERT
+
+A transformer is a particular neural network that has been designed to work with a variable-length sequence input and is implemented as a stack of self-attention and fully-connected layers (Vaswani et al., 2017). Here, we give a brief overview of the transformer which is the basic building block of the proposed approach.
+
+Each token $x _ { t }$ in a sequence of tokens ${ \boldsymbol x } = ( x _ { 1 } , \dots , x _ { N } )$ , representing input text, is first turned into a continuous vector $h _ { t } ^ { 0 } \in \mathbb { R } ^ { H }$ which is the sum of the token and position embedding vectors. This sequence is fed into the first transformer layer which returns another sequence of the same length $\dot { h ^ { 1 } } \in \mathbb { R } ^ { N \times H }$ . We repeat this procedure $L$ times, for a transformer with $L$ layers, to obtain $h ^ { L } = ( h _ { 1 } ^ { L } , \ldots , h _ { N } ^ { L } )$ . We refer to each vector in the hidden sequence at each layer as a word vector to emphasize that there exists a correspondence between each such vector and one of the input words.
+
+Although the transformer was first introduced for the problem of machine translation, Devlin et al.   
+(2018) demonstrated that the transformer can be trained and used as a masked language model.
+
+More specifically, Devlin et al. (2018) showed that the transformer-based masked language model, called BERT, learns a universally useful parameter set that can be finetuned for any downstream task including sequence-level and token-level classification.
+
+In the case of sequence-level classification, a softmax classifier is attached to the word vector $h _ { 1 } ^ { L }$ associated with the special token [CLS], and the entire network, including the softmax classifier and BERT, is finetuned. For token-level classification, we use each $h _ { t } ^ { L }$ as the final hidden reprsentation of the associated $t$ -th word in the input sequence. This strategy of pretraining followed by finetuning, often referred to as transfer learning, has recently become a dominant approach to classification in natural language processing.
+
+# 2.2 POWER-BERT
+
+PoWER-BERT keeps only the topmost $l _ { j }$ word vectors at each layer $j$ by eliminating redundant ones based on the significance score, which is the total amount of attention imposed by a word on the other words (Goyal et al., 2020). $l _ { j }$ is the hyper-parameter determines how many vectors to keep at layer $j$ PoWER-BERT has the same model parameters with BERT, but the extraction layers are interspersed after the self-attention layer in every transformer blocks (Vaswani et al., 2017).
+
+PoWER-BERT reduces inference time successfully, achieving better accuracy-time trade-off than DistilBERT (Sanh et al., 2019), BERT-PKD (Sun et al., 2019), and Head-Prune (Michel et al., 2019). Despite the original intention of maximizing the inference efficiency with the minimal loss in accuracy, it is possible to set up PoWER-BERT to be both more efficient and more accurate compared to the original BERT, which was observed but largely overlooked by Goyal et al. (2020).
+
+Training a PoWER-BERT model consists of three steps: (1) finetuning, (2) length configuration search, and (3) re-training. The finetuning step is just like the standard finetuning step of BERT given a target task. A length configuration is a sequence of retention parameters $\left( l _ { 1 } , \cdots l _ { L } \right)$ , each of which corresponds to the number of word vectors that are kept at each layer. These retention parameters are learned along with all the other parameters to minimize the original task loss together with an extra term that approximately measures the number of retained word vectors across layers. In the re-training step, PoWER-BERT is finetuned with the length configuration fixed to its learned one.
+
+For each computational budget, we must train a separate model going through all three steps described above. Moreover, the length configuration search step above is only approximate, as it relies on relaxation of retention parameters which are inherently discrete. This leads to the lack of guaranteed correlation between the success of this stage and true run-time. Even worse, it is a delicate act to tune the length configuration given a target computational budget, because trade-off is implicitly made via a regularization coefficient. Furthermore, PoWER-BERT has an inherent limitation in that it only applies to sequence-level classification because it eliminates word vectors in intermediate layers.
+
+# 3 LENGTH-ADAPTIVE TRANSFORMER
+
+In this section, we explain our proposed framework which results in a transformer that reduces the length of a sequence at each layer with an arbitrary rate. We call such a resulting transformer a Length-Adaptive Transformer. We train Length-Adaptive Transformer with LengthDrop which randomly samples the number of hidden vectors to be dropped at each layer with the goal of making the final model robust to such drop in the inference time. Once the model is trained, we search for the optimal trade-off between accuracy and efficiency using multi-objective evolutionary search, which allows us to use the model for any given computational budget without finetuning nor re-training. At the end of this section, we describe Drop-and-Restore process as a way to greatly increase the applicability of PoWER-BERT which forms a building block of the proposed framework.
+
+In short, we train a Length-Adaptive Transformer once with LengthDrop and Drop-and-Restore, and use it with an automatically determined length configuration for inference with any target computational budget, on both sequence-level and token-level tasks.
+
+# 3.1 LENGTHDROP
+
+Earlier approaches to efficient inference with transformers have focused on a scenario where the target computational budget for inference is known in advance Sanh et al. (2019); Goyal et al. (2020). This greatly increases the cost of deploying transformers, as it requires us to train a separate transformer for each scenario. Instead, we propose to train one model that could be used for a diverse set of target computational budgets without retraining.
+
+LengthDrop randomly generates a length configuration by sequentially sampling a sequence length $l _ { i + 1 }$ at the $( i + 1 )$ -th layer based on the previous layer’s sequence length $l _ { i }$ , following the uniform distribution $\mathcal { U } ( \lceil ( 1 - p ) l _ { i } \rceil , l _ { i } )$ , where $l _ { 0 }$ is set to the length of the input sequence, and $p$ is the LengthDrop probability. This sequential sampling results in a length configuration $( l _ { 1 } , \cdots , l _ { L } )$ . Length-Adaptive Transformer can be thought of as consisting of a full model and many sub-models corresponding to different length configuration, similarly to a neural network trained with dropout (Srivastava et al., 2014).
+
+LayerDrop From the perspective of each word vector, the proposed LengthDrop could be thought of as skipping the layers between when it was set aside and the final layer where it was restored. The word vector however does not have any information based on which it can determine whether it would be dropped at any particular layer. In our preliminary experiments, we found that this greatly hinders optimization. We address this issue by using LayerDrop (Fan et al., 2019) which skips each layer of a transformer uniformly at random. The LayerDrop encourages each word vector to be agnostic to skipping any number of layers between when it is dropped and when it is restored, just like dropout (Srivastava et al., 2014) prevents hidden neurons from co-adapting with each other by randomly dropping them.
+
+Sandwich Rule and Inplace Distillation We observed that standard supervised training with LengthDrop does not work well in the preliminary experiments. We instead borrow a pair of training techniques developed by Yu & Huang (2019) which are sandwich rule and inplace distillation, for better optimization as well as final generalization. At each update, we update the full model without LengthDrop as usual to minimize the supervised loss function. We simultaneously update $n _ { s }$ randomly-sampled sub-models (which are called sandwiches) and the smallest-possible submodel, which corresponds to keeping only $\lceil ( 1 - p ) l _ { i } \rceil$ word vectors at each layer $i$ , using knowledge distillation (Hinton et al., 2015) from the full model. Here, sub-models mean models with length reduction. They are trained to their prediction close to the full model’s prediction (inplace distillation).
+
+# 3.2 EVOLUTIONARY SEARCH OF LENGTH CONFIGURATIONS
+
+After training a Length-Adaptive Transformer with LengthDrop, we search for appropriate length configurations for possible target computational budgets that will be given at inference time. The length configuration determines the model performance in terms of both accuracy and efficiency. In order to search for the optimal length configuration, we propose to use evolutionary search, similarly to Cai et al. (2019) and Wang et al. (2020). This procedure is efficient, as it only requires a single pass through the relatively small validation set for each length configuration, unlike re-training for a new computational budget which requires multiple passes through a significantly larger training set for each budget.
+
+We initialize the population with constant-ratio configurations. Each configuration is created by $l _ { i + 1 } = \lceil ( 1 - r ) \bar { l _ { i } } \rceil$ for each layer $i$ with $r$ so that the amount of computation within the initial population is uniformly distributed between those of the smallest and full models. At each iteration, we evolve the population to consist only of configurations lie on a newly updated efficiencyaccuracy Pareto frontier by mutation and cross-over. Mutation alters an original length configuration $( l _ { 1 } , \cdots , l _ { L } )$ to $( l _ { 1 } ^ { \prime } , \cdots , l _ { L } ^ { \prime } )$ by sampling $l _ { i } ^ { \prime }$ from the uniform distribution $\bar { \mathcal { U } } ( l _ { i - 1 } ^ { \prime } , l _ { i + 1 } )$ with the probability $p _ { m }$ or keeping the original length ${ \bar { l } } _ { i } ^ { \prime } = l _ { i }$ , sweeping the layers from $i = 1$ to $i = L$ . Crossover takes two length configurations and averages the lengths at each layer. Both of these operations are performed while ensuring the monotonicity of the lengths over the layers. We repeat this iteration $G$ times, while maintaining $n _ { m }$ mutated configurations and $n _ { c }$ crossover’d configurations. Repeating this procedure pushes the Pareto frontier further to identify the best trade-off between two objectives, efficiency and accuracy, without requiring any continuous relaxation of length configurations nor using a proxy objective function.
+
+![](images/320388afaf5c944756a7b3f52eddc7583af0fdd53b75f8ac7bf8c3063dd11f2f.jpg)  
+Figure 1: Illustration of (a) word-vector elimination process in PoWER-BERT (Goyal et al., 2020) and (b) Drop-and-Restore process in Length-Adaptive Transformer. Yellow box and blue boxes imply the output of embedding layer and transformer layers, respectively. Green boxes mean vectors dropped in lower layers and restored at the last layer. Red box is the task-specific layer. Though word-vectors in the middle could be eliminated (or dropped), remaining vectors are left-aligned for the better illustration. In this case, the number of transformer layers is four.
+
+# 3.3 DROP-AND-RESTORE PROCESS
+
+The applicability of the PoWER-BERT, based on which our main contribution above was made, is limited to sequence-level classification, because it eliminates word vectors at each layer. In addition to our main contribution above, we thus propose to extend the PoWER-BERT so that it is applicable to token-level classification, such as span-based question-answering. Our proposal, to which we refer as Drop-and-Restore, does not eliminate word vectors at each layer according to the length configuration but instead sets them aside until the final hidden layer. At the final hidden layer, these word vectors are brought back to form the full hidden sequence, as illustrated graphically in Fig. 1.
+
+# 4 EXPERIMENT SETUP
+
+Datasets We test the proposed approach on both sequence-level and token-level tasks, the latter of which could not have been done with the original PoWER-BERT unless for the proposed Dropand-Restore. We use MNLI-m and SST-2 from GLUE benchmark (Wang et al., 2018), as was done to test PoWER-BERT earlier, for sequence-level classification. We choose them because consistent accuracy scores from standard training on them due to their sufficiently large training set imply that they are reliable to verify our approach. We use SQuAD 1.1 (Rajpurkar et al., 2016) for token-level classification.
+
+Evaluation metrics We use the number of floating operations (FLOPs) as a main metric to measure the inference efficiency given any length configuration, as it is agnostic to the choice of underlying hardware, unlike other alternatives such as hardware-aware latency (Wang et al., 2020) or energy consumption (Henderson et al., 2020). We later demonstrate that FLOPs and wall-clock time on GPU and CPU correlate well with the proposed approach, which is not necessarily the case for other approaches, such as unstructured weight pruning (Han et al., 2015; See et al., 2016).
+
+Pretrained transformers Since BERT was introduced by Devlin et al. (2018), it has become a standard practice to start from a pretrained (masked) language model and finetune it for each downstream task. We follow the same strategy in this paper and test two pretrained transformerbased language models; BERTBASE (Devlin et al., 2018) and DistilBERT (Sanh et al., 2019), which allows us to demonstrate that the usefulness and applicability of our approach are not tied to any specific architectural choice, such as the number of layers and the maximum length of input sequence. Although we focus on BERT-based masked language models here, the proposed approach is readily applicable to any transformer-based models.
+
+Learning We train a Length-Adaptive Transformer with LengthDrop probability and LayerDrop probability both set to 0.2. We use $n _ { s } = 2$ randomly sampled intermediate sub-models in addition to the full model and smallest model for applying the sandwich learning rule.
+
+We start finetuning the pretrained transformer without Drop-and-Restore first, just as Goyal et al. (2020) did with PoWER-BERT. We then continue finetuning it for another five epochs with Drop-andRestore. This is unlike the recommended three epochs by Devlin et al. (2018), as learning progresses slower due to a higher level of stochasticity introduced by LengthDrop and LayerDrop. We use the batch size of 32, the learning rate of $5 e - 5$ for SQuAD v1.1 and $2 e - 5$ for MNLI-m and SST, and the maximum sequence length of 384 for SQuAD v1.1 and 128 for MNLI-m and SST.
+
+![](images/3ea54ad6f6a4d01240155dd50bd06714bd078c67453a78cfd7ce1b9404ef27c2.jpg)  
+Figure 2: Pareto curves of F1 score and FLOPs on SQuAD 1.1 (Rajpurkar et al., 2016). We apply the proposed method to $\mathbf { B E R T _ { B a s e } }$ (solid lines) and DistilBERT (dotted lines). For each model, we draw three curves using (1) standard finetuned transformer with constant-rate length reduction, (2) Length-Adaptive Transformer with constant-rate length reduction, and (3) Length-Adaptive Transformer with length configurations obtained from the evolutionary search.
+
+![](images/4608176aa7c7dba0b4748567c1c64abe798b711bebf826c4b323894a4bfb2b12.jpg)  
+Figure 3: Correlation between FLOPs and latency with different length configurations.
+
+Search We run up to $G = 3 0$ iterations of evolutionary search, using $n _ { m } = 3 0$ mutated configurations with mutation probability $p _ { m } = 0 . 5$ and $n _ { c } = 3 0$ crossover’d configurations, to find the Pareto frontier of accuracy and efficiency.
+
+# 5 RESULTS AND ANALYSIS
+
+Efficiency-accuracy trade-off We use SQuAD 1.1 to examine the effect of the proposed approach on the efficiency-accuracy trade-off. When the underlying classifier was not trained with LengthDrop, as proposed in this paper, the accuracy drops even more dramatically as more word vectors are dropped at each layer. The difference between standard transformer and Length-Adaptive Transformer is stark in Fig. 2. This verifies the importance of training a transformer in a way that makes it malleable for inference-time re-configuration.
+
+When the model was trained with the proposed LengthDrop, we notice the efficacy of the proposed approach of using evolutionary search to find the optimal trade-off between inference efficiency and accuracy. The trade-off curve from the proposed search strategy has a larger area-under-curve (AUC) than when constant-rate length reduction was used to meet a target computational budget. It demonstrates the importance of using both LengthDrop and evolutionary search.
+
+We make a minor observation that the proposed approach ends up with a significantly higher accuracy than DistillBERT when enough computational budget is allowed for inference $( \log { \mathrm { F L O P s } } > 1 0 )$ . This makes our approach desirable in a wide array of scenarios, as it does not require any additional pretraining stage, as does DistilBERT. With a severe constraint on the computational budget, the proposed approach could be used on DistilBERT to significantly improve the efficiency without compromising the accuracy.
+
+Maximizing inference efficiency We consider all three tasks, SQuAD 1.1, MNLI-m and SST-2, and investigate how much efficiency can be gained by the proposed approach with minimal sacrifice of accuracy. First, we look at how much efficiency could be gained without losing on the accuracy. That is, we use the length configuration that maximizes the inference efficiency (i.e., minimize the FLOPs) while ensuring that the accuracy is above or same as the accuracy of the standard approach without any drop of word vectors. The results are presented in the rows marked with Length-Adaptive† from Table 1. For example, in the case of $\mathbf { B E R T _ { B a s e } }$ , the proposed approach reduce FLOPs by more than half across all three tasks.
+
+Table 1: Comparison results of standard Transformer and LengthAdaptive Transformer. Among length configurations on the Pareto frontier of Length-Adaptive Transformer, we pick two representative points: Length-Adaptive? and Length-Adaptive† as the most efficient one while having the highest accuracy and the accuracy higher than (or equal to) standard Transformer, respectively.   
+
+<table><tr><td colspan="2">Model</td><td colspan="2">SQuAD 1.1</td><td colspan="2">MNLI-m</td><td colspan="2">SST-2</td></tr><tr><td>Pretrained Transformer</td><td>Method</td><td>F1</td><td>FLOPs</td><td>Acc</td><td>FLOPs</td><td>Acc</td><td>FLOPs</td></tr><tr><td rowspan="2">BERTBase</td><td>Standard</td><td>88.5</td><td>1.00x</td><td>84.4</td><td>1.00x</td><td>92.8</td><td>1.00x</td></tr><tr><td>Length-Adaptive*</td><td>89.6</td><td>0.89x</td><td>85.0</td><td>0.58x</td><td>93.1</td><td>0.36x</td></tr><tr><td rowspan="2"></td><td>Length-Adaptivet</td><td>88.7</td><td>0.45x</td><td>84.4</td><td>0.35x</td><td>92.8</td><td>0.35x</td></tr><tr><td>Standard</td><td>85.8</td><td>1.00x</td><td>80.9</td><td>1.00x</td><td>90.6</td><td>1.00x</td></tr><tr><td rowspan="2">DistilBERT1</td><td>Length-Adaptive*</td><td>86.3</td><td>0.81x</td><td>81.5</td><td>0.56x</td><td>92.0</td><td>0.55x</td></tr><tr><td>Length-Adaptive†</td><td>85.9</td><td>0.59x</td><td>81.3</td><td>0.54x</td><td>91.7</td><td>0.54x</td></tr></table>
+
+![](images/e4a6ecfc1cdcda5b3130f2509429e44b544d994935e6b44f36893f811295f752.jpg)  
+Figure 4: Example of area under Pareto curve as the evolutionary search of lenth configurations proceeds.
+
+From Fig. 2, we have observed that the proposed Length-Adaptive Transformer generalize better than the standard, base model in some cases. We thus try to maximize both the inference efficiency and accuracy, in order to see whether it is possible for the proposed algorithm to find a length configuration that both maximizes inference efficiency and improves accuracy. We present the results in the rows marked with Length-Adaptive? from Table 1. For all cases, Length-Adaptive Transformer achieves higher accuracy than a standard transformer does while reducing FLOPs significantly. Although it is not apparent from the table, tor MNLI-m and SST-2, the accuracy of the smallest sub-model is already greater than or equal to that of a standard transformer.
+
+FLOPs vs. Latency As has been discussed in recent literature (see, e.g., (Li et al., 2020; Chin et al., 2020)), FLOPs is not a perfect indicator of the real latency measured in wall-clock time, as the latter is affected by the combination of hardware choice and network architecture. To understand the real-world impact of the proposed approach, we study the relationship between FLOPs, obtained by the proposed procedure, and wall-clock time measured on both CPU and GPU by measuring them while varying length configurations. As shown in Fig. 3, FLOPs and latency exhibit near-linear correlation on GPU, when the minibatch size is $\geq 1 6$ , and regardless of the minibatch size, on CPU. In other words, the reduction in FLOPs with the proposed approach directly implies the reduction in wall-clock time.
+
+Convergence of search Although the proposed approach is efficient in that it requires only one round of training, it needs a separate search stage for each target budget. It is important for evolutionary search to converge quickly in the number of forward sweeps of a validation set. As exemplified in Fig. 4, evolutionary search converges after about fifteen iterations.
+
+# 6 RELATED WORK
+
+The main purpose of the proposed algorithm is to improve the inference efficiency of a large-scale transformer. This goal has been pursued from various directions, and in this section, we provide a brief overview of these earlier, and some concurrent, attempts in the context of the proposed approach.
+
+Weight pruning Weight pruning (Han et al., 2015) focuses on reducing the number of parameters which directly reflects the memory footprint of a model and indirectly correlates with inference speed. However, their actual speed-up in runtime is usually not significant, especially while executing a model with parallel computation using GPU devices (Tang et al., 2018; Li et al., 2020).
+
+Adaptive architecture There are three major axes along which computation can be reduced in a neural network; (1) input size/length, (2) network depth and (3) network width. The proposed approach, based on PoWER-BERT, adaptively reduces the input length as the input sequence is processed by the transformer layers. In our knowledge, Goyal et al. (2020) is the first work in this direction for transformers. More recently, Funnel-Transformer (Dai et al., 2020) and multi-scale transformer language models (Subramanian et al., 2020) also successfully reduce sequence length in the middle and rescale to full length for the final computation. However, their inference complexity is fixed unlike PoWER-BERT because they are not designed for the control of efficiency.
+
+LayerDrop (Fan et al., 2019) drops random layers during the training to be robust to pruning inspired by Huang et al. (2016). Word-level adaptive depth in Elbayad et al. (2019) might seemingly resemble with length reduction, but word vectors reached the maximal layer are used for self-attention computation without updating themselves. Escaping a network early (Teerapittayanon et al., 2016; Huang et al., 2017) based on the confidence of the prediction (Xin et al., 2020; Schwartz et al., 2020; Liu et al., 2020) also offers a control over accuracy-efficiency trade-off, but it is difficult to tune a threshold for a desired computational budget because of the example-wise adaptive computation.
+
+DynaBERT (Hou et al., 2020) can run at adaptive width (the number of attention heads and intermediate hidden dimension) and depth. Hardware-aware Transformers (Wang et al., 2020) construct a design space with arbitrary encoder-decoder attention and heterogeneous layers in terms of different numbers of layers, attention heads, hidden dimension, and embedding dimension.
+
+Structured dropout A major innovation we introduce over the existing PoWER-BERT is the use of stochastic, structured regularization to make a transformer robust to the choice of length configuration in the inference time. Rippel et al. (2014) proposes a nested dropout to learn ordered representations. Similar to LengthDrop, it samples an index form a prior distribution and drops all units having a larger index than sampled one.
+
+Search There have been a series of attempts at finding the optimal network configuration by solving a combinatorial optimization problem. In computer vision, Once-for-All (Cai et al., 2019) use an evolutionary search (Real et al., 2019) to find a better configuration in dimensions of depth, width, kernel size, and resolution given computational budget. Similarly but differently, our evolutionary search is mutli-objective to find length configurations on the Pareto accuracy-efficiency frontier to cope with any possible computational budgets. Moreover, we only change the sequence length of hidden vectors instead of architectural model size like dimensions.
+
+# 7 CONCLUSION AND FUTURE WORK
+
+In this work, we propose a new framework for training a transformer once and using it for efficient inference under any computational budget. With the help of training with LengthDrop and Drop-andRestore process followed by the evolutionary search, our proposed Length-Adaptive Transformer allows any given transformer models to be used with any inference-time computational budget for both sequence-level and token-level classification tasks. Our experiments, on SQuAD 1.1, MNLI-m and SST-2, have revealed that the proposed algorithmic framework significantly pushes a better Pareto frontier on the trade-off between inference efficiency and accuracy. Furthermore, we have observed that the proposed Length-Adaptive Transformer could achieve up to $3 \mathbf { x }$ speed-up over the standard transformer without sacrificing accuracy, both in terms of FLOPs and wallclock time.
+
+Although our approach finds an optimal length configuration of a trained classifier per computational budget, it leaves open a question whether the proposed approach could be further extended to support per-instance length configuration by for instance training a small, auxiliary neural network for each computational budget. Yet another aspect we have not investigated in this paper is the applicability of the proposed approach to sequence generation, such as machine translation. We leave both of these research directions for the future.
+
+Our approach is effective, as we have shown in this paper, and also quite simple to implement on top of existing language models. We will release our implementation, which is based on HuggingFace’s Transformers library (Wolf et al., 2019), publicly and plan to adapt it for a broader set of transformerbased models and downstream tasks.
+
+# REFERENCES
+
+Tom B Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al. Language models are few-shot learners. arXiv preprint arXiv:2005.14165, 2020.
+
+Han Cai, Chuang Gan, and Song Han. Once for all: Train one network and specialize it for efficient deployment. arXiv preprint arXiv:1908.09791, 2019.
+
+Ting-Wu Chin, Ruizhou Ding, Cha Zhang, and Diana Marculescu. Towards efficient model compression via learned global ranking. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 1518–1528, 2020.
+
+Zihang Dai, Guokun Lai, Yiming Yang, and Quoc V Le. Funnel-transformer: Filtering out sequential redundancy for efficient language processing. arXiv preprint arXiv:2006.03236, 2020.
+
+Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. Bert: Pre-training of deep bidirectional transformers for language understanding. arXiv preprint arXiv:1810.04805, 2018.
+
+Maha Elbayad, Jiatao Gu, Edouard Grave, and Michael Auli. Depth-adaptive transformer. arXiv preprint arXiv:1910.10073, 2019.
+
+Angela Fan, Edouard Grave, and Armand Joulin. Reducing transformer depth on demand with structured dropout. arXiv preprint arXiv:1909.11556, 2019.
+
+Saurabh Goyal, Anamitra Roy Choudhary, Venkatesan Chakaravarthy, Saurabh ManishRaje, Yogish Sabharwal, and Ashish Verma. Power-bert: Accelerating bert inference for classification tasks. arXiv preprint arXiv:2001.08950, 2020.
+
+Song Han, Huizi Mao, and William J Dally. Deep compression: Compressing deep neural networks with pruning, trained quantization and huffman coding. arXiv preprint arXiv:1510.00149, 2015.
+
+Peter Henderson, Jieru Hu, Joshua Romoff, Emma Brunskill, Dan Jurafsky, and Joelle Pineau. Towards the systematic reporting of the energy and carbon footprints of machine learning. arXiv preprint arXiv:2002.05651, 2020.
+
+Geoffrey Hinton, Oriol Vinyals, and Jeff Dean. Distilling the knowledge in a neural network. arXiv preprint arXiv:1503.02531, 2015.
+
+Lu Hou, Lifeng Shang, Xin Jiang, and Qun Liu. Dynabert: Dynamic bert with adaptive width and depth. arXiv preprint arXiv:2004.04037, 2020.
+
+Gao Huang, Yu Sun, Zhuang Liu, Daniel Sedra, and Kilian Q Weinberger. Deep networks with stochastic depth. In European conference on computer vision, pp. 646–661. Springer, 2016.
+
+Gao Huang, Danlu Chen, Tianhong Li, Felix Wu, Laurens van der Maaten, and Kilian Q Weinberger. Multi-scale dense networks for resource efficient image classification. arXiv preprint arXiv:1703.09844, 2017.
+
+Jared Kaplan, Sam McCandlish, Tom Henighan, Tom B Brown, Benjamin Chess, Rewon Child, Scott Gray, Alec Radford, Jeffrey Wu, and Dario Amodei. Scaling laws for neural language models. arXiv preprint arXiv:2001.08361, 2020.
+
+Zhuohan Li, Eric Wallace, Sheng Shen, Kevin Lin, Kurt Keutzer, Dan Klein, and Joseph E Gonzalez. Train large, then compress: Rethinking model size for efficient training and inference of transformers. arXiv preprint arXiv:2002.11794, 2020.
+
+Weijie Liu, Peng Zhou, Zhe Zhao, Zhiruo Wang, Haotang Deng, and Qi Ju. Fastbert: a self-distilling bert with adaptive inference time. arXiv preprint arXiv:2004.02178, 2020.
+
+Paul Michel, Omer Levy, and Graham Neubig. Are sixteen heads really better than one? In Advances in Neural Information Processing Systems, pp. 14014–14024, 2019.
+
+Matthew E Peters, Mark Neumann, Mohit Iyyer, Matt Gardner, Christopher Clark, Kenton Lee, and Luke Zettlemoyer. Deep contextualized word representations. arXiv preprint arXiv:1802.05365, 2018.
+
+Alec Radford, Jeffrey Wu, Rewon Child, David Luan, Dario Amodei, and Ilya Sutskever. Language models are unsupervised multitask learners. OpenAI Blog, 1(8):9, 2019.
+
+Colin Raffel, Noam Shazeer, Adam Roberts, Katherine Lee, Sharan Narang, Michael Matena, Yanqi Zhou, Wei Li, and Peter J Liu. Exploring the limits of transfer learning with a unified text-to-text transformer. arXiv preprint arXiv:1910.10683, 2019.
+
+Pranav Rajpurkar, Jian Zhang, Konstantin Lopyrev, and Percy Liang. Squad: $^ { 1 0 0 , 0 0 0 + }$ questions for machine comprehension of text. arXiv preprint arXiv:1606.05250, 2016.
+
+Esteban Real, Alok Aggarwal, Yanping Huang, and Quoc V Le. Regularized evolution for image classifier architecture search. In Proceedings of the aaai conference on artificial intelligence, volume 33, pp. 4780–4789, 2019.
+
+Oren Rippel, Michael Gelbart, and Ryan Adams. Learning ordered representations with nested dropout. In International Conference on Machine Learning, pp. 1746–1754, 2014.
+
+Victor Sanh, Lysandre Debut, Julien Chaumond, and Thomas Wolf. Distilbert, a distilled version of bert: smaller, faster, cheaper and lighter. arXiv preprint arXiv:1910.01108, 2019.
+
+Roy Schwartz, Jesse Dodge, Noah A Smith, and Oren Etzioni. Green ai. arXiv preprint arXiv:1907.10597, 2019.
+
+Roy Schwartz, Gabi Stanovsky, Swabha Swayamdipta, Jesse Dodge, and Noah A Smith. The right tool for the job: Matching model and instance complexities. arXiv preprint arXiv:2004.07453, 2020.
+
+Abigail See, Minh-Thang Luong, and Christopher D Manning. Compression of neural machine translation models via pruning. arXiv preprint arXiv:1606.09274, 2016.
+
+Mohammad Shoeybi, Mostofa Patwary, Raul Puri, Patrick LeGresley, Jared Casper, and Bryan Catanzaro. Megatron-lm: Training multi-billion parameter language models using gpu model parallelism. arXiv preprint arXiv:1909.08053, 2019.
+
+Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov. Dropout: a simple way to prevent neural networks from overfitting. The journal of machine learning research, 15(1):1929–1958, 2014.
+
+Emma Strubell, Ananya Ganesh, and Andrew McCallum. Energy and policy considerations for deep learning in nlp. arXiv preprint arXiv:1906.02243, 2019.
+
+Sandeep Subramanian, Ronan Collobert, Marc’Aurelio Ranzato, and Y-Lan Boureau. Multi-scale transformer language models. arXiv preprint arXiv:2005.00581, 2020.
+
+Siqi Sun, Yu Cheng, Zhe Gan, and Jingjing Liu. Patient knowledge distillation for bert model compression. arXiv preprint arXiv:1908.09355, 2019.
+
+Raphael Tang, Ashutosh Adhikari, and Jimmy Lin. Flops as a direct optimization objective for learning sparse neural networks. arXiv preprint arXiv:1811.03060, 2018.
+
+Surat Teerapittayanon, Bradley McDanel, and Hsiang-Tsung Kung. Branchynet: Fast inference via early exiting from deep neural networks. In 2016 23rd International Conference on Pattern Recognition (ICPR), pp. 2464–2469. IEEE, 2016.
+
+Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention is all you need. In Advances in neural information processing systems, pp. 5998–6008, 2017.
+
+Alex Wang, Amanpreet Singh, Julian Michael, Felix Hill, Omer Levy, and Samuel R Bowman. Glue: A multi-task benchmark and analysis platform for natural language understanding. arXiv preprint arXiv:1804.07461, 2018.
+
+Hanrui Wang, Zhanghao Wu, Zhijian Liu, Han Cai, Ligeng Zhu, Chuang Gan, and Song Han. Hat: Hardware-aware transformers for efficient natural language processing. arXiv preprint arXiv:2005.14187, 2020.
+
+Thomas Wolf, Lysandre Debut, Victor Sanh, Julien Chaumond, Clement Delangue, Anthony Moi, Pierric Cistac, Tim Rault, Remi Louf, Morgan Funtowicz, et al. Transformers: State-of-the-art ´ natural language processing. arXiv preprint arXiv:1910.03771, 2019.
+
+Ji Xin, Raphael Tang, Jaejun Lee, Yaoliang Yu, and Jimmy Lin. Deebert: Dynamic early exiting for accelerating bert inference. arXiv preprint arXiv:2004.12993, 2020.
+
+Zhilin Yang, Zihang Dai, Yiming Yang, Jaime Carbonell, Russ R Salakhutdinov, and Quoc V Le. Xlnet: Generalized autoregressive pretraining for language understanding. In Advances in neural information processing systems, pp. 5754–5764, 2019.
+
+Jiahui Yu and Thomas S Huang. Universally slimmable networks and improved training techniques. In Proceedings of the IEEE International Conference on Computer Vision, pp. 1803–1811, 2019.
\ No newline at end of file
diff --git a/parse/train/tqc8n6oHCtZ/tqc8n6oHCtZ_content_list.json b/parse/train/tqc8n6oHCtZ/tqc8n6oHCtZ_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..2a2d84d854deee88724ebaadd6e1ab1505f6f2dd
--- /dev/null
+++ b/parse/train/tqc8n6oHCtZ/tqc8n6oHCtZ_content_list.json
@@ -0,0 +1,1314 @@
+[
+    {
+        "type": "text",
+        "text": "LENGTH-ADAPTIVE TRANSFORMER: TRAIN ONCE WITH LENGTH DROP, USE ANYTIME WITH SEARCH ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            98,
+            823,
+            147
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Anonymous authors Paper under double-blind review ",
+        "bbox": [
+            183,
+            174,
+            398,
+            200
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            238,
+            544,
+            253
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Although transformers have achieved impressive accuracies in various tasks in natural language processing, they often come with a prohibitive computational cost, that prevents their use in scenarios with limited computational resources for inference. This need for computational efficiency in inference has been addressed by for instance PoWER-BERT (Goyal et al., 2020) which gradually decreases the length of a sequence as it is passed through layers. These approaches however often assume that the target computational complexity is known in advance at the time of training. This implies that a separate model must be trained for each inference scenario with its distinct computational budget. In this paper, we extend PoWER-BERT to address this issue of inefficiency and redundancy. The proposed extension enables us to train a large-scale transformer, called Length-Adaptive Transformer, once and uses it for various inference scenarios without re-training it. To do so, we train a transformer with LengthDrop, a structural variant of dropout, which stochastically determines the length of a sequence at each layer. We then use a multi-objective evolutionary search to find a length configuration that maximizes the accuracy and minimizes the computational complexity under any given computational budget. Additionally, we significantly extend the applicability of PoWER-BERT beyond sequence-level classification into token-level classification such as span-based question-answering, by introducing the idea of Drop-and-Restore. With Drop-and-Restore, word-vectors are dropped temporarily in intermediate layers and restored at the last layer if necessary. We empirically verify the utility of the proposed approach by demonstrating the superior accuracyefficiency trade-off under various setups, including SQuAD 1.1, MNLI-m, and SST-2. Upon publication, the code to reproduce our work will be open-sourced. ",
+        "bbox": [
+            232,
+            270,
+            766,
+            602
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            627,
+            336,
+            643
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Pretrained language models (Peters et al., 2018; Devlin et al., 2018; Radford et al., 2019; Yang et al., 2019) have achieved notable improvements in various natural language processing (NLP) tasks. Most of them rely on transformers (Vaswani et al., 2017), and the number of model parameters ranges from hundreds of millions to billions (Shoeybi et al., 2019; Raffel et al., 2019; Kaplan et al., 2020; Brown et al., 2020). Despite this high accuracy, excessive computational overhead during inference, both in terms of time and memory, has hindered its use in real applications. This level of excessive computation has further raised the concern over energy consumption as well (Schwartz et al., 2019; Strubell et al., 2019). ",
+        "bbox": [
+            174,
+            659,
+            826,
+            770
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Recent studies have attempted at addressing these concerns regarding large-scale transformers’ computational and energy efficiency (see $\\ S 6$ for a more extensive discussion.) Among these, we focus on PoWER-BERT (Goyal et al., 2020) which progressively reduces sequence length by eliminating word-vectors based on the attention values as passing layers. PoWER-BERT establishes the superiority of accuracy-time trade-off over earlier approaches (Sanh et al., 2019; Sun et al., 2019; Michel et al., 2019). It however requires us to train a separate model for each efficiency constraint. In this paper, we thus develop a framework based on PoWER-BERT such that we can train a single model that can be adapted in the inference time to meet any given efficiency target. ",
+        "bbox": [
+            174,
+            777,
+            825,
+            888
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In order to train a transformer to cope with a diverse set of computational budgets in the inference time, we propose to train one while reducing the sequence length with a random proportion at each layer. We refer to this procedure as LengthDrop which was motivated by the nested dropout (Rippel et al., 2014). We can extract sub-models of shared weights with any length configuration without requiring extra post-processing nor additional finetuning. ",
+        "bbox": [
+            173,
+            895,
+            821,
+            924
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            103,
+            823,
+            146
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Once a transformer is trained with the proposed LengthDrop, we search for the length configuration that maximizes the accuracy given a computational budget. Because this search is combinatorial and has multiple objectives (accuracy and efficiency), we use an evolutionary search algorithm, which further allows us to obtain a full Pareto frontier of accuracy-efficiency trade-off of each model. ",
+        "bbox": [
+            174,
+            152,
+            823,
+            208
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "It is not trivial to find an optimal length configuration given the inference-time computational budget, although it is extremely important in order to deploy these large-scale transformers in practice. In this work, we propose to use evolutionary search to find a length configuration that maximizes the accuracy within a given computational budget. We can further compute the Pareto frontier of accuracy-efficiency trade-off to obtain a sequence of length configurations with varying efficiency profiles. ",
+        "bbox": [
+            174,
+            215,
+            825,
+            299
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "PoWER-BERT, which forms the foundation of the proposed two-stage procedure, is only applicable to sequence-level classification, because by design it eliminates some of the word vectors at each layer. In other words, it cannot be used for token-level tasks such as span-based question answering (Rajpurkar et al., 2016), because these tasks require hidden representations of the entire input sequence at the final layer. We thus propose to extend PoWER-BERT with a novel Drop-and-Restore process (§3.3), which eliminates this inherent limitation. Word vectors are dropped and set aside, rather than eliminated, in intermediate layers to maintain the saving of computational cost, as was with the original PoWER-BERT. These set-aside vectors are then restored at the final hidden layer and provided as an input to a subsequent task-specific layer, which is unlike the original PoWER-BERT. ",
+        "bbox": [
+            174,
+            306,
+            825,
+            431
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The main contributions of this work are two-fold. First, we introduce LengthDrop, a structured variant of dropout for training a single Length-Adaptive Transformer model that allows us to automatically derive multiple sub-models with different length configurations in the inference time using evolutionary search, without requiring any re-training. Second, we design Drop-and-Restore process that makes PoWER-BERT applicable beyond classification, which enables PoWER-BERT to be applicable to a wider range of NLP tasks such as span-based question answering. We empirically verify Length-Adaptive Transformer works quite well using the variants of BERT on a diverse set of NLP tasks, including SQuAD 1.1 (Rajpurkar et al., 2016) and two sequence-level classification tasks in GLUE benchmark (Wang et al., 2018). Our experiments reveal that the proposed approach grants us a fine-grained control of computational efficiency and a superior accuracy-efficiency trade-off in the inference time, compared to existing approaches. ",
+        "bbox": [
+            174,
+            438,
+            825,
+            590
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 BACKGROUND: TRANSFORMERS AND POWER-BERT ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            611,
+            651,
+            627
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Before we describe our main approach, we review some of the building blocks in this section. In particular, we review transformers, which are a standard backbone used in natural language processing these days, and PoWER-BERT, which was recently proposed as an effective way to train a large-scale, but highly efficient transformer for sequence-level classification. ",
+        "bbox": [
+            174,
+            643,
+            825,
+            699
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1 TRANSFORMERS AND BERT ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            715,
+            413,
+            729
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "A transformer is a particular neural network that has been designed to work with a variable-length sequence input and is implemented as a stack of self-attention and fully-connected layers (Vaswani et al., 2017). Here, we give a brief overview of the transformer which is the basic building block of the proposed approach. ",
+        "bbox": [
+            174,
+            742,
+            825,
+            797
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Each token $x _ { t }$ in a sequence of tokens ${ \\boldsymbol x } = ( x _ { 1 } , \\dots , x _ { N } )$ , representing input text, is first turned into a continuous vector $h _ { t } ^ { 0 } \\in \\mathbb { R } ^ { H }$ which is the sum of the token and position embedding vectors. This sequence is fed into the first transformer layer which returns another sequence of the same length $\\dot { h ^ { 1 } } \\in \\mathbb { R } ^ { N \\times H }$ . We repeat this procedure $L$ times, for a transformer with $L$ layers, to obtain $h ^ { L } = ( h _ { 1 } ^ { L } , \\ldots , h _ { N } ^ { L } )$ . We refer to each vector in the hidden sequence at each layer as a word vector to emphasize that there exists a correspondence between each such vector and one of the input words. ",
+        "bbox": [
+            174,
+            804,
+            825,
+            888
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Although the transformer was first introduced for the problem of machine translation, Devlin et al.   \n(2018) demonstrated that the transformer can be trained and used as a masked language model. ",
+        "bbox": [
+            173,
+            895,
+            823,
+            924
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "More specifically, Devlin et al. (2018) showed that the transformer-based masked language model, called BERT, learns a universally useful parameter set that can be finetuned for any downstream task including sequence-level and token-level classification. ",
+        "bbox": [
+            176,
+            103,
+            823,
+            145
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In the case of sequence-level classification, a softmax classifier is attached to the word vector $h _ { 1 } ^ { L }$ associated with the special token [CLS], and the entire network, including the softmax classifier and BERT, is finetuned. For token-level classification, we use each $h _ { t } ^ { L }$ as the final hidden reprsentation of the associated $t$ -th word in the input sequence. This strategy of pretraining followed by finetuning, often referred to as transfer learning, has recently become a dominant approach to classification in natural language processing. ",
+        "bbox": [
+            174,
+            152,
+            825,
+            237
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2 POWER-BERT ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            273,
+            323,
+            287
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "PoWER-BERT keeps only the topmost $l _ { j }$ word vectors at each layer $j$ by eliminating redundant ones based on the significance score, which is the total amount of attention imposed by a word on the other words (Goyal et al., 2020). $l _ { j }$ is the hyper-parameter determines how many vectors to keep at layer $j$ PoWER-BERT has the same model parameters with BERT, but the extraction layers are interspersed after the self-attention layer in every transformer blocks (Vaswani et al., 2017). ",
+        "bbox": [
+            174,
+            308,
+            825,
+            378
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "PoWER-BERT reduces inference time successfully, achieving better accuracy-time trade-off than DistilBERT (Sanh et al., 2019), BERT-PKD (Sun et al., 2019), and Head-Prune (Michel et al., 2019). Despite the original intention of maximizing the inference efficiency with the minimal loss in accuracy, it is possible to set up PoWER-BERT to be both more efficient and more accurate compared to the original BERT, which was observed but largely overlooked by Goyal et al. (2020). ",
+        "bbox": [
+            174,
+            385,
+            825,
+            455
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Training a PoWER-BERT model consists of three steps: (1) finetuning, (2) length configuration search, and (3) re-training. The finetuning step is just like the standard finetuning step of BERT given a target task. A length configuration is a sequence of retention parameters $\\left( l _ { 1 } , \\cdots l _ { L } \\right)$ , each of which corresponds to the number of word vectors that are kept at each layer. These retention parameters are learned along with all the other parameters to minimize the original task loss together with an extra term that approximately measures the number of retained word vectors across layers. In the re-training step, PoWER-BERT is finetuned with the length configuration fixed to its learned one. ",
+        "bbox": [
+            174,
+            462,
+            825,
+            559
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "For each computational budget, we must train a separate model going through all three steps described above. Moreover, the length configuration search step above is only approximate, as it relies on relaxation of retention parameters which are inherently discrete. This leads to the lack of guaranteed correlation between the success of this stage and true run-time. Even worse, it is a delicate act to tune the length configuration given a target computational budget, because trade-off is implicitly made via a regularization coefficient. Furthermore, PoWER-BERT has an inherent limitation in that it only applies to sequence-level classification because it eliminates word vectors in intermediate layers. ",
+        "bbox": [
+            174,
+            566,
+            825,
+            664
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 LENGTH-ADAPTIVE TRANSFORMER ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            705,
+            504,
+            722
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section, we explain our proposed framework which results in a transformer that reduces the length of a sequence at each layer with an arbitrary rate. We call such a resulting transformer a Length-Adaptive Transformer. We train Length-Adaptive Transformer with LengthDrop which randomly samples the number of hidden vectors to be dropped at each layer with the goal of making the final model robust to such drop in the inference time. Once the model is trained, we search for the optimal trade-off between accuracy and efficiency using multi-objective evolutionary search, which allows us to use the model for any given computational budget without finetuning nor re-training. At the end of this section, we describe Drop-and-Restore process as a way to greatly increase the applicability of PoWER-BERT which forms a building block of the proposed framework. ",
+        "bbox": [
+            174,
+            748,
+            825,
+            875
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In short, we train a Length-Adaptive Transformer once with LengthDrop and Drop-and-Restore, and use it with an automatically determined length configuration for inference with any target computational budget, on both sequence-level and token-level tasks. ",
+        "bbox": [
+            176,
+            882,
+            823,
+            922
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1 LENGTHDROP ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            103,
+            313,
+            117
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Earlier approaches to efficient inference with transformers have focused on a scenario where the target computational budget for inference is known in advance Sanh et al. (2019); Goyal et al. (2020). This greatly increases the cost of deploying transformers, as it requires us to train a separate transformer for each scenario. Instead, we propose to train one model that could be used for a diverse set of target computational budgets without retraining. ",
+        "bbox": [
+            174,
+            128,
+            825,
+            199
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "LengthDrop randomly generates a length configuration by sequentially sampling a sequence length $l _ { i + 1 }$ at the $( i + 1 )$ -th layer based on the previous layer’s sequence length $l _ { i }$ , following the uniform distribution $\\mathcal { U } ( \\lceil ( 1 - p ) l _ { i } \\rceil , l _ { i } )$ , where $l _ { 0 }$ is set to the length of the input sequence, and $p$ is the LengthDrop probability. This sequential sampling results in a length configuration $( l _ { 1 } , \\cdots , l _ { L } )$ . Length-Adaptive Transformer can be thought of as consisting of a full model and many sub-models corresponding to different length configuration, similarly to a neural network trained with dropout (Srivastava et al., 2014). ",
+        "bbox": [
+            173,
+            207,
+            825,
+            304
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "LayerDrop From the perspective of each word vector, the proposed LengthDrop could be thought of as skipping the layers between when it was set aside and the final layer where it was restored. The word vector however does not have any information based on which it can determine whether it would be dropped at any particular layer. In our preliminary experiments, we found that this greatly hinders optimization. We address this issue by using LayerDrop (Fan et al., 2019) which skips each layer of a transformer uniformly at random. The LayerDrop encourages each word vector to be agnostic to skipping any number of layers between when it is dropped and when it is restored, just like dropout (Srivastava et al., 2014) prevents hidden neurons from co-adapting with each other by randomly dropping them. ",
+        "bbox": [
+            173,
+            318,
+            825,
+            444
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Sandwich Rule and Inplace Distillation We observed that standard supervised training with LengthDrop does not work well in the preliminary experiments. We instead borrow a pair of training techniques developed by Yu & Huang (2019) which are sandwich rule and inplace distillation, for better optimization as well as final generalization. At each update, we update the full model without LengthDrop as usual to minimize the supervised loss function. We simultaneously update $n _ { s }$ randomly-sampled sub-models (which are called sandwiches) and the smallest-possible submodel, which corresponds to keeping only $\\lceil ( 1 - p ) l _ { i } \\rceil$ word vectors at each layer $i$ , using knowledge distillation (Hinton et al., 2015) from the full model. Here, sub-models mean models with length reduction. They are trained to their prediction close to the full model’s prediction (inplace distillation). ",
+        "bbox": [
+            174,
+            457,
+            825,
+            583
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2 EVOLUTIONARY SEARCH OF LENGTH CONFIGURATIONS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            598,
+            604,
+            613
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "After training a Length-Adaptive Transformer with LengthDrop, we search for appropriate length configurations for possible target computational budgets that will be given at inference time. The length configuration determines the model performance in terms of both accuracy and efficiency. In order to search for the optimal length configuration, we propose to use evolutionary search, similarly to Cai et al. (2019) and Wang et al. (2020). This procedure is efficient, as it only requires a single pass through the relatively small validation set for each length configuration, unlike re-training for a new computational budget which requires multiple passes through a significantly larger training set for each budget. ",
+        "bbox": [
+            174,
+            625,
+            825,
+            736
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We initialize the population with constant-ratio configurations. Each configuration is created by $l _ { i + 1 } = \\lceil ( 1 - r ) \\bar { l _ { i } } \\rceil$ for each layer $i$ with $r$ so that the amount of computation within the initial population is uniformly distributed between those of the smallest and full models. At each iteration, we evolve the population to consist only of configurations lie on a newly updated efficiencyaccuracy Pareto frontier by mutation and cross-over. Mutation alters an original length configuration $( l _ { 1 } , \\cdots , l _ { L } )$ to $( l _ { 1 } ^ { \\prime } , \\cdots , l _ { L } ^ { \\prime } )$ by sampling $l _ { i } ^ { \\prime }$ from the uniform distribution $\\bar { \\mathcal { U } } ( l _ { i - 1 } ^ { \\prime } , l _ { i + 1 } )$ with the probability $p _ { m }$ or keeping the original length ${ \\bar { l } } _ { i } ^ { \\prime } = l _ { i }$ , sweeping the layers from $i = 1$ to $i = L$ . Crossover takes two length configurations and averages the lengths at each layer. Both of these operations are performed while ensuring the monotonicity of the lengths over the layers. We repeat this iteration $G$ times, while maintaining $n _ { m }$ mutated configurations and $n _ { c }$ crossover’d configurations. Repeating this procedure pushes the Pareto frontier further to identify the best trade-off between two objectives, efficiency and accuracy, without requiring any continuous relaxation of length configurations nor using a proxy objective function. ",
+        "bbox": [
+            173,
+            743,
+            826,
+            924
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/320388afaf5c944756a7b3f52eddc7583af0fdd53b75f8ac7bf8c3063dd11f2f.jpg",
+        "image_caption": [
+            "Figure 1: Illustration of (a) word-vector elimination process in PoWER-BERT (Goyal et al., 2020) and (b) Drop-and-Restore process in Length-Adaptive Transformer. Yellow box and blue boxes imply the output of embedding layer and transformer layers, respectively. Green boxes mean vectors dropped in lower layers and restored at the last layer. Red box is the task-specific layer. Though word-vectors in the middle could be eliminated (or dropped), remaining vectors are left-aligned for the better illustration. In this case, the number of transformer layers is four. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            194,
+            111,
+            803,
+            198
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3 DROP-AND-RESTORE PROCESS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            314,
+            429,
+            328
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The applicability of the PoWER-BERT, based on which our main contribution above was made, is limited to sequence-level classification, because it eliminates word vectors at each layer. In addition to our main contribution above, we thus propose to extend the PoWER-BERT so that it is applicable to token-level classification, such as span-based question-answering. Our proposal, to which we refer as Drop-and-Restore, does not eliminate word vectors at each layer according to the length configuration but instead sets them aside until the final hidden layer. At the final hidden layer, these word vectors are brought back to form the full hidden sequence, as illustrated graphically in Fig. 1. ",
+        "bbox": [
+            174,
+            340,
+            825,
+            438
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4 EXPERIMENT SETUP ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            459,
+            377,
+            474
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Datasets We test the proposed approach on both sequence-level and token-level tasks, the latter of which could not have been done with the original PoWER-BERT unless for the proposed Dropand-Restore. We use MNLI-m and SST-2 from GLUE benchmark (Wang et al., 2018), as was done to test PoWER-BERT earlier, for sequence-level classification. We choose them because consistent accuracy scores from standard training on them due to their sufficiently large training set imply that they are reliable to verify our approach. We use SQuAD 1.1 (Rajpurkar et al., 2016) for token-level classification. ",
+        "bbox": [
+            174,
+            491,
+            825,
+            588
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Evaluation metrics We use the number of floating operations (FLOPs) as a main metric to measure the inference efficiency given any length configuration, as it is agnostic to the choice of underlying hardware, unlike other alternatives such as hardware-aware latency (Wang et al., 2020) or energy consumption (Henderson et al., 2020). We later demonstrate that FLOPs and wall-clock time on GPU and CPU correlate well with the proposed approach, which is not necessarily the case for other approaches, such as unstructured weight pruning (Han et al., 2015; See et al., 2016). ",
+        "bbox": [
+            174,
+            604,
+            825,
+            689
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Pretrained transformers Since BERT was introduced by Devlin et al. (2018), it has become a standard practice to start from a pretrained (masked) language model and finetune it for each downstream task. We follow the same strategy in this paper and test two pretrained transformerbased language models; BERTBASE (Devlin et al., 2018) and DistilBERT (Sanh et al., 2019), which allows us to demonstrate that the usefulness and applicability of our approach are not tied to any specific architectural choice, such as the number of layers and the maximum length of input sequence. Although we focus on BERT-based masked language models here, the proposed approach is readily applicable to any transformer-based models. ",
+        "bbox": [
+            174,
+            704,
+            825,
+            815
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Learning We train a Length-Adaptive Transformer with LengthDrop probability and LayerDrop probability both set to 0.2. We use $n _ { s } = 2$ randomly sampled intermediate sub-models in addition to the full model and smallest model for applying the sandwich learning rule. ",
+        "bbox": [
+            174,
+            833,
+            825,
+            875
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We start finetuning the pretrained transformer without Drop-and-Restore first, just as Goyal et al. (2020) did with PoWER-BERT. We then continue finetuning it for another five epochs with Drop-andRestore. This is unlike the recommended three epochs by Devlin et al. (2018), as learning progresses slower due to a higher level of stochasticity introduced by LengthDrop and LayerDrop. We use the batch size of 32, the learning rate of $5 e - 5$ for SQuAD v1.1 and $2 e - 5$ for MNLI-m and SST, and the maximum sequence length of 384 for SQuAD v1.1 and 128 for MNLI-m and SST. ",
+        "bbox": [
+            176,
+            882,
+            825,
+            924
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/3ea54ad6f6a4d01240155dd50bd06714bd078c67453a78cfd7ce1b9404ef27c2.jpg",
+        "image_caption": [
+            "Figure 2: Pareto curves of F1 score and FLOPs on SQuAD 1.1 (Rajpurkar et al., 2016). We apply the proposed method to $\\mathbf { B E R T _ { B a s e } }$ (solid lines) and DistilBERT (dotted lines). For each model, we draw three curves using (1) standard finetuned transformer with constant-rate length reduction, (2) Length-Adaptive Transformer with constant-rate length reduction, and (3) Length-Adaptive Transformer with length configurations obtained from the evolutionary search. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            181,
+            99,
+            638,
+            349
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/4608176aa7c7dba0b4748567c1c64abe798b711bebf826c4b323894a4bfb2b12.jpg",
+        "image_caption": [
+            "Figure 3: Correlation between FLOPs and latency with different length configurations. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            666,
+            102,
+            812,
+            375
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            173,
+            473,
+            823,
+            516
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Search We run up to $G = 3 0$ iterations of evolutionary search, using $n _ { m } = 3 0$ mutated configurations with mutation probability $p _ { m } = 0 . 5$ and $n _ { c } = 3 0$ crossover’d configurations, to find the Pareto frontier of accuracy and efficiency. ",
+        "bbox": [
+            174,
+            532,
+            825,
+            575
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5 RESULTS AND ANALYSIS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            595,
+            413,
+            612
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Efficiency-accuracy trade-off We use SQuAD 1.1 to examine the effect of the proposed approach on the efficiency-accuracy trade-off. When the underlying classifier was not trained with LengthDrop, as proposed in this paper, the accuracy drops even more dramatically as more word vectors are dropped at each layer. The difference between standard transformer and Length-Adaptive Transformer is stark in Fig. 2. This verifies the importance of training a transformer in a way that makes it malleable for inference-time re-configuration. ",
+        "bbox": [
+            174,
+            627,
+            825,
+            712
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "When the model was trained with the proposed LengthDrop, we notice the efficacy of the proposed approach of using evolutionary search to find the optimal trade-off between inference efficiency and accuracy. The trade-off curve from the proposed search strategy has a larger area-under-curve (AUC) than when constant-rate length reduction was used to meet a target computational budget. It demonstrates the importance of using both LengthDrop and evolutionary search. ",
+        "bbox": [
+            174,
+            718,
+            825,
+            789
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We make a minor observation that the proposed approach ends up with a significantly higher accuracy than DistillBERT when enough computational budget is allowed for inference $( \\log { \\mathrm { F L O P s } } > 1 0 )$ . This makes our approach desirable in a wide array of scenarios, as it does not require any additional pretraining stage, as does DistilBERT. With a severe constraint on the computational budget, the proposed approach could be used on DistilBERT to significantly improve the efficiency without compromising the accuracy. ",
+        "bbox": [
+            174,
+            795,
+            825,
+            878
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Maximizing inference efficiency We consider all three tasks, SQuAD 1.1, MNLI-m and SST-2, and investigate how much efficiency can be gained by the proposed approach with minimal sacrifice of accuracy. First, we look at how much efficiency could be gained without losing on the accuracy. That is, we use the length configuration that maximizes the inference efficiency (i.e., minimize the FLOPs) while ensuring that the accuracy is above or same as the accuracy of the standard approach without any drop of word vectors. The results are presented in the rows marked with Length-Adaptive† from Table 1. For example, in the case of $\\mathbf { B E R T _ { B a s e } }$ , the proposed approach reduce FLOPs by more than half across all three tasks. ",
+        "bbox": [
+            174,
+            895,
+            821,
+            924
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/f0829b1fbd9636baa6152ad5a45e5f7dbf08c6a7333b2fd362453dfa90284833.jpg",
+        "table_caption": [
+            "Table 1: Comparison results of standard Transformer and LengthAdaptive Transformer. Among length configurations on the Pareto frontier of Length-Adaptive Transformer, we pick two representative points: Length-Adaptive? and Length-Adaptive† as the most efficient one while having the highest accuracy and the accuracy higher than (or equal to) standard Transformer, respectively. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"2\">Model</td><td colspan=\"2\">SQuAD 1.1</td><td colspan=\"2\">MNLI-m</td><td colspan=\"2\">SST-2</td></tr><tr><td>Pretrained Transformer</td><td>Method</td><td>F1</td><td>FLOPs</td><td>Acc</td><td>FLOPs</td><td>Acc</td><td>FLOPs</td></tr><tr><td rowspan=\"2\">BERTBase</td><td>Standard</td><td>88.5</td><td>1.00x</td><td>84.4</td><td>1.00x</td><td>92.8</td><td>1.00x</td></tr><tr><td>Length-Adaptive*</td><td>89.6</td><td>0.89x</td><td>85.0</td><td>0.58x</td><td>93.1</td><td>0.36x</td></tr><tr><td rowspan=\"2\"></td><td>Length-Adaptivet</td><td>88.7</td><td>0.45x</td><td>84.4</td><td>0.35x</td><td>92.8</td><td>0.35x</td></tr><tr><td>Standard</td><td>85.8</td><td>1.00x</td><td>80.9</td><td>1.00x</td><td>90.6</td><td>1.00x</td></tr><tr><td rowspan=\"2\">DistilBERT1</td><td>Length-Adaptive*</td><td>86.3</td><td>0.81x</td><td>81.5</td><td>0.56x</td><td>92.0</td><td>0.55x</td></tr><tr><td>Length-Adaptive†</td><td>85.9</td><td>0.59x</td><td>81.3</td><td>0.54x</td><td>91.7</td><td>0.54x</td></tr></table>",
+        "bbox": [
+            183,
+            101,
+            643,
+            239
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/e4a6ecfc1cdcda5b3130f2509429e44b544d994935e6b44f36893f811295f752.jpg",
+        "image_caption": [
+            "Figure 4: Example of area under Pareto curve as the evolutionary search of lenth configurations proceeds. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            669,
+            108,
+            813,
+            229
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            344,
+            826,
+            429
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "From Fig. 2, we have observed that the proposed Length-Adaptive Transformer generalize better than the standard, base model in some cases. We thus try to maximize both the inference efficiency and accuracy, in order to see whether it is possible for the proposed algorithm to find a length configuration that both maximizes inference efficiency and improves accuracy. We present the results in the rows marked with Length-Adaptive? from Table 1. For all cases, Length-Adaptive Transformer achieves higher accuracy than a standard transformer does while reducing FLOPs significantly. Although it is not apparent from the table, tor MNLI-m and SST-2, the accuracy of the smallest sub-model is already greater than or equal to that of a standard transformer. ",
+        "bbox": [
+            173,
+            435,
+            825,
+            547
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "FLOPs vs. Latency As has been discussed in recent literature (see, e.g., (Li et al., 2020; Chin et al., 2020)), FLOPs is not a perfect indicator of the real latency measured in wall-clock time, as the latter is affected by the combination of hardware choice and network architecture. To understand the real-world impact of the proposed approach, we study the relationship between FLOPs, obtained by the proposed procedure, and wall-clock time measured on both CPU and GPU by measuring them while varying length configurations. As shown in Fig. 3, FLOPs and latency exhibit near-linear correlation on GPU, when the minibatch size is $\\geq 1 6$ , and regardless of the minibatch size, on CPU. In other words, the reduction in FLOPs with the proposed approach directly implies the reduction in wall-clock time. ",
+        "bbox": [
+            174,
+            561,
+            825,
+            688
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Convergence of search Although the proposed approach is efficient in that it requires only one round of training, it needs a separate search stage for each target budget. It is important for evolutionary search to converge quickly in the number of forward sweeps of a validation set. As exemplified in Fig. 4, evolutionary search converges after about fifteen iterations. ",
+        "bbox": [
+            174,
+            703,
+            825,
+            758
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "6 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            779,
+            344,
+            795
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The main purpose of the proposed algorithm is to improve the inference efficiency of a large-scale transformer. This goal has been pursued from various directions, and in this section, we provide a brief overview of these earlier, and some concurrent, attempts in the context of the proposed approach. ",
+        "bbox": [
+            174,
+            810,
+            825,
+            852
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Weight pruning Weight pruning (Han et al., 2015) focuses on reducing the number of parameters which directly reflects the memory footprint of a model and indirectly correlates with inference speed. However, their actual speed-up in runtime is usually not significant, especially while executing a model with parallel computation using GPU devices (Tang et al., 2018; Li et al., 2020). ",
+        "bbox": [
+            176,
+            867,
+            825,
+            924
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Adaptive architecture There are three major axes along which computation can be reduced in a neural network; (1) input size/length, (2) network depth and (3) network width. The proposed approach, based on PoWER-BERT, adaptively reduces the input length as the input sequence is processed by the transformer layers. In our knowledge, Goyal et al. (2020) is the first work in this direction for transformers. More recently, Funnel-Transformer (Dai et al., 2020) and multi-scale transformer language models (Subramanian et al., 2020) also successfully reduce sequence length in the middle and rescale to full length for the final computation. However, their inference complexity is fixed unlike PoWER-BERT because they are not designed for the control of efficiency. ",
+        "bbox": [
+            174,
+            103,
+            825,
+            214
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "LayerDrop (Fan et al., 2019) drops random layers during the training to be robust to pruning inspired by Huang et al. (2016). Word-level adaptive depth in Elbayad et al. (2019) might seemingly resemble with length reduction, but word vectors reached the maximal layer are used for self-attention computation without updating themselves. Escaping a network early (Teerapittayanon et al., 2016; Huang et al., 2017) based on the confidence of the prediction (Xin et al., 2020; Schwartz et al., 2020; Liu et al., 2020) also offers a control over accuracy-efficiency trade-off, but it is difficult to tune a threshold for a desired computational budget because of the example-wise adaptive computation. ",
+        "bbox": [
+            174,
+            222,
+            825,
+            319
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "DynaBERT (Hou et al., 2020) can run at adaptive width (the number of attention heads and intermediate hidden dimension) and depth. Hardware-aware Transformers (Wang et al., 2020) construct a design space with arbitrary encoder-decoder attention and heterogeneous layers in terms of different numbers of layers, attention heads, hidden dimension, and embedding dimension. ",
+        "bbox": [
+            174,
+            327,
+            825,
+            382
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Structured dropout A major innovation we introduce over the existing PoWER-BERT is the use of stochastic, structured regularization to make a transformer robust to the choice of length configuration in the inference time. Rippel et al. (2014) proposes a nested dropout to learn ordered representations. Similar to LengthDrop, it samples an index form a prior distribution and drops all units having a larger index than sampled one. ",
+        "bbox": [
+            174,
+            397,
+            825,
+            467
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Search There have been a series of attempts at finding the optimal network configuration by solving a combinatorial optimization problem. In computer vision, Once-for-All (Cai et al., 2019) use an evolutionary search (Real et al., 2019) to find a better configuration in dimensions of depth, width, kernel size, and resolution given computational budget. Similarly but differently, our evolutionary search is mutli-objective to find length configurations on the Pareto accuracy-efficiency frontier to cope with any possible computational budgets. Moreover, we only change the sequence length of hidden vectors instead of architectural model size like dimensions. ",
+        "bbox": [
+            174,
+            482,
+            825,
+            580
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "7 CONCLUSION AND FUTURE WORK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            601,
+            495,
+            617
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this work, we propose a new framework for training a transformer once and using it for efficient inference under any computational budget. With the help of training with LengthDrop and Drop-andRestore process followed by the evolutionary search, our proposed Length-Adaptive Transformer allows any given transformer models to be used with any inference-time computational budget for both sequence-level and token-level classification tasks. Our experiments, on SQuAD 1.1, MNLI-m and SST-2, have revealed that the proposed algorithmic framework significantly pushes a better Pareto frontier on the trade-off between inference efficiency and accuracy. Furthermore, we have observed that the proposed Length-Adaptive Transformer could achieve up to $3 \\mathbf { x }$ speed-up over the standard transformer without sacrificing accuracy, both in terms of FLOPs and wallclock time. ",
+        "bbox": [
+            174,
+            632,
+            825,
+            757
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Although our approach finds an optimal length configuration of a trained classifier per computational budget, it leaves open a question whether the proposed approach could be further extended to support per-instance length configuration by for instance training a small, auxiliary neural network for each computational budget. Yet another aspect we have not investigated in this paper is the applicability of the proposed approach to sequence generation, such as machine translation. We leave both of these research directions for the future. ",
+        "bbox": [
+            174,
+            765,
+            825,
+            848
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Our approach is effective, as we have shown in this paper, and also quite simple to implement on top of existing language models. We will release our implementation, which is based on HuggingFace’s Transformers library (Wolf et al., 2019), publicly and plan to adapt it for a broader set of transformerbased models and downstream tasks. ",
+        "bbox": [
+            176,
+            854,
+            825,
+            910
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "REFERENCES ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            102,
+            287,
+            117
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Tom B Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al. Language models are few-shot learners. arXiv preprint arXiv:2005.14165, 2020. ",
+        "bbox": [
+            176,
+            126,
+            825,
+            169
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Han Cai, Chuang Gan, and Song Han. Once for all: Train one network and specialize it for efficient deployment. arXiv preprint arXiv:1908.09791, 2019. ",
+        "bbox": [
+            171,
+            179,
+            823,
+            208
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Ting-Wu Chin, Ruizhou Ding, Cha Zhang, and Diana Marculescu. Towards efficient model compression via learned global ranking. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 1518–1528, 2020. ",
+        "bbox": [
+            174,
+            218,
+            823,
+            262
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Zihang Dai, Guokun Lai, Yiming Yang, and Quoc V Le. Funnel-transformer: Filtering out sequential redundancy for efficient language processing. arXiv preprint arXiv:2006.03236, 2020. ",
+        "bbox": [
+            173,
+            272,
+            823,
+            303
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. Bert: Pre-training of deep bidirectional transformers for language understanding. arXiv preprint arXiv:1810.04805, 2018. ",
+        "bbox": [
+            173,
+            311,
+            823,
+            342
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Maha Elbayad, Jiatao Gu, Edouard Grave, and Michael Auli. Depth-adaptive transformer. arXiv preprint arXiv:1910.10073, 2019. ",
+        "bbox": [
+            173,
+            351,
+            823,
+            381
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Angela Fan, Edouard Grave, and Armand Joulin. Reducing transformer depth on demand with structured dropout. arXiv preprint arXiv:1909.11556, 2019. ",
+        "bbox": [
+            169,
+            390,
+            825,
+            420
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Saurabh Goyal, Anamitra Roy Choudhary, Venkatesan Chakaravarthy, Saurabh ManishRaje, Yogish Sabharwal, and Ashish Verma. Power-bert: Accelerating bert inference for classification tasks. arXiv preprint arXiv:2001.08950, 2020. ",
+        "bbox": [
+            176,
+            430,
+            823,
+            473
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Song Han, Huizi Mao, and William J Dally. Deep compression: Compressing deep neural networks with pruning, trained quantization and huffman coding. arXiv preprint arXiv:1510.00149, 2015. ",
+        "bbox": [
+            173,
+            483,
+            821,
+            513
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Peter Henderson, Jieru Hu, Joshua Romoff, Emma Brunskill, Dan Jurafsky, and Joelle Pineau. Towards the systematic reporting of the energy and carbon footprints of machine learning. arXiv preprint arXiv:2002.05651, 2020. ",
+        "bbox": [
+            174,
+            522,
+            823,
+            566
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Geoffrey Hinton, Oriol Vinyals, and Jeff Dean. Distilling the knowledge in a neural network. arXiv preprint arXiv:1503.02531, 2015. ",
+        "bbox": [
+            171,
+            577,
+            823,
+            606
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Lu Hou, Lifeng Shang, Xin Jiang, and Qun Liu. Dynabert: Dynamic bert with adaptive width and depth. arXiv preprint arXiv:2004.04037, 2020. ",
+        "bbox": [
+            171,
+            616,
+            825,
+            645
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Gao Huang, Yu Sun, Zhuang Liu, Daniel Sedra, and Kilian Q Weinberger. Deep networks with stochastic depth. In European conference on computer vision, pp. 646–661. Springer, 2016. ",
+        "bbox": [
+            171,
+            655,
+            823,
+            685
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Gao Huang, Danlu Chen, Tianhong Li, Felix Wu, Laurens van der Maaten, and Kilian Q Weinberger. Multi-scale dense networks for resource efficient image classification. arXiv preprint arXiv:1703.09844, 2017. ",
+        "bbox": [
+            173,
+            695,
+            825,
+            738
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Jared Kaplan, Sam McCandlish, Tom Henighan, Tom B Brown, Benjamin Chess, Rewon Child, Scott Gray, Alec Radford, Jeffrey Wu, and Dario Amodei. Scaling laws for neural language models. arXiv preprint arXiv:2001.08361, 2020. ",
+        "bbox": [
+            171,
+            748,
+            826,
+            791
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Zhuohan Li, Eric Wallace, Sheng Shen, Kevin Lin, Kurt Keutzer, Dan Klein, and Joseph E Gonzalez. Train large, then compress: Rethinking model size for efficient training and inference of transformers. arXiv preprint arXiv:2002.11794, 2020. ",
+        "bbox": [
+            173,
+            803,
+            823,
+            844
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Weijie Liu, Peng Zhou, Zhe Zhao, Zhiruo Wang, Haotang Deng, and Qi Ju. Fastbert: a self-distilling bert with adaptive inference time. arXiv preprint arXiv:2004.02178, 2020. ",
+        "bbox": [
+            171,
+            856,
+            823,
+            885
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Paul Michel, Omer Levy, and Graham Neubig. Are sixteen heads really better than one? In Advances in Neural Information Processing Systems, pp. 14014–14024, 2019. ",
+        "bbox": [
+            173,
+            895,
+            821,
+            924
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Matthew E Peters, Mark Neumann, Mohit Iyyer, Matt Gardner, Christopher Clark, Kenton Lee, and Luke Zettlemoyer. Deep contextualized word representations. arXiv preprint arXiv:1802.05365, 2018. ",
+        "bbox": [
+            176,
+            103,
+            823,
+            146
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Alec Radford, Jeffrey Wu, Rewon Child, David Luan, Dario Amodei, and Ilya Sutskever. Language models are unsupervised multitask learners. OpenAI Blog, 1(8):9, 2019. ",
+        "bbox": [
+            173,
+            154,
+            823,
+            184
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Colin Raffel, Noam Shazeer, Adam Roberts, Katherine Lee, Sharan Narang, Michael Matena, Yanqi Zhou, Wei Li, and Peter J Liu. Exploring the limits of transfer learning with a unified text-to-text transformer. arXiv preprint arXiv:1910.10683, 2019. ",
+        "bbox": [
+            178,
+            191,
+            823,
+            234
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Pranav Rajpurkar, Jian Zhang, Konstantin Lopyrev, and Percy Liang. Squad: $^ { 1 0 0 , 0 0 0 + }$ questions for machine comprehension of text. arXiv preprint arXiv:1606.05250, 2016. ",
+        "bbox": [
+            171,
+            242,
+            825,
+            271
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Esteban Real, Alok Aggarwal, Yanping Huang, and Quoc V Le. Regularized evolution for image classifier architecture search. In Proceedings of the aaai conference on artificial intelligence, volume 33, pp. 4780–4789, 2019. ",
+        "bbox": [
+            176,
+            279,
+            825,
+            321
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Oren Rippel, Michael Gelbart, and Ryan Adams. Learning ordered representations with nested dropout. In International Conference on Machine Learning, pp. 1746–1754, 2014. ",
+        "bbox": [
+            173,
+            329,
+            823,
+            359
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Victor Sanh, Lysandre Debut, Julien Chaumond, and Thomas Wolf. Distilbert, a distilled version of bert: smaller, faster, cheaper and lighter. arXiv preprint arXiv:1910.01108, 2019. ",
+        "bbox": [
+            171,
+            367,
+            823,
+            396
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Roy Schwartz, Jesse Dodge, Noah A Smith, and Oren Etzioni. Green ai. arXiv preprint arXiv:1907.10597, 2019. ",
+        "bbox": [
+            171,
+            404,
+            823,
+            433
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Roy Schwartz, Gabi Stanovsky, Swabha Swayamdipta, Jesse Dodge, and Noah A Smith. The right tool for the job: Matching model and instance complexities. arXiv preprint arXiv:2004.07453, 2020. ",
+        "bbox": [
+            174,
+            440,
+            823,
+            483
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Abigail See, Minh-Thang Luong, and Christopher D Manning. Compression of neural machine translation models via pruning. arXiv preprint arXiv:1606.09274, 2016. ",
+        "bbox": [
+            171,
+            492,
+            823,
+            521
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Mohammad Shoeybi, Mostofa Patwary, Raul Puri, Patrick LeGresley, Jared Casper, and Bryan Catanzaro. Megatron-lm: Training multi-billion parameter language models using gpu model parallelism. arXiv preprint arXiv:1909.08053, 2019. ",
+        "bbox": [
+            178,
+            529,
+            821,
+            571
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov. Dropout: a simple way to prevent neural networks from overfitting. The journal of machine learning research, 15(1):1929–1958, 2014. ",
+        "bbox": [
+            176,
+            579,
+            823,
+            623
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Emma Strubell, Ananya Ganesh, and Andrew McCallum. Energy and policy considerations for deep learning in nlp. arXiv preprint arXiv:1906.02243, 2019. ",
+        "bbox": [
+            169,
+            631,
+            823,
+            660
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Sandeep Subramanian, Ronan Collobert, Marc’Aurelio Ranzato, and Y-Lan Boureau. Multi-scale transformer language models. arXiv preprint arXiv:2005.00581, 2020. ",
+        "bbox": [
+            173,
+            667,
+            823,
+            696
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Siqi Sun, Yu Cheng, Zhe Gan, and Jingjing Liu. Patient knowledge distillation for bert model compression. arXiv preprint arXiv:1908.09355, 2019. ",
+        "bbox": [
+            173,
+            704,
+            823,
+            734
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Raphael Tang, Ashutosh Adhikari, and Jimmy Lin. Flops as a direct optimization objective for learning sparse neural networks. arXiv preprint arXiv:1811.03060, 2018. ",
+        "bbox": [
+            171,
+            742,
+            823,
+            771
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Surat Teerapittayanon, Bradley McDanel, and Hsiang-Tsung Kung. Branchynet: Fast inference via early exiting from deep neural networks. In 2016 23rd International Conference on Pattern Recognition (ICPR), pp. 2464–2469. IEEE, 2016. ",
+        "bbox": [
+            176,
+            780,
+            823,
+            821
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention is all you need. In Advances in neural information processing systems, pp. 5998–6008, 2017. ",
+        "bbox": [
+            174,
+            830,
+            823,
+            873
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Alex Wang, Amanpreet Singh, Julian Michael, Felix Hill, Omer Levy, and Samuel R Bowman. Glue: A multi-task benchmark and analysis platform for natural language understanding. arXiv preprint arXiv:1804.07461, 2018. ",
+        "bbox": [
+            174,
+            882,
+            823,
+            922
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Hanrui Wang, Zhanghao Wu, Zhijian Liu, Han Cai, Ligeng Zhu, Chuang Gan, and Song Han. Hat: Hardware-aware transformers for efficient natural language processing. arXiv preprint arXiv:2005.14187, 2020. ",
+        "bbox": [
+            174,
+            103,
+            825,
+            145
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Thomas Wolf, Lysandre Debut, Victor Sanh, Julien Chaumond, Clement Delangue, Anthony Moi, Pierric Cistac, Tim Rault, Remi Louf, Morgan Funtowicz, et al. Transformers: State-of-the-art ´ natural language processing. arXiv preprint arXiv:1910.03771, 2019. ",
+        "bbox": [
+            174,
+            155,
+            823,
+            198
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Ji Xin, Raphael Tang, Jaejun Lee, Yaoliang Yu, and Jimmy Lin. Deebert: Dynamic early exiting for accelerating bert inference. arXiv preprint arXiv:2004.12993, 2020. ",
+        "bbox": [
+            171,
+            205,
+            825,
+            234
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Zhilin Yang, Zihang Dai, Yiming Yang, Jaime Carbonell, Russ R Salakhutdinov, and Quoc V Le. Xlnet: Generalized autoregressive pretraining for language understanding. In Advances in neural information processing systems, pp. 5754–5764, 2019. ",
+        "bbox": [
+            174,
+            244,
+            823,
+            287
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Jiahui Yu and Thomas S Huang. Universally slimmable networks and improved training techniques. In Proceedings of the IEEE International Conference on Computer Vision, pp. 1803–1811, 2019. ",
+        "bbox": [
+            174,
+            295,
+            823,
+            324
+        ],
+        "page_idx": 10
+    }
+]
\ No newline at end of file
diff --git a/parse/train/tqc8n6oHCtZ/tqc8n6oHCtZ_middle.json b/parse/train/tqc8n6oHCtZ/tqc8n6oHCtZ_middle.json
new file mode 100644
index 0000000000000000000000000000000000000000..b45587731e2f902f49fb6ba6a8beff1c16ab8e59
--- /dev/null
+++ b/parse/train/tqc8n6oHCtZ/tqc8n6oHCtZ_middle.json
@@ -0,0 +1,28224 @@
+{
+    "pdf_info": [
+        {
+            "preproc_blocks": [
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        78,
+                        504,
+                        117
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                79,
+                                505,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        79,
+                                        505,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "LENGTH-ADAPTIVE TRANSFORMER: TRAIN ONCE",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                99,
+                                485,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        99,
+                                        485,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "WITH LENGTH DROP, USE ANYTIME WITH SEARCH",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        112,
+                        138,
+                        244,
+                        159
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                113,
+                                138,
+                                201,
+                                150
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        138,
+                                        201,
+                                        150
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Anonymous authors",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                112,
+                                148,
+                                245,
+                                161
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        112,
+                                        148,
+                                        245,
+                                        161
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Paper under double-blind review",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 2.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        278,
+                        189,
+                        333,
+                        201
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                276,
+                                187,
+                                336,
+                                203
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        276,
+                                        187,
+                                        336,
+                                        203
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ABSTRACT",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        142,
+                        214,
+                        469,
+                        477
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                142,
+                                214,
+                                469,
+                                226
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        214,
+                                        469,
+                                        226
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Although transformers have achieved impressive accuracies in various tasks in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                225,
+                                469,
+                                236
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        225,
+                                        469,
+                                        236
+                                    ],
+                                    "score": 1.0,
+                                    "content": "natural language processing, they often come with a prohibitive computational",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                236,
+                                470,
+                                247
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        236,
+                                        470,
+                                        247
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cost, that prevents their use in scenarios with limited computational resources for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                246,
+                                469,
+                                258
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        246,
+                                        469,
+                                        258
+                                    ],
+                                    "score": 1.0,
+                                    "content": "inference. This need for computational efficiency in inference has been addressed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                257,
+                                469,
+                                269
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        257,
+                                        469,
+                                        269
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by for instance PoWER-BERT (Goyal et al., 2020) which gradually decreases the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                268,
+                                470,
+                                280
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        268,
+                                        470,
+                                        280
+                                    ],
+                                    "score": 1.0,
+                                    "content": "length of a sequence as it is passed through layers. These approaches however",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                279,
+                                470,
+                                291
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        279,
+                                        470,
+                                        291
+                                    ],
+                                    "score": 1.0,
+                                    "content": "often assume that the target computational complexity is known in advance at",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                290,
+                                469,
+                                302
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        290,
+                                        469,
+                                        302
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the time of training. This implies that a separate model must be trained for each",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                302,
+                                469,
+                                313
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        302,
+                                        469,
+                                        313
+                                    ],
+                                    "score": 1.0,
+                                    "content": "inference scenario with its distinct computational budget. In this paper, we extend",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                312,
+                                469,
+                                325
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        312,
+                                        469,
+                                        325
+                                    ],
+                                    "score": 1.0,
+                                    "content": "PoWER-BERT to address this issue of inefficiency and redundancy. The proposed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                323,
+                                469,
+                                335
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        323,
+                                        469,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "extension enables us to train a large-scale transformer, called Length-Adaptive",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                333,
+                                470,
+                                347
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        333,
+                                        470,
+                                        347
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Transformer, once and uses it for various inference scenarios without re-training",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                140,
+                                344,
+                                470,
+                                357
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        140,
+                                        344,
+                                        470,
+                                        357
+                                    ],
+                                    "score": 1.0,
+                                    "content": "it. To do so, we train a transformer with LengthDrop, a structural variant of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                356,
+                                470,
+                                368
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        356,
+                                        470,
+                                        368
+                                    ],
+                                    "score": 1.0,
+                                    "content": "dropout, which stochastically determines the length of a sequence at each layer.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                366,
+                                469,
+                                379
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        366,
+                                        469,
+                                        379
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We then use a multi-objective evolutionary search to find a length configuration",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                378,
+                                470,
+                                390
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        378,
+                                        470,
+                                        390
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that maximizes the accuracy and minimizes the computational complexity under",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                389,
+                                470,
+                                401
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        389,
+                                        470,
+                                        401
+                                    ],
+                                    "score": 1.0,
+                                    "content": "any given computational budget. Additionally, we significantly extend the appli-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                400,
+                                470,
+                                412
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        400,
+                                        470,
+                                        412
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cability of PoWER-BERT beyond sequence-level classification into token-level",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                411,
+                                470,
+                                424
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        411,
+                                        470,
+                                        424
+                                    ],
+                                    "score": 1.0,
+                                    "content": "classification such as span-based question-answering, by introducing the idea of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                421,
+                                470,
+                                434
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        421,
+                                        470,
+                                        434
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Drop-and-Restore. With Drop-and-Restore, word-vectors are dropped temporarily",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                432,
+                                469,
+                                446
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        432,
+                                        469,
+                                        446
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in intermediate layers and restored at the last layer if necessary. We empirically",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                443,
+                                470,
+                                457
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        443,
+                                        470,
+                                        457
+                                    ],
+                                    "score": 1.0,
+                                    "content": "verify the utility of the proposed approach by demonstrating the superior accuracy-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                455,
+                                470,
+                                466
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        455,
+                                        470,
+                                        466
+                                    ],
+                                    "score": 1.0,
+                                    "content": "efficiency trade-off under various setups, including SQuAD 1.1, MNLI-m, and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                465,
+                                462,
+                                478
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        465,
+                                        462,
+                                        478
+                                    ],
+                                    "score": 1.0,
+                                    "content": "SST-2. Upon publication, the code to reproduce our work will be open-sourced.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 16.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        497,
+                        206,
+                        510
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                496,
+                                208,
+                                513
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        496,
+                                        208,
+                                        513
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1 INTRODUCTION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 29
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        522,
+                        506,
+                        610
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                521,
+                                506,
+                                535
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        521,
+                                        506,
+                                        535
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Pretrained language models (Peters et al., 2018; Devlin et al., 2018; Radford et al., 2019; Yang et al.,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                532,
+                                506,
+                                547
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        532,
+                                        506,
+                                        547
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2019) have achieved notable improvements in various natural language processing (NLP) tasks. Most",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                543,
+                                506,
+                                558
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        543,
+                                        506,
+                                        558
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of them rely on transformers (Vaswani et al., 2017), and the number of model parameters ranges",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                555,
+                                506,
+                                567
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        555,
+                                        506,
+                                        567
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from hundreds of millions to billions (Shoeybi et al., 2019; Raffel et al., 2019; Kaplan et al., 2020;",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                565,
+                                507,
+                                579
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        565,
+                                        507,
+                                        579
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Brown et al., 2020). Despite this high accuracy, excessive computational overhead during inference,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                577,
+                                506,
+                                589
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        577,
+                                        506,
+                                        589
+                                    ],
+                                    "score": 1.0,
+                                    "content": "both in terms of time and memory, has hindered its use in real applications. This level of excessive",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                588,
+                                506,
+                                600
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        588,
+                                        506,
+                                        600
+                                    ],
+                                    "score": 1.0,
+                                    "content": "computation has further raised the concern over energy consumption as well (Schwartz et al., 2019;",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                599,
+                                193,
+                                611
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        599,
+                                        193,
+                                        611
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Strubell et al., 2019).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 33.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        616,
+                        505,
+                        704
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                615,
+                                507,
+                                630
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        615,
+                                        507,
+                                        630
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Recent studies have attempted at addressing these concerns regarding large-scale transformers’",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                627,
+                                505,
+                                639
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        627,
+                                        277,
+                                        639
+                                    ],
+                                    "score": 1.0,
+                                    "content": "computational and energy efficiency (see",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        278,
+                                        627,
+                                        289,
+                                        639
+                                    ],
+                                    "score": 0.62,
+                                    "content": "\\ S 6",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        290,
+                                        627,
+                                        505,
+                                        639
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for a more extensive discussion.) Among these, we",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                637,
+                                505,
+                                651
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        637,
+                                        505,
+                                        651
+                                    ],
+                                    "score": 1.0,
+                                    "content": "focus on PoWER-BERT (Goyal et al., 2020) which progressively reduces sequence length by",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                648,
+                                506,
+                                661
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        648,
+                                        506,
+                                        661
+                                    ],
+                                    "score": 1.0,
+                                    "content": "eliminating word-vectors based on the attention values as passing layers. PoWER-BERT establishes",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                660,
+                                506,
+                                672
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        660,
+                                        506,
+                                        672
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the superiority of accuracy-time trade-off over earlier approaches (Sanh et al., 2019; Sun et al., 2019;",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                670,
+                                507,
+                                684
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        670,
+                                        507,
+                                        684
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Michel et al., 2019). It however requires us to train a separate model for each efficiency constraint.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                681,
+                                506,
+                                695
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        681,
+                                        506,
+                                        695
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In this paper, we thus develop a framework based on PoWER-BERT such that we can train a single",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                692,
+                                439,
+                                706
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        692,
+                                        439,
+                                        706
+                                    ],
+                                    "score": 1.0,
+                                    "content": "model that can be adapted in the inference time to meet any given efficiency target.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        }
+                    ],
+                    "index": 41.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        709,
+                        503,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                709,
+                                505,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        709,
+                                        505,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In order to train a transformer to cope with a diverse set of computational budgets in the inference",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                721,
+                                504,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        721,
+                                        504,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "time, we propose to train one while reducing the sequence length with a random proportion at each",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        }
+                    ],
+                    "index": 46.5
+                }
+            ],
+            "page_idx": 0,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        751,
+                        308,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                302,
+                                751,
+                                308,
+                                761
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        302,
+                                        751,
+                                        308,
+                                        761
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        307,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                308,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        308,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Under review as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        78,
+                        504,
+                        117
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                79,
+                                505,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        79,
+                                        505,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "LENGTH-ADAPTIVE TRANSFORMER: TRAIN ONCE",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                99,
+                                485,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        99,
+                                        485,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "WITH LENGTH DROP, USE ANYTIME WITH SEARCH",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        112,
+                        138,
+                        244,
+                        159
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                113,
+                                138,
+                                201,
+                                150
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        138,
+                                        201,
+                                        150
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Anonymous authors",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                112,
+                                148,
+                                245,
+                                161
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        112,
+                                        148,
+                                        245,
+                                        161
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Paper under double-blind review",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 2.5,
+                    "bbox_fs": [
+                        112,
+                        138,
+                        245,
+                        161
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        278,
+                        189,
+                        333,
+                        201
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                276,
+                                187,
+                                336,
+                                203
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        276,
+                                        187,
+                                        336,
+                                        203
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ABSTRACT",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        142,
+                        214,
+                        469,
+                        477
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                142,
+                                214,
+                                469,
+                                226
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        214,
+                                        469,
+                                        226
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Although transformers have achieved impressive accuracies in various tasks in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                225,
+                                469,
+                                236
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        225,
+                                        469,
+                                        236
+                                    ],
+                                    "score": 1.0,
+                                    "content": "natural language processing, they often come with a prohibitive computational",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                236,
+                                470,
+                                247
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        236,
+                                        470,
+                                        247
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cost, that prevents their use in scenarios with limited computational resources for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                246,
+                                469,
+                                258
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        246,
+                                        469,
+                                        258
+                                    ],
+                                    "score": 1.0,
+                                    "content": "inference. This need for computational efficiency in inference has been addressed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                257,
+                                469,
+                                269
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        257,
+                                        469,
+                                        269
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by for instance PoWER-BERT (Goyal et al., 2020) which gradually decreases the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                268,
+                                470,
+                                280
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        268,
+                                        470,
+                                        280
+                                    ],
+                                    "score": 1.0,
+                                    "content": "length of a sequence as it is passed through layers. These approaches however",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                279,
+                                470,
+                                291
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        279,
+                                        470,
+                                        291
+                                    ],
+                                    "score": 1.0,
+                                    "content": "often assume that the target computational complexity is known in advance at",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                290,
+                                469,
+                                302
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        290,
+                                        469,
+                                        302
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the time of training. This implies that a separate model must be trained for each",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                302,
+                                469,
+                                313
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        302,
+                                        469,
+                                        313
+                                    ],
+                                    "score": 1.0,
+                                    "content": "inference scenario with its distinct computational budget. In this paper, we extend",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                312,
+                                469,
+                                325
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        312,
+                                        469,
+                                        325
+                                    ],
+                                    "score": 1.0,
+                                    "content": "PoWER-BERT to address this issue of inefficiency and redundancy. The proposed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                323,
+                                469,
+                                335
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        323,
+                                        469,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "extension enables us to train a large-scale transformer, called Length-Adaptive",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                333,
+                                470,
+                                347
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        333,
+                                        470,
+                                        347
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Transformer, once and uses it for various inference scenarios without re-training",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                140,
+                                344,
+                                470,
+                                357
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        140,
+                                        344,
+                                        470,
+                                        357
+                                    ],
+                                    "score": 1.0,
+                                    "content": "it. To do so, we train a transformer with LengthDrop, a structural variant of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                356,
+                                470,
+                                368
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        356,
+                                        470,
+                                        368
+                                    ],
+                                    "score": 1.0,
+                                    "content": "dropout, which stochastically determines the length of a sequence at each layer.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                366,
+                                469,
+                                379
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        366,
+                                        469,
+                                        379
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We then use a multi-objective evolutionary search to find a length configuration",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                378,
+                                470,
+                                390
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        378,
+                                        470,
+                                        390
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that maximizes the accuracy and minimizes the computational complexity under",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                389,
+                                470,
+                                401
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        389,
+                                        470,
+                                        401
+                                    ],
+                                    "score": 1.0,
+                                    "content": "any given computational budget. Additionally, we significantly extend the appli-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                400,
+                                470,
+                                412
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        400,
+                                        470,
+                                        412
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cability of PoWER-BERT beyond sequence-level classification into token-level",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                411,
+                                470,
+                                424
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        411,
+                                        470,
+                                        424
+                                    ],
+                                    "score": 1.0,
+                                    "content": "classification such as span-based question-answering, by introducing the idea of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                421,
+                                470,
+                                434
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        421,
+                                        470,
+                                        434
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Drop-and-Restore. With Drop-and-Restore, word-vectors are dropped temporarily",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                432,
+                                469,
+                                446
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        432,
+                                        469,
+                                        446
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in intermediate layers and restored at the last layer if necessary. We empirically",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                141,
+                                443,
+                                470,
+                                457
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        141,
+                                        443,
+                                        470,
+                                        457
+                                    ],
+                                    "score": 1.0,
+                                    "content": "verify the utility of the proposed approach by demonstrating the superior accuracy-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                455,
+                                470,
+                                466
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        455,
+                                        470,
+                                        466
+                                    ],
+                                    "score": 1.0,
+                                    "content": "efficiency trade-off under various setups, including SQuAD 1.1, MNLI-m, and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                142,
+                                465,
+                                462,
+                                478
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        465,
+                                        462,
+                                        478
+                                    ],
+                                    "score": 1.0,
+                                    "content": "SST-2. Upon publication, the code to reproduce our work will be open-sourced.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 16.5,
+                    "bbox_fs": [
+                        140,
+                        214,
+                        470,
+                        478
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        497,
+                        206,
+                        510
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                496,
+                                208,
+                                513
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        496,
+                                        208,
+                                        513
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1 INTRODUCTION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 29
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        522,
+                        506,
+                        610
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                521,
+                                506,
+                                535
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        521,
+                                        506,
+                                        535
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Pretrained language models (Peters et al., 2018; Devlin et al., 2018; Radford et al., 2019; Yang et al.,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                532,
+                                506,
+                                547
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        532,
+                                        506,
+                                        547
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2019) have achieved notable improvements in various natural language processing (NLP) tasks. Most",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                543,
+                                506,
+                                558
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        543,
+                                        506,
+                                        558
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of them rely on transformers (Vaswani et al., 2017), and the number of model parameters ranges",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                555,
+                                506,
+                                567
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        555,
+                                        506,
+                                        567
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from hundreds of millions to billions (Shoeybi et al., 2019; Raffel et al., 2019; Kaplan et al., 2020;",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                565,
+                                507,
+                                579
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        565,
+                                        507,
+                                        579
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Brown et al., 2020). Despite this high accuracy, excessive computational overhead during inference,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                577,
+                                506,
+                                589
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        577,
+                                        506,
+                                        589
+                                    ],
+                                    "score": 1.0,
+                                    "content": "both in terms of time and memory, has hindered its use in real applications. This level of excessive",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                588,
+                                506,
+                                600
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        588,
+                                        506,
+                                        600
+                                    ],
+                                    "score": 1.0,
+                                    "content": "computation has further raised the concern over energy consumption as well (Schwartz et al., 2019;",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                599,
+                                193,
+                                611
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        599,
+                                        193,
+                                        611
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Strubell et al., 2019).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 33.5,
+                    "bbox_fs": [
+                        104,
+                        521,
+                        507,
+                        611
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        616,
+                        505,
+                        704
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                615,
+                                507,
+                                630
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        615,
+                                        507,
+                                        630
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Recent studies have attempted at addressing these concerns regarding large-scale transformers’",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                627,
+                                505,
+                                639
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        627,
+                                        277,
+                                        639
+                                    ],
+                                    "score": 1.0,
+                                    "content": "computational and energy efficiency (see",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        278,
+                                        627,
+                                        289,
+                                        639
+                                    ],
+                                    "score": 0.62,
+                                    "content": "\\ S 6",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        290,
+                                        627,
+                                        505,
+                                        639
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for a more extensive discussion.) Among these, we",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                637,
+                                505,
+                                651
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        637,
+                                        505,
+                                        651
+                                    ],
+                                    "score": 1.0,
+                                    "content": "focus on PoWER-BERT (Goyal et al., 2020) which progressively reduces sequence length by",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                648,
+                                506,
+                                661
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        648,
+                                        506,
+                                        661
+                                    ],
+                                    "score": 1.0,
+                                    "content": "eliminating word-vectors based on the attention values as passing layers. PoWER-BERT establishes",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                660,
+                                506,
+                                672
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        660,
+                                        506,
+                                        672
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the superiority of accuracy-time trade-off over earlier approaches (Sanh et al., 2019; Sun et al., 2019;",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                670,
+                                507,
+                                684
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        670,
+                                        507,
+                                        684
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Michel et al., 2019). It however requires us to train a separate model for each efficiency constraint.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                681,
+                                506,
+                                695
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        681,
+                                        506,
+                                        695
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In this paper, we thus develop a framework based on PoWER-BERT such that we can train a single",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                692,
+                                439,
+                                706
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        692,
+                                        439,
+                                        706
+                                    ],
+                                    "score": 1.0,
+                                    "content": "model that can be adapted in the inference time to meet any given efficiency target.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        }
+                    ],
+                    "index": 41.5,
+                    "bbox_fs": [
+                        105,
+                        615,
+                        507,
+                        706
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        709,
+                        503,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                709,
+                                505,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        709,
+                                        505,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In order to train a transformer to cope with a diverse set of computational budgets in the inference",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                721,
+                                504,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        721,
+                                        504,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "time, we propose to train one while reducing the sequence length with a random proportion at each",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                82,
+                                505,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        82,
+                                        505,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "layer. We refer to this procedure as LengthDrop which was motivated by the nested dropout (Rippel",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                93,
+                                505,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        93,
+                                        505,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "et al., 2014). We can extract sub-models of shared weights with any length configuration without",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                105,
+                                336,
+                                118
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        105,
+                                        336,
+                                        118
+                                    ],
+                                    "score": 1.0,
+                                    "content": "requiring extra post-processing nor additional finetuning.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 46.5,
+                    "bbox_fs": [
+                        105,
+                        709,
+                        505,
+                        732
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        82,
+                        504,
+                        116
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                82,
+                                505,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        82,
+                                        505,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "layer. We refer to this procedure as LengthDrop which was motivated by the nested dropout (Rippel",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                93,
+                                505,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        93,
+                                        505,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "et al., 2014). We can extract sub-models of shared weights with any length configuration without",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                105,
+                                336,
+                                118
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        105,
+                                        336,
+                                        118
+                                    ],
+                                    "score": 1.0,
+                                    "content": "requiring extra post-processing nor additional finetuning.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        121,
+                        504,
+                        165
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                121,
+                                506,
+                                134
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        121,
+                                        506,
+                                        134
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Once a transformer is trained with the proposed LengthDrop, we search for the length configuration",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                132,
+                                506,
+                                145
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        132,
+                                        506,
+                                        145
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that maximizes the accuracy given a computational budget. Because this search is combinatorial and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                143,
+                                506,
+                                156
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        143,
+                                        506,
+                                        156
+                                    ],
+                                    "score": 1.0,
+                                    "content": "has multiple objectives (accuracy and efficiency), we use an evolutionary search algorithm, which",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                154,
+                                486,
+                                166
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        154,
+                                        486,
+                                        166
+                                    ],
+                                    "score": 1.0,
+                                    "content": "further allows us to obtain a full Pareto frontier of accuracy-efficiency trade-off of each model.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 4.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        171,
+                        505,
+                        237
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                170,
+                                506,
+                                184
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        170,
+                                        506,
+                                        184
+                                    ],
+                                    "score": 1.0,
+                                    "content": "It is not trivial to find an optimal length configuration given the inference-time computational budget,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                182,
+                                506,
+                                195
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        182,
+                                        506,
+                                        195
+                                    ],
+                                    "score": 1.0,
+                                    "content": "although it is extremely important in order to deploy these large-scale transformers in practice. In",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                193,
+                                506,
+                                206
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        193,
+                                        506,
+                                        206
+                                    ],
+                                    "score": 1.0,
+                                    "content": "this work, we propose to use evolutionary search to find a length configuration that maximizes",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                204,
+                                506,
+                                217
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        204,
+                                        506,
+                                        217
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the accuracy within a given computational budget. We can further compute the Pareto frontier of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                214,
+                                505,
+                                229
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        214,
+                                        505,
+                                        229
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accuracy-efficiency trade-off to obtain a sequence of length configurations with varying efficiency",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                226,
+                                142,
+                                239
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        226,
+                                        142,
+                                        239
+                                    ],
+                                    "score": 1.0,
+                                    "content": "profiles.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "index": 9.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        243,
+                        505,
+                        342
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                243,
+                                505,
+                                256
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        243,
+                                        505,
+                                        256
+                                    ],
+                                    "score": 1.0,
+                                    "content": "PoWER-BERT, which forms the foundation of the proposed two-stage procedure, is only applicable",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                254,
+                                505,
+                                266
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        254,
+                                        505,
+                                        266
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to sequence-level classification, because by design it eliminates some of the word vectors at each",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                264,
+                                506,
+                                279
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        264,
+                                        506,
+                                        279
+                                    ],
+                                    "score": 1.0,
+                                    "content": "layer. In other words, it cannot be used for token-level tasks such as span-based question answering",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                275,
+                                505,
+                                290
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        275,
+                                        505,
+                                        290
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(Rajpurkar et al., 2016), because these tasks require hidden representations of the entire input sequence",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                286,
+                                505,
+                                300
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        286,
+                                        505,
+                                        300
+                                    ],
+                                    "score": 1.0,
+                                    "content": "at the final layer. We thus propose to extend PoWER-BERT with a novel Drop-and-Restore process",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                298,
+                                505,
+                                310
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        298,
+                                        505,
+                                        310
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(§3.3), which eliminates this inherent limitation. Word vectors are dropped and set aside, rather",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                308,
+                                505,
+                                321
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        308,
+                                        505,
+                                        321
+                                    ],
+                                    "score": 1.0,
+                                    "content": "than eliminated, in intermediate layers to maintain the saving of computational cost, as was with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                320,
+                                505,
+                                332
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        320,
+                                        505,
+                                        332
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the original PoWER-BERT. These set-aside vectors are then restored at the final hidden layer and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                330,
+                                506,
+                                343
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        330,
+                                        506,
+                                        343
+                                    ],
+                                    "score": 1.0,
+                                    "content": "provided as an input to a subsequent task-specific layer, which is unlike the original PoWER-BERT.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        347,
+                        505,
+                        468
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                347,
+                                505,
+                                360
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        347,
+                                        505,
+                                        360
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The main contributions of this work are two-fold. First, we introduce LengthDrop, a structured",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                359,
+                                506,
+                                371
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        359,
+                                        506,
+                                        371
+                                    ],
+                                    "score": 1.0,
+                                    "content": "variant of dropout for training a single Length-Adaptive Transformer model that allows us to au-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                370,
+                                505,
+                                382
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        370,
+                                        505,
+                                        382
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tomatically derive multiple sub-models with different length configurations in the inference time",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                381,
+                                506,
+                                393
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        381,
+                                        506,
+                                        393
+                                    ],
+                                    "score": 1.0,
+                                    "content": "using evolutionary search, without requiring any re-training. Second, we design Drop-and-Restore",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                390,
+                                506,
+                                405
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        390,
+                                        506,
+                                        405
+                                    ],
+                                    "score": 1.0,
+                                    "content": "process that makes PoWER-BERT applicable beyond classification, which enables PoWER-BERT to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                403,
+                                505,
+                                415
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        403,
+                                        505,
+                                        415
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be applicable to a wider range of NLP tasks such as span-based question answering. We empirically",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                414,
+                                506,
+                                426
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        414,
+                                        506,
+                                        426
+                                    ],
+                                    "score": 1.0,
+                                    "content": "verify Length-Adaptive Transformer works quite well using the variants of BERT on a diverse set of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                424,
+                                505,
+                                437
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        424,
+                                        505,
+                                        437
+                                    ],
+                                    "score": 1.0,
+                                    "content": "NLP tasks, including SQuAD 1.1 (Rajpurkar et al., 2016) and two sequence-level classification tasks",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                435,
+                                505,
+                                448
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        435,
+                                        505,
+                                        448
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in GLUE benchmark (Wang et al., 2018). Our experiments reveal that the proposed approach grants",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                446,
+                                506,
+                                460
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        446,
+                                        506,
+                                        460
+                                    ],
+                                    "score": 1.0,
+                                    "content": "us a fine-grained control of computational efficiency and a superior accuracy-efficiency trade-off in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                458,
+                                319,
+                                469
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        458,
+                                        319,
+                                        469
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the inference time, compared to existing approaches.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 27
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        484,
+                        399,
+                        497
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                484,
+                                401,
+                                499
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        484,
+                                        401,
+                                        499
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2 BACKGROUND: TRANSFORMERS AND POWER-BERT",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 33
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        510,
+                        505,
+                        554
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                510,
+                                505,
+                                522
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        510,
+                                        505,
+                                        522
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Before we describe our main approach, we review some of the building blocks in this section. In",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                520,
+                                505,
+                                534
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        520,
+                                        505,
+                                        534
+                                    ],
+                                    "score": 1.0,
+                                    "content": "particular, we review transformers, which are a standard backbone used in natural language processing",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                531,
+                                507,
+                                545
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        531,
+                                        507,
+                                        545
+                                    ],
+                                    "score": 1.0,
+                                    "content": "these days, and PoWER-BERT, which was recently proposed as an effective way to train a large-scale,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                543,
+                                366,
+                                555
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        543,
+                                        366,
+                                        555
+                                    ],
+                                    "score": 1.0,
+                                    "content": "but highly efficient transformer for sequence-level classification.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 35.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        567,
+                        253,
+                        578
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                567,
+                                254,
+                                580
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        567,
+                                        254,
+                                        580
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2.1 TRANSFORMERS AND BERT",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        }
+                    ],
+                    "index": 38
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        588,
+                        505,
+                        632
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                588,
+                                504,
+                                599
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        588,
+                                        504,
+                                        599
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A transformer is a particular neural network that has been designed to work with a variable-length",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                599,
+                                505,
+                                611
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        599,
+                                        505,
+                                        611
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sequence input and is implemented as a stack of self-attention and fully-connected layers (Vaswani",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                610,
+                                506,
+                                623
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        610,
+                                        506,
+                                        623
+                                    ],
+                                    "score": 1.0,
+                                    "content": "et al., 2017). Here, we give a brief overview of the transformer which is the basic building block of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                622,
+                                201,
+                                633
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        622,
+                                        201,
+                                        633
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the proposed approach.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        }
+                    ],
+                    "index": 40.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        637,
+                        505,
+                        704
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                637,
+                                505,
+                                651
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        637,
+                                        155,
+                                        651
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Each token",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        155,
+                                        640,
+                                        166,
+                                        649
+                                    ],
+                                    "score": 0.84,
+                                    "content": "x _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        166,
+                                        637,
+                                        268,
+                                        651
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in a sequence of tokens",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        269,
+                                        638,
+                                        344,
+                                        650
+                                    ],
+                                    "score": 0.91,
+                                    "content": "{ \\boldsymbol x } = ( x _ { 1 } , \\dots , x _ { N } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        345,
+                                        637,
+                                        505,
+                                        651
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", representing input text, is first turned",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                646,
+                                507,
+                                662
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        646,
+                                        208,
+                                        662
+                                    ],
+                                    "score": 1.0,
+                                    "content": "into a continuous vector",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        208,
+                                        648,
+                                        246,
+                                        660
+                                    ],
+                                    "score": 0.93,
+                                    "content": "h _ { t } ^ { 0 } \\in \\mathbb { R } ^ { H }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        247,
+                                        646,
+                                        507,
+                                        662
+                                    ],
+                                    "score": 1.0,
+                                    "content": "which is the sum of the token and position embedding vectors.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                659,
+                                505,
+                                673
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        659,
+                                        505,
+                                        673
+                                    ],
+                                    "score": 1.0,
+                                    "content": "This sequence is fed into the first transformer layer which returns another sequence of the same",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                667,
+                                507,
+                                685
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        667,
+                                        135,
+                                        685
+                                    ],
+                                    "score": 1.0,
+                                    "content": "length",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        135,
+                                        670,
+                                        187,
+                                        681
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\dot { h ^ { 1 } } \\in \\mathbb { R } ^ { N \\times H }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        188,
+                                        667,
+                                        297,
+                                        685
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". We repeat this procedure",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        297,
+                                        671,
+                                        306,
+                                        681
+                                    ],
+                                    "score": 0.81,
+                                    "content": "L",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        667,
+                                        427,
+                                        685
+                                    ],
+                                    "score": 1.0,
+                                    "content": "times, for a transformer with",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        427,
+                                        671,
+                                        435,
+                                        681
+                                    ],
+                                    "score": 0.75,
+                                    "content": "L",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        436,
+                                        667,
+                                        507,
+                                        685
+                                    ],
+                                    "score": 1.0,
+                                    "content": "layers, to obtain",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                679,
+                                506,
+                                696
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        681,
+                                        188,
+                                        694
+                                    ],
+                                    "score": 0.89,
+                                    "content": "h ^ { L } = ( h _ { 1 } ^ { L } , \\ldots , h _ { N } ^ { L } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        188,
+                                        679,
+                                        506,
+                                        696
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". We refer to each vector in the hidden sequence at each layer as a word vector to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                692,
+                                504,
+                                705
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        692,
+                                        504,
+                                        705
+                                    ],
+                                    "score": 1.0,
+                                    "content": "emphasize that there exists a correspondence between each such vector and one of the input words.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        }
+                    ],
+                    "index": 45.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        709,
+                        504,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                710,
+                                506,
+                                721
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        710,
+                                        506,
+                                        721
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Although the transformer was first introduced for the problem of machine translation, Devlin et al.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                720,
+                                506,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        720,
+                                        506,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(2018) demonstrated that the transformer can be trained and used as a masked language model.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50
+                        }
+                    ],
+                    "index": 49.5
+                }
+            ],
+            "page_idx": 1,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        108,
+                        27,
+                        306,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                308,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        308,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Under review as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        751,
+                        309,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                301,
+                                750,
+                                310,
+                                763
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        301,
+                                        750,
+                                        310,
+                                        763
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        82,
+                        504,
+                        116
+                    ],
+                    "lines": [],
+                    "index": 1,
+                    "bbox_fs": [
+                        105,
+                        82,
+                        505,
+                        118
+                    ],
+                    "lines_deleted": true
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        121,
+                        504,
+                        165
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                121,
+                                506,
+                                134
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        121,
+                                        506,
+                                        134
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Once a transformer is trained with the proposed LengthDrop, we search for the length configuration",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                132,
+                                506,
+                                145
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        132,
+                                        506,
+                                        145
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that maximizes the accuracy given a computational budget. Because this search is combinatorial and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                143,
+                                506,
+                                156
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        143,
+                                        506,
+                                        156
+                                    ],
+                                    "score": 1.0,
+                                    "content": "has multiple objectives (accuracy and efficiency), we use an evolutionary search algorithm, which",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                154,
+                                486,
+                                166
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        154,
+                                        486,
+                                        166
+                                    ],
+                                    "score": 1.0,
+                                    "content": "further allows us to obtain a full Pareto frontier of accuracy-efficiency trade-off of each model.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 4.5,
+                    "bbox_fs": [
+                        105,
+                        121,
+                        506,
+                        166
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        171,
+                        505,
+                        237
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                170,
+                                506,
+                                184
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        170,
+                                        506,
+                                        184
+                                    ],
+                                    "score": 1.0,
+                                    "content": "It is not trivial to find an optimal length configuration given the inference-time computational budget,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                182,
+                                506,
+                                195
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        182,
+                                        506,
+                                        195
+                                    ],
+                                    "score": 1.0,
+                                    "content": "although it is extremely important in order to deploy these large-scale transformers in practice. In",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                193,
+                                506,
+                                206
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        193,
+                                        506,
+                                        206
+                                    ],
+                                    "score": 1.0,
+                                    "content": "this work, we propose to use evolutionary search to find a length configuration that maximizes",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                204,
+                                506,
+                                217
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        204,
+                                        506,
+                                        217
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the accuracy within a given computational budget. We can further compute the Pareto frontier of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                214,
+                                505,
+                                229
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        214,
+                                        505,
+                                        229
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accuracy-efficiency trade-off to obtain a sequence of length configurations with varying efficiency",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                226,
+                                142,
+                                239
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        226,
+                                        142,
+                                        239
+                                    ],
+                                    "score": 1.0,
+                                    "content": "profiles.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "index": 9.5,
+                    "bbox_fs": [
+                        104,
+                        170,
+                        506,
+                        239
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        243,
+                        505,
+                        342
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                243,
+                                505,
+                                256
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        243,
+                                        505,
+                                        256
+                                    ],
+                                    "score": 1.0,
+                                    "content": "PoWER-BERT, which forms the foundation of the proposed two-stage procedure, is only applicable",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                254,
+                                505,
+                                266
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        254,
+                                        505,
+                                        266
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to sequence-level classification, because by design it eliminates some of the word vectors at each",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                264,
+                                506,
+                                279
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        264,
+                                        506,
+                                        279
+                                    ],
+                                    "score": 1.0,
+                                    "content": "layer. In other words, it cannot be used for token-level tasks such as span-based question answering",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                275,
+                                505,
+                                290
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        275,
+                                        505,
+                                        290
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(Rajpurkar et al., 2016), because these tasks require hidden representations of the entire input sequence",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                286,
+                                505,
+                                300
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        286,
+                                        505,
+                                        300
+                                    ],
+                                    "score": 1.0,
+                                    "content": "at the final layer. We thus propose to extend PoWER-BERT with a novel Drop-and-Restore process",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                298,
+                                505,
+                                310
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        298,
+                                        505,
+                                        310
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(§3.3), which eliminates this inherent limitation. Word vectors are dropped and set aside, rather",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                308,
+                                505,
+                                321
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        308,
+                                        505,
+                                        321
+                                    ],
+                                    "score": 1.0,
+                                    "content": "than eliminated, in intermediate layers to maintain the saving of computational cost, as was with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                320,
+                                505,
+                                332
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        320,
+                                        505,
+                                        332
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the original PoWER-BERT. These set-aside vectors are then restored at the final hidden layer and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                330,
+                                506,
+                                343
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        330,
+                                        506,
+                                        343
+                                    ],
+                                    "score": 1.0,
+                                    "content": "provided as an input to a subsequent task-specific layer, which is unlike the original PoWER-BERT.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 17,
+                    "bbox_fs": [
+                        105,
+                        243,
+                        506,
+                        343
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        347,
+                        505,
+                        468
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                347,
+                                505,
+                                360
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        347,
+                                        505,
+                                        360
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The main contributions of this work are two-fold. First, we introduce LengthDrop, a structured",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                359,
+                                506,
+                                371
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        359,
+                                        506,
+                                        371
+                                    ],
+                                    "score": 1.0,
+                                    "content": "variant of dropout for training a single Length-Adaptive Transformer model that allows us to au-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                370,
+                                505,
+                                382
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        370,
+                                        505,
+                                        382
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tomatically derive multiple sub-models with different length configurations in the inference time",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                381,
+                                506,
+                                393
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        381,
+                                        506,
+                                        393
+                                    ],
+                                    "score": 1.0,
+                                    "content": "using evolutionary search, without requiring any re-training. Second, we design Drop-and-Restore",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                390,
+                                506,
+                                405
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        390,
+                                        506,
+                                        405
+                                    ],
+                                    "score": 1.0,
+                                    "content": "process that makes PoWER-BERT applicable beyond classification, which enables PoWER-BERT to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                403,
+                                505,
+                                415
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        403,
+                                        505,
+                                        415
+                                    ],
+                                    "score": 1.0,
+                                    "content": "be applicable to a wider range of NLP tasks such as span-based question answering. We empirically",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                414,
+                                506,
+                                426
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        414,
+                                        506,
+                                        426
+                                    ],
+                                    "score": 1.0,
+                                    "content": "verify Length-Adaptive Transformer works quite well using the variants of BERT on a diverse set of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                424,
+                                505,
+                                437
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        424,
+                                        505,
+                                        437
+                                    ],
+                                    "score": 1.0,
+                                    "content": "NLP tasks, including SQuAD 1.1 (Rajpurkar et al., 2016) and two sequence-level classification tasks",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                435,
+                                505,
+                                448
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        435,
+                                        505,
+                                        448
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in GLUE benchmark (Wang et al., 2018). Our experiments reveal that the proposed approach grants",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                446,
+                                506,
+                                460
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        446,
+                                        506,
+                                        460
+                                    ],
+                                    "score": 1.0,
+                                    "content": "us a fine-grained control of computational efficiency and a superior accuracy-efficiency trade-off in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                458,
+                                319,
+                                469
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        458,
+                                        319,
+                                        469
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the inference time, compared to existing approaches.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 27,
+                    "bbox_fs": [
+                        105,
+                        347,
+                        506,
+                        469
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        484,
+                        399,
+                        497
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                484,
+                                401,
+                                499
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        484,
+                                        401,
+                                        499
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2 BACKGROUND: TRANSFORMERS AND POWER-BERT",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 33
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        510,
+                        505,
+                        554
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                510,
+                                505,
+                                522
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        510,
+                                        505,
+                                        522
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Before we describe our main approach, we review some of the building blocks in this section. In",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                520,
+                                505,
+                                534
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        520,
+                                        505,
+                                        534
+                                    ],
+                                    "score": 1.0,
+                                    "content": "particular, we review transformers, which are a standard backbone used in natural language processing",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                531,
+                                507,
+                                545
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        531,
+                                        507,
+                                        545
+                                    ],
+                                    "score": 1.0,
+                                    "content": "these days, and PoWER-BERT, which was recently proposed as an effective way to train a large-scale,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                543,
+                                366,
+                                555
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        543,
+                                        366,
+                                        555
+                                    ],
+                                    "score": 1.0,
+                                    "content": "but highly efficient transformer for sequence-level classification.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 35.5,
+                    "bbox_fs": [
+                        105,
+                        510,
+                        507,
+                        555
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        567,
+                        253,
+                        578
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                567,
+                                254,
+                                580
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        567,
+                                        254,
+                                        580
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2.1 TRANSFORMERS AND BERT",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        }
+                    ],
+                    "index": 38
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        588,
+                        505,
+                        632
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                588,
+                                504,
+                                599
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        588,
+                                        504,
+                                        599
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A transformer is a particular neural network that has been designed to work with a variable-length",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                599,
+                                505,
+                                611
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        599,
+                                        505,
+                                        611
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sequence input and is implemented as a stack of self-attention and fully-connected layers (Vaswani",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                610,
+                                506,
+                                623
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        610,
+                                        506,
+                                        623
+                                    ],
+                                    "score": 1.0,
+                                    "content": "et al., 2017). Here, we give a brief overview of the transformer which is the basic building block of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                622,
+                                201,
+                                633
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        622,
+                                        201,
+                                        633
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the proposed approach.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        }
+                    ],
+                    "index": 40.5,
+                    "bbox_fs": [
+                        105,
+                        588,
+                        506,
+                        633
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        637,
+                        505,
+                        704
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                637,
+                                505,
+                                651
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        637,
+                                        155,
+                                        651
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Each token",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        155,
+                                        640,
+                                        166,
+                                        649
+                                    ],
+                                    "score": 0.84,
+                                    "content": "x _ { t }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        166,
+                                        637,
+                                        268,
+                                        651
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in a sequence of tokens",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        269,
+                                        638,
+                                        344,
+                                        650
+                                    ],
+                                    "score": 0.91,
+                                    "content": "{ \\boldsymbol x } = ( x _ { 1 } , \\dots , x _ { N } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        345,
+                                        637,
+                                        505,
+                                        651
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", representing input text, is first turned",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                646,
+                                507,
+                                662
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        646,
+                                        208,
+                                        662
+                                    ],
+                                    "score": 1.0,
+                                    "content": "into a continuous vector",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        208,
+                                        648,
+                                        246,
+                                        660
+                                    ],
+                                    "score": 0.93,
+                                    "content": "h _ { t } ^ { 0 } \\in \\mathbb { R } ^ { H }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        247,
+                                        646,
+                                        507,
+                                        662
+                                    ],
+                                    "score": 1.0,
+                                    "content": "which is the sum of the token and position embedding vectors.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                659,
+                                505,
+                                673
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        659,
+                                        505,
+                                        673
+                                    ],
+                                    "score": 1.0,
+                                    "content": "This sequence is fed into the first transformer layer which returns another sequence of the same",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                667,
+                                507,
+                                685
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        667,
+                                        135,
+                                        685
+                                    ],
+                                    "score": 1.0,
+                                    "content": "length",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        135,
+                                        670,
+                                        187,
+                                        681
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\dot { h ^ { 1 } } \\in \\mathbb { R } ^ { N \\times H }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        188,
+                                        667,
+                                        297,
+                                        685
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". We repeat this procedure",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        297,
+                                        671,
+                                        306,
+                                        681
+                                    ],
+                                    "score": 0.81,
+                                    "content": "L",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        667,
+                                        427,
+                                        685
+                                    ],
+                                    "score": 1.0,
+                                    "content": "times, for a transformer with",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        427,
+                                        671,
+                                        435,
+                                        681
+                                    ],
+                                    "score": 0.75,
+                                    "content": "L",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        436,
+                                        667,
+                                        507,
+                                        685
+                                    ],
+                                    "score": 1.0,
+                                    "content": "layers, to obtain",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                679,
+                                506,
+                                696
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        681,
+                                        188,
+                                        694
+                                    ],
+                                    "score": 0.89,
+                                    "content": "h ^ { L } = ( h _ { 1 } ^ { L } , \\ldots , h _ { N } ^ { L } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        188,
+                                        679,
+                                        506,
+                                        696
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". We refer to each vector in the hidden sequence at each layer as a word vector to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                692,
+                                504,
+                                705
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        692,
+                                        504,
+                                        705
+                                    ],
+                                    "score": 1.0,
+                                    "content": "emphasize that there exists a correspondence between each such vector and one of the input words.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        }
+                    ],
+                    "index": 45.5,
+                    "bbox_fs": [
+                        104,
+                        637,
+                        507,
+                        705
+                    ]
+                },
+                {
+                    "type": "list",
+                    "bbox": [
+                        106,
+                        709,
+                        504,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                710,
+                                506,
+                                721
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        710,
+                                        506,
+                                        721
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Although the transformer was first introduced for the problem of machine translation, Devlin et al.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                720,
+                                506,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        720,
+                                        506,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(2018) demonstrated that the transformer can be trained and used as a masked language model.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50,
+                            "is_list_start_line": true,
+                            "is_list_end_line": true
+                        }
+                    ],
+                    "index": 49.5,
+                    "bbox_fs": [
+                        106,
+                        710,
+                        506,
+                        733
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        82,
+                        504,
+                        115
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                81,
+                                506,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        81,
+                                        506,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "More specifically, Devlin et al. (2018) showed that the transformer-based masked language model,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                93,
+                                506,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        93,
+                                        506,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "called BERT, learns a universally useful parameter set that can be finetuned for any downstream task",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                104,
+                                329,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        104,
+                                        329,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "including sequence-level and token-level classification.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        121,
+                        505,
+                        188
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                120,
+                                504,
+                                134
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        120,
+                                        491,
+                                        134
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In the case of sequence-level classification, a softmax classifier is attached to the word vector",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        491,
+                                        120,
+                                        504,
+                                        133
+                                    ],
+                                    "score": 0.89,
+                                    "content": "h _ { 1 } ^ { L }",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                132,
+                                505,
+                                144
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        132,
+                                        505,
+                                        144
+                                    ],
+                                    "score": 1.0,
+                                    "content": "associated with the special token [CLS], and the entire network, including the softmax classifier and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                143,
+                                506,
+                                156
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        143,
+                                        353,
+                                        156
+                                    ],
+                                    "score": 1.0,
+                                    "content": "BERT, is finetuned. For token-level classification, we use each",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        353,
+                                        143,
+                                        366,
+                                        155
+                                    ],
+                                    "score": 0.91,
+                                    "content": "h _ { t } ^ { L }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        366,
+                                        143,
+                                        506,
+                                        156
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as the final hidden reprsentation of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                152,
+                                507,
+                                168
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        152,
+                                        165,
+                                        168
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the associated",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        165,
+                                        155,
+                                        170,
+                                        164
+                                    ],
+                                    "score": 0.73,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        171,
+                                        152,
+                                        507,
+                                        168
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-th word in the input sequence. This strategy of pretraining followed by finetuning,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                164,
+                                505,
+                                178
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        164,
+                                        505,
+                                        178
+                                    ],
+                                    "score": 1.0,
+                                    "content": "often referred to as transfer learning, has recently become a dominant approach to classification in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                176,
+                                222,
+                                189
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        176,
+                                        222,
+                                        189
+                                    ],
+                                    "score": 1.0,
+                                    "content": "natural language processing.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 5.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        217,
+                        198,
+                        228
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                217,
+                                199,
+                                231
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        217,
+                                        199,
+                                        231
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2.2 POWER-BERT",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        244,
+                        505,
+                        300
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                244,
+                                506,
+                                258
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        244,
+                                        261,
+                                        258
+                                    ],
+                                    "score": 1.0,
+                                    "content": "PoWER-BERT keeps only the topmost",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        262,
+                                        245,
+                                        270,
+                                        257
+                                    ],
+                                    "score": 0.87,
+                                    "content": "l _ { j }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        270,
+                                        244,
+                                        376,
+                                        258
+                                    ],
+                                    "score": 1.0,
+                                    "content": "word vectors at each layer",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        376,
+                                        246,
+                                        383,
+                                        256
+                                    ],
+                                    "score": 0.83,
+                                    "content": "j",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        383,
+                                        244,
+                                        506,
+                                        258
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by eliminating redundant ones",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                256,
+                                505,
+                                268
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        256,
+                                        505,
+                                        268
+                                    ],
+                                    "score": 1.0,
+                                    "content": "based on the significance score, which is the total amount of attention imposed by a word on the other",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                266,
+                                503,
+                                280
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        266,
+                                        214,
+                                        280
+                                    ],
+                                    "score": 1.0,
+                                    "content": "words (Goyal et al., 2020).",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        214,
+                                        267,
+                                        223,
+                                        279
+                                    ],
+                                    "score": 0.86,
+                                    "content": "l _ { j }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        223,
+                                        266,
+                                        497,
+                                        280
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the hyper-parameter determines how many vectors to keep at layer",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        497,
+                                        268,
+                                        503,
+                                        279
+                                    ],
+                                    "score": 0.8,
+                                    "content": "j",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                278,
+                                506,
+                                291
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        278,
+                                        506,
+                                        291
+                                    ],
+                                    "score": 1.0,
+                                    "content": "PoWER-BERT has the same model parameters with BERT, but the extraction layers are interspersed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                289,
+                                423,
+                                301
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        289,
+                                        423,
+                                        301
+                                    ],
+                                    "score": 1.0,
+                                    "content": "after the self-attention layer in every transformer blocks (Vaswani et al., 2017).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        305,
+                        505,
+                        361
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                305,
+                                505,
+                                318
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        305,
+                                        505,
+                                        318
+                                    ],
+                                    "score": 1.0,
+                                    "content": "PoWER-BERT reduces inference time successfully, achieving better accuracy-time trade-off than",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                317,
+                                506,
+                                329
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        317,
+                                        506,
+                                        329
+                                    ],
+                                    "score": 1.0,
+                                    "content": "DistilBERT (Sanh et al., 2019), BERT-PKD (Sun et al., 2019), and Head-Prune (Michel et al.,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                328,
+                                505,
+                                340
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        328,
+                                        505,
+                                        340
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2019). Despite the original intention of maximizing the inference efficiency with the minimal loss in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                338,
+                                505,
+                                351
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        338,
+                                        505,
+                                        351
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accuracy, it is possible to set up PoWER-BERT to be both more efficient and more accurate compared",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                350,
+                                461,
+                                362
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        350,
+                                        461,
+                                        362
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to the original BERT, which was observed but largely overlooked by Goyal et al. (2020).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        366,
+                        505,
+                        443
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                366,
+                                505,
+                                380
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        366,
+                                        505,
+                                        380
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Training a PoWER-BERT model consists of three steps: (1) finetuning, (2) length configuration",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                378,
+                                505,
+                                390
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        378,
+                                        505,
+                                        390
+                                    ],
+                                    "score": 1.0,
+                                    "content": "search, and (3) re-training. The finetuning step is just like the standard finetuning step of BERT given",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                389,
+                                505,
+                                401
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        389,
+                                        401,
+                                        401
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a target task. A length configuration is a sequence of retention parameters",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        401,
+                                        389,
+                                        443,
+                                        401
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\left( l _ { 1 } , \\cdots l _ { L } \\right)",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        443,
+                                        389,
+                                        505,
+                                        401
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", each of which",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                399,
+                                506,
+                                413
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        399,
+                                        506,
+                                        413
+                                    ],
+                                    "score": 1.0,
+                                    "content": "corresponds to the number of word vectors that are kept at each layer. These retention parameters",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                410,
+                                505,
+                                423
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        410,
+                                        505,
+                                        423
+                                    ],
+                                    "score": 1.0,
+                                    "content": "are learned along with all the other parameters to minimize the original task loss together with an",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                421,
+                                505,
+                                433
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        421,
+                                        505,
+                                        433
+                                    ],
+                                    "score": 1.0,
+                                    "content": "extra term that approximately measures the number of retained word vectors across layers. In the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                433,
+                                498,
+                                444
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        433,
+                                        498,
+                                        444
+                                    ],
+                                    "score": 1.0,
+                                    "content": "re-training step, PoWER-BERT is finetuned with the length configuration fixed to its learned one.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 23
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        449,
+                        505,
+                        526
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                449,
+                                506,
+                                462
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        449,
+                                        506,
+                                        462
+                                    ],
+                                    "score": 1.0,
+                                    "content": "For each computational budget, we must train a separate model going through all three steps described",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                460,
+                                505,
+                                473
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        460,
+                                        505,
+                                        473
+                                    ],
+                                    "score": 1.0,
+                                    "content": "above. Moreover, the length configuration search step above is only approximate, as it relies on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                471,
+                                505,
+                                483
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        471,
+                                        505,
+                                        483
+                                    ],
+                                    "score": 1.0,
+                                    "content": "relaxation of retention parameters which are inherently discrete. This leads to the lack of guaranteed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                483,
+                                505,
+                                494
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        483,
+                                        505,
+                                        494
+                                    ],
+                                    "score": 1.0,
+                                    "content": "correlation between the success of this stage and true run-time. Even worse, it is a delicate act to tune",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                493,
+                                506,
+                                505
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        493,
+                                        506,
+                                        505
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the length configuration given a target computational budget, because trade-off is implicitly made via",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                504,
+                                505,
+                                516
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        504,
+                                        505,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a regularization coefficient. Furthermore, PoWER-BERT has an inherent limitation in that it only",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                515,
+                                495,
+                                528
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        515,
+                                        495,
+                                        528
+                                    ],
+                                    "score": 1.0,
+                                    "content": "applies to sequence-level classification because it eliminates word vectors in intermediate layers.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 30
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        559,
+                        309,
+                        572
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                558,
+                                311,
+                                574
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        558,
+                                        311,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3 LENGTH-ADAPTIVE TRANSFORMER",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        }
+                    ],
+                    "index": 34
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        593,
+                        505,
+                        693
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                593,
+                                505,
+                                607
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        593,
+                                        505,
+                                        607
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In this section, we explain our proposed framework which results in a transformer that reduces",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                605,
+                                505,
+                                617
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        605,
+                                        505,
+                                        617
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the length of a sequence at each layer with an arbitrary rate. We call such a resulting transformer",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                616,
+                                505,
+                                629
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        616,
+                                        505,
+                                        629
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a Length-Adaptive Transformer. We train Length-Adaptive Transformer with LengthDrop which",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                625,
+                                506,
+                                641
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        625,
+                                        506,
+                                        641
+                                    ],
+                                    "score": 1.0,
+                                    "content": "randomly samples the number of hidden vectors to be dropped at each layer with the goal of making",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                637,
+                                506,
+                                650
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        637,
+                                        506,
+                                        650
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the final model robust to such drop in the inference time. Once the model is trained, we search for the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                649,
+                                505,
+                                662
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        649,
+                                        505,
+                                        662
+                                    ],
+                                    "score": 1.0,
+                                    "content": "optimal trade-off between accuracy and efficiency using multi-objective evolutionary search, which",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                659,
+                                506,
+                                674
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        659,
+                                        506,
+                                        674
+                                    ],
+                                    "score": 1.0,
+                                    "content": "allows us to use the model for any given computational budget without finetuning nor re-training.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                670,
+                                506,
+                                684
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        670,
+                                        506,
+                                        684
+                                    ],
+                                    "score": 1.0,
+                                    "content": "At the end of this section, we describe Drop-and-Restore process as a way to greatly increase the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                681,
+                                465,
+                                695
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        681,
+                                        465,
+                                        695
+                                    ],
+                                    "score": 1.0,
+                                    "content": "applicability of PoWER-BERT which forms a building block of the proposed framework.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        }
+                    ],
+                    "index": 39
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        699,
+                        504,
+                        731
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                698,
+                                506,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        698,
+                                        506,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In short, we train a Length-Adaptive Transformer once with LengthDrop and Drop-and-Restore,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                709,
+                                506,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        709,
+                                        506,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and use it with an automatically determined length configuration for inference with any target",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                721,
+                                381,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        721,
+                                        381,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "computational budget, on both sequence-level and token-level tasks.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        }
+                    ],
+                    "index": 45
+                }
+            ],
+            "page_idx": 2,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        303,
+                        751,
+                        309,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                301,
+                                750,
+                                310,
+                                762
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        301,
+                                        750,
+                                        310,
+                                        762
+                                    ],
+                                    "score": 1.0,
+                                    "content": "",
+                                    "type": "text",
+                                    "height": 12,
+                                    "width": 9
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        307,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                308,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        308,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Under review as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        82,
+                        504,
+                        115
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                81,
+                                506,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        81,
+                                        506,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "More specifically, Devlin et al. (2018) showed that the transformer-based masked language model,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                93,
+                                506,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        93,
+                                        506,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "called BERT, learns a universally useful parameter set that can be finetuned for any downstream task",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                104,
+                                329,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        104,
+                                        329,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "including sequence-level and token-level classification.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1,
+                    "bbox_fs": [
+                        105,
+                        81,
+                        506,
+                        117
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        121,
+                        505,
+                        188
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                120,
+                                504,
+                                134
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        120,
+                                        491,
+                                        134
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In the case of sequence-level classification, a softmax classifier is attached to the word vector",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        491,
+                                        120,
+                                        504,
+                                        133
+                                    ],
+                                    "score": 0.89,
+                                    "content": "h _ { 1 } ^ { L }",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                132,
+                                505,
+                                144
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        132,
+                                        505,
+                                        144
+                                    ],
+                                    "score": 1.0,
+                                    "content": "associated with the special token [CLS], and the entire network, including the softmax classifier and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                143,
+                                506,
+                                156
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        143,
+                                        353,
+                                        156
+                                    ],
+                                    "score": 1.0,
+                                    "content": "BERT, is finetuned. For token-level classification, we use each",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        353,
+                                        143,
+                                        366,
+                                        155
+                                    ],
+                                    "score": 0.91,
+                                    "content": "h _ { t } ^ { L }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        366,
+                                        143,
+                                        506,
+                                        156
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as the final hidden reprsentation of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                152,
+                                507,
+                                168
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        152,
+                                        165,
+                                        168
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the associated",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        165,
+                                        155,
+                                        170,
+                                        164
+                                    ],
+                                    "score": 0.73,
+                                    "content": "t",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        171,
+                                        152,
+                                        507,
+                                        168
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-th word in the input sequence. This strategy of pretraining followed by finetuning,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                164,
+                                505,
+                                178
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        164,
+                                        505,
+                                        178
+                                    ],
+                                    "score": 1.0,
+                                    "content": "often referred to as transfer learning, has recently become a dominant approach to classification in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                176,
+                                222,
+                                189
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        176,
+                                        222,
+                                        189
+                                    ],
+                                    "score": 1.0,
+                                    "content": "natural language processing.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 5.5,
+                    "bbox_fs": [
+                        105,
+                        120,
+                        507,
+                        189
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        217,
+                        198,
+                        228
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                217,
+                                199,
+                                231
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        217,
+                                        199,
+                                        231
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2.2 POWER-BERT",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        244,
+                        505,
+                        300
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                244,
+                                506,
+                                258
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        244,
+                                        261,
+                                        258
+                                    ],
+                                    "score": 1.0,
+                                    "content": "PoWER-BERT keeps only the topmost",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        262,
+                                        245,
+                                        270,
+                                        257
+                                    ],
+                                    "score": 0.87,
+                                    "content": "l _ { j }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        270,
+                                        244,
+                                        376,
+                                        258
+                                    ],
+                                    "score": 1.0,
+                                    "content": "word vectors at each layer",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        376,
+                                        246,
+                                        383,
+                                        256
+                                    ],
+                                    "score": 0.83,
+                                    "content": "j",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        383,
+                                        244,
+                                        506,
+                                        258
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by eliminating redundant ones",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                256,
+                                505,
+                                268
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        256,
+                                        505,
+                                        268
+                                    ],
+                                    "score": 1.0,
+                                    "content": "based on the significance score, which is the total amount of attention imposed by a word on the other",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                266,
+                                503,
+                                280
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        266,
+                                        214,
+                                        280
+                                    ],
+                                    "score": 1.0,
+                                    "content": "words (Goyal et al., 2020).",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        214,
+                                        267,
+                                        223,
+                                        279
+                                    ],
+                                    "score": 0.86,
+                                    "content": "l _ { j }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        223,
+                                        266,
+                                        497,
+                                        280
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the hyper-parameter determines how many vectors to keep at layer",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        497,
+                                        268,
+                                        503,
+                                        279
+                                    ],
+                                    "score": 0.8,
+                                    "content": "j",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                278,
+                                506,
+                                291
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        278,
+                                        506,
+                                        291
+                                    ],
+                                    "score": 1.0,
+                                    "content": "PoWER-BERT has the same model parameters with BERT, but the extraction layers are interspersed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                289,
+                                423,
+                                301
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        289,
+                                        423,
+                                        301
+                                    ],
+                                    "score": 1.0,
+                                    "content": "after the self-attention layer in every transformer blocks (Vaswani et al., 2017).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 12,
+                    "bbox_fs": [
+                        105,
+                        244,
+                        506,
+                        301
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        305,
+                        505,
+                        361
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                305,
+                                505,
+                                318
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        305,
+                                        505,
+                                        318
+                                    ],
+                                    "score": 1.0,
+                                    "content": "PoWER-BERT reduces inference time successfully, achieving better accuracy-time trade-off than",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                317,
+                                506,
+                                329
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        317,
+                                        506,
+                                        329
+                                    ],
+                                    "score": 1.0,
+                                    "content": "DistilBERT (Sanh et al., 2019), BERT-PKD (Sun et al., 2019), and Head-Prune (Michel et al.,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                328,
+                                505,
+                                340
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        328,
+                                        505,
+                                        340
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2019). Despite the original intention of maximizing the inference efficiency with the minimal loss in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                338,
+                                505,
+                                351
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        338,
+                                        505,
+                                        351
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accuracy, it is possible to set up PoWER-BERT to be both more efficient and more accurate compared",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                350,
+                                461,
+                                362
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        350,
+                                        461,
+                                        362
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to the original BERT, which was observed but largely overlooked by Goyal et al. (2020).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 17,
+                    "bbox_fs": [
+                        105,
+                        305,
+                        506,
+                        362
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        366,
+                        505,
+                        443
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                366,
+                                505,
+                                380
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        366,
+                                        505,
+                                        380
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Training a PoWER-BERT model consists of three steps: (1) finetuning, (2) length configuration",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                378,
+                                505,
+                                390
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        378,
+                                        505,
+                                        390
+                                    ],
+                                    "score": 1.0,
+                                    "content": "search, and (3) re-training. The finetuning step is just like the standard finetuning step of BERT given",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                389,
+                                505,
+                                401
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        389,
+                                        401,
+                                        401
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a target task. A length configuration is a sequence of retention parameters",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        401,
+                                        389,
+                                        443,
+                                        401
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\left( l _ { 1 } , \\cdots l _ { L } \\right)",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        443,
+                                        389,
+                                        505,
+                                        401
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", each of which",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                399,
+                                506,
+                                413
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        399,
+                                        506,
+                                        413
+                                    ],
+                                    "score": 1.0,
+                                    "content": "corresponds to the number of word vectors that are kept at each layer. These retention parameters",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                410,
+                                505,
+                                423
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        410,
+                                        505,
+                                        423
+                                    ],
+                                    "score": 1.0,
+                                    "content": "are learned along with all the other parameters to minimize the original task loss together with an",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                421,
+                                505,
+                                433
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        421,
+                                        505,
+                                        433
+                                    ],
+                                    "score": 1.0,
+                                    "content": "extra term that approximately measures the number of retained word vectors across layers. In the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                433,
+                                498,
+                                444
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        433,
+                                        498,
+                                        444
+                                    ],
+                                    "score": 1.0,
+                                    "content": "re-training step, PoWER-BERT is finetuned with the length configuration fixed to its learned one.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 23,
+                    "bbox_fs": [
+                        105,
+                        366,
+                        506,
+                        444
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        449,
+                        505,
+                        526
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                449,
+                                506,
+                                462
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        449,
+                                        506,
+                                        462
+                                    ],
+                                    "score": 1.0,
+                                    "content": "For each computational budget, we must train a separate model going through all three steps described",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                460,
+                                505,
+                                473
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        460,
+                                        505,
+                                        473
+                                    ],
+                                    "score": 1.0,
+                                    "content": "above. Moreover, the length configuration search step above is only approximate, as it relies on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                471,
+                                505,
+                                483
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        471,
+                                        505,
+                                        483
+                                    ],
+                                    "score": 1.0,
+                                    "content": "relaxation of retention parameters which are inherently discrete. This leads to the lack of guaranteed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                483,
+                                505,
+                                494
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        483,
+                                        505,
+                                        494
+                                    ],
+                                    "score": 1.0,
+                                    "content": "correlation between the success of this stage and true run-time. Even worse, it is a delicate act to tune",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                493,
+                                506,
+                                505
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        493,
+                                        506,
+                                        505
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the length configuration given a target computational budget, because trade-off is implicitly made via",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                504,
+                                505,
+                                516
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        504,
+                                        505,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a regularization coefficient. Furthermore, PoWER-BERT has an inherent limitation in that it only",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                515,
+                                495,
+                                528
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        515,
+                                        495,
+                                        528
+                                    ],
+                                    "score": 1.0,
+                                    "content": "applies to sequence-level classification because it eliminates word vectors in intermediate layers.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 30,
+                    "bbox_fs": [
+                        105,
+                        449,
+                        506,
+                        528
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        559,
+                        309,
+                        572
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                558,
+                                311,
+                                574
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        558,
+                                        311,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3 LENGTH-ADAPTIVE TRANSFORMER",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        }
+                    ],
+                    "index": 34
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        593,
+                        505,
+                        693
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                593,
+                                505,
+                                607
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        593,
+                                        505,
+                                        607
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In this section, we explain our proposed framework which results in a transformer that reduces",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                605,
+                                505,
+                                617
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        605,
+                                        505,
+                                        617
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the length of a sequence at each layer with an arbitrary rate. We call such a resulting transformer",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                616,
+                                505,
+                                629
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        616,
+                                        505,
+                                        629
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a Length-Adaptive Transformer. We train Length-Adaptive Transformer with LengthDrop which",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                625,
+                                506,
+                                641
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        625,
+                                        506,
+                                        641
+                                    ],
+                                    "score": 1.0,
+                                    "content": "randomly samples the number of hidden vectors to be dropped at each layer with the goal of making",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                637,
+                                506,
+                                650
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        637,
+                                        506,
+                                        650
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the final model robust to such drop in the inference time. Once the model is trained, we search for the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                649,
+                                505,
+                                662
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        649,
+                                        505,
+                                        662
+                                    ],
+                                    "score": 1.0,
+                                    "content": "optimal trade-off between accuracy and efficiency using multi-objective evolutionary search, which",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                659,
+                                506,
+                                674
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        659,
+                                        506,
+                                        674
+                                    ],
+                                    "score": 1.0,
+                                    "content": "allows us to use the model for any given computational budget without finetuning nor re-training.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                670,
+                                506,
+                                684
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        670,
+                                        506,
+                                        684
+                                    ],
+                                    "score": 1.0,
+                                    "content": "At the end of this section, we describe Drop-and-Restore process as a way to greatly increase the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                681,
+                                465,
+                                695
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        681,
+                                        465,
+                                        695
+                                    ],
+                                    "score": 1.0,
+                                    "content": "applicability of PoWER-BERT which forms a building block of the proposed framework.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        }
+                    ],
+                    "index": 39,
+                    "bbox_fs": [
+                        104,
+                        593,
+                        506,
+                        695
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        699,
+                        504,
+                        731
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                698,
+                                506,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        698,
+                                        506,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In short, we train a Length-Adaptive Transformer once with LengthDrop and Drop-and-Restore,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                709,
+                                506,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        709,
+                                        506,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and use it with an automatically determined length configuration for inference with any target",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                721,
+                                381,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        721,
+                                        381,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "computational budget, on both sequence-level and token-level tasks.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        }
+                    ],
+                    "index": 45,
+                    "bbox_fs": [
+                        105,
+                        698,
+                        506,
+                        732
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        82,
+                        192,
+                        93
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                82,
+                                194,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        82,
+                                        194,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3.1 LENGTHDROP",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        102,
+                        505,
+                        158
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                103,
+                                505,
+                                115
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        103,
+                                        505,
+                                        115
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Earlier approaches to efficient inference with transformers have focused on a scenario where the target",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                114,
+                                505,
+                                127
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        114,
+                                        505,
+                                        127
+                                    ],
+                                    "score": 1.0,
+                                    "content": "computational budget for inference is known in advance Sanh et al. (2019); Goyal et al. (2020). This",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                125,
+                                506,
+                                137
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        125,
+                                        506,
+                                        137
+                                    ],
+                                    "score": 1.0,
+                                    "content": "greatly increases the cost of deploying transformers, as it requires us to train a separate transformer",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                136,
+                                505,
+                                149
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        136,
+                                        505,
+                                        149
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for each scenario. Instead, we propose to train one model that could be used for a diverse set of target",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                147,
+                                275,
+                                160
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        147,
+                                        275,
+                                        160
+                                    ],
+                                    "score": 1.0,
+                                    "content": "computational budgets without retraining.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        164,
+                        505,
+                        241
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                163,
+                                505,
+                                177
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        163,
+                                        505,
+                                        177
+                                    ],
+                                    "score": 1.0,
+                                    "content": "LengthDrop randomly generates a length configuration by sequentially sampling a sequence length",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                174,
+                                506,
+                                188
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        175,
+                                        124,
+                                        186
+                                    ],
+                                    "score": 0.91,
+                                    "content": "l _ { i + 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        124,
+                                        174,
+                                        150,
+                                        188
+                                    ],
+                                    "score": 1.0,
+                                    "content": "at the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        151,
+                                        175,
+                                        179,
+                                        186
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( i + 1 )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        180,
+                                        174,
+                                        402,
+                                        188
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-th layer based on the previous layer’s sequence length",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        402,
+                                        175,
+                                        409,
+                                        186
+                                    ],
+                                    "score": 0.86,
+                                    "content": "l _ { i }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        410,
+                                        174,
+                                        506,
+                                        188
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", following the uniform",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                185,
+                                506,
+                                199
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        185,
+                                        156,
+                                        199
+                                    ],
+                                    "score": 1.0,
+                                    "content": "distribution",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        157,
+                                        186,
+                                        230,
+                                        198
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\mathcal { U } ( \\lceil ( 1 - p ) l _ { i } \\rceil , l _ { i } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        230,
+                                        185,
+                                        263,
+                                        199
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        264,
+                                        186,
+                                        273,
+                                        197
+                                    ],
+                                    "score": 0.85,
+                                    "content": "l _ { 0 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        273,
+                                        185,
+                                        471,
+                                        199
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is set to the length of the input sequence, and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        471,
+                                        187,
+                                        478,
+                                        197
+                                    ],
+                                    "score": 0.77,
+                                    "content": "p",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        478,
+                                        185,
+                                        506,
+                                        199
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                196,
+                                506,
+                                210
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        196,
+                                        454,
+                                        210
+                                    ],
+                                    "score": 1.0,
+                                    "content": "LengthDrop probability. This sequential sampling results in a length configuration",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        454,
+                                        197,
+                                        503,
+                                        209
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( l _ { 1 } , \\cdots , l _ { L } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        503,
+                                        196,
+                                        506,
+                                        210
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                207,
+                                506,
+                                220
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        207,
+                                        506,
+                                        220
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Length-Adaptive Transformer can be thought of as consisting of a full model and many sub-models",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                218,
+                                506,
+                                232
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        218,
+                                        506,
+                                        232
+                                    ],
+                                    "score": 1.0,
+                                    "content": "corresponding to different length configuration, similarly to a neural network trained with dropout",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                230,
+                                205,
+                                242
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        230,
+                                        205,
+                                        242
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(Srivastava et al., 2014).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        252,
+                        505,
+                        352
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                252,
+                                505,
+                                265
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        252,
+                                        505,
+                                        265
+                                    ],
+                                    "score": 1.0,
+                                    "content": "LayerDrop From the perspective of each word vector, the proposed LengthDrop could be thought",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                264,
+                                506,
+                                276
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        264,
+                                        506,
+                                        276
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of as skipping the layers between when it was set aside and the final layer where it was restored.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                274,
+                                506,
+                                286
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        274,
+                                        506,
+                                        286
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The word vector however does not have any information based on which it can determine whether it",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                285,
+                                505,
+                                298
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        285,
+                                        505,
+                                        298
+                                    ],
+                                    "score": 1.0,
+                                    "content": "would be dropped at any particular layer. In our preliminary experiments, we found that this greatly",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                296,
+                                505,
+                                309
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        296,
+                                        505,
+                                        309
+                                    ],
+                                    "score": 1.0,
+                                    "content": "hinders optimization. We address this issue by using LayerDrop (Fan et al., 2019) which skips each",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                307,
+                                506,
+                                320
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        307,
+                                        506,
+                                        320
+                                    ],
+                                    "score": 1.0,
+                                    "content": "layer of a transformer uniformly at random. The LayerDrop encourages each word vector to be",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                318,
+                                506,
+                                331
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        318,
+                                        506,
+                                        331
+                                    ],
+                                    "score": 1.0,
+                                    "content": "agnostic to skipping any number of layers between when it is dropped and when it is restored, just",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                328,
+                                505,
+                                342
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        328,
+                                        505,
+                                        342
+                                    ],
+                                    "score": 1.0,
+                                    "content": "like dropout (Srivastava et al., 2014) prevents hidden neurons from co-adapting with each other by",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                340,
+                                210,
+                                354
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        340,
+                                        210,
+                                        354
+                                    ],
+                                    "score": 1.0,
+                                    "content": "randomly dropping them.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        362,
+                        505,
+                        462
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                362,
+                                505,
+                                375
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        362,
+                                        505,
+                                        375
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sandwich Rule and Inplace Distillation We observed that standard supervised training with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                373,
+                                506,
+                                388
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        373,
+                                        506,
+                                        388
+                                    ],
+                                    "score": 1.0,
+                                    "content": "LengthDrop does not work well in the preliminary experiments. We instead borrow a pair of training",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                384,
+                                506,
+                                398
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        384,
+                                        506,
+                                        398
+                                    ],
+                                    "score": 1.0,
+                                    "content": "techniques developed by Yu & Huang (2019) which are sandwich rule and inplace distillation,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                395,
+                                506,
+                                408
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        395,
+                                        506,
+                                        408
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for better optimization as well as final generalization. At each update, we update the full model",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                407,
+                                505,
+                                419
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        407,
+                                        505,
+                                        419
+                                    ],
+                                    "score": 1.0,
+                                    "content": "without LengthDrop as usual to minimize the supervised loss function. We simultaneously update",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                417,
+                                506,
+                                431
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        420,
+                                        118,
+                                        429
+                                    ],
+                                    "score": 0.83,
+                                    "content": "n _ { s }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        118,
+                                        417,
+                                        506,
+                                        431
+                                    ],
+                                    "score": 1.0,
+                                    "content": "randomly-sampled sub-models (which are called sandwiches) and the smallest-possible sub-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                429,
+                                505,
+                                442
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        429,
+                                        276,
+                                        442
+                                    ],
+                                    "score": 1.0,
+                                    "content": "model, which corresponds to keeping only",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        276,
+                                        429,
+                                        321,
+                                        441
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\lceil ( 1 - p ) l _ { i } \\rceil",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        321,
+                                        429,
+                                        428,
+                                        442
+                                    ],
+                                    "score": 1.0,
+                                    "content": "word vectors at each layer",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        428,
+                                        430,
+                                        433,
+                                        439
+                                    ],
+                                    "score": 0.69,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        433,
+                                        429,
+                                        505,
+                                        442
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", using knowledge",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                439,
+                                505,
+                                452
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        439,
+                                        505,
+                                        452
+                                    ],
+                                    "score": 1.0,
+                                    "content": "distillation (Hinton et al., 2015) from the full model. Here, sub-models mean models with length",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                451,
+                                506,
+                                464
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        451,
+                                        506,
+                                        464
+                                    ],
+                                    "score": 1.0,
+                                    "content": "reduction. They are trained to their prediction close to the full model’s prediction (inplace distillation).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 26
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        474,
+                        370,
+                        486
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                474,
+                                371,
+                                487
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        474,
+                                        371,
+                                        487
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3.2 EVOLUTIONARY SEARCH OF LENGTH CONFIGURATIONS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        }
+                    ],
+                    "index": 31
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        495,
+                        505,
+                        583
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                495,
+                                505,
+                                509
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        495,
+                                        505,
+                                        509
+                                    ],
+                                    "score": 1.0,
+                                    "content": "After training a Length-Adaptive Transformer with LengthDrop, we search for appropriate length",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                506,
+                                505,
+                                518
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        506,
+                                        505,
+                                        518
+                                    ],
+                                    "score": 1.0,
+                                    "content": "configurations for possible target computational budgets that will be given at inference time. The",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                517,
+                                505,
+                                531
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        517,
+                                        505,
+                                        531
+                                    ],
+                                    "score": 1.0,
+                                    "content": "length configuration determines the model performance in terms of both accuracy and efficiency. In",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                528,
+                                505,
+                                541
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        528,
+                                        505,
+                                        541
+                                    ],
+                                    "score": 1.0,
+                                    "content": "order to search for the optimal length configuration, we propose to use evolutionary search, similarly",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                539,
+                                505,
+                                552
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        539,
+                                        505,
+                                        552
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to Cai et al. (2019) and Wang et al. (2020). This procedure is efficient, as it only requires a single",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                550,
+                                507,
+                                564
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        550,
+                                        507,
+                                        564
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pass through the relatively small validation set for each length configuration, unlike re-training for a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                561,
+                                505,
+                                575
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        561,
+                                        505,
+                                        575
+                                    ],
+                                    "score": 1.0,
+                                    "content": "new computational budget which requires multiple passes through a significantly larger training set",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                572,
+                                173,
+                                585
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        572,
+                                        173,
+                                        585
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for each budget.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 35.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        589,
+                        506,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                588,
+                                505,
+                                602
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        588,
+                                        505,
+                                        602
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We initialize the population with constant-ratio configurations. Each configuration is created by",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                599,
+                                506,
+                                613
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        600,
+                                        187,
+                                        612
+                                    ],
+                                    "score": 0.92,
+                                    "content": "l _ { i + 1 } = \\lceil ( 1 - r ) \\bar { l _ { i } } \\rceil",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        187,
+                                        599,
+                                        250,
+                                        613
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for each layer",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        250,
+                                        601,
+                                        255,
+                                        610
+                                    ],
+                                    "score": 0.74,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        255,
+                                        599,
+                                        278,
+                                        613
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        279,
+                                        603,
+                                        285,
+                                        610
+                                    ],
+                                    "score": 0.7,
+                                    "content": "r",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        285,
+                                        599,
+                                        506,
+                                        613
+                                    ],
+                                    "score": 1.0,
+                                    "content": "so that the amount of computation within the initial",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                610,
+                                507,
+                                624
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        610,
+                                        507,
+                                        624
+                                    ],
+                                    "score": 1.0,
+                                    "content": "population is uniformly distributed between those of the smallest and full models. At each itera-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                620,
+                                507,
+                                636
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        620,
+                                        507,
+                                        636
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tion, we evolve the population to consist only of configurations lie on a newly updated efficiency-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                633,
+                                506,
+                                646
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        633,
+                                        506,
+                                        646
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accuracy Pareto frontier by mutation and cross-over. Mutation alters an original length configuration",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                643,
+                                507,
+                                658
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        644,
+                                        154,
+                                        656
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( l _ { 1 } , \\cdots , l _ { L } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        155,
+                                        643,
+                                        166,
+                                        658
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        167,
+                                        644,
+                                        214,
+                                        656
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( l _ { 1 } ^ { \\prime } , \\cdots , l _ { L } ^ { \\prime } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        215,
+                                        643,
+                                        267,
+                                        658
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by sampling",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        267,
+                                        644,
+                                        275,
+                                        655
+                                    ],
+                                    "score": 0.84,
+                                    "content": "l _ { i } ^ { \\prime }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        275,
+                                        643,
+                                        393,
+                                        658
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from the uniform distribution",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        394,
+                                        644,
+                                        447,
+                                        656
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\bar { \\mathcal { U } } ( l _ { i - 1 } ^ { \\prime } , l _ { i + 1 } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        447,
+                                        643,
+                                        507,
+                                        658
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with the prob-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                654,
+                                506,
+                                668
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        654,
+                                        134,
+                                        668
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        134,
+                                        657,
+                                        147,
+                                        667
+                                    ],
+                                    "score": 0.85,
+                                    "content": "p _ { m }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        148,
+                                        654,
+                                        267,
+                                        668
+                                    ],
+                                    "score": 1.0,
+                                    "content": "or keeping the original length",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        268,
+                                        655,
+                                        294,
+                                        667
+                                    ],
+                                    "score": 0.9,
+                                    "content": "{ \\bar { l } } _ { i } ^ { \\prime } = l _ { i }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        295,
+                                        654,
+                                        400,
+                                        668
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", sweeping the layers from",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        400,
+                                        656,
+                                        423,
+                                        665
+                                    ],
+                                    "score": 0.88,
+                                    "content": "i = 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        423,
+                                        654,
+                                        434,
+                                        668
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        434,
+                                        655,
+                                        459,
+                                        665
+                                    ],
+                                    "score": 0.9,
+                                    "content": "i = L",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        459,
+                                        654,
+                                        506,
+                                        668
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Crossover",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                666,
+                                505,
+                                678
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        666,
+                                        505,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "takes two length configurations and averages the lengths at each layer. Both of these operations are",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                677,
+                                504,
+                                689
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        677,
+                                        495,
+                                        689
+                                    ],
+                                    "score": 1.0,
+                                    "content": "performed while ensuring the monotonicity of the lengths over the layers. We repeat this iteration",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        495,
+                                        677,
+                                        504,
+                                        687
+                                    ],
+                                    "score": 0.79,
+                                    "content": "G",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                687,
+                                506,
+                                701
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        687,
+                                        209,
+                                        701
+                                    ],
+                                    "score": 1.0,
+                                    "content": "times, while maintaining",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        209,
+                                        689,
+                                        223,
+                                        699
+                                    ],
+                                    "score": 0.83,
+                                    "content": "n _ { m }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        224,
+                                        687,
+                                        337,
+                                        701
+                                    ],
+                                    "score": 1.0,
+                                    "content": "mutated configurations and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        338,
+                                        689,
+                                        348,
+                                        699
+                                    ],
+                                    "score": 0.79,
+                                    "content": "n _ { c }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        349,
+                                        687,
+                                        506,
+                                        701
+                                    ],
+                                    "score": 1.0,
+                                    "content": "crossover’d configurations. Repeating",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                699,
+                                506,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        699,
+                                        506,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "this procedure pushes the Pareto frontier further to identify the best trade-off between two objectives,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                709,
+                                506,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        709,
+                                        506,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "efficiency and accuracy, without requiring any continuous relaxation of length configurations nor",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 51
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                721,
+                                240,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        721,
+                                        240,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "using a proxy objective function.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 52
+                        }
+                    ],
+                    "index": 46
+                }
+            ],
+            "page_idx": 3,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        307,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                25,
+                                308,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        25,
+                                        308,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Under review as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        752,
+                        308,
+                        759
+                    ],
+                    "lines": []
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        82,
+                        192,
+                        93
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                82,
+                                194,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        82,
+                                        194,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3.1 LENGTHDROP",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        102,
+                        505,
+                        158
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                103,
+                                505,
+                                115
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        103,
+                                        505,
+                                        115
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Earlier approaches to efficient inference with transformers have focused on a scenario where the target",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                114,
+                                505,
+                                127
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        114,
+                                        505,
+                                        127
+                                    ],
+                                    "score": 1.0,
+                                    "content": "computational budget for inference is known in advance Sanh et al. (2019); Goyal et al. (2020). This",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                125,
+                                506,
+                                137
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        125,
+                                        506,
+                                        137
+                                    ],
+                                    "score": 1.0,
+                                    "content": "greatly increases the cost of deploying transformers, as it requires us to train a separate transformer",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                136,
+                                505,
+                                149
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        136,
+                                        505,
+                                        149
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for each scenario. Instead, we propose to train one model that could be used for a diverse set of target",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                147,
+                                275,
+                                160
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        147,
+                                        275,
+                                        160
+                                    ],
+                                    "score": 1.0,
+                                    "content": "computational budgets without retraining.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        }
+                    ],
+                    "index": 3,
+                    "bbox_fs": [
+                        105,
+                        103,
+                        506,
+                        160
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        164,
+                        505,
+                        241
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                163,
+                                505,
+                                177
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        163,
+                                        505,
+                                        177
+                                    ],
+                                    "score": 1.0,
+                                    "content": "LengthDrop randomly generates a length configuration by sequentially sampling a sequence length",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                174,
+                                506,
+                                188
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        175,
+                                        124,
+                                        186
+                                    ],
+                                    "score": 0.91,
+                                    "content": "l _ { i + 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        124,
+                                        174,
+                                        150,
+                                        188
+                                    ],
+                                    "score": 1.0,
+                                    "content": "at the",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        151,
+                                        175,
+                                        179,
+                                        186
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( i + 1 )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        180,
+                                        174,
+                                        402,
+                                        188
+                                    ],
+                                    "score": 1.0,
+                                    "content": "-th layer based on the previous layer’s sequence length",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        402,
+                                        175,
+                                        409,
+                                        186
+                                    ],
+                                    "score": 0.86,
+                                    "content": "l _ { i }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        410,
+                                        174,
+                                        506,
+                                        188
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", following the uniform",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                185,
+                                506,
+                                199
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        185,
+                                        156,
+                                        199
+                                    ],
+                                    "score": 1.0,
+                                    "content": "distribution",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        157,
+                                        186,
+                                        230,
+                                        198
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\mathcal { U } ( \\lceil ( 1 - p ) l _ { i } \\rceil , l _ { i } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        230,
+                                        185,
+                                        263,
+                                        199
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        264,
+                                        186,
+                                        273,
+                                        197
+                                    ],
+                                    "score": 0.85,
+                                    "content": "l _ { 0 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        273,
+                                        185,
+                                        471,
+                                        199
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is set to the length of the input sequence, and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        471,
+                                        187,
+                                        478,
+                                        197
+                                    ],
+                                    "score": 0.77,
+                                    "content": "p",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        478,
+                                        185,
+                                        506,
+                                        199
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                196,
+                                506,
+                                210
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        196,
+                                        454,
+                                        210
+                                    ],
+                                    "score": 1.0,
+                                    "content": "LengthDrop probability. This sequential sampling results in a length configuration",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        454,
+                                        197,
+                                        503,
+                                        209
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( l _ { 1 } , \\cdots , l _ { L } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        503,
+                                        196,
+                                        506,
+                                        210
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                207,
+                                506,
+                                220
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        207,
+                                        506,
+                                        220
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Length-Adaptive Transformer can be thought of as consisting of a full model and many sub-models",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                218,
+                                506,
+                                232
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        218,
+                                        506,
+                                        232
+                                    ],
+                                    "score": 1.0,
+                                    "content": "corresponding to different length configuration, similarly to a neural network trained with dropout",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                230,
+                                205,
+                                242
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        230,
+                                        205,
+                                        242
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(Srivastava et al., 2014).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "index": 9,
+                    "bbox_fs": [
+                        105,
+                        163,
+                        506,
+                        242
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        252,
+                        505,
+                        352
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                252,
+                                505,
+                                265
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        252,
+                                        505,
+                                        265
+                                    ],
+                                    "score": 1.0,
+                                    "content": "LayerDrop From the perspective of each word vector, the proposed LengthDrop could be thought",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                264,
+                                506,
+                                276
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        264,
+                                        506,
+                                        276
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of as skipping the layers between when it was set aside and the final layer where it was restored.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                274,
+                                506,
+                                286
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        274,
+                                        506,
+                                        286
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The word vector however does not have any information based on which it can determine whether it",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                285,
+                                505,
+                                298
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        285,
+                                        505,
+                                        298
+                                    ],
+                                    "score": 1.0,
+                                    "content": "would be dropped at any particular layer. In our preliminary experiments, we found that this greatly",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                296,
+                                505,
+                                309
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        296,
+                                        505,
+                                        309
+                                    ],
+                                    "score": 1.0,
+                                    "content": "hinders optimization. We address this issue by using LayerDrop (Fan et al., 2019) which skips each",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                307,
+                                506,
+                                320
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        307,
+                                        506,
+                                        320
+                                    ],
+                                    "score": 1.0,
+                                    "content": "layer of a transformer uniformly at random. The LayerDrop encourages each word vector to be",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                318,
+                                506,
+                                331
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        318,
+                                        506,
+                                        331
+                                    ],
+                                    "score": 1.0,
+                                    "content": "agnostic to skipping any number of layers between when it is dropped and when it is restored, just",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                328,
+                                505,
+                                342
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        328,
+                                        505,
+                                        342
+                                    ],
+                                    "score": 1.0,
+                                    "content": "like dropout (Srivastava et al., 2014) prevents hidden neurons from co-adapting with each other by",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                340,
+                                210,
+                                354
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        340,
+                                        210,
+                                        354
+                                    ],
+                                    "score": 1.0,
+                                    "content": "randomly dropping them.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 17,
+                    "bbox_fs": [
+                        105,
+                        252,
+                        506,
+                        354
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        362,
+                        505,
+                        462
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                362,
+                                505,
+                                375
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        362,
+                                        505,
+                                        375
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sandwich Rule and Inplace Distillation We observed that standard supervised training with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                373,
+                                506,
+                                388
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        373,
+                                        506,
+                                        388
+                                    ],
+                                    "score": 1.0,
+                                    "content": "LengthDrop does not work well in the preliminary experiments. We instead borrow a pair of training",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                384,
+                                506,
+                                398
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        384,
+                                        506,
+                                        398
+                                    ],
+                                    "score": 1.0,
+                                    "content": "techniques developed by Yu & Huang (2019) which are sandwich rule and inplace distillation,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                395,
+                                506,
+                                408
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        395,
+                                        506,
+                                        408
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for better optimization as well as final generalization. At each update, we update the full model",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                407,
+                                505,
+                                419
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        407,
+                                        505,
+                                        419
+                                    ],
+                                    "score": 1.0,
+                                    "content": "without LengthDrop as usual to minimize the supervised loss function. We simultaneously update",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                417,
+                                506,
+                                431
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        420,
+                                        118,
+                                        429
+                                    ],
+                                    "score": 0.83,
+                                    "content": "n _ { s }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        118,
+                                        417,
+                                        506,
+                                        431
+                                    ],
+                                    "score": 1.0,
+                                    "content": "randomly-sampled sub-models (which are called sandwiches) and the smallest-possible sub-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                429,
+                                505,
+                                442
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        429,
+                                        276,
+                                        442
+                                    ],
+                                    "score": 1.0,
+                                    "content": "model, which corresponds to keeping only",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        276,
+                                        429,
+                                        321,
+                                        441
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\lceil ( 1 - p ) l _ { i } \\rceil",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        321,
+                                        429,
+                                        428,
+                                        442
+                                    ],
+                                    "score": 1.0,
+                                    "content": "word vectors at each layer",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        428,
+                                        430,
+                                        433,
+                                        439
+                                    ],
+                                    "score": 0.69,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        433,
+                                        429,
+                                        505,
+                                        442
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", using knowledge",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                439,
+                                505,
+                                452
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        439,
+                                        505,
+                                        452
+                                    ],
+                                    "score": 1.0,
+                                    "content": "distillation (Hinton et al., 2015) from the full model. Here, sub-models mean models with length",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                451,
+                                506,
+                                464
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        451,
+                                        506,
+                                        464
+                                    ],
+                                    "score": 1.0,
+                                    "content": "reduction. They are trained to their prediction close to the full model’s prediction (inplace distillation).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 26,
+                    "bbox_fs": [
+                        105,
+                        362,
+                        506,
+                        464
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        474,
+                        370,
+                        486
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                474,
+                                371,
+                                487
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        474,
+                                        371,
+                                        487
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3.2 EVOLUTIONARY SEARCH OF LENGTH CONFIGURATIONS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        }
+                    ],
+                    "index": 31
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        495,
+                        505,
+                        583
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                495,
+                                505,
+                                509
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        495,
+                                        505,
+                                        509
+                                    ],
+                                    "score": 1.0,
+                                    "content": "After training a Length-Adaptive Transformer with LengthDrop, we search for appropriate length",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                506,
+                                505,
+                                518
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        506,
+                                        505,
+                                        518
+                                    ],
+                                    "score": 1.0,
+                                    "content": "configurations for possible target computational budgets that will be given at inference time. The",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                517,
+                                505,
+                                531
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        517,
+                                        505,
+                                        531
+                                    ],
+                                    "score": 1.0,
+                                    "content": "length configuration determines the model performance in terms of both accuracy and efficiency. In",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                528,
+                                505,
+                                541
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        528,
+                                        505,
+                                        541
+                                    ],
+                                    "score": 1.0,
+                                    "content": "order to search for the optimal length configuration, we propose to use evolutionary search, similarly",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                539,
+                                505,
+                                552
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        539,
+                                        505,
+                                        552
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to Cai et al. (2019) and Wang et al. (2020). This procedure is efficient, as it only requires a single",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                550,
+                                507,
+                                564
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        550,
+                                        507,
+                                        564
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pass through the relatively small validation set for each length configuration, unlike re-training for a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                561,
+                                505,
+                                575
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        561,
+                                        505,
+                                        575
+                                    ],
+                                    "score": 1.0,
+                                    "content": "new computational budget which requires multiple passes through a significantly larger training set",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                572,
+                                173,
+                                585
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        572,
+                                        173,
+                                        585
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for each budget.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 35.5,
+                    "bbox_fs": [
+                        104,
+                        495,
+                        507,
+                        585
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        589,
+                        506,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                588,
+                                505,
+                                602
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        588,
+                                        505,
+                                        602
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We initialize the population with constant-ratio configurations. Each configuration is created by",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                599,
+                                506,
+                                613
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        600,
+                                        187,
+                                        612
+                                    ],
+                                    "score": 0.92,
+                                    "content": "l _ { i + 1 } = \\lceil ( 1 - r ) \\bar { l _ { i } } \\rceil",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        187,
+                                        599,
+                                        250,
+                                        613
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for each layer",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        250,
+                                        601,
+                                        255,
+                                        610
+                                    ],
+                                    "score": 0.74,
+                                    "content": "i",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        255,
+                                        599,
+                                        278,
+                                        613
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        279,
+                                        603,
+                                        285,
+                                        610
+                                    ],
+                                    "score": 0.7,
+                                    "content": "r",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        285,
+                                        599,
+                                        506,
+                                        613
+                                    ],
+                                    "score": 1.0,
+                                    "content": "so that the amount of computation within the initial",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                610,
+                                507,
+                                624
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        610,
+                                        507,
+                                        624
+                                    ],
+                                    "score": 1.0,
+                                    "content": "population is uniformly distributed between those of the smallest and full models. At each itera-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                620,
+                                507,
+                                636
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        620,
+                                        507,
+                                        636
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tion, we evolve the population to consist only of configurations lie on a newly updated efficiency-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                633,
+                                506,
+                                646
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        633,
+                                        506,
+                                        646
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accuracy Pareto frontier by mutation and cross-over. Mutation alters an original length configuration",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                643,
+                                507,
+                                658
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        644,
+                                        154,
+                                        656
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( l _ { 1 } , \\cdots , l _ { L } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        155,
+                                        643,
+                                        166,
+                                        658
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        167,
+                                        644,
+                                        214,
+                                        656
+                                    ],
+                                    "score": 0.91,
+                                    "content": "( l _ { 1 } ^ { \\prime } , \\cdots , l _ { L } ^ { \\prime } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        215,
+                                        643,
+                                        267,
+                                        658
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by sampling",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        267,
+                                        644,
+                                        275,
+                                        655
+                                    ],
+                                    "score": 0.84,
+                                    "content": "l _ { i } ^ { \\prime }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        275,
+                                        643,
+                                        393,
+                                        658
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from the uniform distribution",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        394,
+                                        644,
+                                        447,
+                                        656
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\bar { \\mathcal { U } } ( l _ { i - 1 } ^ { \\prime } , l _ { i + 1 } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        447,
+                                        643,
+                                        507,
+                                        658
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with the prob-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                654,
+                                506,
+                                668
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        654,
+                                        134,
+                                        668
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        134,
+                                        657,
+                                        147,
+                                        667
+                                    ],
+                                    "score": 0.85,
+                                    "content": "p _ { m }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        148,
+                                        654,
+                                        267,
+                                        668
+                                    ],
+                                    "score": 1.0,
+                                    "content": "or keeping the original length",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        268,
+                                        655,
+                                        294,
+                                        667
+                                    ],
+                                    "score": 0.9,
+                                    "content": "{ \\bar { l } } _ { i } ^ { \\prime } = l _ { i }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        295,
+                                        654,
+                                        400,
+                                        668
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", sweeping the layers from",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        400,
+                                        656,
+                                        423,
+                                        665
+                                    ],
+                                    "score": 0.88,
+                                    "content": "i = 1",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        423,
+                                        654,
+                                        434,
+                                        668
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        434,
+                                        655,
+                                        459,
+                                        665
+                                    ],
+                                    "score": 0.9,
+                                    "content": "i = L",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        459,
+                                        654,
+                                        506,
+                                        668
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Crossover",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                666,
+                                505,
+                                678
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        666,
+                                        505,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "takes two length configurations and averages the lengths at each layer. Both of these operations are",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                677,
+                                504,
+                                689
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        677,
+                                        495,
+                                        689
+                                    ],
+                                    "score": 1.0,
+                                    "content": "performed while ensuring the monotonicity of the lengths over the layers. We repeat this iteration",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        495,
+                                        677,
+                                        504,
+                                        687
+                                    ],
+                                    "score": 0.79,
+                                    "content": "G",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                687,
+                                506,
+                                701
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        687,
+                                        209,
+                                        701
+                                    ],
+                                    "score": 1.0,
+                                    "content": "times, while maintaining",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        209,
+                                        689,
+                                        223,
+                                        699
+                                    ],
+                                    "score": 0.83,
+                                    "content": "n _ { m }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        224,
+                                        687,
+                                        337,
+                                        701
+                                    ],
+                                    "score": 1.0,
+                                    "content": "mutated configurations and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        338,
+                                        689,
+                                        348,
+                                        699
+                                    ],
+                                    "score": 0.79,
+                                    "content": "n _ { c }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        349,
+                                        687,
+                                        506,
+                                        701
+                                    ],
+                                    "score": 1.0,
+                                    "content": "crossover’d configurations. Repeating",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                699,
+                                506,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        699,
+                                        506,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "this procedure pushes the Pareto frontier further to identify the best trade-off between two objectives,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                709,
+                                506,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        709,
+                                        506,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "efficiency and accuracy, without requiring any continuous relaxation of length configurations nor",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 51
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                721,
+                                240,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        721,
+                                        240,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "using a proxy objective function.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 52
+                        }
+                    ],
+                    "index": 46,
+                    "bbox_fs": [
+                        104,
+                        588,
+                        507,
+                        733
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "image",
+                    "bbox": [
+                        119,
+                        88,
+                        492,
+                        157
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                119,
+                                88,
+                                492,
+                                157
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        119,
+                                        88,
+                                        492,
+                                        157
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                119,
+                                                88,
+                                                492,
+                                                157
+                                            ],
+                                            "score": 0.963,
+                                            "type": "image",
+                                            "image_path": "320388afaf5c944756a7b3f52eddc7583af0fdd53b75f8ac7bf8c3063dd11f2f.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        119,
+                                        88,
+                                        492,
+                                        111.0
+                                    ],
+                                    "spans": [],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        119,
+                                        111.0,
+                                        492,
+                                        134.0
+                                    ],
+                                    "spans": [],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        119,
+                                        134.0,
+                                        492,
+                                        157.0
+                                    ],
+                                    "spans": [],
+                                    "index": 2
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                106,
+                                165,
+                                505,
+                                232
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        166,
+                                        506,
+                                        179
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                166,
+                                                506,
+                                                179
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 1: Illustration of (a) word-vector elimination process in PoWER-BERT (Goyal et al., 2020)",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        177,
+                                        506,
+                                        190
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                177,
+                                                506,
+                                                190
+                                            ],
+                                            "score": 1.0,
+                                            "content": "and (b) Drop-and-Restore process in Length-Adaptive Transformer. Yellow box and blue boxes",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        189,
+                                        505,
+                                        200
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                189,
+                                                505,
+                                                200
+                                            ],
+                                            "score": 1.0,
+                                            "content": "imply the output of embedding layer and transformer layers, respectively. Green boxes mean vectors",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 5
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        199,
+                                        505,
+                                        212
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                199,
+                                                505,
+                                                212
+                                            ],
+                                            "score": 1.0,
+                                            "content": "dropped in lower layers and restored at the last layer. Red box is the task-specific layer. Though",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 6
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        210,
+                                        506,
+                                        223
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                210,
+                                                506,
+                                                223
+                                            ],
+                                            "score": 1.0,
+                                            "content": "word-vectors in the middle could be eliminated (or dropped), remaining vectors are left-aligned for",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 7
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        220,
+                                        408,
+                                        234
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                220,
+                                                408,
+                                                234
+                                            ],
+                                            "score": 1.0,
+                                            "content": "the better illustration. In this case, the number of transformer layers is four.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 8
+                                }
+                            ],
+                            "index": 5.5
+                        }
+                    ],
+                    "index": 3.25
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        249,
+                        263,
+                        260
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                248,
+                                265,
+                                262
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        248,
+                                        265,
+                                        262
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3.3 DROP-AND-RESTORE PROCESS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        270,
+                        505,
+                        347
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                271,
+                                506,
+                                283
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        271,
+                                        506,
+                                        283
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The applicability of the PoWER-BERT, based on which our main contribution above was made, is",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                281,
+                                506,
+                                294
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        281,
+                                        506,
+                                        294
+                                    ],
+                                    "score": 1.0,
+                                    "content": "limited to sequence-level classification, because it eliminates word vectors at each layer. In addition",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                293,
+                                504,
+                                304
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        293,
+                                        504,
+                                        304
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to our main contribution above, we thus propose to extend the PoWER-BERT so that it is applicable",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                303,
+                                505,
+                                316
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        303,
+                                        505,
+                                        316
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to token-level classification, such as span-based question-answering. Our proposal, to which we",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                313,
+                                505,
+                                326
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        313,
+                                        505,
+                                        326
+                                    ],
+                                    "score": 1.0,
+                                    "content": "refer as Drop-and-Restore, does not eliminate word vectors at each layer according to the length",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                326,
+                                505,
+                                337
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        326,
+                                        505,
+                                        337
+                                    ],
+                                    "score": 1.0,
+                                    "content": "configuration but instead sets them aside until the final hidden layer. At the final hidden layer, these",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                336,
+                                504,
+                                349
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        336,
+                                        504,
+                                        349
+                                    ],
+                                    "score": 1.0,
+                                    "content": "word vectors are brought back to form the full hidden sequence, as illustrated graphically in Fig. 1.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        364,
+                        231,
+                        376
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                363,
+                                232,
+                                378
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        363,
+                                        232,
+                                        378
+                                    ],
+                                    "score": 1.0,
+                                    "content": "4 EXPERIMENT SETUP",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        389,
+                        505,
+                        466
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                389,
+                                506,
+                                402
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        389,
+                                        506,
+                                        402
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Datasets We test the proposed approach on both sequence-level and token-level tasks, the latter",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                399,
+                                507,
+                                414
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        399,
+                                        507,
+                                        414
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of which could not have been done with the original PoWER-BERT unless for the proposed Drop-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                411,
+                                505,
+                                424
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        411,
+                                        505,
+                                        424
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and-Restore. We use MNLI-m and SST-2 from GLUE benchmark (Wang et al., 2018), as was done",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                422,
+                                506,
+                                435
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        422,
+                                        506,
+                                        435
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to test PoWER-BERT earlier, for sequence-level classification. We choose them because consistent",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                434,
+                                505,
+                                446
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        434,
+                                        505,
+                                        446
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accuracy scores from standard training on them due to their sufficiently large training set imply that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                444,
+                                506,
+                                457
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        444,
+                                        506,
+                                        457
+                                    ],
+                                    "score": 1.0,
+                                    "content": "they are reliable to verify our approach. We use SQuAD 1.1 (Rajpurkar et al., 2016) for token-level",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                455,
+                                164,
+                                467
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        455,
+                                        164,
+                                        467
+                                    ],
+                                    "score": 1.0,
+                                    "content": "classification.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 21
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        479,
+                        505,
+                        546
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                478,
+                                505,
+                                492
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        478,
+                                        505,
+                                        492
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Evaluation metrics We use the number of floating operations (FLOPs) as a main metric to measure",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                489,
+                                506,
+                                505
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        489,
+                                        506,
+                                        505
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the inference efficiency given any length configuration, as it is agnostic to the choice of underlying",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                499,
+                                506,
+                                516
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        499,
+                                        506,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "hardware, unlike other alternatives such as hardware-aware latency (Wang et al., 2020) or energy",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                512,
+                                506,
+                                525
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        512,
+                                        506,
+                                        525
+                                    ],
+                                    "score": 1.0,
+                                    "content": "consumption (Henderson et al., 2020). We later demonstrate that FLOPs and wall-clock time on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                523,
+                                506,
+                                536
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        523,
+                                        506,
+                                        536
+                                    ],
+                                    "score": 1.0,
+                                    "content": "GPU and CPU correlate well with the proposed approach, which is not necessarily the case for other",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                535,
+                                444,
+                                547
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        535,
+                                        444,
+                                        547
+                                    ],
+                                    "score": 1.0,
+                                    "content": "approaches, such as unstructured weight pruning (Han et al., 2015; See et al., 2016).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 27.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        558,
+                        505,
+                        646
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                559,
+                                505,
+                                571
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        559,
+                                        505,
+                                        571
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Pretrained transformers Since BERT was introduced by Devlin et al. (2018), it has become",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                570,
+                                505,
+                                582
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        570,
+                                        505,
+                                        582
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a standard practice to start from a pretrained (masked) language model and finetune it for each",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                580,
+                                506,
+                                594
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        580,
+                                        506,
+                                        594
+                                    ],
+                                    "score": 1.0,
+                                    "content": "downstream task. We follow the same strategy in this paper and test two pretrained transformer-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                591,
+                                506,
+                                604
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        591,
+                                        506,
+                                        604
+                                    ],
+                                    "score": 1.0,
+                                    "content": "based language models; BERTBASE (Devlin et al., 2018) and DistilBERT (Sanh et al., 2019), which",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                601,
+                                505,
+                                616
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        601,
+                                        505,
+                                        616
+                                    ],
+                                    "score": 1.0,
+                                    "content": "allows us to demonstrate that the usefulness and applicability of our approach are not tied to any",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                613,
+                                506,
+                                627
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        613,
+                                        506,
+                                        627
+                                    ],
+                                    "score": 1.0,
+                                    "content": "specific architectural choice, such as the number of layers and the maximum length of input sequence.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                624,
+                                505,
+                                637
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        624,
+                                        505,
+                                        637
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Although we focus on BERT-based masked language models here, the proposed approach is readily",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                636,
+                                286,
+                                647
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        636,
+                                        286,
+                                        647
+                                    ],
+                                    "score": 1.0,
+                                    "content": "applicable to any transformer-based models.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        }
+                    ],
+                    "index": 34.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        660,
+                        505,
+                        693
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                659,
+                                505,
+                                673
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        659,
+                                        505,
+                                        673
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Learning We train a Length-Adaptive Transformer with LengthDrop probability and LayerDrop",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                671,
+                                505,
+                                683
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        671,
+                                        244,
+                                        683
+                                    ],
+                                    "score": 1.0,
+                                    "content": "probability both set to 0.2. We use",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        245,
+                                        671,
+                                        275,
+                                        682
+                                    ],
+                                    "score": 0.9,
+                                    "content": "n _ { s } = 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        275,
+                                        671,
+                                        505,
+                                        683
+                                    ],
+                                    "score": 1.0,
+                                    "content": "randomly sampled intermediate sub-models in addition to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                681,
+                                406,
+                                694
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        681,
+                                        406,
+                                        694
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the full model and smallest model for applying the sandwich learning rule.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        }
+                    ],
+                    "index": 40
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        699,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                699,
+                                506,
+                                711
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        699,
+                                        506,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We start finetuning the pretrained transformer without Drop-and-Restore first, just as Goyal et al.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                709,
+                                506,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        709,
+                                        506,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(2020) did with PoWER-BERT. We then continue finetuning it for another five epochs with Drop-and-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                720,
+                                505,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        720,
+                                        505,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Restore. This is unlike the recommended three epochs by Devlin et al. (2018), as learning progresses",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        }
+                    ],
+                    "index": 43
+                }
+            ],
+            "page_idx": 4,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        307,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                308,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        308,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Under review as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        751,
+                        308,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                302,
+                                750,
+                                309,
+                                763
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        302,
+                                        750,
+                                        309,
+                                        763
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "image",
+                    "bbox": [
+                        119,
+                        88,
+                        492,
+                        157
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                119,
+                                88,
+                                492,
+                                157
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        119,
+                                        88,
+                                        492,
+                                        157
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                119,
+                                                88,
+                                                492,
+                                                157
+                                            ],
+                                            "score": 0.963,
+                                            "type": "image",
+                                            "image_path": "320388afaf5c944756a7b3f52eddc7583af0fdd53b75f8ac7bf8c3063dd11f2f.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        119,
+                                        88,
+                                        492,
+                                        111.0
+                                    ],
+                                    "spans": [],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        119,
+                                        111.0,
+                                        492,
+                                        134.0
+                                    ],
+                                    "spans": [],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        119,
+                                        134.0,
+                                        492,
+                                        157.0
+                                    ],
+                                    "spans": [],
+                                    "index": 2
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                106,
+                                165,
+                                505,
+                                232
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        166,
+                                        506,
+                                        179
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                166,
+                                                506,
+                                                179
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 1: Illustration of (a) word-vector elimination process in PoWER-BERT (Goyal et al., 2020)",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        177,
+                                        506,
+                                        190
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                177,
+                                                506,
+                                                190
+                                            ],
+                                            "score": 1.0,
+                                            "content": "and (b) Drop-and-Restore process in Length-Adaptive Transformer. Yellow box and blue boxes",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        189,
+                                        505,
+                                        200
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                189,
+                                                505,
+                                                200
+                                            ],
+                                            "score": 1.0,
+                                            "content": "imply the output of embedding layer and transformer layers, respectively. Green boxes mean vectors",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 5
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        199,
+                                        505,
+                                        212
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                199,
+                                                505,
+                                                212
+                                            ],
+                                            "score": 1.0,
+                                            "content": "dropped in lower layers and restored at the last layer. Red box is the task-specific layer. Though",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 6
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        210,
+                                        506,
+                                        223
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                210,
+                                                506,
+                                                223
+                                            ],
+                                            "score": 1.0,
+                                            "content": "word-vectors in the middle could be eliminated (or dropped), remaining vectors are left-aligned for",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 7
+                                },
+                                {
+                                    "bbox": [
+                                        105,
+                                        220,
+                                        408,
+                                        234
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                105,
+                                                220,
+                                                408,
+                                                234
+                                            ],
+                                            "score": 1.0,
+                                            "content": "the better illustration. In this case, the number of transformer layers is four.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 8
+                                }
+                            ],
+                            "index": 5.5
+                        }
+                    ],
+                    "index": 3.25
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        249,
+                        263,
+                        260
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                248,
+                                265,
+                                262
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        248,
+                                        265,
+                                        262
+                                    ],
+                                    "score": 1.0,
+                                    "content": "3.3 DROP-AND-RESTORE PROCESS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        270,
+                        505,
+                        347
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                271,
+                                506,
+                                283
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        271,
+                                        506,
+                                        283
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The applicability of the PoWER-BERT, based on which our main contribution above was made, is",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                281,
+                                506,
+                                294
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        281,
+                                        506,
+                                        294
+                                    ],
+                                    "score": 1.0,
+                                    "content": "limited to sequence-level classification, because it eliminates word vectors at each layer. In addition",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                293,
+                                504,
+                                304
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        293,
+                                        504,
+                                        304
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to our main contribution above, we thus propose to extend the PoWER-BERT so that it is applicable",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                303,
+                                505,
+                                316
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        303,
+                                        505,
+                                        316
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to token-level classification, such as span-based question-answering. Our proposal, to which we",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                313,
+                                505,
+                                326
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        313,
+                                        505,
+                                        326
+                                    ],
+                                    "score": 1.0,
+                                    "content": "refer as Drop-and-Restore, does not eliminate word vectors at each layer according to the length",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                326,
+                                505,
+                                337
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        326,
+                                        505,
+                                        337
+                                    ],
+                                    "score": 1.0,
+                                    "content": "configuration but instead sets them aside until the final hidden layer. At the final hidden layer, these",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                336,
+                                504,
+                                349
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        336,
+                                        504,
+                                        349
+                                    ],
+                                    "score": 1.0,
+                                    "content": "word vectors are brought back to form the full hidden sequence, as illustrated graphically in Fig. 1.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 13,
+                    "bbox_fs": [
+                        105,
+                        271,
+                        506,
+                        349
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        364,
+                        231,
+                        376
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                363,
+                                232,
+                                378
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        363,
+                                        232,
+                                        378
+                                    ],
+                                    "score": 1.0,
+                                    "content": "4 EXPERIMENT SETUP",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        389,
+                        505,
+                        466
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                389,
+                                506,
+                                402
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        389,
+                                        506,
+                                        402
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Datasets We test the proposed approach on both sequence-level and token-level tasks, the latter",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                399,
+                                507,
+                                414
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        399,
+                                        507,
+                                        414
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of which could not have been done with the original PoWER-BERT unless for the proposed Drop-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                411,
+                                505,
+                                424
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        411,
+                                        505,
+                                        424
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and-Restore. We use MNLI-m and SST-2 from GLUE benchmark (Wang et al., 2018), as was done",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                422,
+                                506,
+                                435
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        422,
+                                        506,
+                                        435
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to test PoWER-BERT earlier, for sequence-level classification. We choose them because consistent",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                434,
+                                505,
+                                446
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        434,
+                                        505,
+                                        446
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accuracy scores from standard training on them due to their sufficiently large training set imply that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                444,
+                                506,
+                                457
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        444,
+                                        506,
+                                        457
+                                    ],
+                                    "score": 1.0,
+                                    "content": "they are reliable to verify our approach. We use SQuAD 1.1 (Rajpurkar et al., 2016) for token-level",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                455,
+                                164,
+                                467
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        455,
+                                        164,
+                                        467
+                                    ],
+                                    "score": 1.0,
+                                    "content": "classification.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 21,
+                    "bbox_fs": [
+                        105,
+                        389,
+                        507,
+                        467
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        479,
+                        505,
+                        546
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                478,
+                                505,
+                                492
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        478,
+                                        505,
+                                        492
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Evaluation metrics We use the number of floating operations (FLOPs) as a main metric to measure",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                489,
+                                506,
+                                505
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        489,
+                                        506,
+                                        505
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the inference efficiency given any length configuration, as it is agnostic to the choice of underlying",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                499,
+                                506,
+                                516
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        499,
+                                        506,
+                                        516
+                                    ],
+                                    "score": 1.0,
+                                    "content": "hardware, unlike other alternatives such as hardware-aware latency (Wang et al., 2020) or energy",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                512,
+                                506,
+                                525
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        512,
+                                        506,
+                                        525
+                                    ],
+                                    "score": 1.0,
+                                    "content": "consumption (Henderson et al., 2020). We later demonstrate that FLOPs and wall-clock time on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                523,
+                                506,
+                                536
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        523,
+                                        506,
+                                        536
+                                    ],
+                                    "score": 1.0,
+                                    "content": "GPU and CPU correlate well with the proposed approach, which is not necessarily the case for other",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                535,
+                                444,
+                                547
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        535,
+                                        444,
+                                        547
+                                    ],
+                                    "score": 1.0,
+                                    "content": "approaches, such as unstructured weight pruning (Han et al., 2015; See et al., 2016).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 27.5,
+                    "bbox_fs": [
+                        105,
+                        478,
+                        506,
+                        547
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        558,
+                        505,
+                        646
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                559,
+                                505,
+                                571
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        559,
+                                        505,
+                                        571
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Pretrained transformers Since BERT was introduced by Devlin et al. (2018), it has become",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                570,
+                                505,
+                                582
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        570,
+                                        505,
+                                        582
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a standard practice to start from a pretrained (masked) language model and finetune it for each",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                580,
+                                506,
+                                594
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        580,
+                                        506,
+                                        594
+                                    ],
+                                    "score": 1.0,
+                                    "content": "downstream task. We follow the same strategy in this paper and test two pretrained transformer-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                591,
+                                506,
+                                604
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        591,
+                                        506,
+                                        604
+                                    ],
+                                    "score": 1.0,
+                                    "content": "based language models; BERTBASE (Devlin et al., 2018) and DistilBERT (Sanh et al., 2019), which",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                601,
+                                505,
+                                616
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        601,
+                                        505,
+                                        616
+                                    ],
+                                    "score": 1.0,
+                                    "content": "allows us to demonstrate that the usefulness and applicability of our approach are not tied to any",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                613,
+                                506,
+                                627
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        613,
+                                        506,
+                                        627
+                                    ],
+                                    "score": 1.0,
+                                    "content": "specific architectural choice, such as the number of layers and the maximum length of input sequence.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                624,
+                                505,
+                                637
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        624,
+                                        505,
+                                        637
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Although we focus on BERT-based masked language models here, the proposed approach is readily",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                636,
+                                286,
+                                647
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        636,
+                                        286,
+                                        647
+                                    ],
+                                    "score": 1.0,
+                                    "content": "applicable to any transformer-based models.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        }
+                    ],
+                    "index": 34.5,
+                    "bbox_fs": [
+                        105,
+                        559,
+                        506,
+                        647
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        660,
+                        505,
+                        693
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                659,
+                                505,
+                                673
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        659,
+                                        505,
+                                        673
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Learning We train a Length-Adaptive Transformer with LengthDrop probability and LayerDrop",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                671,
+                                505,
+                                683
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        671,
+                                        244,
+                                        683
+                                    ],
+                                    "score": 1.0,
+                                    "content": "probability both set to 0.2. We use",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        245,
+                                        671,
+                                        275,
+                                        682
+                                    ],
+                                    "score": 0.9,
+                                    "content": "n _ { s } = 2",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        275,
+                                        671,
+                                        505,
+                                        683
+                                    ],
+                                    "score": 1.0,
+                                    "content": "randomly sampled intermediate sub-models in addition to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                681,
+                                406,
+                                694
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        681,
+                                        406,
+                                        694
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the full model and smallest model for applying the sandwich learning rule.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        }
+                    ],
+                    "index": 40,
+                    "bbox_fs": [
+                        105,
+                        659,
+                        505,
+                        694
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        699,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                699,
+                                506,
+                                711
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        699,
+                                        506,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We start finetuning the pretrained transformer without Drop-and-Restore first, just as Goyal et al.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                709,
+                                506,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        709,
+                                        506,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(2020) did with PoWER-BERT. We then continue finetuning it for another five epochs with Drop-and-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                720,
+                                505,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        720,
+                                        505,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Restore. This is unlike the recommended three epochs by Devlin et al. (2018), as learning progresses",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                375,
+                                505,
+                                389
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        375,
+                                        505,
+                                        389
+                                    ],
+                                    "score": 1.0,
+                                    "content": "slower due to a higher level of stochasticity introduced by LengthDrop and LayerDrop. We use the",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                387,
+                                505,
+                                399
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        387,
+                                        252,
+                                        399
+                                    ],
+                                    "score": 1.0,
+                                    "content": "batch size of 32, the learning rate of",
+                                    "type": "text",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        253,
+                                        387,
+                                        281,
+                                        397
+                                    ],
+                                    "score": 0.85,
+                                    "content": "5 e - 5",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        281,
+                                        387,
+                                        367,
+                                        399
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for SQuAD v1.1 and",
+                                    "type": "text",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        367,
+                                        387,
+                                        396,
+                                        397
+                                    ],
+                                    "score": 0.84,
+                                    "content": "2 e - 5",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        396,
+                                        387,
+                                        505,
+                                        399
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for MNLI-m and SST, and",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                398,
+                                453,
+                                410
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        398,
+                                        453,
+                                        410
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the maximum sequence length of 384 for SQuAD v1.1 and 128 for MNLI-m and SST.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 43,
+                    "bbox_fs": [
+                        105,
+                        699,
+                        506,
+                        733
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "image",
+                    "bbox": [
+                        111,
+                        79,
+                        391,
+                        277
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                111,
+                                79,
+                                391,
+                                277
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        79,
+                                        391,
+                                        277
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                111,
+                                                79,
+                                                391,
+                                                277
+                                            ],
+                                            "score": 0.935,
+                                            "type": "image",
+                                            "image_path": "3ea54ad6f6a4d01240155dd50bd06714bd078c67453a78cfd7ce1b9404ef27c2.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        79,
+                                        391,
+                                        145.0
+                                    ],
+                                    "spans": [],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        111,
+                                        145.0,
+                                        391,
+                                        211.0
+                                    ],
+                                    "spans": [],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        111,
+                                        211.0,
+                                        391,
+                                        277.0
+                                    ],
+                                    "spans": [],
+                                    "index": 2
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                108,
+                                285,
+                                396,
+                                363
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        285,
+                                        397,
+                                        298
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                107,
+                                                285,
+                                                397,
+                                                298
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 2: Pareto curves of F1 score and FLOPs on SQuAD 1.1 (Rajpurkar",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        107,
+                                        297,
+                                        396,
+                                        309
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                107,
+                                                297,
+                                                291,
+                                                309
+                                            ],
+                                            "score": 1.0,
+                                            "content": "et al., 2016). We apply the proposed method to",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
+                                                291,
+                                                297,
+                                                331,
+                                                308
+                                            ],
+                                            "score": 0.77,
+                                            "content": "\\mathbf { B E R T _ { B a s e } }",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
+                                                331,
+                                                297,
+                                                396,
+                                                309
+                                            ],
+                                            "score": 1.0,
+                                            "content": "(solid lines) and",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        306,
+                                        397,
+                                        321
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                306,
+                                                397,
+                                                321
+                                            ],
+                                            "score": 1.0,
+                                            "content": "DistilBERT (dotted lines). For each model, we draw three curves using",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 6
+                                },
+                                {
+                                    "bbox": [
+                                        107,
+                                        318,
+                                        397,
+                                        332
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                107,
+                                                318,
+                                                397,
+                                                332
+                                            ],
+                                            "score": 1.0,
+                                            "content": "(1) standard finetuned transformer with constant-rate length reduction, (2)",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 7
+                                },
+                                {
+                                    "bbox": [
+                                        107,
+                                        330,
+                                        397,
+                                        342
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                107,
+                                                330,
+                                                397,
+                                                342
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Length-Adaptive Transformer with constant-rate length reduction, and",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 8
+                                },
+                                {
+                                    "bbox": [
+                                        107,
+                                        341,
+                                        396,
+                                        353
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                107,
+                                                341,
+                                                396,
+                                                353
+                                            ],
+                                            "score": 1.0,
+                                            "content": "(3) Length-Adaptive Transformer with length configurations obtained",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 9
+                                },
+                                {
+                                    "bbox": [
+                                        108,
+                                        352,
+                                        227,
+                                        364
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                108,
+                                                352,
+                                                227,
+                                                364
+                                            ],
+                                            "score": 1.0,
+                                            "content": "from the evolutionary search.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 10
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 4.0
+                },
+                {
+                    "type": "image",
+                    "bbox": [
+                        408,
+                        81,
+                        497,
+                        297
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                408,
+                                81,
+                                497,
+                                297
+                            ],
+                            "group_id": 1,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        408,
+                                        81,
+                                        497,
+                                        297
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                408,
+                                                81,
+                                                497,
+                                                297
+                                            ],
+                                            "score": 0.934,
+                                            "type": "image",
+                                            "image_path": "4608176aa7c7dba0b4748567c1c64abe798b711bebf826c4b323894a4bfb2b12.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        408,
+                                        81,
+                                        497,
+                                        297
+                                    ],
+                                    "spans": [],
+                                    "index": 5
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                408,
+                                305,
+                                498,
+                                350
+                            ],
+                            "group_id": 1,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        407,
+                                        305,
+                                        498,
+                                        317
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                407,
+                                                305,
+                                                498,
+                                                317
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 3: Correlation",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 11
+                                },
+                                {
+                                    "bbox": [
+                                        408,
+                                        316,
+                                        498,
+                                        328
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                408,
+                                                316,
+                                                498,
+                                                328
+                                            ],
+                                            "score": 1.0,
+                                            "content": "between FLOPs and",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 12
+                                },
+                                {
+                                    "bbox": [
+                                        408,
+                                        327,
+                                        498,
+                                        339
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                408,
+                                                327,
+                                                498,
+                                                339
+                                            ],
+                                            "score": 1.0,
+                                            "content": "latency with different",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 13
+                                },
+                                {
+                                    "bbox": [
+                                        408,
+                                        338,
+                                        498,
+                                        351
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                408,
+                                                338,
+                                                498,
+                                                351
+                                            ],
+                                            "score": 1.0,
+                                            "content": "length configurations.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 14
+                                }
+                            ],
+                            "index": 12.5
+                        }
+                    ],
+                    "index": 8.75
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        375,
+                        504,
+                        409
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                375,
+                                505,
+                                389
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        375,
+                                        505,
+                                        389
+                                    ],
+                                    "score": 1.0,
+                                    "content": "slower due to a higher level of stochasticity introduced by LengthDrop and LayerDrop. We use the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                387,
+                                505,
+                                399
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        387,
+                                        252,
+                                        399
+                                    ],
+                                    "score": 1.0,
+                                    "content": "batch size of 32, the learning rate of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        253,
+                                        387,
+                                        281,
+                                        397
+                                    ],
+                                    "score": 0.85,
+                                    "content": "5 e - 5",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        281,
+                                        387,
+                                        367,
+                                        399
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for SQuAD v1.1 and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        367,
+                                        387,
+                                        396,
+                                        397
+                                    ],
+                                    "score": 0.84,
+                                    "content": "2 e - 5",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        396,
+                                        387,
+                                        505,
+                                        399
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for MNLI-m and SST, and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                398,
+                                453,
+                                410
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        398,
+                                        453,
+                                        410
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the maximum sequence length of 384 for SQuAD v1.1 and 128 for MNLI-m and SST.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        422,
+                        505,
+                        456
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                421,
+                                507,
+                                435
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        421,
+                                        199,
+                                        435
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Search We run up to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        200,
+                                        422,
+                                        232,
+                                        432
+                                    ],
+                                    "score": 0.9,
+                                    "content": "G = 3 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        232,
+                                        421,
+                                        389,
+                                        435
+                                    ],
+                                    "score": 1.0,
+                                    "content": "iterations of evolutionary search, using",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        389,
+                                        423,
+                                        428,
+                                        433
+                                    ],
+                                    "score": 0.9,
+                                    "content": "n _ { m } = 3 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        428,
+                                        421,
+                                        507,
+                                        435
+                                    ],
+                                    "score": 1.0,
+                                    "content": "mutated configura-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                433,
+                                505,
+                                446
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        433,
+                                        231,
+                                        446
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tions with mutation probability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        232,
+                                        433,
+                                        272,
+                                        445
+                                    ],
+                                    "score": 0.9,
+                                    "content": "p _ { m } = 0 . 5",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        272,
+                                        433,
+                                        289,
+                                        446
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        290,
+                                        433,
+                                        325,
+                                        444
+                                    ],
+                                    "score": 0.91,
+                                    "content": "n _ { c } = 3 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        325,
+                                        433,
+                                        505,
+                                        446
+                                    ],
+                                    "score": 1.0,
+                                    "content": "crossover’d configurations, to find the Pareto",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                443,
+                                248,
+                                457
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        443,
+                                        248,
+                                        457
+                                    ],
+                                    "score": 1.0,
+                                    "content": "frontier of accuracy and efficiency.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 19
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        472,
+                        253,
+                        485
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                471,
+                                255,
+                                487
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        471,
+                                        255,
+                                        487
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5 RESULTS AND ANALYSIS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 21
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        497,
+                        505,
+                        564
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                498,
+                                505,
+                                510
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        498,
+                                        505,
+                                        510
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Efficiency-accuracy trade-off We use SQuAD 1.1 to examine the effect of the proposed approach",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                508,
+                                507,
+                                523
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        508,
+                                        507,
+                                        523
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on the efficiency-accuracy trade-off. When the underlying classifier was not trained with LengthDrop,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                520,
+                                506,
+                                533
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        520,
+                                        506,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as proposed in this paper, the accuracy drops even more dramatically as more word vectors are dropped",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                530,
+                                506,
+                                543
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        530,
+                                        506,
+                                        543
+                                    ],
+                                    "score": 1.0,
+                                    "content": "at each layer. The difference between standard transformer and Length-Adaptive Transformer is stark",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                541,
+                                506,
+                                555
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        541,
+                                        506,
+                                        555
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in Fig. 2. This verifies the importance of training a transformer in a way that makes it malleable for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                553,
+                                236,
+                                565
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        553,
+                                        236,
+                                        565
+                                    ],
+                                    "score": 1.0,
+                                    "content": "inference-time re-configuration.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 24.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        569,
+                        505,
+                        625
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                569,
+                                505,
+                                583
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        569,
+                                        505,
+                                        583
+                                    ],
+                                    "score": 1.0,
+                                    "content": "When the model was trained with the proposed LengthDrop, we notice the efficacy of the proposed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                579,
+                                506,
+                                595
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        579,
+                                        506,
+                                        595
+                                    ],
+                                    "score": 1.0,
+                                    "content": "approach of using evolutionary search to find the optimal trade-off between inference efficiency",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                591,
+                                505,
+                                605
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        591,
+                                        505,
+                                        605
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and accuracy. The trade-off curve from the proposed search strategy has a larger area-under-curve",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                603,
+                                505,
+                                615
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        603,
+                                        505,
+                                        615
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(AUC) than when constant-rate length reduction was used to meet a target computational budget. It",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                613,
+                                429,
+                                627
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        613,
+                                        429,
+                                        627
+                                    ],
+                                    "score": 1.0,
+                                    "content": "demonstrates the importance of using both LengthDrop and evolutionary search.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 30
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        630,
+                        505,
+                        696
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                629,
+                                506,
+                                644
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        629,
+                                        506,
+                                        644
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We make a minor observation that the proposed approach ends up with a significantly higher accuracy",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                641,
+                                506,
+                                654
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        641,
+                                        429,
+                                        654
+                                    ],
+                                    "score": 1.0,
+                                    "content": "than DistillBERT when enough computational budget is allowed for inference",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        430,
+                                        641,
+                                        502,
+                                        653
+                                    ],
+                                    "score": 0.8,
+                                    "content": "( \\log { \\mathrm { F L O P s } } > 1 0 )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        502,
+                                        641,
+                                        506,
+                                        654
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                651,
+                                506,
+                                665
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        651,
+                                        506,
+                                        665
+                                    ],
+                                    "score": 1.0,
+                                    "content": "This makes our approach desirable in a wide array of scenarios, as it does not require any additional",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                662,
+                                506,
+                                676
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        662,
+                                        506,
+                                        676
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pretraining stage, as does DistilBERT. With a severe constraint on the computational budget, the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                674,
+                                506,
+                                687
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        674,
+                                        506,
+                                        687
+                                    ],
+                                    "score": 1.0,
+                                    "content": "proposed approach could be used on DistilBERT to significantly improve the efficiency without",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                685,
+                                221,
+                                699
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        685,
+                                        221,
+                                        699
+                                    ],
+                                    "score": 1.0,
+                                    "content": "compromising the accuracy.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        }
+                    ],
+                    "index": 35.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        709,
+                        503,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                709,
+                                505,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        709,
+                                        505,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Maximizing inference efficiency We consider all three tasks, SQuAD 1.1, MNLI-m and SST-2,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                720,
+                                505,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        720,
+                                        505,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and investigate how much efficiency can be gained by the proposed approach with minimal sacrifice of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        }
+                    ],
+                    "index": 39.5
+                }
+            ],
+            "page_idx": 5,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        307,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                25,
+                                308,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        25,
+                                        308,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Under review as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        752,
+                        308,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                302,
+                                751,
+                                309,
+                                762
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        302,
+                                        751,
+                                        309,
+                                        762
+                                    ],
+                                    "score": 1.0,
+                                    "content": "6",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "image",
+                    "bbox": [
+                        111,
+                        79,
+                        391,
+                        277
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                111,
+                                79,
+                                391,
+                                277
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        79,
+                                        391,
+                                        277
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                111,
+                                                79,
+                                                391,
+                                                277
+                                            ],
+                                            "score": 0.935,
+                                            "type": "image",
+                                            "image_path": "3ea54ad6f6a4d01240155dd50bd06714bd078c67453a78cfd7ce1b9404ef27c2.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        79,
+                                        391,
+                                        145.0
+                                    ],
+                                    "spans": [],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        111,
+                                        145.0,
+                                        391,
+                                        211.0
+                                    ],
+                                    "spans": [],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        111,
+                                        211.0,
+                                        391,
+                                        277.0
+                                    ],
+                                    "spans": [],
+                                    "index": 2
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                108,
+                                285,
+                                396,
+                                363
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        285,
+                                        397,
+                                        298
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                107,
+                                                285,
+                                                397,
+                                                298
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 2: Pareto curves of F1 score and FLOPs on SQuAD 1.1 (Rajpurkar",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        107,
+                                        297,
+                                        396,
+                                        309
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                107,
+                                                297,
+                                                291,
+                                                309
+                                            ],
+                                            "score": 1.0,
+                                            "content": "et al., 2016). We apply the proposed method to",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
+                                                291,
+                                                297,
+                                                331,
+                                                308
+                                            ],
+                                            "score": 0.77,
+                                            "content": "\\mathbf { B E R T _ { B a s e } }",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
+                                                331,
+                                                297,
+                                                396,
+                                                309
+                                            ],
+                                            "score": 1.0,
+                                            "content": "(solid lines) and",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        106,
+                                        306,
+                                        397,
+                                        321
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                106,
+                                                306,
+                                                397,
+                                                321
+                                            ],
+                                            "score": 1.0,
+                                            "content": "DistilBERT (dotted lines). For each model, we draw three curves using",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 6
+                                },
+                                {
+                                    "bbox": [
+                                        107,
+                                        318,
+                                        397,
+                                        332
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                107,
+                                                318,
+                                                397,
+                                                332
+                                            ],
+                                            "score": 1.0,
+                                            "content": "(1) standard finetuned transformer with constant-rate length reduction, (2)",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 7
+                                },
+                                {
+                                    "bbox": [
+                                        107,
+                                        330,
+                                        397,
+                                        342
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                107,
+                                                330,
+                                                397,
+                                                342
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Length-Adaptive Transformer with constant-rate length reduction, and",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 8
+                                },
+                                {
+                                    "bbox": [
+                                        107,
+                                        341,
+                                        396,
+                                        353
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                107,
+                                                341,
+                                                396,
+                                                353
+                                            ],
+                                            "score": 1.0,
+                                            "content": "(3) Length-Adaptive Transformer with length configurations obtained",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 9
+                                },
+                                {
+                                    "bbox": [
+                                        108,
+                                        352,
+                                        227,
+                                        364
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                108,
+                                                352,
+                                                227,
+                                                364
+                                            ],
+                                            "score": 1.0,
+                                            "content": "from the evolutionary search.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 10
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 4.0
+                },
+                {
+                    "type": "image",
+                    "bbox": [
+                        408,
+                        81,
+                        497,
+                        297
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                408,
+                                81,
+                                497,
+                                297
+                            ],
+                            "group_id": 1,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        408,
+                                        81,
+                                        497,
+                                        297
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                408,
+                                                81,
+                                                497,
+                                                297
+                                            ],
+                                            "score": 0.934,
+                                            "type": "image",
+                                            "image_path": "4608176aa7c7dba0b4748567c1c64abe798b711bebf826c4b323894a4bfb2b12.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        408,
+                                        81,
+                                        497,
+                                        297
+                                    ],
+                                    "spans": [],
+                                    "index": 5
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                408,
+                                305,
+                                498,
+                                350
+                            ],
+                            "group_id": 1,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        407,
+                                        305,
+                                        498,
+                                        317
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                407,
+                                                305,
+                                                498,
+                                                317
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 3: Correlation",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 11
+                                },
+                                {
+                                    "bbox": [
+                                        408,
+                                        316,
+                                        498,
+                                        328
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                408,
+                                                316,
+                                                498,
+                                                328
+                                            ],
+                                            "score": 1.0,
+                                            "content": "between FLOPs and",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 12
+                                },
+                                {
+                                    "bbox": [
+                                        408,
+                                        327,
+                                        498,
+                                        339
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                408,
+                                                327,
+                                                498,
+                                                339
+                                            ],
+                                            "score": 1.0,
+                                            "content": "latency with different",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 13
+                                },
+                                {
+                                    "bbox": [
+                                        408,
+                                        338,
+                                        498,
+                                        351
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                408,
+                                                338,
+                                                498,
+                                                351
+                                            ],
+                                            "score": 1.0,
+                                            "content": "length configurations.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 14
+                                }
+                            ],
+                            "index": 12.5
+                        }
+                    ],
+                    "index": 8.75
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        375,
+                        504,
+                        409
+                    ],
+                    "lines": [],
+                    "index": 16,
+                    "bbox_fs": [
+                        105,
+                        375,
+                        505,
+                        410
+                    ],
+                    "lines_deleted": true
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        422,
+                        505,
+                        456
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                421,
+                                507,
+                                435
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        421,
+                                        199,
+                                        435
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Search We run up to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        200,
+                                        422,
+                                        232,
+                                        432
+                                    ],
+                                    "score": 0.9,
+                                    "content": "G = 3 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        232,
+                                        421,
+                                        389,
+                                        435
+                                    ],
+                                    "score": 1.0,
+                                    "content": "iterations of evolutionary search, using",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        389,
+                                        423,
+                                        428,
+                                        433
+                                    ],
+                                    "score": 0.9,
+                                    "content": "n _ { m } = 3 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        428,
+                                        421,
+                                        507,
+                                        435
+                                    ],
+                                    "score": 1.0,
+                                    "content": "mutated configura-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                433,
+                                505,
+                                446
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        433,
+                                        231,
+                                        446
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tions with mutation probability",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        232,
+                                        433,
+                                        272,
+                                        445
+                                    ],
+                                    "score": 0.9,
+                                    "content": "p _ { m } = 0 . 5",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        272,
+                                        433,
+                                        289,
+                                        446
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        290,
+                                        433,
+                                        325,
+                                        444
+                                    ],
+                                    "score": 0.91,
+                                    "content": "n _ { c } = 3 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        325,
+                                        433,
+                                        505,
+                                        446
+                                    ],
+                                    "score": 1.0,
+                                    "content": "crossover’d configurations, to find the Pareto",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                443,
+                                248,
+                                457
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        443,
+                                        248,
+                                        457
+                                    ],
+                                    "score": 1.0,
+                                    "content": "frontier of accuracy and efficiency.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 19,
+                    "bbox_fs": [
+                        105,
+                        421,
+                        507,
+                        457
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        472,
+                        253,
+                        485
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                471,
+                                255,
+                                487
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        471,
+                                        255,
+                                        487
+                                    ],
+                                    "score": 1.0,
+                                    "content": "5 RESULTS AND ANALYSIS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 21
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        497,
+                        505,
+                        564
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                498,
+                                505,
+                                510
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        498,
+                                        505,
+                                        510
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Efficiency-accuracy trade-off We use SQuAD 1.1 to examine the effect of the proposed approach",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                508,
+                                507,
+                                523
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        508,
+                                        507,
+                                        523
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on the efficiency-accuracy trade-off. When the underlying classifier was not trained with LengthDrop,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                520,
+                                506,
+                                533
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        520,
+                                        506,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as proposed in this paper, the accuracy drops even more dramatically as more word vectors are dropped",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                530,
+                                506,
+                                543
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        530,
+                                        506,
+                                        543
+                                    ],
+                                    "score": 1.0,
+                                    "content": "at each layer. The difference between standard transformer and Length-Adaptive Transformer is stark",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                541,
+                                506,
+                                555
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        541,
+                                        506,
+                                        555
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in Fig. 2. This verifies the importance of training a transformer in a way that makes it malleable for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                553,
+                                236,
+                                565
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        553,
+                                        236,
+                                        565
+                                    ],
+                                    "score": 1.0,
+                                    "content": "inference-time re-configuration.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 24.5,
+                    "bbox_fs": [
+                        105,
+                        498,
+                        507,
+                        565
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        569,
+                        505,
+                        625
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                569,
+                                505,
+                                583
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        569,
+                                        505,
+                                        583
+                                    ],
+                                    "score": 1.0,
+                                    "content": "When the model was trained with the proposed LengthDrop, we notice the efficacy of the proposed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                579,
+                                506,
+                                595
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        579,
+                                        506,
+                                        595
+                                    ],
+                                    "score": 1.0,
+                                    "content": "approach of using evolutionary search to find the optimal trade-off between inference efficiency",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                591,
+                                505,
+                                605
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        591,
+                                        505,
+                                        605
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and accuracy. The trade-off curve from the proposed search strategy has a larger area-under-curve",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                603,
+                                505,
+                                615
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        603,
+                                        505,
+                                        615
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(AUC) than when constant-rate length reduction was used to meet a target computational budget. It",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                613,
+                                429,
+                                627
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        613,
+                                        429,
+                                        627
+                                    ],
+                                    "score": 1.0,
+                                    "content": "demonstrates the importance of using both LengthDrop and evolutionary search.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 30,
+                    "bbox_fs": [
+                        105,
+                        569,
+                        506,
+                        627
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        630,
+                        505,
+                        696
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                629,
+                                506,
+                                644
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        629,
+                                        506,
+                                        644
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We make a minor observation that the proposed approach ends up with a significantly higher accuracy",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                641,
+                                506,
+                                654
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        641,
+                                        429,
+                                        654
+                                    ],
+                                    "score": 1.0,
+                                    "content": "than DistillBERT when enough computational budget is allowed for inference",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        430,
+                                        641,
+                                        502,
+                                        653
+                                    ],
+                                    "score": 0.8,
+                                    "content": "( \\log { \\mathrm { F L O P s } } > 1 0 )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        502,
+                                        641,
+                                        506,
+                                        654
+                                    ],
+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                651,
+                                506,
+                                665
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        651,
+                                        506,
+                                        665
+                                    ],
+                                    "score": 1.0,
+                                    "content": "This makes our approach desirable in a wide array of scenarios, as it does not require any additional",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                662,
+                                506,
+                                676
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        662,
+                                        506,
+                                        676
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pretraining stage, as does DistilBERT. With a severe constraint on the computational budget, the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                674,
+                                506,
+                                687
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        674,
+                                        506,
+                                        687
+                                    ],
+                                    "score": 1.0,
+                                    "content": "proposed approach could be used on DistilBERT to significantly improve the efficiency without",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                685,
+                                221,
+                                699
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        685,
+                                        221,
+                                        699
+                                    ],
+                                    "score": 1.0,
+                                    "content": "compromising the accuracy.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        }
+                    ],
+                    "index": 35.5,
+                    "bbox_fs": [
+                        104,
+                        629,
+                        506,
+                        699
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        709,
+                        503,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                709,
+                                505,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        709,
+                                        505,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Maximizing inference efficiency We consider all three tasks, SQuAD 1.1, MNLI-m and SST-2,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                720,
+                                505,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        720,
+                                        505,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and investigate how much efficiency can be gained by the proposed approach with minimal sacrifice of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                274,
+                                506,
+                                286
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        274,
+                                        506,
+                                        286
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accuracy. First, we look at how much efficiency could be gained without losing on the accuracy. That",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                285,
+                                506,
+                                297
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        285,
+                                        506,
+                                        297
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is, we use the length configuration that maximizes the inference efficiency (i.e., minimize the FLOPs)",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                296,
+                                506,
+                                308
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        296,
+                                        506,
+                                        308
+                                    ],
+                                    "score": 1.0,
+                                    "content": "while ensuring that the accuracy is above or same as the accuracy of the standard approach without",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                306,
+                                505,
+                                319
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        306,
+                                        505,
+                                        319
+                                    ],
+                                    "score": 1.0,
+                                    "content": "any drop of word vectors. The results are presented in the rows marked with Length-Adaptive† from",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                317,
+                                506,
+                                331
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        317,
+                                        252,
+                                        331
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Table 1. For example, in the case of",
+                                    "type": "text",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        252,
+                                        318,
+                                        292,
+                                        329
+                                    ],
+                                    "score": 0.62,
+                                    "content": "\\mathbf { B E R T _ { B a s e } }",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        292,
+                                        317,
+                                        506,
+                                        331
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the proposed approach reduce FLOPs by more than",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                329,
+                                211,
+                                340
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        329,
+                                        211,
+                                        340
+                                    ],
+                                    "score": 1.0,
+                                    "content": "half across all three tasks.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 39.5,
+                    "bbox_fs": [
+                        105,
+                        709,
+                        505,
+                        732
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "table",
+                    "bbox": [
+                        112,
+                        80,
+                        394,
+                        190
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                112,
+                                80,
+                                394,
+                                190
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        112,
+                                        80,
+                                        394,
+                                        190
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                112,
+                                                80,
+                                                394,
+                                                190
+                                            ],
+                                            "score": 0.981,
+                                            "html": "<table><tr><td colspan=\"2\">Model</td><td colspan=\"2\">SQuAD 1.1</td><td colspan=\"2\">MNLI-m</td><td colspan=\"2\">SST-2</td></tr><tr><td>Pretrained Transformer</td><td>Method</td><td>F1</td><td>FLOPs</td><td>Acc</td><td>FLOPs</td><td>Acc</td><td>FLOPs</td></tr><tr><td rowspan=\"2\">BERTBase</td><td>Standard</td><td>88.5</td><td>1.00x</td><td>84.4</td><td>1.00x</td><td>92.8</td><td>1.00x</td></tr><tr><td>Length-Adaptive*</td><td>89.6</td><td>0.89x</td><td>85.0</td><td>0.58x</td><td>93.1</td><td>0.36x</td></tr><tr><td rowspan=\"2\"></td><td>Length-Adaptivet</td><td>88.7</td><td>0.45x</td><td>84.4</td><td>0.35x</td><td>92.8</td><td>0.35x</td></tr><tr><td>Standard</td><td>85.8</td><td>1.00x</td><td>80.9</td><td>1.00x</td><td>90.6</td><td>1.00x</td></tr><tr><td rowspan=\"2\">DistilBERT1</td><td>Length-Adaptive*</td><td>86.3</td><td>0.81x</td><td>81.5</td><td>0.56x</td><td>92.0</td><td>0.55x</td></tr><tr><td>Length-Adaptive†</td><td>85.9</td><td>0.59x</td><td>81.3</td><td>0.54x</td><td>91.7</td><td>0.54x</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "f0829b1fbd9636baa6152ad5a45e5f7dbf08c6a7333b2fd362453dfa90284833.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        112,
+                                        80,
+                                        394,
+                                        116.66666666666666
+                                    ],
+                                    "spans": [],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        112,
+                                        116.66666666666666,
+                                        394,
+                                        153.33333333333331
+                                    ],
+                                    "spans": [],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        112,
+                                        153.33333333333331,
+                                        394,
+                                        189.99999999999997
+                                    ],
+                                    "spans": [],
+                                    "index": 2
+                                }
+                            ]
+                        },
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                109,
+                                198,
+                                398,
+                                264
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        108,
+                                        197,
+                                        398,
+                                        210
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                108,
+                                                197,
+                                                398,
+                                                210
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 1: Comparison results of standard Transformer and Length-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        109,
+                                        208,
+                                        398,
+                                        221
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                109,
+                                                208,
+                                                398,
+                                                221
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Adaptive Transformer. Among length configurations on the Pareto fron-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        108,
+                                        219,
+                                        399,
+                                        232
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                108,
+                                                219,
+                                                399,
+                                                232
+                                            ],
+                                            "score": 1.0,
+                                            "content": "tier of Length-Adaptive Transformer, we pick two representative points:",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 5
+                                },
+                                {
+                                    "bbox": [
+                                        108,
+                                        231,
+                                        398,
+                                        242
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                108,
+                                                231,
+                                                398,
+                                                242
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Length-Adaptive? and Length-Adaptive† as the most efficient one while",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 6
+                                },
+                                {
+                                    "bbox": [
+                                        108,
+                                        241,
+                                        398,
+                                        255
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                108,
+                                                241,
+                                                398,
+                                                255
+                                            ],
+                                            "score": 1.0,
+                                            "content": "having the highest accuracy and the accuracy higher than (or equal to)",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 7
+                                },
+                                {
+                                    "bbox": [
+                                        108,
+                                        252,
+                                        252,
+                                        266
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                108,
+                                                252,
+                                                252,
+                                                266
+                                            ],
+                                            "score": 1.0,
+                                            "content": "standard Transformer, respectively.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 8
+                                }
+                            ],
+                            "index": 5.5
+                        }
+                    ],
+                    "index": 3.25
+                },
+                {
+                    "type": "image",
+                    "bbox": [
+                        410,
+                        86,
+                        498,
+                        182
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                410,
+                                86,
+                                498,
+                                182
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        410,
+                                        86,
+                                        498,
+                                        182
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                410,
+                                                86,
+                                                498,
+                                                182
+                                            ],
+                                            "score": 0.961,
+                                            "type": "image",
+                                            "image_path": "e4a6ecfc1cdcda5b3130f2509429e44b544d994935e6b44f36893f811295f752.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 9.5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        410,
+                                        86,
+                                        498,
+                                        134.0
+                                    ],
+                                    "spans": [],
+                                    "index": 9
+                                },
+                                {
+                                    "bbox": [
+                                        410,
+                                        134.0,
+                                        498,
+                                        182.0
+                                    ],
+                                    "spans": [],
+                                    "index": 10
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                409,
+                                191,
+                                500,
+                                257
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        408,
+                                        188,
+                                        502,
+                                        203
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                408,
+                                                188,
+                                                502,
+                                                203
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 4: Exam-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 11
+                                },
+                                {
+                                    "bbox": [
+                                        408,
+                                        201,
+                                        501,
+                                        213
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                408,
+                                                201,
+                                                501,
+                                                213
+                                            ],
+                                            "score": 1.0,
+                                            "content": "ple of area under",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 12
+                                },
+                                {
+                                    "bbox": [
+                                        409,
+                                        213,
+                                        499,
+                                        223
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                409,
+                                                213,
+                                                499,
+                                                223
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Pareto curve as the",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 13
+                                },
+                                {
+                                    "bbox": [
+                                        409,
+                                        223,
+                                        500,
+                                        235
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                409,
+                                                223,
+                                                500,
+                                                235
+                                            ],
+                                            "score": 1.0,
+                                            "content": "evolutionary search of",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 14
+                                },
+                                {
+                                    "bbox": [
+                                        408,
+                                        233,
+                                        500,
+                                        246
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                408,
+                                                233,
+                                                500,
+                                                246
+                                            ],
+                                            "score": 1.0,
+                                            "content": "lenth configurations",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 15
+                                },
+                                {
+                                    "bbox": [
+                                        408,
+                                        246,
+                                        450,
+                                        257
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                408,
+                                                246,
+                                                450,
+                                                257
+                                            ],
+                                            "score": 1.0,
+                                            "content": "proceeds.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 16
+                                }
+                            ],
+                            "index": 13.5
+                        }
+                    ],
+                    "index": 11.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        273,
+                        506,
+                        340
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                274,
+                                506,
+                                286
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        274,
+                                        506,
+                                        286
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accuracy. First, we look at how much efficiency could be gained without losing on the accuracy. That",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                285,
+                                506,
+                                297
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        285,
+                                        506,
+                                        297
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is, we use the length configuration that maximizes the inference efficiency (i.e., minimize the FLOPs)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                296,
+                                506,
+                                308
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        296,
+                                        506,
+                                        308
+                                    ],
+                                    "score": 1.0,
+                                    "content": "while ensuring that the accuracy is above or same as the accuracy of the standard approach without",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                306,
+                                505,
+                                319
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        306,
+                                        505,
+                                        319
+                                    ],
+                                    "score": 1.0,
+                                    "content": "any drop of word vectors. The results are presented in the rows marked with Length-Adaptive† from",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                317,
+                                506,
+                                331
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        317,
+                                        252,
+                                        331
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Table 1. For example, in the case of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        252,
+                                        318,
+                                        292,
+                                        329
+                                    ],
+                                    "score": 0.62,
+                                    "content": "\\mathbf { B E R T _ { B a s e } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        292,
+                                        317,
+                                        506,
+                                        331
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the proposed approach reduce FLOPs by more than",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                329,
+                                211,
+                                340
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        329,
+                                        211,
+                                        340
+                                    ],
+                                    "score": 1.0,
+                                    "content": "half across all three tasks.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 19.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        345,
+                        505,
+                        434
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                346,
+                                504,
+                                358
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        346,
+                                        504,
+                                        358
+                                    ],
+                                    "score": 1.0,
+                                    "content": "From Fig. 2, we have observed that the proposed Length-Adaptive Transformer generalize better than",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                357,
+                                505,
+                                369
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        357,
+                                        505,
+                                        369
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the standard, base model in some cases. We thus try to maximize both the inference efficiency and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                368,
+                                505,
+                                380
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        368,
+                                        505,
+                                        380
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accuracy, in order to see whether it is possible for the proposed algorithm to find a length configuration",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                378,
+                                505,
+                                391
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        378,
+                                        505,
+                                        391
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that both maximizes inference efficiency and improves accuracy. We present the results in the rows",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                389,
+                                505,
+                                402
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        389,
+                                        505,
+                                        402
+                                    ],
+                                    "score": 1.0,
+                                    "content": "marked with Length-Adaptive? from Table 1. For all cases, Length-Adaptive Transformer achieves",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                401,
+                                506,
+                                413
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        401,
+                                        506,
+                                        413
+                                    ],
+                                    "score": 1.0,
+                                    "content": "higher accuracy than a standard transformer does while reducing FLOPs significantly. Although it",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                411,
+                                505,
+                                424
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        411,
+                                        505,
+                                        424
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is not apparent from the table, tor MNLI-m and SST-2, the accuracy of the smallest sub-model is",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                423,
+                                356,
+                                435
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        423,
+                                        356,
+                                        435
+                                    ],
+                                    "score": 1.0,
+                                    "content": "already greater than or equal to that of a standard transformer.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 26.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        445,
+                        505,
+                        545
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                445,
+                                506,
+                                458
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        445,
+                                        506,
+                                        458
+                                    ],
+                                    "score": 1.0,
+                                    "content": "FLOPs vs. Latency As has been discussed in recent literature (see, e.g., (Li et al., 2020; Chin",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                456,
+                                505,
+                                469
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        456,
+                                        505,
+                                        469
+                                    ],
+                                    "score": 1.0,
+                                    "content": "et al., 2020)), FLOPs is not a perfect indicator of the real latency measured in wall-clock time, as the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                468,
+                                504,
+                                478
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        468,
+                                        504,
+                                        478
+                                    ],
+                                    "score": 1.0,
+                                    "content": "latter is affected by the combination of hardware choice and network architecture. To understand",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                478,
+                                505,
+                                492
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        478,
+                                        505,
+                                        492
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the real-world impact of the proposed approach, we study the relationship between FLOPs, obtained",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                488,
+                                506,
+                                504
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        488,
+                                        506,
+                                        504
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by the proposed procedure, and wall-clock time measured on both CPU and GPU by measuring",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                501,
+                                505,
+                                512
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        501,
+                                        505,
+                                        512
+                                    ],
+                                    "score": 1.0,
+                                    "content": "them while varying length configurations. As shown in Fig. 3, FLOPs and latency exhibit near-linear",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                512,
+                                506,
+                                524
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        512,
+                                        297,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": "correlation on GPU, when the minibatch size is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        297,
+                                        512,
+                                        319,
+                                        523
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\geq 1 6",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        319,
+                                        512,
+                                        506,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and regardless of the minibatch size, on CPU.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                522,
+                                506,
+                                536
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        522,
+                                        506,
+                                        536
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In other words, the reduction in FLOPs with the proposed approach directly implies the reduction in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                532,
+                                173,
+                                546
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        532,
+                                        173,
+                                        546
+                                    ],
+                                    "score": 1.0,
+                                    "content": "wall-clock time.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 35
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        557,
+                        505,
+                        601
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                556,
+                                505,
+                                570
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        556,
+                                        505,
+                                        570
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Convergence of search Although the proposed approach is efficient in that it requires only one",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                569,
+                                506,
+                                581
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        569,
+                                        506,
+                                        581
+                                    ],
+                                    "score": 1.0,
+                                    "content": "round of training, it needs a separate search stage for each target budget. It is important for evolution-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                579,
+                                505,
+                                591
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        579,
+                                        505,
+                                        591
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ary search to converge quickly in the number of forward sweeps of a validation set. As exemplified in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                591,
+                                372,
+                                602
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        591,
+                                        372,
+                                        602
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Fig. 4, evolutionary search converges after about fifteen iterations.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        }
+                    ],
+                    "index": 41.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        617,
+                        211,
+                        630
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                616,
+                                213,
+                                632
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        616,
+                                        213,
+                                        632
+                                    ],
+                                    "score": 1.0,
+                                    "content": "6 RELATED WORK",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        }
+                    ],
+                    "index": 44
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        642,
+                        505,
+                        675
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                641,
+                                505,
+                                655
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        641,
+                                        505,
+                                        655
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The main purpose of the proposed algorithm is to improve the inference efficiency of a large-scale",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                653,
+                                505,
+                                666
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        653,
+                                        505,
+                                        666
+                                    ],
+                                    "score": 1.0,
+                                    "content": "transformer. This goal has been pursued from various directions, and in this section, we provide a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                664,
+                                506,
+                                677
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        664,
+                                        506,
+                                        677
+                                    ],
+                                    "score": 1.0,
+                                    "content": "brief overview of these earlier, and some concurrent, attempts in the context of the proposed approach.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        }
+                    ],
+                    "index": 46
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        687,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                687,
+                                505,
+                                701
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        687,
+                                        505,
+                                        701
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Weight pruning Weight pruning (Han et al., 2015) focuses on reducing the number of parameters",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                698,
+                                506,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        698,
+                                        506,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "which directly reflects the memory footprint of a model and indirectly correlates with inference speed.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                709,
+                                506,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        709,
+                                        506,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "However, their actual speed-up in runtime is usually not significant, especially while executing a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                721,
+                                456,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        721,
+                                        456,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "model with parallel computation using GPU devices (Tang et al., 2018; Li et al., 2020).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 51
+                        }
+                    ],
+                    "index": 49.5
+                }
+            ],
+            "page_idx": 6,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        307,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                308,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        308,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Under review as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        751,
+                        308,
+                        759
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                302,
+                                750,
+                                309,
+                                762
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        302,
+                                        750,
+                                        309,
+                                        762
+                                    ],
+                                    "score": 1.0,
+                                    "content": "7",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "table",
+                    "bbox": [
+                        112,
+                        80,
+                        394,
+                        190
+                    ],
+                    "blocks": [
+                        {
+                            "type": "table_body",
+                            "bbox": [
+                                112,
+                                80,
+                                394,
+                                190
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        112,
+                                        80,
+                                        394,
+                                        190
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                112,
+                                                80,
+                                                394,
+                                                190
+                                            ],
+                                            "score": 0.981,
+                                            "html": "<table><tr><td colspan=\"2\">Model</td><td colspan=\"2\">SQuAD 1.1</td><td colspan=\"2\">MNLI-m</td><td colspan=\"2\">SST-2</td></tr><tr><td>Pretrained Transformer</td><td>Method</td><td>F1</td><td>FLOPs</td><td>Acc</td><td>FLOPs</td><td>Acc</td><td>FLOPs</td></tr><tr><td rowspan=\"2\">BERTBase</td><td>Standard</td><td>88.5</td><td>1.00x</td><td>84.4</td><td>1.00x</td><td>92.8</td><td>1.00x</td></tr><tr><td>Length-Adaptive*</td><td>89.6</td><td>0.89x</td><td>85.0</td><td>0.58x</td><td>93.1</td><td>0.36x</td></tr><tr><td rowspan=\"2\"></td><td>Length-Adaptivet</td><td>88.7</td><td>0.45x</td><td>84.4</td><td>0.35x</td><td>92.8</td><td>0.35x</td></tr><tr><td>Standard</td><td>85.8</td><td>1.00x</td><td>80.9</td><td>1.00x</td><td>90.6</td><td>1.00x</td></tr><tr><td rowspan=\"2\">DistilBERT1</td><td>Length-Adaptive*</td><td>86.3</td><td>0.81x</td><td>81.5</td><td>0.56x</td><td>92.0</td><td>0.55x</td></tr><tr><td>Length-Adaptive†</td><td>85.9</td><td>0.59x</td><td>81.3</td><td>0.54x</td><td>91.7</td><td>0.54x</td></tr></table>",
+                                            "type": "table",
+                                            "image_path": "f0829b1fbd9636baa6152ad5a45e5f7dbf08c6a7333b2fd362453dfa90284833.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        112,
+                                        80,
+                                        394,
+                                        116.66666666666666
+                                    ],
+                                    "spans": [],
+                                    "index": 0
+                                },
+                                {
+                                    "bbox": [
+                                        112,
+                                        116.66666666666666,
+                                        394,
+                                        153.33333333333331
+                                    ],
+                                    "spans": [],
+                                    "index": 1
+                                },
+                                {
+                                    "bbox": [
+                                        112,
+                                        153.33333333333331,
+                                        394,
+                                        189.99999999999997
+                                    ],
+                                    "spans": [],
+                                    "index": 2
+                                }
+                            ]
+                        },
+                        {
+                            "type": "table_caption",
+                            "bbox": [
+                                109,
+                                198,
+                                398,
+                                264
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        108,
+                                        197,
+                                        398,
+                                        210
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                108,
+                                                197,
+                                                398,
+                                                210
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Table 1: Comparison results of standard Transformer and Length-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 3
+                                },
+                                {
+                                    "bbox": [
+                                        109,
+                                        208,
+                                        398,
+                                        221
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                109,
+                                                208,
+                                                398,
+                                                221
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Adaptive Transformer. Among length configurations on the Pareto fron-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 4
+                                },
+                                {
+                                    "bbox": [
+                                        108,
+                                        219,
+                                        399,
+                                        232
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                108,
+                                                219,
+                                                399,
+                                                232
+                                            ],
+                                            "score": 1.0,
+                                            "content": "tier of Length-Adaptive Transformer, we pick two representative points:",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 5
+                                },
+                                {
+                                    "bbox": [
+                                        108,
+                                        231,
+                                        398,
+                                        242
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                108,
+                                                231,
+                                                398,
+                                                242
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Length-Adaptive? and Length-Adaptive† as the most efficient one while",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 6
+                                },
+                                {
+                                    "bbox": [
+                                        108,
+                                        241,
+                                        398,
+                                        255
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                108,
+                                                241,
+                                                398,
+                                                255
+                                            ],
+                                            "score": 1.0,
+                                            "content": "having the highest accuracy and the accuracy higher than (or equal to)",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 7
+                                },
+                                {
+                                    "bbox": [
+                                        108,
+                                        252,
+                                        252,
+                                        266
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                108,
+                                                252,
+                                                252,
+                                                266
+                                            ],
+                                            "score": 1.0,
+                                            "content": "standard Transformer, respectively.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 8
+                                }
+                            ],
+                            "index": 5.5
+                        }
+                    ],
+                    "index": 3.25
+                },
+                {
+                    "type": "image",
+                    "bbox": [
+                        410,
+                        86,
+                        498,
+                        182
+                    ],
+                    "blocks": [
+                        {
+                            "type": "image_body",
+                            "bbox": [
+                                410,
+                                86,
+                                498,
+                                182
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        410,
+                                        86,
+                                        498,
+                                        182
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                410,
+                                                86,
+                                                498,
+                                                182
+                                            ],
+                                            "score": 0.961,
+                                            "type": "image",
+                                            "image_path": "e4a6ecfc1cdcda5b3130f2509429e44b544d994935e6b44f36893f811295f752.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 9.5,
+                            "virtual_lines": [
+                                {
+                                    "bbox": [
+                                        410,
+                                        86,
+                                        498,
+                                        134.0
+                                    ],
+                                    "spans": [],
+                                    "index": 9
+                                },
+                                {
+                                    "bbox": [
+                                        410,
+                                        134.0,
+                                        498,
+                                        182.0
+                                    ],
+                                    "spans": [],
+                                    "index": 10
+                                }
+                            ]
+                        },
+                        {
+                            "type": "image_caption",
+                            "bbox": [
+                                409,
+                                191,
+                                500,
+                                257
+                            ],
+                            "group_id": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        408,
+                                        188,
+                                        502,
+                                        203
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                408,
+                                                188,
+                                                502,
+                                                203
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Figure 4: Exam-",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 11
+                                },
+                                {
+                                    "bbox": [
+                                        408,
+                                        201,
+                                        501,
+                                        213
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                408,
+                                                201,
+                                                501,
+                                                213
+                                            ],
+                                            "score": 1.0,
+                                            "content": "ple of area under",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 12
+                                },
+                                {
+                                    "bbox": [
+                                        409,
+                                        213,
+                                        499,
+                                        223
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                409,
+                                                213,
+                                                499,
+                                                223
+                                            ],
+                                            "score": 1.0,
+                                            "content": "Pareto curve as the",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 13
+                                },
+                                {
+                                    "bbox": [
+                                        409,
+                                        223,
+                                        500,
+                                        235
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                409,
+                                                223,
+                                                500,
+                                                235
+                                            ],
+                                            "score": 1.0,
+                                            "content": "evolutionary search of",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 14
+                                },
+                                {
+                                    "bbox": [
+                                        408,
+                                        233,
+                                        500,
+                                        246
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                408,
+                                                233,
+                                                500,
+                                                246
+                                            ],
+                                            "score": 1.0,
+                                            "content": "lenth configurations",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 15
+                                },
+                                {
+                                    "bbox": [
+                                        408,
+                                        246,
+                                        450,
+                                        257
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                408,
+                                                246,
+                                                450,
+                                                257
+                                            ],
+                                            "score": 1.0,
+                                            "content": "proceeds.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 16
+                                }
+                            ],
+                            "index": 13.5
+                        }
+                    ],
+                    "index": 11.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        273,
+                        506,
+                        340
+                    ],
+                    "lines": [],
+                    "index": 19.5,
+                    "bbox_fs": [
+                        105,
+                        274,
+                        506,
+                        340
+                    ],
+                    "lines_deleted": true
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        345,
+                        505,
+                        434
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                346,
+                                504,
+                                358
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        346,
+                                        504,
+                                        358
+                                    ],
+                                    "score": 1.0,
+                                    "content": "From Fig. 2, we have observed that the proposed Length-Adaptive Transformer generalize better than",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                357,
+                                505,
+                                369
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        357,
+                                        505,
+                                        369
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the standard, base model in some cases. We thus try to maximize both the inference efficiency and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                368,
+                                505,
+                                380
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        368,
+                                        505,
+                                        380
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accuracy, in order to see whether it is possible for the proposed algorithm to find a length configuration",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                378,
+                                505,
+                                391
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        378,
+                                        505,
+                                        391
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that both maximizes inference efficiency and improves accuracy. We present the results in the rows",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                389,
+                                505,
+                                402
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        389,
+                                        505,
+                                        402
+                                    ],
+                                    "score": 1.0,
+                                    "content": "marked with Length-Adaptive? from Table 1. For all cases, Length-Adaptive Transformer achieves",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                401,
+                                506,
+                                413
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        401,
+                                        506,
+                                        413
+                                    ],
+                                    "score": 1.0,
+                                    "content": "higher accuracy than a standard transformer does while reducing FLOPs significantly. Although it",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                411,
+                                505,
+                                424
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        411,
+                                        505,
+                                        424
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is not apparent from the table, tor MNLI-m and SST-2, the accuracy of the smallest sub-model is",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                423,
+                                356,
+                                435
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        423,
+                                        356,
+                                        435
+                                    ],
+                                    "score": 1.0,
+                                    "content": "already greater than or equal to that of a standard transformer.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 26.5,
+                    "bbox_fs": [
+                        105,
+                        346,
+                        506,
+                        435
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        445,
+                        505,
+                        545
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                445,
+                                506,
+                                458
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        445,
+                                        506,
+                                        458
+                                    ],
+                                    "score": 1.0,
+                                    "content": "FLOPs vs. Latency As has been discussed in recent literature (see, e.g., (Li et al., 2020; Chin",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                456,
+                                505,
+                                469
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        456,
+                                        505,
+                                        469
+                                    ],
+                                    "score": 1.0,
+                                    "content": "et al., 2020)), FLOPs is not a perfect indicator of the real latency measured in wall-clock time, as the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                468,
+                                504,
+                                478
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        468,
+                                        504,
+                                        478
+                                    ],
+                                    "score": 1.0,
+                                    "content": "latter is affected by the combination of hardware choice and network architecture. To understand",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                478,
+                                505,
+                                492
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        478,
+                                        505,
+                                        492
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the real-world impact of the proposed approach, we study the relationship between FLOPs, obtained",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                488,
+                                506,
+                                504
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        488,
+                                        506,
+                                        504
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by the proposed procedure, and wall-clock time measured on both CPU and GPU by measuring",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                501,
+                                505,
+                                512
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        501,
+                                        505,
+                                        512
+                                    ],
+                                    "score": 1.0,
+                                    "content": "them while varying length configurations. As shown in Fig. 3, FLOPs and latency exhibit near-linear",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                512,
+                                506,
+                                524
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        512,
+                                        297,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": "correlation on GPU, when the minibatch size is",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        297,
+                                        512,
+                                        319,
+                                        523
+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\geq 1 6",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        319,
+                                        512,
+                                        506,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and regardless of the minibatch size, on CPU.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                522,
+                                506,
+                                536
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        522,
+                                        506,
+                                        536
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In other words, the reduction in FLOPs with the proposed approach directly implies the reduction in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                532,
+                                173,
+                                546
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        532,
+                                        173,
+                                        546
+                                    ],
+                                    "score": 1.0,
+                                    "content": "wall-clock time.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 35,
+                    "bbox_fs": [
+                        105,
+                        445,
+                        506,
+                        546
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        557,
+                        505,
+                        601
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                556,
+                                505,
+                                570
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        556,
+                                        505,
+                                        570
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Convergence of search Although the proposed approach is efficient in that it requires only one",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                569,
+                                506,
+                                581
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        569,
+                                        506,
+                                        581
+                                    ],
+                                    "score": 1.0,
+                                    "content": "round of training, it needs a separate search stage for each target budget. It is important for evolution-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                579,
+                                505,
+                                591
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        579,
+                                        505,
+                                        591
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ary search to converge quickly in the number of forward sweeps of a validation set. As exemplified in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                591,
+                                372,
+                                602
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        591,
+                                        372,
+                                        602
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Fig. 4, evolutionary search converges after about fifteen iterations.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        }
+                    ],
+                    "index": 41.5,
+                    "bbox_fs": [
+                        105,
+                        556,
+                        506,
+                        602
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        617,
+                        211,
+                        630
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                616,
+                                213,
+                                632
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        616,
+                                        213,
+                                        632
+                                    ],
+                                    "score": 1.0,
+                                    "content": "6 RELATED WORK",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        }
+                    ],
+                    "index": 44
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        642,
+                        505,
+                        675
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                641,
+                                505,
+                                655
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        641,
+                                        505,
+                                        655
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The main purpose of the proposed algorithm is to improve the inference efficiency of a large-scale",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                653,
+                                505,
+                                666
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        653,
+                                        505,
+                                        666
+                                    ],
+                                    "score": 1.0,
+                                    "content": "transformer. This goal has been pursued from various directions, and in this section, we provide a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                664,
+                                506,
+                                677
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        664,
+                                        506,
+                                        677
+                                    ],
+                                    "score": 1.0,
+                                    "content": "brief overview of these earlier, and some concurrent, attempts in the context of the proposed approach.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        }
+                    ],
+                    "index": 46,
+                    "bbox_fs": [
+                        105,
+                        641,
+                        506,
+                        677
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        687,
+                        505,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                687,
+                                505,
+                                701
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        687,
+                                        505,
+                                        701
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Weight pruning Weight pruning (Han et al., 2015) focuses on reducing the number of parameters",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                698,
+                                506,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        698,
+                                        506,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "which directly reflects the memory footprint of a model and indirectly correlates with inference speed.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                709,
+                                506,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        709,
+                                        506,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "However, their actual speed-up in runtime is usually not significant, especially while executing a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                721,
+                                456,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        721,
+                                        456,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "model with parallel computation using GPU devices (Tang et al., 2018; Li et al., 2020).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 51
+                        }
+                    ],
+                    "index": 49.5,
+                    "bbox_fs": [
+                        105,
+                        687,
+                        506,
+                        732
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        82,
+                        505,
+                        170
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                82,
+                                505,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        82,
+                                        505,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Adaptive architecture There are three major axes along which computation can be reduced in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                94,
+                                505,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        94,
+                                        505,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a neural network; (1) input size/length, (2) network depth and (3) network width. The proposed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                105,
+                                506,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        105,
+                                        506,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "approach, based on PoWER-BERT, adaptively reduces the input length as the input sequence is",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                115,
+                                506,
+                                128
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        115,
+                                        506,
+                                        128
+                                    ],
+                                    "score": 1.0,
+                                    "content": "processed by the transformer layers. In our knowledge, Goyal et al. (2020) is the first work in this",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                127,
+                                505,
+                                138
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        127,
+                                        505,
+                                        138
+                                    ],
+                                    "score": 1.0,
+                                    "content": "direction for transformers. More recently, Funnel-Transformer (Dai et al., 2020) and multi-scale",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                136,
+                                505,
+                                150
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        136,
+                                        505,
+                                        150
+                                    ],
+                                    "score": 1.0,
+                                    "content": "transformer language models (Subramanian et al., 2020) also successfully reduce sequence length in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                148,
+                                505,
+                                161
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        148,
+                                        505,
+                                        161
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the middle and rescale to full length for the final computation. However, their inference complexity is",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                158,
+                                455,
+                                173
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        158,
+                                        455,
+                                        173
+                                    ],
+                                    "score": 1.0,
+                                    "content": "fixed unlike PoWER-BERT because they are not designed for the control of efficiency.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 3.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        176,
+                        505,
+                        253
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                175,
+                                505,
+                                190
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        175,
+                                        505,
+                                        190
+                                    ],
+                                    "score": 1.0,
+                                    "content": "LayerDrop (Fan et al., 2019) drops random layers during the training to be robust to pruning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                186,
+                                504,
+                                200
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        186,
+                                        504,
+                                        200
+                                    ],
+                                    "score": 1.0,
+                                    "content": "inspired by Huang et al. (2016). Word-level adaptive depth in Elbayad et al. (2019) might seemingly",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                198,
+                                505,
+                                210
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        198,
+                                        505,
+                                        210
+                                    ],
+                                    "score": 1.0,
+                                    "content": "resemble with length reduction, but word vectors reached the maximal layer are used for self-attention",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                210,
+                                506,
+                                221
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        210,
+                                        506,
+                                        221
+                                    ],
+                                    "score": 1.0,
+                                    "content": "computation without updating themselves. Escaping a network early (Teerapittayanon et al., 2016;",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                220,
+                                506,
+                                232
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        220,
+                                        506,
+                                        232
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Huang et al., 2017) based on the confidence of the prediction (Xin et al., 2020; Schwartz et al., 2020;",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                231,
+                                506,
+                                243
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        231,
+                                        506,
+                                        243
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Liu et al., 2020) also offers a control over accuracy-efficiency trade-off, but it is difficult to tune a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                242,
+                                495,
+                                254
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        242,
+                                        495,
+                                        254
+                                    ],
+                                    "score": 1.0,
+                                    "content": "threshold for a desired computational budget because of the example-wise adaptive computation.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        259,
+                        505,
+                        303
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                258,
+                                507,
+                                272
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        258,
+                                        507,
+                                        272
+                                    ],
+                                    "score": 1.0,
+                                    "content": "DynaBERT (Hou et al., 2020) can run at adaptive width (the number of attention heads and interme-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                270,
+                                506,
+                                282
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        270,
+                                        506,
+                                        282
+                                    ],
+                                    "score": 1.0,
+                                    "content": "diate hidden dimension) and depth. Hardware-aware Transformers (Wang et al., 2020) construct a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                281,
+                                504,
+                                293
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        281,
+                                        504,
+                                        293
+                                    ],
+                                    "score": 1.0,
+                                    "content": "design space with arbitrary encoder-decoder attention and heterogeneous layers in terms of different",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                291,
+                                434,
+                                304
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        291,
+                                        434,
+                                        304
+                                    ],
+                                    "score": 1.0,
+                                    "content": "numbers of layers, attention heads, hidden dimension, and embedding dimension.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 16.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        315,
+                        505,
+                        370
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                315,
+                                505,
+                                327
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        315,
+                                        505,
+                                        327
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Structured dropout A major innovation we introduce over the existing PoWER-BERT is the use of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                326,
+                                505,
+                                339
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        326,
+                                        505,
+                                        339
+                                    ],
+                                    "score": 1.0,
+                                    "content": "stochastic, structured regularization to make a transformer robust to the choice of length configuration",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                336,
+                                507,
+                                351
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        336,
+                                        507,
+                                        351
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in the inference time. Rippel et al. (2014) proposes a nested dropout to learn ordered representations.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                346,
+                                507,
+                                362
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        346,
+                                        507,
+                                        362
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Similar to LengthDrop, it samples an index form a prior distribution and drops all units having a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                359,
+                                231,
+                                373
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        359,
+                                        231,
+                                        373
+                                    ],
+                                    "score": 1.0,
+                                    "content": "larger index than sampled one.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 21
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        382,
+                        505,
+                        460
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                381,
+                                506,
+                                397
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        381,
+                                        506,
+                                        397
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Search There have been a series of attempts at finding the optimal network configuration by solving",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                394,
+                                506,
+                                406
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        394,
+                                        506,
+                                        406
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a combinatorial optimization problem. In computer vision, Once-for-All (Cai et al., 2019) use an",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                405,
+                                506,
+                                416
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        405,
+                                        506,
+                                        416
+                                    ],
+                                    "score": 1.0,
+                                    "content": "evolutionary search (Real et al., 2019) to find a better configuration in dimensions of depth, width,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                414,
+                                506,
+                                430
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        414,
+                                        506,
+                                        430
+                                    ],
+                                    "score": 1.0,
+                                    "content": "kernel size, and resolution given computational budget. Similarly but differently, our evolutionary",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                426,
+                                505,
+                                439
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        426,
+                                        505,
+                                        439
+                                    ],
+                                    "score": 1.0,
+                                    "content": "search is mutli-objective to find length configurations on the Pareto accuracy-efficiency frontier to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                438,
+                                506,
+                                451
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        438,
+                                        506,
+                                        451
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cope with any possible computational budgets. Moreover, we only change the sequence length of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                448,
+                                374,
+                                461
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        448,
+                                        374,
+                                        461
+                                    ],
+                                    "score": 1.0,
+                                    "content": "hidden vectors instead of architectural model size like dimensions.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 27
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        476,
+                        303,
+                        489
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                474,
+                                304,
+                                491
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        474,
+                                        304,
+                                        491
+                                    ],
+                                    "score": 1.0,
+                                    "content": "7 CONCLUSION AND FUTURE WORK",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        }
+                    ],
+                    "index": 31
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        501,
+                        505,
+                        600
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                500,
+                                506,
+                                514
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        500,
+                                        506,
+                                        514
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In this work, we propose a new framework for training a transformer once and using it for efficient",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                511,
+                                506,
+                                525
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        511,
+                                        506,
+                                        525
+                                    ],
+                                    "score": 1.0,
+                                    "content": "inference under any computational budget. With the help of training with LengthDrop and Drop-and-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                523,
+                                505,
+                                536
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        523,
+                                        505,
+                                        536
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Restore process followed by the evolutionary search, our proposed Length-Adaptive Transformer",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                533,
+                                505,
+                                547
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        533,
+                                        505,
+                                        547
+                                    ],
+                                    "score": 1.0,
+                                    "content": "allows any given transformer models to be used with any inference-time computational budget for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                545,
+                                505,
+                                558
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        545,
+                                        505,
+                                        558
+                                    ],
+                                    "score": 1.0,
+                                    "content": "both sequence-level and token-level classification tasks. Our experiments, on SQuAD 1.1, MNLI-m",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                556,
+                                506,
+                                569
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        556,
+                                        506,
+                                        569
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and SST-2, have revealed that the proposed algorithmic framework significantly pushes a better Pareto",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                566,
+                                505,
+                                580
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        566,
+                                        505,
+                                        580
+                                    ],
+                                    "score": 1.0,
+                                    "content": "frontier on the trade-off between inference efficiency and accuracy. Furthermore, we have observed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                577,
+                                506,
+                                591
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        577,
+                                        382,
+                                        591
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that the proposed Length-Adaptive Transformer could achieve up to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        382,
+                                        578,
+                                        394,
+                                        588
+                                    ],
+                                    "score": 0.55,
+                                    "content": "3 \\mathbf { x }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        394,
+                                        577,
+                                        506,
+                                        591
+                                    ],
+                                    "score": 1.0,
+                                    "content": "speed-up over the standard",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                589,
+                                449,
+                                601
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        589,
+                                        449,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": "transformer without sacrificing accuracy, both in terms of FLOPs and wallclock time.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        }
+                    ],
+                    "index": 36
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        606,
+                        505,
+                        672
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                605,
+                                505,
+                                618
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        605,
+                                        505,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Although our approach finds an optimal length configuration of a trained classifier per computational",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                617,
+                                505,
+                                629
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        617,
+                                        505,
+                                        629
+                                    ],
+                                    "score": 1.0,
+                                    "content": "budget, it leaves open a question whether the proposed approach could be further extended to support",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                628,
+                                505,
+                                640
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        628,
+                                        505,
+                                        640
+                                    ],
+                                    "score": 1.0,
+                                    "content": "per-instance length configuration by for instance training a small, auxiliary neural network for each",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                639,
+                                506,
+                                651
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        639,
+                                        506,
+                                        651
+                                    ],
+                                    "score": 1.0,
+                                    "content": "computational budget. Yet another aspect we have not investigated in this paper is the applicability of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                649,
+                                505,
+                                662
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        649,
+                                        505,
+                                        662
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the proposed approach to sequence generation, such as machine translation. We leave both of these",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                660,
+                                242,
+                                673
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        660,
+                                        242,
+                                        673
+                                    ],
+                                    "score": 1.0,
+                                    "content": "research directions for the future.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        }
+                    ],
+                    "index": 43.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        677,
+                        505,
+                        721
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                676,
+                                505,
+                                691
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        676,
+                                        505,
+                                        691
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Our approach is effective, as we have shown in this paper, and also quite simple to implement on top",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                688,
+                                505,
+                                700
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        688,
+                                        505,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of existing language models. We will release our implementation, which is based on HuggingFace’s",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                699,
+                                507,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        699,
+                                        507,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Transformers library (Wolf et al., 2019), publicly and plan to adapt it for a broader set of transformer-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                711,
+                                255,
+                                721
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        711,
+                                        255,
+                                        721
+                                    ],
+                                    "score": 1.0,
+                                    "content": "based models and downstream tasks.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50
+                        }
+                    ],
+                    "index": 48.5
+                }
+            ],
+            "page_idx": 7,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        108,
+                        27,
+                        306,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                308,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        308,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Under review as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        752,
+                        308,
+                        759
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                302,
+                                750,
+                                309,
+                                761
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        302,
+                                        750,
+                                        309,
+                                        761
+                                    ],
+                                    "score": 1.0,
+                                    "content": "8",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        82,
+                        505,
+                        170
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                82,
+                                505,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        82,
+                                        505,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Adaptive architecture There are three major axes along which computation can be reduced in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                94,
+                                505,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        94,
+                                        505,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a neural network; (1) input size/length, (2) network depth and (3) network width. The proposed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                105,
+                                506,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        105,
+                                        506,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "approach, based on PoWER-BERT, adaptively reduces the input length as the input sequence is",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                115,
+                                506,
+                                128
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        115,
+                                        506,
+                                        128
+                                    ],
+                                    "score": 1.0,
+                                    "content": "processed by the transformer layers. In our knowledge, Goyal et al. (2020) is the first work in this",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                127,
+                                505,
+                                138
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        127,
+                                        505,
+                                        138
+                                    ],
+                                    "score": 1.0,
+                                    "content": "direction for transformers. More recently, Funnel-Transformer (Dai et al., 2020) and multi-scale",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                136,
+                                505,
+                                150
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        136,
+                                        505,
+                                        150
+                                    ],
+                                    "score": 1.0,
+                                    "content": "transformer language models (Subramanian et al., 2020) also successfully reduce sequence length in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                148,
+                                505,
+                                161
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        148,
+                                        505,
+                                        161
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the middle and rescale to full length for the final computation. However, their inference complexity is",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                158,
+                                455,
+                                173
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        158,
+                                        455,
+                                        173
+                                    ],
+                                    "score": 1.0,
+                                    "content": "fixed unlike PoWER-BERT because they are not designed for the control of efficiency.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 3.5,
+                    "bbox_fs": [
+                        105,
+                        82,
+                        506,
+                        173
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        176,
+                        505,
+                        253
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                175,
+                                505,
+                                190
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        175,
+                                        505,
+                                        190
+                                    ],
+                                    "score": 1.0,
+                                    "content": "LayerDrop (Fan et al., 2019) drops random layers during the training to be robust to pruning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                186,
+                                504,
+                                200
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        186,
+                                        504,
+                                        200
+                                    ],
+                                    "score": 1.0,
+                                    "content": "inspired by Huang et al. (2016). Word-level adaptive depth in Elbayad et al. (2019) might seemingly",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                198,
+                                505,
+                                210
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        198,
+                                        505,
+                                        210
+                                    ],
+                                    "score": 1.0,
+                                    "content": "resemble with length reduction, but word vectors reached the maximal layer are used for self-attention",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                210,
+                                506,
+                                221
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        210,
+                                        506,
+                                        221
+                                    ],
+                                    "score": 1.0,
+                                    "content": "computation without updating themselves. Escaping a network early (Teerapittayanon et al., 2016;",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                220,
+                                506,
+                                232
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        220,
+                                        506,
+                                        232
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Huang et al., 2017) based on the confidence of the prediction (Xin et al., 2020; Schwartz et al., 2020;",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                231,
+                                506,
+                                243
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        231,
+                                        506,
+                                        243
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Liu et al., 2020) also offers a control over accuracy-efficiency trade-off, but it is difficult to tune a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                242,
+                                495,
+                                254
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        242,
+                                        495,
+                                        254
+                                    ],
+                                    "score": 1.0,
+                                    "content": "threshold for a desired computational budget because of the example-wise adaptive computation.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 11,
+                    "bbox_fs": [
+                        105,
+                        175,
+                        506,
+                        254
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        259,
+                        505,
+                        303
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                258,
+                                507,
+                                272
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        258,
+                                        507,
+                                        272
+                                    ],
+                                    "score": 1.0,
+                                    "content": "DynaBERT (Hou et al., 2020) can run at adaptive width (the number of attention heads and interme-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                270,
+                                506,
+                                282
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        270,
+                                        506,
+                                        282
+                                    ],
+                                    "score": 1.0,
+                                    "content": "diate hidden dimension) and depth. Hardware-aware Transformers (Wang et al., 2020) construct a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                281,
+                                504,
+                                293
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        281,
+                                        504,
+                                        293
+                                    ],
+                                    "score": 1.0,
+                                    "content": "design space with arbitrary encoder-decoder attention and heterogeneous layers in terms of different",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                291,
+                                434,
+                                304
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        291,
+                                        434,
+                                        304
+                                    ],
+                                    "score": 1.0,
+                                    "content": "numbers of layers, attention heads, hidden dimension, and embedding dimension.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 16.5,
+                    "bbox_fs": [
+                        105,
+                        258,
+                        507,
+                        304
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        315,
+                        505,
+                        370
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                315,
+                                505,
+                                327
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        315,
+                                        505,
+                                        327
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Structured dropout A major innovation we introduce over the existing PoWER-BERT is the use of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                326,
+                                505,
+                                339
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        326,
+                                        505,
+                                        339
+                                    ],
+                                    "score": 1.0,
+                                    "content": "stochastic, structured regularization to make a transformer robust to the choice of length configuration",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                336,
+                                507,
+                                351
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        336,
+                                        507,
+                                        351
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in the inference time. Rippel et al. (2014) proposes a nested dropout to learn ordered representations.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                346,
+                                507,
+                                362
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        346,
+                                        507,
+                                        362
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Similar to LengthDrop, it samples an index form a prior distribution and drops all units having a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                359,
+                                231,
+                                373
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        359,
+                                        231,
+                                        373
+                                    ],
+                                    "score": 1.0,
+                                    "content": "larger index than sampled one.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 21,
+                    "bbox_fs": [
+                        105,
+                        315,
+                        507,
+                        373
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        382,
+                        505,
+                        460
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                381,
+                                506,
+                                397
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        381,
+                                        506,
+                                        397
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Search There have been a series of attempts at finding the optimal network configuration by solving",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                394,
+                                506,
+                                406
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        394,
+                                        506,
+                                        406
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a combinatorial optimization problem. In computer vision, Once-for-All (Cai et al., 2019) use an",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                405,
+                                506,
+                                416
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        405,
+                                        506,
+                                        416
+                                    ],
+                                    "score": 1.0,
+                                    "content": "evolutionary search (Real et al., 2019) to find a better configuration in dimensions of depth, width,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                414,
+                                506,
+                                430
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        414,
+                                        506,
+                                        430
+                                    ],
+                                    "score": 1.0,
+                                    "content": "kernel size, and resolution given computational budget. Similarly but differently, our evolutionary",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                426,
+                                505,
+                                439
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        426,
+                                        505,
+                                        439
+                                    ],
+                                    "score": 1.0,
+                                    "content": "search is mutli-objective to find length configurations on the Pareto accuracy-efficiency frontier to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                438,
+                                506,
+                                451
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        438,
+                                        506,
+                                        451
+                                    ],
+                                    "score": 1.0,
+                                    "content": "cope with any possible computational budgets. Moreover, we only change the sequence length of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                448,
+                                374,
+                                461
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        448,
+                                        374,
+                                        461
+                                    ],
+                                    "score": 1.0,
+                                    "content": "hidden vectors instead of architectural model size like dimensions.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 27,
+                    "bbox_fs": [
+                        105,
+                        381,
+                        506,
+                        461
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        476,
+                        303,
+                        489
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                474,
+                                304,
+                                491
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        474,
+                                        304,
+                                        491
+                                    ],
+                                    "score": 1.0,
+                                    "content": "7 CONCLUSION AND FUTURE WORK",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        }
+                    ],
+                    "index": 31
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        501,
+                        505,
+                        600
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                500,
+                                506,
+                                514
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        500,
+                                        506,
+                                        514
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In this work, we propose a new framework for training a transformer once and using it for efficient",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                511,
+                                506,
+                                525
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        511,
+                                        506,
+                                        525
+                                    ],
+                                    "score": 1.0,
+                                    "content": "inference under any computational budget. With the help of training with LengthDrop and Drop-and-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                523,
+                                505,
+                                536
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        523,
+                                        505,
+                                        536
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Restore process followed by the evolutionary search, our proposed Length-Adaptive Transformer",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                533,
+                                505,
+                                547
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        533,
+                                        505,
+                                        547
+                                    ],
+                                    "score": 1.0,
+                                    "content": "allows any given transformer models to be used with any inference-time computational budget for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                545,
+                                505,
+                                558
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        545,
+                                        505,
+                                        558
+                                    ],
+                                    "score": 1.0,
+                                    "content": "both sequence-level and token-level classification tasks. Our experiments, on SQuAD 1.1, MNLI-m",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                556,
+                                506,
+                                569
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        556,
+                                        506,
+                                        569
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and SST-2, have revealed that the proposed algorithmic framework significantly pushes a better Pareto",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                566,
+                                505,
+                                580
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        566,
+                                        505,
+                                        580
+                                    ],
+                                    "score": 1.0,
+                                    "content": "frontier on the trade-off between inference efficiency and accuracy. Furthermore, we have observed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                577,
+                                506,
+                                591
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        577,
+                                        382,
+                                        591
+                                    ],
+                                    "score": 1.0,
+                                    "content": "that the proposed Length-Adaptive Transformer could achieve up to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        382,
+                                        578,
+                                        394,
+                                        588
+                                    ],
+                                    "score": 0.55,
+                                    "content": "3 \\mathbf { x }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        394,
+                                        577,
+                                        506,
+                                        591
+                                    ],
+                                    "score": 1.0,
+                                    "content": "speed-up over the standard",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                589,
+                                449,
+                                601
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        589,
+                                        449,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": "transformer without sacrificing accuracy, both in terms of FLOPs and wallclock time.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        }
+                    ],
+                    "index": 36,
+                    "bbox_fs": [
+                        105,
+                        500,
+                        506,
+                        601
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        606,
+                        505,
+                        672
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                605,
+                                505,
+                                618
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        605,
+                                        505,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Although our approach finds an optimal length configuration of a trained classifier per computational",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                617,
+                                505,
+                                629
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        617,
+                                        505,
+                                        629
+                                    ],
+                                    "score": 1.0,
+                                    "content": "budget, it leaves open a question whether the proposed approach could be further extended to support",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                628,
+                                505,
+                                640
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        628,
+                                        505,
+                                        640
+                                    ],
+                                    "score": 1.0,
+                                    "content": "per-instance length configuration by for instance training a small, auxiliary neural network for each",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                639,
+                                506,
+                                651
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        639,
+                                        506,
+                                        651
+                                    ],
+                                    "score": 1.0,
+                                    "content": "computational budget. Yet another aspect we have not investigated in this paper is the applicability of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                649,
+                                505,
+                                662
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        649,
+                                        505,
+                                        662
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the proposed approach to sequence generation, such as machine translation. We leave both of these",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                660,
+                                242,
+                                673
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        660,
+                                        242,
+                                        673
+                                    ],
+                                    "score": 1.0,
+                                    "content": "research directions for the future.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        }
+                    ],
+                    "index": 43.5,
+                    "bbox_fs": [
+                        105,
+                        605,
+                        506,
+                        673
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        677,
+                        505,
+                        721
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                676,
+                                505,
+                                691
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        676,
+                                        505,
+                                        691
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Our approach is effective, as we have shown in this paper, and also quite simple to implement on top",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                688,
+                                505,
+                                700
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        688,
+                                        505,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of existing language models. We will release our implementation, which is based on HuggingFace’s",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                699,
+                                507,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        699,
+                                        507,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Transformers library (Wolf et al., 2019), publicly and plan to adapt it for a broader set of transformer-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                711,
+                                255,
+                                721
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        711,
+                                        255,
+                                        721
+                                    ],
+                                    "score": 1.0,
+                                    "content": "based models and downstream tasks.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50
+                        }
+                    ],
+                    "index": 48.5,
+                    "bbox_fs": [
+                        105,
+                        676,
+                        507,
+                        721
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        81,
+                        176,
+                        93
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                82,
+                                176,
+                                94
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        82,
+                                        176,
+                                        94
+                                    ],
+                                    "score": 1.0,
+                                    "content": "REFERENCES",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        100,
+                        505,
+                        134
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                100,
+                                506,
+                                113
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        100,
+                                        506,
+                                        113
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Tom B Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared Kaplan, Prafulla Dhariwal,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                111,
+                                505,
+                                125
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        111,
+                                        505,
+                                        125
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al. Language models are",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                123,
+                                353,
+                                135
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        123,
+                                        353,
+                                        135
+                                    ],
+                                    "score": 1.0,
+                                    "content": "few-shot learners. arXiv preprint arXiv:2005.14165, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        142,
+                        504,
+                        165
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                143,
+                                505,
+                                156
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        143,
+                                        505,
+                                        156
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Han Cai, Chuang Gan, and Song Han. Once for all: Train one network and specialize it for efficient",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                154,
+                                331,
+                                166
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        154,
+                                        331,
+                                        166
+                                    ],
+                                    "score": 1.0,
+                                    "content": "deployment. arXiv preprint arXiv:1908.09791, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        }
+                    ],
+                    "index": 4.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        173,
+                        504,
+                        208
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                173,
+                                506,
+                                187
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        173,
+                                        506,
+                                        187
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Ting-Wu Chin, Ruizhou Ding, Cha Zhang, and Diana Marculescu. Towards efficient model compres-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                185,
+                                505,
+                                197
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        185,
+                                        505,
+                                        197
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sion via learned global ranking. In Proceedings of the IEEE/CVF Conference on Computer Vision",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                196,
+                                308,
+                                209
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        196,
+                                        308,
+                                        209
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and Pattern Recognition, pp. 1518–1528, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        216,
+                        504,
+                        240
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                216,
+                                505,
+                                229
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        216,
+                                        505,
+                                        229
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Zihang Dai, Guokun Lai, Yiming Yang, and Quoc V Le. Funnel-transformer: Filtering out sequential",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                227,
+                                464,
+                                240
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        227,
+                                        464,
+                                        240
+                                    ],
+                                    "score": 1.0,
+                                    "content": "redundancy for efficient language processing. arXiv preprint arXiv:2006.03236, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 9.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        247,
+                        504,
+                        271
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                246,
+                                505,
+                                261
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        246,
+                                        505,
+                                        261
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. Bert: Pre-training of deep",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                258,
+                                500,
+                                272
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        258,
+                                        500,
+                                        272
+                                    ],
+                                    "score": 1.0,
+                                    "content": "bidirectional transformers for language understanding. arXiv preprint arXiv:1810.04805, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "index": 11.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        278,
+                        504,
+                        302
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                279,
+                                505,
+                                292
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        279,
+                                        505,
+                                        292
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Maha Elbayad, Jiatao Gu, Edouard Grave, and Michael Auli. Depth-adaptive transformer. arXiv",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                290,
+                                254,
+                                302
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        290,
+                                        254,
+                                        302
+                                    ],
+                                    "score": 1.0,
+                                    "content": "preprint arXiv:1910.10073, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 13.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        309,
+                        505,
+                        333
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                310,
+                                505,
+                                323
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        310,
+                                        505,
+                                        323
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Angela Fan, Edouard Grave, and Armand Joulin. Reducing transformer depth on demand with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                321,
+                                358,
+                                334
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        321,
+                                        358,
+                                        334
+                                    ],
+                                    "score": 1.0,
+                                    "content": "structured dropout. arXiv preprint arXiv:1909.11556, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 15.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        341,
+                        504,
+                        375
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                342,
+                                505,
+                                354
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        342,
+                                        505,
+                                        354
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Saurabh Goyal, Anamitra Roy Choudhary, Venkatesan Chakaravarthy, Saurabh ManishRaje, Yogish",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                353,
+                                506,
+                                365
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        353,
+                                        506,
+                                        365
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sabharwal, and Ashish Verma. Power-bert: Accelerating bert inference for classification tasks.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                363,
+                                279,
+                                376
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        363,
+                                        279,
+                                        376
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv preprint arXiv:2001.08950, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        383,
+                        503,
+                        407
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                384,
+                                505,
+                                397
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        384,
+                                        505,
+                                        397
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Song Han, Huizi Mao, and William J Dally. Deep compression: Compressing deep neural networks",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                395,
+                                503,
+                                407
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        395,
+                                        503,
+                                        407
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with pruning, trained quantization and huffman coding. arXiv preprint arXiv:1510.00149, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 20.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        414,
+                        504,
+                        449
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                414,
+                                505,
+                                428
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        414,
+                                        505,
+                                        428
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Peter Henderson, Jieru Hu, Joshua Romoff, Emma Brunskill, Dan Jurafsky, and Joelle Pineau.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                426,
+                                505,
+                                439
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        426,
+                                        505,
+                                        439
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Towards the systematic reporting of the energy and carbon footprints of machine learning. arXiv",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                438,
+                                254,
+                                449
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        438,
+                                        254,
+                                        449
+                                    ],
+                                    "score": 1.0,
+                                    "content": "preprint arXiv:2002.05651, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 23
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        457,
+                        504,
+                        480
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                457,
+                                505,
+                                470
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        457,
+                                        505,
+                                        470
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Geoffrey Hinton, Oriol Vinyals, and Jeff Dean. Distilling the knowledge in a neural network. arXiv",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                469,
+                                254,
+                                480
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        469,
+                                        254,
+                                        480
+                                    ],
+                                    "score": 1.0,
+                                    "content": "preprint arXiv:1503.02531, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 25.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        488,
+                        505,
+                        511
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                488,
+                                506,
+                                502
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        488,
+                                        506,
+                                        502
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lu Hou, Lifeng Shang, Xin Jiang, and Qun Liu. Dynabert: Dynamic bert with adaptive width and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                500,
+                                306,
+                                512
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        500,
+                                        306,
+                                        512
+                                    ],
+                                    "score": 1.0,
+                                    "content": "depth. arXiv preprint arXiv:2004.04037, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 27.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        519,
+                        504,
+                        543
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                520,
+                                505,
+                                532
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        520,
+                                        505,
+                                        532
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Gao Huang, Yu Sun, Zhuang Liu, Daniel Sedra, and Kilian Q Weinberger. Deep networks with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                530,
+                                484,
+                                544
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        530,
+                                        484,
+                                        544
+                                    ],
+                                    "score": 1.0,
+                                    "content": "stochastic depth. In European conference on computer vision, pp. 646–661. Springer, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 29.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        551,
+                        505,
+                        585
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                551,
+                                506,
+                                563
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        551,
+                                        506,
+                                        563
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Gao Huang, Danlu Chen, Tianhong Li, Felix Wu, Laurens van der Maaten, and Kilian Q Wein-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                562,
+                                505,
+                                575
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        562,
+                                        505,
+                                        575
+                                    ],
+                                    "score": 1.0,
+                                    "content": "berger. Multi-scale dense networks for resource efficient image classification. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                573,
+                                220,
+                                584
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        573,
+                                        220,
+                                        584
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1703.09844, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 32
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        593,
+                        506,
+                        627
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                594,
+                                505,
+                                606
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        594,
+                                        505,
+                                        606
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Jared Kaplan, Sam McCandlish, Tom Henighan, Tom B Brown, Benjamin Chess, Rewon Child, Scott",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                605,
+                                507,
+                                617
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        605,
+                                        507,
+                                        617
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Gray, Alec Radford, Jeffrey Wu, and Dario Amodei. Scaling laws for neural language models.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                616,
+                                279,
+                                627
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        616,
+                                        279,
+                                        627
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv preprint arXiv:2001.08361, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 35
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        636,
+                        504,
+                        669
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                636,
+                                506,
+                                649
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        636,
+                                        506,
+                                        649
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Zhuohan Li, Eric Wallace, Sheng Shen, Kevin Lin, Kurt Keutzer, Dan Klein, and Joseph E Gon-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                647,
+                                506,
+                                659
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        647,
+                                        506,
+                                        659
+                                    ],
+                                    "score": 1.0,
+                                    "content": "zalez. Train large, then compress: Rethinking model size for efficient training and inference of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                658,
+                                335,
+                                669
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        658,
+                                        335,
+                                        669
+                                    ],
+                                    "score": 1.0,
+                                    "content": "transformers. arXiv preprint arXiv:2002.11794, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 38
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        678,
+                        504,
+                        701
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                677,
+                                505,
+                                691
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        677,
+                                        505,
+                                        691
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Weijie Liu, Peng Zhou, Zhe Zhao, Zhiruo Wang, Haotang Deng, and Qi Ju. Fastbert: a self-distilling",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                689,
+                                416,
+                                701
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        689,
+                                        416,
+                                        701
+                                    ],
+                                    "score": 1.0,
+                                    "content": "bert with adaptive inference time. arXiv preprint arXiv:2004.02178, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        }
+                    ],
+                    "index": 40.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        709,
+                        503,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                708,
+                                505,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        708,
+                                        505,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Paul Michel, Omer Levy, and Graham Neubig. Are sixteen heads really better than one? In Advances",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                720,
+                                389,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        720,
+                                        389,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in Neural Information Processing Systems, pp. 14014–14024, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        }
+                    ],
+                    "index": 42.5
+                }
+            ],
+            "page_idx": 8,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        302,
+                        751,
+                        309,
+                        759
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                302,
+                                751,
+                                309,
+                                762
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        302,
+                                        751,
+                                        309,
+                                        762
+                                    ],
+                                    "score": 1.0,
+                                    "content": "9",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        307,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                308,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        308,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Under review as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        81,
+                        176,
+                        93
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                82,
+                                176,
+                                94
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        82,
+                                        176,
+                                        94
+                                    ],
+                                    "score": 1.0,
+                                    "content": "REFERENCES",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        100,
+                        505,
+                        134
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                100,
+                                506,
+                                113
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        100,
+                                        506,
+                                        113
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Tom B Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared Kaplan, Prafulla Dhariwal,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                111,
+                                505,
+                                125
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        111,
+                                        505,
+                                        125
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al. Language models are",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                123,
+                                353,
+                                135
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        123,
+                                        353,
+                                        135
+                                    ],
+                                    "score": 1.0,
+                                    "content": "few-shot learners. arXiv preprint arXiv:2005.14165, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 2,
+                    "bbox_fs": [
+                        106,
+                        100,
+                        506,
+                        135
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        142,
+                        504,
+                        165
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                143,
+                                505,
+                                156
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        143,
+                                        505,
+                                        156
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Han Cai, Chuang Gan, and Song Han. Once for all: Train one network and specialize it for efficient",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                154,
+                                331,
+                                166
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        154,
+                                        331,
+                                        166
+                                    ],
+                                    "score": 1.0,
+                                    "content": "deployment. arXiv preprint arXiv:1908.09791, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        }
+                    ],
+                    "index": 4.5,
+                    "bbox_fs": [
+                        106,
+                        143,
+                        505,
+                        166
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        173,
+                        504,
+                        208
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                173,
+                                506,
+                                187
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        173,
+                                        506,
+                                        187
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Ting-Wu Chin, Ruizhou Ding, Cha Zhang, and Diana Marculescu. Towards efficient model compres-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                185,
+                                505,
+                                197
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        185,
+                                        505,
+                                        197
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sion via learned global ranking. In Proceedings of the IEEE/CVF Conference on Computer Vision",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                196,
+                                308,
+                                209
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        196,
+                                        308,
+                                        209
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and Pattern Recognition, pp. 1518–1528, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 7,
+                    "bbox_fs": [
+                        106,
+                        173,
+                        506,
+                        209
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        216,
+                        504,
+                        240
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                216,
+                                505,
+                                229
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        216,
+                                        505,
+                                        229
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Zihang Dai, Guokun Lai, Yiming Yang, and Quoc V Le. Funnel-transformer: Filtering out sequential",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                227,
+                                464,
+                                240
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        227,
+                                        464,
+                                        240
+                                    ],
+                                    "score": 1.0,
+                                    "content": "redundancy for efficient language processing. arXiv preprint arXiv:2006.03236, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 9.5,
+                    "bbox_fs": [
+                        106,
+                        216,
+                        505,
+                        240
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        247,
+                        504,
+                        271
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                246,
+                                505,
+                                261
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        246,
+                                        505,
+                                        261
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. Bert: Pre-training of deep",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                258,
+                                500,
+                                272
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        258,
+                                        500,
+                                        272
+                                    ],
+                                    "score": 1.0,
+                                    "content": "bidirectional transformers for language understanding. arXiv preprint arXiv:1810.04805, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "index": 11.5,
+                    "bbox_fs": [
+                        105,
+                        246,
+                        505,
+                        272
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        278,
+                        504,
+                        302
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                279,
+                                505,
+                                292
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        279,
+                                        505,
+                                        292
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Maha Elbayad, Jiatao Gu, Edouard Grave, and Michael Auli. Depth-adaptive transformer. arXiv",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                290,
+                                254,
+                                302
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        290,
+                                        254,
+                                        302
+                                    ],
+                                    "score": 1.0,
+                                    "content": "preprint arXiv:1910.10073, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 13.5,
+                    "bbox_fs": [
+                        105,
+                        279,
+                        505,
+                        302
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        309,
+                        505,
+                        333
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                310,
+                                505,
+                                323
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        310,
+                                        505,
+                                        323
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Angela Fan, Edouard Grave, and Armand Joulin. Reducing transformer depth on demand with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                321,
+                                358,
+                                334
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        321,
+                                        358,
+                                        334
+                                    ],
+                                    "score": 1.0,
+                                    "content": "structured dropout. arXiv preprint arXiv:1909.11556, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 15.5,
+                    "bbox_fs": [
+                        106,
+                        310,
+                        505,
+                        334
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        341,
+                        504,
+                        375
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                342,
+                                505,
+                                354
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        342,
+                                        505,
+                                        354
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Saurabh Goyal, Anamitra Roy Choudhary, Venkatesan Chakaravarthy, Saurabh ManishRaje, Yogish",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                353,
+                                506,
+                                365
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        353,
+                                        506,
+                                        365
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sabharwal, and Ashish Verma. Power-bert: Accelerating bert inference for classification tasks.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                363,
+                                279,
+                                376
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        363,
+                                        279,
+                                        376
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv preprint arXiv:2001.08950, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 18,
+                    "bbox_fs": [
+                        106,
+                        342,
+                        506,
+                        376
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        383,
+                        503,
+                        407
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                384,
+                                505,
+                                397
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        384,
+                                        505,
+                                        397
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Song Han, Huizi Mao, and William J Dally. Deep compression: Compressing deep neural networks",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                395,
+                                503,
+                                407
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        395,
+                                        503,
+                                        407
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with pruning, trained quantization and huffman coding. arXiv preprint arXiv:1510.00149, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 20.5,
+                    "bbox_fs": [
+                        106,
+                        384,
+                        505,
+                        407
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        414,
+                        504,
+                        449
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                414,
+                                505,
+                                428
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        414,
+                                        505,
+                                        428
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Peter Henderson, Jieru Hu, Joshua Romoff, Emma Brunskill, Dan Jurafsky, and Joelle Pineau.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                426,
+                                505,
+                                439
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        426,
+                                        505,
+                                        439
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Towards the systematic reporting of the energy and carbon footprints of machine learning. arXiv",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                438,
+                                254,
+                                449
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        438,
+                                        254,
+                                        449
+                                    ],
+                                    "score": 1.0,
+                                    "content": "preprint arXiv:2002.05651, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 23,
+                    "bbox_fs": [
+                        105,
+                        414,
+                        505,
+                        449
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        457,
+                        504,
+                        480
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                457,
+                                505,
+                                470
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        457,
+                                        505,
+                                        470
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Geoffrey Hinton, Oriol Vinyals, and Jeff Dean. Distilling the knowledge in a neural network. arXiv",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                469,
+                                254,
+                                480
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        469,
+                                        254,
+                                        480
+                                    ],
+                                    "score": 1.0,
+                                    "content": "preprint arXiv:1503.02531, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 25.5,
+                    "bbox_fs": [
+                        106,
+                        457,
+                        505,
+                        480
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        488,
+                        505,
+                        511
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                488,
+                                506,
+                                502
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        488,
+                                        506,
+                                        502
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lu Hou, Lifeng Shang, Xin Jiang, and Qun Liu. Dynabert: Dynamic bert with adaptive width and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                500,
+                                306,
+                                512
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        500,
+                                        306,
+                                        512
+                                    ],
+                                    "score": 1.0,
+                                    "content": "depth. arXiv preprint arXiv:2004.04037, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 27.5,
+                    "bbox_fs": [
+                        105,
+                        488,
+                        506,
+                        512
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        519,
+                        504,
+                        543
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                520,
+                                505,
+                                532
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        520,
+                                        505,
+                                        532
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Gao Huang, Yu Sun, Zhuang Liu, Daniel Sedra, and Kilian Q Weinberger. Deep networks with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                530,
+                                484,
+                                544
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        530,
+                                        484,
+                                        544
+                                    ],
+                                    "score": 1.0,
+                                    "content": "stochastic depth. In European conference on computer vision, pp. 646–661. Springer, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 29.5,
+                    "bbox_fs": [
+                        106,
+                        520,
+                        505,
+                        544
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        551,
+                        505,
+                        585
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                551,
+                                506,
+                                563
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        551,
+                                        506,
+                                        563
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Gao Huang, Danlu Chen, Tianhong Li, Felix Wu, Laurens van der Maaten, and Kilian Q Wein-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                562,
+                                505,
+                                575
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        562,
+                                        505,
+                                        575
+                                    ],
+                                    "score": 1.0,
+                                    "content": "berger. Multi-scale dense networks for resource efficient image classification. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                573,
+                                220,
+                                584
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        573,
+                                        220,
+                                        584
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1703.09844, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 32,
+                    "bbox_fs": [
+                        106,
+                        551,
+                        506,
+                        584
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        593,
+                        506,
+                        627
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                594,
+                                505,
+                                606
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        594,
+                                        505,
+                                        606
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Jared Kaplan, Sam McCandlish, Tom Henighan, Tom B Brown, Benjamin Chess, Rewon Child, Scott",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                605,
+                                507,
+                                617
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        605,
+                                        507,
+                                        617
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Gray, Alec Radford, Jeffrey Wu, and Dario Amodei. Scaling laws for neural language models.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                616,
+                                279,
+                                627
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        616,
+                                        279,
+                                        627
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv preprint arXiv:2001.08361, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 35,
+                    "bbox_fs": [
+                        106,
+                        594,
+                        507,
+                        627
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        636,
+                        504,
+                        669
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                636,
+                                506,
+                                649
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        636,
+                                        506,
+                                        649
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Zhuohan Li, Eric Wallace, Sheng Shen, Kevin Lin, Kurt Keutzer, Dan Klein, and Joseph E Gon-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                647,
+                                506,
+                                659
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        647,
+                                        506,
+                                        659
+                                    ],
+                                    "score": 1.0,
+                                    "content": "zalez. Train large, then compress: Rethinking model size for efficient training and inference of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                658,
+                                335,
+                                669
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        658,
+                                        335,
+                                        669
+                                    ],
+                                    "score": 1.0,
+                                    "content": "transformers. arXiv preprint arXiv:2002.11794, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 38,
+                    "bbox_fs": [
+                        106,
+                        636,
+                        506,
+                        669
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        678,
+                        504,
+                        701
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                677,
+                                505,
+                                691
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        677,
+                                        505,
+                                        691
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Weijie Liu, Peng Zhou, Zhe Zhao, Zhiruo Wang, Haotang Deng, and Qi Ju. Fastbert: a self-distilling",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                689,
+                                416,
+                                701
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        689,
+                                        416,
+                                        701
+                                    ],
+                                    "score": 1.0,
+                                    "content": "bert with adaptive inference time. arXiv preprint arXiv:2004.02178, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        }
+                    ],
+                    "index": 40.5,
+                    "bbox_fs": [
+                        106,
+                        677,
+                        505,
+                        701
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        709,
+                        503,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                708,
+                                505,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        708,
+                                        505,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Paul Michel, Omer Levy, and Graham Neubig. Are sixteen heads really better than one? In Advances",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                720,
+                                389,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        720,
+                                        389,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in Neural Information Processing Systems, pp. 14014–14024, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        }
+                    ],
+                    "index": 42.5,
+                    "bbox_fs": [
+                        105,
+                        708,
+                        505,
+                        732
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        82,
+                        504,
+                        116
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                82,
+                                506,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        82,
+                                        506,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Matthew E Peters, Mark Neumann, Mohit Iyyer, Matt Gardner, Christopher Clark, Kenton Lee, and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                93,
+                                506,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        93,
+                                        506,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Luke Zettlemoyer. Deep contextualized word representations. arXiv preprint arXiv:1802.05365,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                103,
+                                143,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        103,
+                                        143,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        122,
+                        504,
+                        146
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                121,
+                                506,
+                                137
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        121,
+                                        506,
+                                        137
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Alec Radford, Jeffrey Wu, Rewon Child, David Luan, Dario Amodei, and Ilya Sutskever. Language",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                134,
+                                406,
+                                147
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        134,
+                                        406,
+                                        147
+                                    ],
+                                    "score": 1.0,
+                                    "content": "models are unsupervised multitask learners. OpenAI Blog, 1(8):9, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 3.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        109,
+                        152,
+                        504,
+                        186
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                150,
+                                505,
+                                166
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        150,
+                                        505,
+                                        166
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Colin Raffel, Noam Shazeer, Adam Roberts, Katherine Lee, Sharan Narang, Michael Matena, Yanqi",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                163,
+                                505,
+                                176
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        163,
+                                        505,
+                                        176
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Zhou, Wei Li, and Peter J Liu. Exploring the limits of transfer learning with a unified text-to-text",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                174,
+                                331,
+                                186
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        174,
+                                        331,
+                                        186
+                                    ],
+                                    "score": 1.0,
+                                    "content": "transformer. arXiv preprint arXiv:1910.10683, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        192,
+                        505,
+                        215
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                192,
+                                505,
+                                205
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        192,
+                                        412,
+                                        205
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Pranav Rajpurkar, Jian Zhang, Konstantin Lopyrev, and Percy Liang. Squad:",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        412,
+                                        193,
+                                        451,
+                                        204
+                                    ],
+                                    "score": 0.73,
+                                    "content": "^ { 1 0 0 , 0 0 0 + }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        451,
+                                        192,
+                                        505,
+                                        205
+                                    ],
+                                    "score": 1.0,
+                                    "content": "questions for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                204,
+                                410,
+                                216
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        204,
+                                        410,
+                                        216
+                                    ],
+                                    "score": 1.0,
+                                    "content": "machine comprehension of text. arXiv preprint arXiv:1606.05250, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 8.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        221,
+                        505,
+                        255
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                219,
+                                505,
+                                236
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        219,
+                                        505,
+                                        236
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Esteban Real, Alok Aggarwal, Yanping Huang, and Quoc V Le. Regularized evolution for image",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                232,
+                                506,
+                                246
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        232,
+                                        506,
+                                        246
+                                    ],
+                                    "score": 1.0,
+                                    "content": "classifier architecture search. In Proceedings of the aaai conference on artificial intelligence,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                244,
+                                253,
+                                256
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        244,
+                                        253,
+                                        256
+                                    ],
+                                    "score": 1.0,
+                                    "content": "volume 33, pp. 4780–4789, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        261,
+                        504,
+                        285
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                262,
+                                505,
+                                275
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        262,
+                                        505,
+                                        275
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Oren Rippel, Michael Gelbart, and Ryan Adams. Learning ordered representations with nested",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                273,
+                                448,
+                                285
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        273,
+                                        448,
+                                        285
+                                    ],
+                                    "score": 1.0,
+                                    "content": "dropout. In International Conference on Machine Learning, pp. 1746–1754, 2014.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 13.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        291,
+                        504,
+                        314
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                292,
+                                505,
+                                303
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        292,
+                                        505,
+                                        303
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Victor Sanh, Lysandre Debut, Julien Chaumond, and Thomas Wolf. Distilbert, a distilled version of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                302,
+                                443,
+                                315
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        302,
+                                        443,
+                                        315
+                                    ],
+                                    "score": 1.0,
+                                    "content": "bert: smaller, faster, cheaper and lighter. arXiv preprint arXiv:1910.01108, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 15.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        320,
+                        504,
+                        343
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                318,
+                                505,
+                                334
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        318,
+                                        505,
+                                        334
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Roy Schwartz, Jesse Dodge, Noah A Smith, and Oren Etzioni. Green ai. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                331,
+                                219,
+                                344
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        331,
+                                        219,
+                                        344
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1907.10597, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 17.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        349,
+                        504,
+                        383
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                350,
+                                505,
+                                362
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        350,
+                                        505,
+                                        362
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Roy Schwartz, Gabi Stanovsky, Swabha Swayamdipta, Jesse Dodge, and Noah A Smith. The right",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                360,
+                                507,
+                                374
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        360,
+                                        507,
+                                        374
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tool for the job: Matching model and instance complexities. arXiv preprint arXiv:2004.07453,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                370,
+                                142,
+                                385
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        370,
+                                        142,
+                                        385
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 20
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        390,
+                        504,
+                        413
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                390,
+                                505,
+                                403
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        390,
+                                        505,
+                                        403
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Abigail See, Minh-Thang Luong, and Christopher D Manning. Compression of neural machine",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                401,
+                                406,
+                                414
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        401,
+                                        406,
+                                        414
+                                    ],
+                                    "score": 1.0,
+                                    "content": "translation models via pruning. arXiv preprint arXiv:1606.09274, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 22.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        109,
+                        419,
+                        503,
+                        453
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                419,
+                                505,
+                                432
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        419,
+                                        505,
+                                        432
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Mohammad Shoeybi, Mostofa Patwary, Raul Puri, Patrick LeGresley, Jared Casper, and Bryan",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                430,
+                                505,
+                                444
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        430,
+                                        505,
+                                        444
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Catanzaro. Megatron-lm: Training multi-billion parameter language models using gpu model",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                442,
+                                330,
+                                454
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        442,
+                                        330,
+                                        454
+                                    ],
+                                    "score": 1.0,
+                                    "content": "parallelism. arXiv preprint arXiv:1909.08053, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        459,
+                        504,
+                        494
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                459,
+                                506,
+                                473
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        459,
+                                        506,
+                                        473
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                472,
+                                505,
+                                484
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        472,
+                                        505,
+                                        484
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Dropout: a simple way to prevent neural networks from overfitting. The journal of machine",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                482,
+                                291,
+                                495
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        482,
+                                        291,
+                                        495
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning research, 15(1):1929–1958, 2014.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 28
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        500,
+                        504,
+                        523
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                498,
+                                505,
+                                515
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        498,
+                                        505,
+                                        515
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Emma Strubell, Ananya Ganesh, and Andrew McCallum. Energy and policy considerations for deep",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                511,
+                                343,
+                                524
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        511,
+                                        343,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning in nlp. arXiv preprint arXiv:1906.02243, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        }
+                    ],
+                    "index": 30.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        529,
+                        504,
+                        552
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                530,
+                                505,
+                                542
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        530,
+                                        505,
+                                        542
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sandeep Subramanian, Ronan Collobert, Marc’Aurelio Ranzato, and Y-Lan Boureau. Multi-scale",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                540,
+                                401,
+                                553
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        540,
+                                        401,
+                                        553
+                                    ],
+                                    "score": 1.0,
+                                    "content": "transformer language models. arXiv preprint arXiv:2005.00581, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 32.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        558,
+                        504,
+                        582
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                558,
+                                504,
+                                571
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        558,
+                                        504,
+                                        571
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Siqi Sun, Yu Cheng, Zhe Gan, and Jingjing Liu. Patient knowledge distillation for bert model",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                570,
+                                335,
+                                582
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        570,
+                                        335,
+                                        582
+                                    ],
+                                    "score": 1.0,
+                                    "content": "compression. arXiv preprint arXiv:1908.09355, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        }
+                    ],
+                    "index": 34.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        588,
+                        504,
+                        611
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                588,
+                                505,
+                                601
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        588,
+                                        505,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Raphael Tang, Ashutosh Adhikari, and Jimmy Lin. Flops as a direct optimization objective for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                599,
+                                411,
+                                613
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        599,
+                                        411,
+                                        613
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning sparse neural networks. arXiv preprint arXiv:1811.03060, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 36.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        618,
+                        504,
+                        651
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                617,
+                                506,
+                                632
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        617,
+                                        506,
+                                        632
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Surat Teerapittayanon, Bradley McDanel, and Hsiang-Tsung Kung. Branchynet: Fast inference",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                628,
+                                506,
+                                642
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        628,
+                                        506,
+                                        642
+                                    ],
+                                    "score": 1.0,
+                                    "content": "via early exiting from deep neural networks. In 2016 23rd International Conference on Pattern",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                639,
+                                317,
+                                653
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        639,
+                                        317,
+                                        653
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Recognition (ICPR), pp. 2464–2469. IEEE, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        }
+                    ],
+                    "index": 39
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        658,
+                        504,
+                        692
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                658,
+                                505,
+                                671
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        658,
+                                        505,
+                                        671
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                669,
+                                505,
+                                681
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        669,
+                                        505,
+                                        681
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Kaiser, and Illia Polosukhin. Attention is all you need. In Advances in neural information",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                681,
+                                287,
+                                692
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        681,
+                                        287,
+                                        692
+                                    ],
+                                    "score": 1.0,
+                                    "content": "processing systems, pp. 5998–6008, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        }
+                    ],
+                    "index": 42
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        699,
+                        504,
+                        731
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                699,
+                                506,
+                                711
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        699,
+                                        506,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Alex Wang, Amanpreet Singh, Julian Michael, Felix Hill, Omer Levy, and Samuel R Bowman. Glue:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                709,
+                                505,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        709,
+                                        505,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A multi-task benchmark and analysis platform for natural language understanding. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                721,
+                                219,
+                                731
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        721,
+                                        219,
+                                        731
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1804.07461, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        }
+                    ],
+                    "index": 45
+                }
+            ],
+            "page_idx": 9,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        307,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                308,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        308,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Under review as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        311,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                312,
+                                764
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        312,
+                                        764
+                                    ],
+                                    "score": 1.0,
+                                    "content": "10",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        82,
+                        504,
+                        116
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                82,
+                                506,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        82,
+                                        506,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Matthew E Peters, Mark Neumann, Mohit Iyyer, Matt Gardner, Christopher Clark, Kenton Lee, and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                93,
+                                506,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        93,
+                                        506,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Luke Zettlemoyer. Deep contextualized word representations. arXiv preprint arXiv:1802.05365,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                103,
+                                143,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        103,
+                                        143,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1,
+                    "bbox_fs": [
+                        105,
+                        82,
+                        506,
+                        117
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        122,
+                        504,
+                        146
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                121,
+                                506,
+                                137
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        121,
+                                        506,
+                                        137
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Alec Radford, Jeffrey Wu, Rewon Child, David Luan, Dario Amodei, and Ilya Sutskever. Language",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                134,
+                                406,
+                                147
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        134,
+                                        406,
+                                        147
+                                    ],
+                                    "score": 1.0,
+                                    "content": "models are unsupervised multitask learners. OpenAI Blog, 1(8):9, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 3.5,
+                    "bbox_fs": [
+                        105,
+                        121,
+                        506,
+                        147
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        109,
+                        152,
+                        504,
+                        186
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                150,
+                                505,
+                                166
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        150,
+                                        505,
+                                        166
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Colin Raffel, Noam Shazeer, Adam Roberts, Katherine Lee, Sharan Narang, Michael Matena, Yanqi",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                163,
+                                505,
+                                176
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        163,
+                                        505,
+                                        176
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Zhou, Wei Li, and Peter J Liu. Exploring the limits of transfer learning with a unified text-to-text",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                174,
+                                331,
+                                186
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        174,
+                                        331,
+                                        186
+                                    ],
+                                    "score": 1.0,
+                                    "content": "transformer. arXiv preprint arXiv:1910.10683, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 6,
+                    "bbox_fs": [
+                        105,
+                        150,
+                        505,
+                        186
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        192,
+                        505,
+                        215
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                192,
+                                505,
+                                205
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        192,
+                                        412,
+                                        205
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Pranav Rajpurkar, Jian Zhang, Konstantin Lopyrev, and Percy Liang. Squad:",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        412,
+                                        193,
+                                        451,
+                                        204
+                                    ],
+                                    "score": 0.73,
+                                    "content": "^ { 1 0 0 , 0 0 0 + }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        451,
+                                        192,
+                                        505,
+                                        205
+                                    ],
+                                    "score": 1.0,
+                                    "content": "questions for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                204,
+                                410,
+                                216
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        204,
+                                        410,
+                                        216
+                                    ],
+                                    "score": 1.0,
+                                    "content": "machine comprehension of text. arXiv preprint arXiv:1606.05250, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 8.5,
+                    "bbox_fs": [
+                        106,
+                        192,
+                        505,
+                        216
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        221,
+                        505,
+                        255
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                219,
+                                505,
+                                236
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        219,
+                                        505,
+                                        236
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Esteban Real, Alok Aggarwal, Yanping Huang, and Quoc V Le. Regularized evolution for image",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                232,
+                                506,
+                                246
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        232,
+                                        506,
+                                        246
+                                    ],
+                                    "score": 1.0,
+                                    "content": "classifier architecture search. In Proceedings of the aaai conference on artificial intelligence,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                244,
+                                253,
+                                256
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        244,
+                                        253,
+                                        256
+                                    ],
+                                    "score": 1.0,
+                                    "content": "volume 33, pp. 4780–4789, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "index": 11,
+                    "bbox_fs": [
+                        105,
+                        219,
+                        506,
+                        256
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        261,
+                        504,
+                        285
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                262,
+                                505,
+                                275
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        262,
+                                        505,
+                                        275
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Oren Rippel, Michael Gelbart, and Ryan Adams. Learning ordered representations with nested",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                273,
+                                448,
+                                285
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        273,
+                                        448,
+                                        285
+                                    ],
+                                    "score": 1.0,
+                                    "content": "dropout. In International Conference on Machine Learning, pp. 1746–1754, 2014.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 13.5,
+                    "bbox_fs": [
+                        107,
+                        262,
+                        505,
+                        285
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        291,
+                        504,
+                        314
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                292,
+                                505,
+                                303
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        292,
+                                        505,
+                                        303
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Victor Sanh, Lysandre Debut, Julien Chaumond, and Thomas Wolf. Distilbert, a distilled version of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                302,
+                                443,
+                                315
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        302,
+                                        443,
+                                        315
+                                    ],
+                                    "score": 1.0,
+                                    "content": "bert: smaller, faster, cheaper and lighter. arXiv preprint arXiv:1910.01108, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 15.5,
+                    "bbox_fs": [
+                        107,
+                        292,
+                        505,
+                        315
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        320,
+                        504,
+                        343
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                318,
+                                505,
+                                334
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        318,
+                                        505,
+                                        334
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Roy Schwartz, Jesse Dodge, Noah A Smith, and Oren Etzioni. Green ai. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                331,
+                                219,
+                                344
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        331,
+                                        219,
+                                        344
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1907.10597, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 17.5,
+                    "bbox_fs": [
+                        105,
+                        318,
+                        505,
+                        344
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        349,
+                        504,
+                        383
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                350,
+                                505,
+                                362
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        350,
+                                        505,
+                                        362
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Roy Schwartz, Gabi Stanovsky, Swabha Swayamdipta, Jesse Dodge, and Noah A Smith. The right",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                360,
+                                507,
+                                374
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        360,
+                                        507,
+                                        374
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tool for the job: Matching model and instance complexities. arXiv preprint arXiv:2004.07453,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                370,
+                                142,
+                                385
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        370,
+                                        142,
+                                        385
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 20,
+                    "bbox_fs": [
+                        106,
+                        350,
+                        507,
+                        385
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        390,
+                        504,
+                        413
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                390,
+                                505,
+                                403
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        390,
+                                        505,
+                                        403
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Abigail See, Minh-Thang Luong, and Christopher D Manning. Compression of neural machine",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                401,
+                                406,
+                                414
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        401,
+                                        406,
+                                        414
+                                    ],
+                                    "score": 1.0,
+                                    "content": "translation models via pruning. arXiv preprint arXiv:1606.09274, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 22.5,
+                    "bbox_fs": [
+                        106,
+                        390,
+                        505,
+                        414
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        109,
+                        419,
+                        503,
+                        453
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                419,
+                                505,
+                                432
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        419,
+                                        505,
+                                        432
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Mohammad Shoeybi, Mostofa Patwary, Raul Puri, Patrick LeGresley, Jared Casper, and Bryan",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                430,
+                                505,
+                                444
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        430,
+                                        505,
+                                        444
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Catanzaro. Megatron-lm: Training multi-billion parameter language models using gpu model",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                442,
+                                330,
+                                454
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        442,
+                                        330,
+                                        454
+                                    ],
+                                    "score": 1.0,
+                                    "content": "parallelism. arXiv preprint arXiv:1909.08053, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 25,
+                    "bbox_fs": [
+                        106,
+                        419,
+                        505,
+                        454
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        459,
+                        504,
+                        494
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                459,
+                                506,
+                                473
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        459,
+                                        506,
+                                        473
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                472,
+                                505,
+                                484
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        472,
+                                        505,
+                                        484
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Dropout: a simple way to prevent neural networks from overfitting. The journal of machine",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                482,
+                                291,
+                                495
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        482,
+                                        291,
+                                        495
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning research, 15(1):1929–1958, 2014.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 28,
+                    "bbox_fs": [
+                        106,
+                        459,
+                        506,
+                        495
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        500,
+                        504,
+                        523
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                498,
+                                505,
+                                515
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        498,
+                                        505,
+                                        515
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Emma Strubell, Ananya Ganesh, and Andrew McCallum. Energy and policy considerations for deep",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                511,
+                                343,
+                                524
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        511,
+                                        343,
+                                        524
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning in nlp. arXiv preprint arXiv:1906.02243, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        }
+                    ],
+                    "index": 30.5,
+                    "bbox_fs": [
+                        105,
+                        498,
+                        505,
+                        524
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        529,
+                        504,
+                        552
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                530,
+                                505,
+                                542
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        530,
+                                        505,
+                                        542
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sandeep Subramanian, Ronan Collobert, Marc’Aurelio Ranzato, and Y-Lan Boureau. Multi-scale",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                540,
+                                401,
+                                553
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        540,
+                                        401,
+                                        553
+                                    ],
+                                    "score": 1.0,
+                                    "content": "transformer language models. arXiv preprint arXiv:2005.00581, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 32.5,
+                    "bbox_fs": [
+                        107,
+                        530,
+                        505,
+                        553
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        558,
+                        504,
+                        582
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                558,
+                                504,
+                                571
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        558,
+                                        504,
+                                        571
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Siqi Sun, Yu Cheng, Zhe Gan, and Jingjing Liu. Patient knowledge distillation for bert model",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                570,
+                                335,
+                                582
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        570,
+                                        335,
+                                        582
+                                    ],
+                                    "score": 1.0,
+                                    "content": "compression. arXiv preprint arXiv:1908.09355, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        }
+                    ],
+                    "index": 34.5,
+                    "bbox_fs": [
+                        106,
+                        558,
+                        504,
+                        582
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        588,
+                        504,
+                        611
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                588,
+                                505,
+                                601
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        588,
+                                        505,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Raphael Tang, Ashutosh Adhikari, and Jimmy Lin. Flops as a direct optimization objective for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                599,
+                                411,
+                                613
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        599,
+                                        411,
+                                        613
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning sparse neural networks. arXiv preprint arXiv:1811.03060, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 36.5,
+                    "bbox_fs": [
+                        106,
+                        588,
+                        505,
+                        613
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        618,
+                        504,
+                        651
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                617,
+                                506,
+                                632
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        617,
+                                        506,
+                                        632
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Surat Teerapittayanon, Bradley McDanel, and Hsiang-Tsung Kung. Branchynet: Fast inference",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                628,
+                                506,
+                                642
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        628,
+                                        506,
+                                        642
+                                    ],
+                                    "score": 1.0,
+                                    "content": "via early exiting from deep neural networks. In 2016 23rd International Conference on Pattern",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                639,
+                                317,
+                                653
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        639,
+                                        317,
+                                        653
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Recognition (ICPR), pp. 2464–2469. IEEE, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        }
+                    ],
+                    "index": 39,
+                    "bbox_fs": [
+                        105,
+                        617,
+                        506,
+                        653
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        658,
+                        504,
+                        692
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                658,
+                                505,
+                                671
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        658,
+                                        505,
+                                        671
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                669,
+                                505,
+                                681
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        669,
+                                        505,
+                                        681
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Kaiser, and Illia Polosukhin. Attention is all you need. In Advances in neural information",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                681,
+                                287,
+                                692
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        681,
+                                        287,
+                                        692
+                                    ],
+                                    "score": 1.0,
+                                    "content": "processing systems, pp. 5998–6008, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        }
+                    ],
+                    "index": 42,
+                    "bbox_fs": [
+                        105,
+                        658,
+                        505,
+                        692
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        699,
+                        504,
+                        731
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                699,
+                                506,
+                                711
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        699,
+                                        506,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Alex Wang, Amanpreet Singh, Julian Michael, Felix Hill, Omer Levy, and Samuel R Bowman. Glue:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                709,
+                                505,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        709,
+                                        505,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A multi-task benchmark and analysis platform for natural language understanding. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                721,
+                                219,
+                                731
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        721,
+                                        219,
+                                        731
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1804.07461, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        }
+                    ],
+                    "index": 45,
+                    "bbox_fs": [
+                        106,
+                        699,
+                        506,
+                        731
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        82,
+                        505,
+                        115
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                81,
+                                506,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        81,
+                                        506,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Hanrui Wang, Zhanghao Wu, Zhijian Liu, Han Cai, Ligeng Zhu, Chuang Gan, and Song Han.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                93,
+                                505,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        93,
+                                        505,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Hat: Hardware-aware transformers for efficient natural language processing. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                105,
+                                219,
+                                115
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        105,
+                                        219,
+                                        115
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:2005.14187, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        123,
+                        504,
+                        157
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                122,
+                                506,
+                                136
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        122,
+                                        506,
+                                        136
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Thomas Wolf, Lysandre Debut, Victor Sanh, Julien Chaumond, Clement Delangue, Anthony Moi,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                135,
+                                505,
+                                146
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        135,
+                                        505,
+                                        146
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Pierric Cistac, Tim Rault, Remi Louf, Morgan Funtowicz, et al. Transformers: State-of-the-art ´",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                145,
+                                396,
+                                158
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        145,
+                                        396,
+                                        158
+                                    ],
+                                    "score": 1.0,
+                                    "content": "natural language processing. arXiv preprint arXiv:1910.03771, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        163,
+                        505,
+                        186
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                164,
+                                505,
+                                177
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        164,
+                                        505,
+                                        177
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Ji Xin, Raphael Tang, Jaejun Lee, Yaoliang Yu, and Jimmy Lin. Deebert: Dynamic early exiting for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                175,
+                                390,
+                                187
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        175,
+                                        390,
+                                        187
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accelerating bert inference. arXiv preprint arXiv:2004.12993, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 6.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        194,
+                        504,
+                        228
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                193,
+                                506,
+                                207
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        193,
+                                        506,
+                                        207
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Zhilin Yang, Zihang Dai, Yiming Yang, Jaime Carbonell, Russ R Salakhutdinov, and Quoc V Le.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                204,
+                                506,
+                                218
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        204,
+                                        506,
+                                        218
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Xlnet: Generalized autoregressive pretraining for language understanding. In Advances in neural",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                216,
+                                336,
+                                228
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        216,
+                                        336,
+                                        228
+                                    ],
+                                    "score": 1.0,
+                                    "content": "information processing systems, pp. 5754–5764, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        234,
+                        504,
+                        257
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                234,
+                                506,
+                                248
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        234,
+                                        506,
+                                        248
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Jiahui Yu and Thomas S Huang. Universally slimmable networks and improved training techniques.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                245,
+                                506,
+                                258
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        245,
+                                        506,
+                                        258
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In Proceedings of the IEEE International Conference on Computer Vision, pp. 1803–1811, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "index": 11.5
+                }
+            ],
+            "page_idx": 10,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        309,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                312,
+                                765
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        312,
+                                        765
+                                    ],
+                                    "score": 1.0,
+                                    "content": "",
+                                    "type": "text",
+                                    "height": 15,
+                                    "width": 13
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        307,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                308,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        308,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Under review as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        82,
+                        505,
+                        115
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                81,
+                                506,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        81,
+                                        506,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Hanrui Wang, Zhanghao Wu, Zhijian Liu, Han Cai, Ligeng Zhu, Chuang Gan, and Song Han.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                93,
+                                505,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        93,
+                                        505,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Hat: Hardware-aware transformers for efficient natural language processing. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                105,
+                                219,
+                                115
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        105,
+                                        219,
+                                        115
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:2005.14187, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1,
+                    "bbox_fs": [
+                        105,
+                        81,
+                        506,
+                        115
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        123,
+                        504,
+                        157
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                122,
+                                506,
+                                136
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        122,
+                                        506,
+                                        136
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Thomas Wolf, Lysandre Debut, Victor Sanh, Julien Chaumond, Clement Delangue, Anthony Moi,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                135,
+                                505,
+                                146
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        135,
+                                        505,
+                                        146
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Pierric Cistac, Tim Rault, Remi Louf, Morgan Funtowicz, et al. Transformers: State-of-the-art ´",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                145,
+                                396,
+                                158
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        145,
+                                        396,
+                                        158
+                                    ],
+                                    "score": 1.0,
+                                    "content": "natural language processing. arXiv preprint arXiv:1910.03771, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        }
+                    ],
+                    "index": 4,
+                    "bbox_fs": [
+                        105,
+                        122,
+                        506,
+                        158
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        163,
+                        505,
+                        186
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                164,
+                                505,
+                                177
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        164,
+                                        505,
+                                        177
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Ji Xin, Raphael Tang, Jaejun Lee, Yaoliang Yu, and Jimmy Lin. Deebert: Dynamic early exiting for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                175,
+                                390,
+                                187
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        175,
+                                        390,
+                                        187
+                                    ],
+                                    "score": 1.0,
+                                    "content": "accelerating bert inference. arXiv preprint arXiv:2004.12993, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 6.5,
+                    "bbox_fs": [
+                        106,
+                        164,
+                        505,
+                        187
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        194,
+                        504,
+                        228
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                193,
+                                506,
+                                207
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        193,
+                                        506,
+                                        207
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Zhilin Yang, Zihang Dai, Yiming Yang, Jaime Carbonell, Russ R Salakhutdinov, and Quoc V Le.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                204,
+                                506,
+                                218
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        204,
+                                        506,
+                                        218
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Xlnet: Generalized autoregressive pretraining for language understanding. In Advances in neural",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                216,
+                                336,
+                                228
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        216,
+                                        336,
+                                        228
+                                    ],
+                                    "score": 1.0,
+                                    "content": "information processing systems, pp. 5754–5764, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 9,
+                    "bbox_fs": [
+                        105,
+                        193,
+                        506,
+                        228
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        234,
+                        504,
+                        257
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                234,
+                                506,
+                                248
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        234,
+                                        506,
+                                        248
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Jiahui Yu and Thomas S Huang. Universally slimmable networks and improved training techniques.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                245,
+                                506,
+                                258
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        245,
+                                        506,
+                                        258
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In Proceedings of the IEEE International Conference on Computer Vision, pp. 1803–1811, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "index": 11.5,
+                    "bbox_fs": [
+                        105,
+                        234,
+                        506,
+                        258
+                    ]
+                }
+            ]
+        }
+    ],
+    "_backend": "pipeline",
+    "_version_name": "2.2.2"
+}
\ No newline at end of file
diff --git a/parse/train/tqc8n6oHCtZ/tqc8n6oHCtZ_model.json b/parse/train/tqc8n6oHCtZ/tqc8n6oHCtZ_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..c1b7f31b51e54a8734ba2a32236f80950875a702
--- /dev/null
+++ b/parse/train/tqc8n6oHCtZ/tqc8n6oHCtZ_model.json
@@ -0,0 +1,12984 @@
+[
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    397,
+                    596,
+                    1303,
+                    596,
+                    1303,
+                    1326,
+                    397,
+                    1326
+                ],
+                "score": 0.983
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1712,
+                    1404,
+                    1712,
+                    1404,
+                    1957,
+                    298,
+                    1957
+                ],
+                "score": 0.981
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    299,
+                    219,
+                    1402,
+                    219,
+                    1402,
+                    325,
+                    299,
+                    325
+                ],
+                "score": 0.961
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1451,
+                    1406,
+                    1451,
+                    1406,
+                    1696,
+                    298,
+                    1696
+                ],
+                "score": 0.951
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1972,
+                    1398,
+                    1972,
+                    1398,
+                    2034,
+                    297,
+                    2034
+                ],
+                "score": 0.935
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    313,
+                    384,
+                    680,
+                    384,
+                    680,
+                    444,
+                    313,
+                    444
+                ],
+                "score": 0.929
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    302,
+                    1382,
+                    573,
+                    1382,
+                    573,
+                    1417,
+                    302,
+                    1417
+                ],
+                "score": 0.894
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    773,
+                    525,
+                    927,
+                    525,
+                    927,
+                    560,
+                    773,
+                    560
+                ],
+                "score": 0.874
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    75,
+                    854,
+                    75,
+                    854,
+                    105,
+                    298,
+                    105
+                ],
+                "score": 0.76
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2088,
+                    856,
+                    2088,
+                    856,
+                    2112,
+                    841,
+                    2112
+                ],
+                "score": 0.729
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    75,
+                    854,
+                    75,
+                    854,
+                    105,
+                    298,
+                    105
+                ],
+                "score": 0.131
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    773,
+                    1743,
+                    805,
+                    1743,
+                    805,
+                    1775,
+                    773,
+                    1775
+                ],
+                "score": 0.62,
+                "latex": "\\ S 6"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    221.0,
+                    1403.0,
+                    221.0,
+                    1403.0,
+                    269.0,
+                    295.0,
+                    269.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    275.0,
+                    1349.0,
+                    275.0,
+                    1349.0,
+                    327.0,
+                    295.0,
+                    327.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1379.0,
+                    579.0,
+                    1379.0,
+                    579.0,
+                    1426.0,
+                    294.0,
+                    1426.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    768.0,
+                    522.0,
+                    934.0,
+                    522.0,
+                    934.0,
+                    565.0,
+                    768.0,
+                    565.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    73.0,
+                    857.0,
+                    73.0,
+                    857.0,
+                    108.0,
+                    297.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    840.0,
+                    2088.0,
+                    857.0,
+                    2088.0,
+                    857.0,
+                    2116.0,
+                    840.0,
+                    2116.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    73.0,
+                    857.0,
+                    73.0,
+                    857.0,
+                    108.0,
+                    297.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    397.0,
+                    596.0,
+                    1304.0,
+                    596.0,
+                    1304.0,
+                    628.0,
+                    397.0,
+                    628.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    626.0,
+                    1304.0,
+                    626.0,
+                    1304.0,
+                    658.0,
+                    393.0,
+                    658.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    656.0,
+                    1306.0,
+                    656.0,
+                    1306.0,
+                    688.0,
+                    393.0,
+                    688.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    685.0,
+                    1304.0,
+                    685.0,
+                    1304.0,
+                    719.0,
+                    393.0,
+                    719.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    715.0,
+                    1304.0,
+                    715.0,
+                    1304.0,
+                    749.0,
+                    393.0,
+                    749.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    746.0,
+                    1306.0,
+                    746.0,
+                    1306.0,
+                    780.0,
+                    392.0,
+                    780.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    776.0,
+                    1307.0,
+                    776.0,
+                    1307.0,
+                    811.0,
+                    394.0,
+                    811.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    395.0,
+                    808.0,
+                    1305.0,
+                    808.0,
+                    1305.0,
+                    841.0,
+                    395.0,
+                    841.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    395.0,
+                    839.0,
+                    1305.0,
+                    839.0,
+                    1305.0,
+                    871.0,
+                    395.0,
+                    871.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    867.0,
+                    1305.0,
+                    867.0,
+                    1305.0,
+                    903.0,
+                    393.0,
+                    903.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    898.0,
+                    1304.0,
+                    898.0,
+                    1304.0,
+                    933.0,
+                    393.0,
+                    933.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    927.0,
+                    1306.0,
+                    927.0,
+                    1306.0,
+                    966.0,
+                    392.0,
+                    966.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    391.0,
+                    957.0,
+                    1307.0,
+                    957.0,
+                    1307.0,
+                    994.0,
+                    391.0,
+                    994.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    989.0,
+                    1307.0,
+                    989.0,
+                    1307.0,
+                    1023.0,
+                    393.0,
+                    1023.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    1018.0,
+                    1305.0,
+                    1018.0,
+                    1305.0,
+                    1055.0,
+                    392.0,
+                    1055.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    1050.0,
+                    1307.0,
+                    1050.0,
+                    1307.0,
+                    1085.0,
+                    393.0,
+                    1085.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1083.0,
+                    1307.0,
+                    1083.0,
+                    1307.0,
+                    1115.0,
+                    394.0,
+                    1115.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    395.0,
+                    1112.0,
+                    1306.0,
+                    1112.0,
+                    1306.0,
+                    1145.0,
+                    395.0,
+                    1145.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    394.0,
+                    1143.0,
+                    1307.0,
+                    1143.0,
+                    1307.0,
+                    1178.0,
+                    394.0,
+                    1178.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    1172.0,
+                    1306.0,
+                    1172.0,
+                    1306.0,
+                    1208.0,
+                    392.0,
+                    1208.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    392.0,
+                    1202.0,
+                    1305.0,
+                    1202.0,
+                    1305.0,
+                    1240.0,
+                    392.0,
+                    1240.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    393.0,
+                    1231.0,
+                    1308.0,
+                    1231.0,
+                    1308.0,
+                    1272.0,
+                    393.0,
+                    1272.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    396.0,
+                    1265.0,
+                    1306.0,
+                    1265.0,
+                    1306.0,
+                    1297.0,
+                    396.0,
+                    1297.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    395.0,
+                    1294.0,
+                    1285.0,
+                    1294.0,
+                    1285.0,
+                    1329.0,
+                    395.0,
+                    1329.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1710.0,
+                    1409.0,
+                    1710.0,
+                    1409.0,
+                    1751.0,
+                    292.0,
+                    1751.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1743.0,
+                    772.0,
+                    1743.0,
+                    772.0,
+                    1777.0,
+                    294.0,
+                    1777.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    806.0,
+                    1743.0,
+                    1404.0,
+                    1743.0,
+                    1404.0,
+                    1777.0,
+                    806.0,
+                    1777.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1771.0,
+                    1405.0,
+                    1771.0,
+                    1405.0,
+                    1811.0,
+                    292.0,
+                    1811.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1802.0,
+                    1407.0,
+                    1802.0,
+                    1407.0,
+                    1838.0,
+                    292.0,
+                    1838.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1836.0,
+                    1408.0,
+                    1836.0,
+                    1408.0,
+                    1869.0,
+                    294.0,
+                    1869.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1862.0,
+                    1409.0,
+                    1862.0,
+                    1409.0,
+                    1902.0,
+                    292.0,
+                    1902.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1893.0,
+                    1406.0,
+                    1893.0,
+                    1406.0,
+                    1932.0,
+                    292.0,
+                    1932.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1924.0,
+                    1222.0,
+                    1924.0,
+                    1222.0,
+                    1963.0,
+                    292.0,
+                    1963.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1449.0,
+                    1408.0,
+                    1449.0,
+                    1408.0,
+                    1488.0,
+                    292.0,
+                    1488.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1479.0,
+                    1408.0,
+                    1479.0,
+                    1408.0,
+                    1520.0,
+                    292.0,
+                    1520.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1510.0,
+                    1407.0,
+                    1510.0,
+                    1407.0,
+                    1550.0,
+                    292.0,
+                    1550.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1544.0,
+                    1407.0,
+                    1544.0,
+                    1407.0,
+                    1577.0,
+                    295.0,
+                    1577.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1571.0,
+                    1409.0,
+                    1571.0,
+                    1409.0,
+                    1611.0,
+                    291.0,
+                    1611.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1605.0,
+                    1406.0,
+                    1605.0,
+                    1406.0,
+                    1638.0,
+                    295.0,
+                    1638.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1636.0,
+                    1408.0,
+                    1636.0,
+                    1408.0,
+                    1669.0,
+                    295.0,
+                    1669.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1666.0,
+                    537.0,
+                    1666.0,
+                    537.0,
+                    1699.0,
+                    295.0,
+                    1699.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1970.0,
+                    1403.0,
+                    1970.0,
+                    1403.0,
+                    2008.0,
+                    293.0,
+                    2008.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    2004.0,
+                    1402.0,
+                    2004.0,
+                    1402.0,
+                    2036.0,
+                    297.0,
+                    2036.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    315.0,
+                    385.0,
+                    560.0,
+                    385.0,
+                    560.0,
+                    417.0,
+                    315.0,
+                    417.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    312.0,
+                    413.0,
+                    681.0,
+                    413.0,
+                    681.0,
+                    448.0,
+                    312.0,
+                    448.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 0,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    965,
+                    1405,
+                    965,
+                    1405,
+                    1302,
+                    298,
+                    1302
+                ],
+                "score": 0.983
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    476,
+                    1404,
+                    476,
+                    1404,
+                    659,
+                    298,
+                    659
+                ],
+                "score": 0.978
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    676,
+                    1404,
+                    676,
+                    1404,
+                    951,
+                    298,
+                    951
+                ],
+                "score": 0.978
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1772,
+                    1403,
+                    1772,
+                    1403,
+                    1957,
+                    299,
+                    1957
+                ],
+                "score": 0.976
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1417,
+                    1405,
+                    1417,
+                    1405,
+                    1539,
+                    299,
+                    1539
+                ],
+                "score": 0.976
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1634,
+                    1403,
+                    1634,
+                    1403,
+                    1758,
+                    299,
+                    1758
+                ],
+                "score": 0.975
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    338,
+                    1402,
+                    338,
+                    1402,
+                    460,
+                    298,
+                    460
+                ],
+                "score": 0.973
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    229,
+                    1401,
+                    229,
+                    1401,
+                    323,
+                    298,
+                    323
+                ],
+                "score": 0.963
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1972,
+                    1402,
+                    1972,
+                    1402,
+                    2034,
+                    297,
+                    2034
+                ],
+                "score": 0.941
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    301,
+                    1576,
+                    703,
+                    1576,
+                    703,
+                    1608,
+                    301,
+                    1608
+                ],
+                "score": 0.894
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    299,
+                    1347,
+                    1111,
+                    1347,
+                    1111,
+                    1383,
+                    299,
+                    1383
+                ],
+                "score": 0.889
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    300,
+                    76,
+                    852,
+                    76,
+                    852,
+                    104,
+                    300,
+                    104
+                ],
+                "score": 0.794
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2088,
+                    858,
+                    2088,
+                    858,
+                    2112,
+                    841,
+                    2112
+                ],
+                "score": 0.693
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2088,
+                    859,
+                    2088,
+                    859,
+                    2112,
+                    841,
+                    2112
+                ],
+                "score": 0.187
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    579,
+                    1802,
+                    686,
+                    1802,
+                    686,
+                    1836,
+                    579,
+                    1836
+                ],
+                "score": 0.93,
+                "latex": "h _ { t } ^ { 0 } \\in \\mathbb { R } ^ { H }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    748,
+                    1773,
+                    958,
+                    1773,
+                    958,
+                    1807,
+                    748,
+                    1807
+                ],
+                "score": 0.91,
+                "latex": "{ \\boldsymbol x } = ( x _ { 1 } , \\dots , x _ { N } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    376,
+                    1862,
+                    522,
+                    1862,
+                    522,
+                    1892,
+                    376,
+                    1892
+                ],
+                "score": 0.91,
+                "latex": "\\dot { h ^ { 1 } } \\in \\mathbb { R } ^ { N \\times H }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    1893,
+                    523,
+                    1893,
+                    523,
+                    1928,
+                    298,
+                    1928
+                ],
+                "score": 0.89,
+                "latex": "h ^ { L } = ( h _ { 1 } ^ { L } , \\ldots , h _ { N } ^ { L } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    433,
+                    1779,
+                    462,
+                    1779,
+                    462,
+                    1804,
+                    433,
+                    1804
+                ],
+                "score": 0.84,
+                "latex": "x _ { t }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    827,
+                    1866,
+                    850,
+                    1866,
+                    850,
+                    1892,
+                    827,
+                    1892
+                ],
+                "score": 0.81,
+                "latex": "L"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1188,
+                    1866,
+                    1211,
+                    1866,
+                    1211,
+                    1892,
+                    1188,
+                    1892
+                ],
+                "score": 0.75,
+                "latex": "L"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1576.0,
+                    706.0,
+                    1576.0,
+                    706.0,
+                    1612.0,
+                    295.0,
+                    1612.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1345.0,
+                    1115.0,
+                    1345.0,
+                    1115.0,
+                    1388.0,
+                    292.0,
+                    1388.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    73.0,
+                    856.0,
+                    73.0,
+                    856.0,
+                    108.0,
+                    297.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    839.0,
+                    2085.0,
+                    862.0,
+                    2085.0,
+                    862.0,
+                    2120.0,
+                    839.0,
+                    2120.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    838.0,
+                    2085.0,
+                    862.0,
+                    2085.0,
+                    862.0,
+                    2120.0,
+                    838.0,
+                    2120.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    966.0,
+                    1405.0,
+                    966.0,
+                    1405.0,
+                    1001.0,
+                    295.0,
+                    1001.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    998.0,
+                    1408.0,
+                    998.0,
+                    1408.0,
+                    1033.0,
+                    295.0,
+                    1033.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1028.0,
+                    1405.0,
+                    1028.0,
+                    1405.0,
+                    1063.0,
+                    295.0,
+                    1063.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1059.0,
+                    1406.0,
+                    1059.0,
+                    1406.0,
+                    1094.0,
+                    293.0,
+                    1094.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1086.0,
+                    1406.0,
+                    1086.0,
+                    1406.0,
+                    1125.0,
+                    292.0,
+                    1125.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1120.0,
+                    1405.0,
+                    1120.0,
+                    1405.0,
+                    1155.0,
+                    295.0,
+                    1155.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1150.0,
+                    1406.0,
+                    1150.0,
+                    1406.0,
+                    1184.0,
+                    295.0,
+                    1184.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1179.0,
+                    1405.0,
+                    1179.0,
+                    1405.0,
+                    1214.0,
+                    293.0,
+                    1214.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1209.0,
+                    1403.0,
+                    1209.0,
+                    1403.0,
+                    1246.0,
+                    293.0,
+                    1246.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1240.0,
+                    1406.0,
+                    1240.0,
+                    1406.0,
+                    1279.0,
+                    293.0,
+                    1279.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1274.0,
+                    887.0,
+                    1274.0,
+                    887.0,
+                    1305.0,
+                    296.0,
+                    1305.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    474.0,
+                    1408.0,
+                    474.0,
+                    1408.0,
+                    512.0,
+                    292.0,
+                    512.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    506.0,
+                    1406.0,
+                    506.0,
+                    1406.0,
+                    542.0,
+                    293.0,
+                    542.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    537.0,
+                    1406.0,
+                    537.0,
+                    1406.0,
+                    573.0,
+                    294.0,
+                    573.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    569.0,
+                    1406.0,
+                    569.0,
+                    1406.0,
+                    604.0,
+                    294.0,
+                    604.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    597.0,
+                    1405.0,
+                    597.0,
+                    1405.0,
+                    637.0,
+                    291.0,
+                    637.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    629.0,
+                    395.0,
+                    629.0,
+                    395.0,
+                    664.0,
+                    294.0,
+                    664.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    675.0,
+                    1405.0,
+                    675.0,
+                    1405.0,
+                    712.0,
+                    293.0,
+                    712.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    708.0,
+                    1404.0,
+                    708.0,
+                    1404.0,
+                    741.0,
+                    294.0,
+                    741.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    734.0,
+                    1406.0,
+                    734.0,
+                    1406.0,
+                    777.0,
+                    292.0,
+                    777.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    765.0,
+                    1405.0,
+                    765.0,
+                    1405.0,
+                    806.0,
+                    293.0,
+                    806.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    795.0,
+                    1405.0,
+                    795.0,
+                    1405.0,
+                    834.0,
+                    292.0,
+                    834.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    829.0,
+                    1405.0,
+                    829.0,
+                    1405.0,
+                    862.0,
+                    296.0,
+                    862.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    858.0,
+                    1405.0,
+                    858.0,
+                    1405.0,
+                    894.0,
+                    294.0,
+                    894.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    890.0,
+                    1404.0,
+                    890.0,
+                    1404.0,
+                    923.0,
+                    296.0,
+                    923.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    919.0,
+                    1407.0,
+                    919.0,
+                    1407.0,
+                    955.0,
+                    293.0,
+                    955.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1770.0,
+                    432.0,
+                    1770.0,
+                    432.0,
+                    1809.0,
+                    293.0,
+                    1809.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    463.0,
+                    1770.0,
+                    747.0,
+                    1770.0,
+                    747.0,
+                    1809.0,
+                    463.0,
+                    1809.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    959.0,
+                    1770.0,
+                    1405.0,
+                    1770.0,
+                    1405.0,
+                    1809.0,
+                    959.0,
+                    1809.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1797.0,
+                    578.0,
+                    1797.0,
+                    578.0,
+                    1839.0,
+                    292.0,
+                    1839.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    687.0,
+                    1797.0,
+                    1410.0,
+                    1797.0,
+                    1410.0,
+                    1839.0,
+                    687.0,
+                    1839.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1831.0,
+                    1405.0,
+                    1831.0,
+                    1405.0,
+                    1870.0,
+                    293.0,
+                    1870.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    290.0,
+                    1853.0,
+                    375.0,
+                    1853.0,
+                    375.0,
+                    1904.0,
+                    290.0,
+                    1904.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    523.0,
+                    1853.0,
+                    826.0,
+                    1853.0,
+                    826.0,
+                    1904.0,
+                    523.0,
+                    1904.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    851.0,
+                    1853.0,
+                    1187.0,
+                    1853.0,
+                    1187.0,
+                    1904.0,
+                    851.0,
+                    1904.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1212.0,
+                    1853.0,
+                    1409.0,
+                    1853.0,
+                    1409.0,
+                    1904.0,
+                    1212.0,
+                    1904.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1887.0,
+                    297.0,
+                    1887.0,
+                    297.0,
+                    1936.0,
+                    292.0,
+                    1936.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    524.0,
+                    1887.0,
+                    1408.0,
+                    1887.0,
+                    1408.0,
+                    1936.0,
+                    524.0,
+                    1936.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1924.0,
+                    1400.0,
+                    1924.0,
+                    1400.0,
+                    1960.0,
+                    295.0,
+                    1960.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1418.0,
+                    1403.0,
+                    1418.0,
+                    1403.0,
+                    1450.0,
+                    295.0,
+                    1450.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1446.0,
+                    1405.0,
+                    1446.0,
+                    1405.0,
+                    1485.0,
+                    293.0,
+                    1485.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1476.0,
+                    1410.0,
+                    1476.0,
+                    1410.0,
+                    1514.0,
+                    293.0,
+                    1514.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1509.0,
+                    1017.0,
+                    1509.0,
+                    1017.0,
+                    1542.0,
+                    295.0,
+                    1542.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1636.0,
+                    1402.0,
+                    1636.0,
+                    1402.0,
+                    1666.0,
+                    295.0,
+                    1666.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1666.0,
+                    1404.0,
+                    1666.0,
+                    1404.0,
+                    1699.0,
+                    293.0,
+                    1699.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1695.0,
+                    1407.0,
+                    1695.0,
+                    1407.0,
+                    1731.0,
+                    293.0,
+                    1731.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1728.0,
+                    560.0,
+                    1728.0,
+                    560.0,
+                    1761.0,
+                    295.0,
+                    1761.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    338.0,
+                    1406.0,
+                    338.0,
+                    1406.0,
+                    374.0,
+                    294.0,
+                    374.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    368.0,
+                    1406.0,
+                    368.0,
+                    1406.0,
+                    404.0,
+                    293.0,
+                    404.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    399.0,
+                    1406.0,
+                    399.0,
+                    1406.0,
+                    434.0,
+                    293.0,
+                    434.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    430.0,
+                    1350.0,
+                    430.0,
+                    1350.0,
+                    463.0,
+                    294.0,
+                    463.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    229.0,
+                    1405.0,
+                    229.0,
+                    1405.0,
+                    266.0,
+                    293.0,
+                    266.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    261.0,
+                    1405.0,
+                    261.0,
+                    1405.0,
+                    295.0,
+                    294.0,
+                    295.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    292.0,
+                    936.0,
+                    292.0,
+                    936.0,
+                    329.0,
+                    293.0,
+                    329.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1973.0,
+                    1406.0,
+                    1973.0,
+                    1406.0,
+                    2004.0,
+                    296.0,
+                    2004.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    2002.0,
+                    1408.0,
+                    2002.0,
+                    1408.0,
+                    2037.0,
+                    295.0,
+                    2037.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 1,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1649,
+                    1404,
+                    1649,
+                    1404,
+                    1926,
+                    298,
+                    1926
+                ],
+                "score": 0.982
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1018,
+                    1403,
+                    1018,
+                    1403,
+                    1233,
+                    298,
+                    1233
+                ],
+                "score": 0.98
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1249,
+                    1404,
+                    1249,
+                    1404,
+                    1463,
+                    298,
+                    1463
+                ],
+                "score": 0.979
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    337,
+                    1404,
+                    337,
+                    1404,
+                    523,
+                    299,
+                    523
+                ],
+                "score": 0.977
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    680,
+                    1404,
+                    680,
+                    1404,
+                    834,
+                    299,
+                    834
+                ],
+                "score": 0.976
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    849,
+                    1403,
+                    849,
+                    1403,
+                    1003,
+                    299,
+                    1003
+                ],
+                "score": 0.976
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    300,
+                    1942,
+                    1402,
+                    1942,
+                    1402,
+                    2033,
+                    300,
+                    2033
+                ],
+                "score": 0.971
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    300,
+                    229,
+                    1402,
+                    229,
+                    1402,
+                    322,
+                    300,
+                    322
+                ],
+                "score": 0.962
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    299,
+                    1554,
+                    861,
+                    1554,
+                    861,
+                    1589,
+                    299,
+                    1589
+                ],
+                "score": 0.909
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    299,
+                    605,
+                    550,
+                    605,
+                    550,
+                    636,
+                    299,
+                    636
+                ],
+                "score": 0.89
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    300,
+                    76,
+                    852,
+                    76,
+                    852,
+                    104,
+                    300,
+                    104
+                ],
+                "score": 0.732
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    842,
+                    2088,
+                    858,
+                    2088,
+                    858,
+                    2112,
+                    842,
+                    2112
+                ],
+                "score": 0.57
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    842,
+                    2088,
+                    859,
+                    2088,
+                    859,
+                    2111,
+                    842,
+                    2111
+                ],
+                "score": 0.433
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    299,
+                    76,
+                    853,
+                    76,
+                    853,
+                    104,
+                    299,
+                    104
+                ],
+                "score": 0.15
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1115,
+                    1081,
+                    1232,
+                    1081,
+                    1232,
+                    1114,
+                    1115,
+                    1114
+                ],
+                "score": 0.91,
+                "latex": "\\left( l _ { 1 } , \\cdots l _ { L } \\right)"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    982,
+                    398,
+                    1018,
+                    398,
+                    1018,
+                    432,
+                    982,
+                    432
+                ],
+                "score": 0.91,
+                "latex": "h _ { t } ^ { L }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1365,
+                    336,
+                    1400,
+                    336,
+                    1400,
+                    372,
+                    1365,
+                    372
+                ],
+                "score": 0.89,
+                "latex": "h _ { 1 } ^ { L }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    728,
+                    683,
+                    751,
+                    683,
+                    751,
+                    715,
+                    728,
+                    715
+                ],
+                "score": 0.87,
+                "latex": "l _ { j }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    597,
+                    744,
+                    620,
+                    744,
+                    620,
+                    776,
+                    597,
+                    776
+                ],
+                "score": 0.86,
+                "latex": "l _ { j }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1047,
+                    684,
+                    1064,
+                    684,
+                    1064,
+                    713,
+                    1047,
+                    713
+                ],
+                "score": 0.83,
+                "latex": "j"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1382,
+                    745,
+                    1398,
+                    745,
+                    1398,
+                    775,
+                    1382,
+                    775
+                ],
+                "score": 0.8,
+                "latex": "j"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    461,
+                    432,
+                    474,
+                    432,
+                    474,
+                    457,
+                    461,
+                    457
+                ],
+                "score": 0.73,
+                "latex": "t"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1551.0,
+                    866.0,
+                    1551.0,
+                    866.0,
+                    1595.0,
+                    292.0,
+                    1595.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    603.0,
+                    555.0,
+                    603.0,
+                    555.0,
+                    642.0,
+                    294.0,
+                    642.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    73.0,
+                    856.0,
+                    73.0,
+                    856.0,
+                    108.0,
+                    297.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    838.0,
+                    2085.0,
+                    862.0,
+                    2085.0,
+                    862.0,
+                    2118.0,
+                    838.0,
+                    2118.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    839.0,
+                    2086.0,
+                    860.0,
+                    2086.0,
+                    860.0,
+                    2117.0,
+                    839.0,
+                    2117.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    73.0,
+                    856.0,
+                    73.0,
+                    856.0,
+                    108.0,
+                    297.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1649.0,
+                    1405.0,
+                    1649.0,
+                    1405.0,
+                    1687.0,
+                    293.0,
+                    1687.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1683.0,
+                    1405.0,
+                    1683.0,
+                    1405.0,
+                    1716.0,
+                    296.0,
+                    1716.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1712.0,
+                    1405.0,
+                    1712.0,
+                    1405.0,
+                    1748.0,
+                    293.0,
+                    1748.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1738.0,
+                    1406.0,
+                    1738.0,
+                    1406.0,
+                    1781.0,
+                    291.0,
+                    1781.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1770.0,
+                    1406.0,
+                    1770.0,
+                    1406.0,
+                    1808.0,
+                    293.0,
+                    1808.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1803.0,
+                    1405.0,
+                    1803.0,
+                    1405.0,
+                    1840.0,
+                    294.0,
+                    1840.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1831.0,
+                    1406.0,
+                    1831.0,
+                    1406.0,
+                    1873.0,
+                    292.0,
+                    1873.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1862.0,
+                    1406.0,
+                    1862.0,
+                    1406.0,
+                    1901.0,
+                    293.0,
+                    1901.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1892.0,
+                    1294.0,
+                    1892.0,
+                    1294.0,
+                    1931.0,
+                    292.0,
+                    1931.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1018.0,
+                    1404.0,
+                    1018.0,
+                    1404.0,
+                    1057.0,
+                    293.0,
+                    1057.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1050.0,
+                    1404.0,
+                    1050.0,
+                    1404.0,
+                    1085.0,
+                    294.0,
+                    1085.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1081.0,
+                    1114.0,
+                    1081.0,
+                    1114.0,
+                    1116.0,
+                    294.0,
+                    1116.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1233.0,
+                    1081.0,
+                    1404.0,
+                    1081.0,
+                    1404.0,
+                    1116.0,
+                    1233.0,
+                    1116.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1110.0,
+                    1407.0,
+                    1110.0,
+                    1407.0,
+                    1148.0,
+                    293.0,
+                    1148.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1141.0,
+                    1405.0,
+                    1141.0,
+                    1405.0,
+                    1176.0,
+                    294.0,
+                    1176.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1172.0,
+                    1405.0,
+                    1172.0,
+                    1405.0,
+                    1205.0,
+                    293.0,
+                    1205.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1203.0,
+                    1386.0,
+                    1203.0,
+                    1386.0,
+                    1236.0,
+                    292.0,
+                    1236.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1248.0,
+                    1406.0,
+                    1248.0,
+                    1406.0,
+                    1286.0,
+                    293.0,
+                    1286.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1279.0,
+                    1405.0,
+                    1279.0,
+                    1405.0,
+                    1314.0,
+                    293.0,
+                    1314.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1309.0,
+                    1405.0,
+                    1309.0,
+                    1405.0,
+                    1342.0,
+                    293.0,
+                    1342.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1343.0,
+                    1404.0,
+                    1343.0,
+                    1404.0,
+                    1373.0,
+                    296.0,
+                    1373.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1371.0,
+                    1406.0,
+                    1371.0,
+                    1406.0,
+                    1405.0,
+                    294.0,
+                    1405.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1401.0,
+                    1404.0,
+                    1401.0,
+                    1404.0,
+                    1436.0,
+                    293.0,
+                    1436.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1431.0,
+                    1377.0,
+                    1431.0,
+                    1377.0,
+                    1468.0,
+                    293.0,
+                    1468.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    334.0,
+                    1364.0,
+                    334.0,
+                    1364.0,
+                    374.0,
+                    293.0,
+                    374.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1401.0,
+                    334.0,
+                    1404.0,
+                    334.0,
+                    1404.0,
+                    374.0,
+                    1401.0,
+                    374.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    369.0,
+                    1405.0,
+                    369.0,
+                    1405.0,
+                    401.0,
+                    294.0,
+                    401.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    398.0,
+                    981.0,
+                    398.0,
+                    981.0,
+                    434.0,
+                    294.0,
+                    434.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1019.0,
+                    398.0,
+                    1406.0,
+                    398.0,
+                    1406.0,
+                    434.0,
+                    1019.0,
+                    434.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    424.0,
+                    460.0,
+                    424.0,
+                    460.0,
+                    468.0,
+                    293.0,
+                    468.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    475.0,
+                    424.0,
+                    1409.0,
+                    424.0,
+                    1409.0,
+                    468.0,
+                    475.0,
+                    468.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    458.0,
+                    1405.0,
+                    458.0,
+                    1405.0,
+                    496.0,
+                    294.0,
+                    496.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    491.0,
+                    618.0,
+                    491.0,
+                    618.0,
+                    526.0,
+                    296.0,
+                    526.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    679.0,
+                    727.0,
+                    679.0,
+                    727.0,
+                    717.0,
+                    293.0,
+                    717.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    752.0,
+                    679.0,
+                    1046.0,
+                    679.0,
+                    1046.0,
+                    717.0,
+                    752.0,
+                    717.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1065.0,
+                    679.0,
+                    1406.0,
+                    679.0,
+                    1406.0,
+                    717.0,
+                    1065.0,
+                    717.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    713.0,
+                    1405.0,
+                    713.0,
+                    1405.0,
+                    746.0,
+                    297.0,
+                    746.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    741.0,
+                    596.0,
+                    741.0,
+                    596.0,
+                    780.0,
+                    293.0,
+                    780.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    621.0,
+                    741.0,
+                    1381.0,
+                    741.0,
+                    1381.0,
+                    780.0,
+                    621.0,
+                    780.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1399.0,
+                    741.0,
+                    1409.0,
+                    741.0,
+                    1409.0,
+                    780.0,
+                    1399.0,
+                    780.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    773.0,
+                    1406.0,
+                    773.0,
+                    1406.0,
+                    810.0,
+                    294.0,
+                    810.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    805.0,
+                    1175.0,
+                    805.0,
+                    1175.0,
+                    838.0,
+                    295.0,
+                    838.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    849.0,
+                    1404.0,
+                    849.0,
+                    1404.0,
+                    885.0,
+                    294.0,
+                    885.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    881.0,
+                    1407.0,
+                    881.0,
+                    1407.0,
+                    914.0,
+                    295.0,
+                    914.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    913.0,
+                    1405.0,
+                    913.0,
+                    1405.0,
+                    946.0,
+                    297.0,
+                    946.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    941.0,
+                    1405.0,
+                    941.0,
+                    1405.0,
+                    976.0,
+                    293.0,
+                    976.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    974.0,
+                    1281.0,
+                    974.0,
+                    1281.0,
+                    1007.0,
+                    295.0,
+                    1007.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1939.0,
+                    1407.0,
+                    1939.0,
+                    1407.0,
+                    1979.0,
+                    293.0,
+                    1979.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1971.0,
+                    1406.0,
+                    1971.0,
+                    1406.0,
+                    2008.0,
+                    295.0,
+                    2008.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    2003.0,
+                    1059.0,
+                    2003.0,
+                    1059.0,
+                    2035.0,
+                    295.0,
+                    2035.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    227.0,
+                    1407.0,
+                    227.0,
+                    1407.0,
+                    266.0,
+                    293.0,
+                    266.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    261.0,
+                    1406.0,
+                    261.0,
+                    1406.0,
+                    295.0,
+                    295.0,
+                    295.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    291.0,
+                    915.0,
+                    291.0,
+                    915.0,
+                    325.0,
+                    295.0,
+                    325.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 2,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    702,
+                    1404,
+                    702,
+                    1404,
+                    978,
+                    297,
+                    978
+                ],
+                "score": 0.983
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1637,
+                    1406,
+                    1637,
+                    1406,
+                    2034,
+                    297,
+                    2034
+                ],
+                "score": 0.983
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1376,
+                    1404,
+                    1376,
+                    1404,
+                    1622,
+                    298,
+                    1622
+                ],
+                "score": 0.981
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1008,
+                    1405,
+                    1008,
+                    1405,
+                    1285,
+                    298,
+                    1285
+                ],
+                "score": 0.98
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    456,
+                    1405,
+                    456,
+                    1405,
+                    670,
+                    297,
+                    670
+                ],
+                "score": 0.979
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    286,
+                    1403,
+                    286,
+                    1403,
+                    441,
+                    298,
+                    441
+                ],
+                "score": 0.977
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    299,
+                    229,
+                    535,
+                    229,
+                    535,
+                    261,
+                    299,
+                    261
+                ],
+                "score": 0.885
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    300,
+                    1319,
+                    1030,
+                    1319,
+                    1030,
+                    1351,
+                    300,
+                    1351
+                ],
+                "score": 0.841
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    299,
+                    75,
+                    854,
+                    75,
+                    854,
+                    104,
+                    299,
+                    104
+                ],
+                "score": 0.836
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    840,
+                    2089,
+                    857,
+                    2089,
+                    857,
+                    2111,
+                    840,
+                    2111
+                ],
+                "score": 0.765
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    300,
+                    76,
+                    853,
+                    76,
+                    853,
+                    104,
+                    300,
+                    104
+                ],
+                "score": 0.164
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    769,
+                    1192,
+                    893,
+                    1192,
+                    893,
+                    1226,
+                    769,
+                    1226
+                ],
+                "score": 0.92,
+                "latex": "\\lceil ( 1 - p ) l _ { i } \\rceil"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    437,
+                    517,
+                    640,
+                    517,
+                    640,
+                    551,
+                    437,
+                    551
+                ],
+                "score": 0.92,
+                "latex": "\\mathcal { U } ( \\lceil ( 1 - p ) l _ { i } \\rceil , l _ { i } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    297,
+                    1667,
+                    520,
+                    1667,
+                    520,
+                    1702,
+                    297,
+                    1702
+                ],
+                "score": 0.92,
+                "latex": "l _ { i + 1 } = \\lceil ( 1 - r ) \\bar { l _ { i } } \\rceil"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    464,
+                    1789,
+                    597,
+                    1789,
+                    597,
+                    1824,
+                    464,
+                    1824
+                ],
+                "score": 0.91,
+                "latex": "( l _ { 1 } ^ { \\prime } , \\cdots , l _ { L } ^ { \\prime } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    487,
+                    345,
+                    487,
+                    345,
+                    519,
+                    298,
+                    519
+                ],
+                "score": 0.91,
+                "latex": "l _ { i + 1 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1263,
+                    548,
+                    1398,
+                    548,
+                    1398,
+                    581,
+                    1263,
+                    581
+                ],
+                "score": 0.91,
+                "latex": "( l _ { 1 } , \\cdots , l _ { L } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1095,
+                    1789,
+                    1242,
+                    1789,
+                    1242,
+                    1824,
+                    1095,
+                    1824
+                ],
+                "score": 0.91,
+                "latex": "\\bar { \\mathcal { U } } ( l _ { i - 1 } ^ { \\prime } , l _ { i + 1 } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    420,
+                    487,
+                    499,
+                    487,
+                    499,
+                    519,
+                    420,
+                    519
+                ],
+                "score": 0.91,
+                "latex": "( i + 1 )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    295,
+                    1789,
+                    430,
+                    1789,
+                    430,
+                    1823,
+                    295,
+                    1823
+                ],
+                "score": 0.91,
+                "latex": "( l _ { 1 } , \\cdots , l _ { L } )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    745,
+                    1821,
+                    819,
+                    1821,
+                    819,
+                    1854,
+                    745,
+                    1854
+                ],
+                "score": 0.9,
+                "latex": "{ \\bar { l } } _ { i } ^ { \\prime } = l _ { i }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1208,
+                    1822,
+                    1276,
+                    1822,
+                    1276,
+                    1848,
+                    1208,
+                    1848
+                ],
+                "score": 0.9,
+                "latex": "i = L"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1113,
+                    1824,
+                    1176,
+                    1824,
+                    1176,
+                    1848,
+                    1113,
+                    1848
+                ],
+                "score": 0.88,
+                "latex": "i = 1"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1118,
+                    488,
+                    1138,
+                    488,
+                    1138,
+                    517,
+                    1118,
+                    517
+                ],
+                "score": 0.86,
+                "latex": "l _ { i }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    734,
+                    519,
+                    759,
+                    519,
+                    759,
+                    548,
+                    734,
+                    548
+                ],
+                "score": 0.85,
+                "latex": "l _ { 0 }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    374,
+                    1826,
+                    411,
+                    1826,
+                    411,
+                    1853,
+                    374,
+                    1853
+                ],
+                "score": 0.85,
+                "latex": "p _ { m }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    744,
+                    1790,
+                    764,
+                    1790,
+                    764,
+                    1822,
+                    744,
+                    1822
+                ],
+                "score": 0.84,
+                "latex": "l _ { i } ^ { \\prime }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    298,
+                    1167,
+                    329,
+                    1167,
+                    329,
+                    1193,
+                    298,
+                    1193
+                ],
+                "score": 0.83,
+                "latex": "n _ { s }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    582,
+                    1916,
+                    622,
+                    1916,
+                    622,
+                    1943,
+                    582,
+                    1943
+                ],
+                "score": 0.83,
+                "latex": "n _ { m }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1376,
+                    1883,
+                    1401,
+                    1883,
+                    1401,
+                    1909,
+                    1376,
+                    1909
+                ],
+                "score": 0.79,
+                "latex": "G"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    939,
+                    1916,
+                    969,
+                    1916,
+                    969,
+                    1943,
+                    939,
+                    1943
+                ],
+                "score": 0.79,
+                "latex": "n _ { c }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1310,
+                    522,
+                    1328,
+                    522,
+                    1328,
+                    549,
+                    1310,
+                    549
+                ],
+                "score": 0.77,
+                "latex": "p"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    696,
+                    1671,
+                    710,
+                    1671,
+                    710,
+                    1696,
+                    696,
+                    1696
+                ],
+                "score": 0.74,
+                "latex": "i"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    775,
+                    1675,
+                    792,
+                    1675,
+                    792,
+                    1696,
+                    775,
+                    1696
+                ],
+                "score": 0.7,
+                "latex": "r"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1190,
+                    1195,
+                    1203,
+                    1195,
+                    1203,
+                    1221,
+                    1190,
+                    1221
+                ],
+                "score": 0.69,
+                "latex": "i"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    228.0,
+                    539.0,
+                    228.0,
+                    539.0,
+                    265.0,
+                    294.0,
+                    265.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1319.0,
+                    1033.0,
+                    1319.0,
+                    1033.0,
+                    1355.0,
+                    295.0,
+                    1355.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    72.0,
+                    857.0,
+                    72.0,
+                    857.0,
+                    108.0,
+                    297.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    838.0,
+                    2086.0,
+                    862.0,
+                    2086.0,
+                    862.0,
+                    2118.0,
+                    838.0,
+                    2118.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    73.0,
+                    856.0,
+                    73.0,
+                    856.0,
+                    108.0,
+                    297.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    702.0,
+                    1405.0,
+                    702.0,
+                    1405.0,
+                    738.0,
+                    294.0,
+                    738.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    734.0,
+                    1406.0,
+                    734.0,
+                    1406.0,
+                    767.0,
+                    295.0,
+                    767.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    762.0,
+                    1407.0,
+                    762.0,
+                    1407.0,
+                    797.0,
+                    294.0,
+                    797.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    792.0,
+                    1405.0,
+                    792.0,
+                    1405.0,
+                    830.0,
+                    292.0,
+                    830.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    824.0,
+                    1405.0,
+                    824.0,
+                    1405.0,
+                    861.0,
+                    294.0,
+                    861.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    854.0,
+                    1406.0,
+                    854.0,
+                    1406.0,
+                    891.0,
+                    294.0,
+                    891.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    886.0,
+                    1406.0,
+                    886.0,
+                    1406.0,
+                    922.0,
+                    294.0,
+                    922.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    913.0,
+                    1404.0,
+                    913.0,
+                    1404.0,
+                    952.0,
+                    294.0,
+                    952.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    947.0,
+                    585.0,
+                    947.0,
+                    585.0,
+                    984.0,
+                    294.0,
+                    984.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1635.0,
+                    1404.0,
+                    1635.0,
+                    1404.0,
+                    1674.0,
+                    294.0,
+                    1674.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1666.0,
+                    296.0,
+                    1666.0,
+                    296.0,
+                    1703.0,
+                    291.0,
+                    1703.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    521.0,
+                    1666.0,
+                    695.0,
+                    1666.0,
+                    695.0,
+                    1703.0,
+                    521.0,
+                    1703.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    711.0,
+                    1666.0,
+                    774.0,
+                    1666.0,
+                    774.0,
+                    1703.0,
+                    711.0,
+                    1703.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    793.0,
+                    1666.0,
+                    1407.0,
+                    1666.0,
+                    1407.0,
+                    1703.0,
+                    793.0,
+                    1703.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1697.0,
+                    1409.0,
+                    1697.0,
+                    1409.0,
+                    1735.0,
+                    291.0,
+                    1735.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1724.0,
+                    1409.0,
+                    1724.0,
+                    1409.0,
+                    1767.0,
+                    291.0,
+                    1767.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1759.0,
+                    1406.0,
+                    1759.0,
+                    1406.0,
+                    1795.0,
+                    294.0,
+                    1795.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    431.0,
+                    1788.0,
+                    463.0,
+                    1788.0,
+                    463.0,
+                    1828.0,
+                    431.0,
+                    1828.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    598.0,
+                    1788.0,
+                    743.0,
+                    1788.0,
+                    743.0,
+                    1828.0,
+                    598.0,
+                    1828.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    765.0,
+                    1788.0,
+                    1094.0,
+                    1788.0,
+                    1094.0,
+                    1828.0,
+                    765.0,
+                    1828.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1243.0,
+                    1788.0,
+                    1409.0,
+                    1788.0,
+                    1409.0,
+                    1828.0,
+                    1243.0,
+                    1828.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1817.0,
+                    373.0,
+                    1817.0,
+                    373.0,
+                    1858.0,
+                    292.0,
+                    1858.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    412.0,
+                    1817.0,
+                    744.0,
+                    1817.0,
+                    744.0,
+                    1858.0,
+                    412.0,
+                    1858.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    820.0,
+                    1817.0,
+                    1112.0,
+                    1817.0,
+                    1112.0,
+                    1858.0,
+                    820.0,
+                    1858.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1177.0,
+                    1817.0,
+                    1207.0,
+                    1817.0,
+                    1207.0,
+                    1858.0,
+                    1177.0,
+                    1858.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1277.0,
+                    1817.0,
+                    1407.0,
+                    1817.0,
+                    1407.0,
+                    1858.0,
+                    1277.0,
+                    1858.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1850.0,
+                    1404.0,
+                    1850.0,
+                    1404.0,
+                    1886.0,
+                    294.0,
+                    1886.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1882.0,
+                    1375.0,
+                    1882.0,
+                    1375.0,
+                    1916.0,
+                    294.0,
+                    1916.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1402.0,
+                    1882.0,
+                    1406.0,
+                    1882.0,
+                    1406.0,
+                    1916.0,
+                    1402.0,
+                    1916.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1909.0,
+                    581.0,
+                    1909.0,
+                    581.0,
+                    1949.0,
+                    294.0,
+                    1949.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    623.0,
+                    1909.0,
+                    938.0,
+                    1909.0,
+                    938.0,
+                    1949.0,
+                    623.0,
+                    1949.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    970.0,
+                    1909.0,
+                    1406.0,
+                    1909.0,
+                    1406.0,
+                    1949.0,
+                    970.0,
+                    1949.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1942.0,
+                    1408.0,
+                    1942.0,
+                    1408.0,
+                    1979.0,
+                    294.0,
+                    1979.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1970.0,
+                    1406.0,
+                    1970.0,
+                    1406.0,
+                    2010.0,
+                    294.0,
+                    2010.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    2005.0,
+                    668.0,
+                    2005.0,
+                    668.0,
+                    2037.0,
+                    296.0,
+                    2037.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1376.0,
+                    1405.0,
+                    1376.0,
+                    1405.0,
+                    1414.0,
+                    293.0,
+                    1414.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1408.0,
+                    1405.0,
+                    1408.0,
+                    1405.0,
+                    1440.0,
+                    293.0,
+                    1440.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1438.0,
+                    1405.0,
+                    1438.0,
+                    1405.0,
+                    1475.0,
+                    293.0,
+                    1475.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1468.0,
+                    1404.0,
+                    1468.0,
+                    1404.0,
+                    1505.0,
+                    293.0,
+                    1505.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1498.0,
+                    1405.0,
+                    1498.0,
+                    1405.0,
+                    1536.0,
+                    292.0,
+                    1536.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1528.0,
+                    1409.0,
+                    1528.0,
+                    1409.0,
+                    1567.0,
+                    291.0,
+                    1567.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1559.0,
+                    1405.0,
+                    1559.0,
+                    1405.0,
+                    1598.0,
+                    292.0,
+                    1598.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1589.0,
+                    483.0,
+                    1589.0,
+                    483.0,
+                    1627.0,
+                    294.0,
+                    1627.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1006.0,
+                    1405.0,
+                    1006.0,
+                    1405.0,
+                    1044.0,
+                    293.0,
+                    1044.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1037.0,
+                    1406.0,
+                    1037.0,
+                    1406.0,
+                    1080.0,
+                    292.0,
+                    1080.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1069.0,
+                    1408.0,
+                    1069.0,
+                    1408.0,
+                    1107.0,
+                    292.0,
+                    1107.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1098.0,
+                    1406.0,
+                    1098.0,
+                    1406.0,
+                    1136.0,
+                    292.0,
+                    1136.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1131.0,
+                    1405.0,
+                    1131.0,
+                    1405.0,
+                    1166.0,
+                    293.0,
+                    1166.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1160.0,
+                    297.0,
+                    1160.0,
+                    297.0,
+                    1198.0,
+                    291.0,
+                    1198.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    330.0,
+                    1160.0,
+                    1408.0,
+                    1160.0,
+                    1408.0,
+                    1198.0,
+                    330.0,
+                    1198.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1192.0,
+                    768.0,
+                    1192.0,
+                    768.0,
+                    1229.0,
+                    293.0,
+                    1229.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    894.0,
+                    1192.0,
+                    1189.0,
+                    1192.0,
+                    1189.0,
+                    1229.0,
+                    894.0,
+                    1229.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1204.0,
+                    1192.0,
+                    1405.0,
+                    1192.0,
+                    1405.0,
+                    1229.0,
+                    1204.0,
+                    1229.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1220.0,
+                    1405.0,
+                    1220.0,
+                    1405.0,
+                    1258.0,
+                    293.0,
+                    1258.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1253.0,
+                    1407.0,
+                    1253.0,
+                    1407.0,
+                    1289.0,
+                    295.0,
+                    1289.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    455.0,
+                    1403.0,
+                    455.0,
+                    1403.0,
+                    493.0,
+                    294.0,
+                    493.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    346.0,
+                    486.0,
+                    419.0,
+                    486.0,
+                    419.0,
+                    524.0,
+                    346.0,
+                    524.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    500.0,
+                    486.0,
+                    1117.0,
+                    486.0,
+                    1117.0,
+                    524.0,
+                    500.0,
+                    524.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1139.0,
+                    486.0,
+                    1406.0,
+                    486.0,
+                    1406.0,
+                    524.0,
+                    1139.0,
+                    524.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    516.0,
+                    436.0,
+                    516.0,
+                    436.0,
+                    554.0,
+                    294.0,
+                    554.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    641.0,
+                    516.0,
+                    733.0,
+                    516.0,
+                    733.0,
+                    554.0,
+                    641.0,
+                    554.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    760.0,
+                    516.0,
+                    1309.0,
+                    516.0,
+                    1309.0,
+                    554.0,
+                    760.0,
+                    554.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1329.0,
+                    516.0,
+                    1406.0,
+                    516.0,
+                    1406.0,
+                    554.0,
+                    1329.0,
+                    554.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    547.0,
+                    1262.0,
+                    547.0,
+                    1262.0,
+                    585.0,
+                    294.0,
+                    585.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1399.0,
+                    547.0,
+                    1408.0,
+                    547.0,
+                    1408.0,
+                    585.0,
+                    1399.0,
+                    585.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    577.0,
+                    1406.0,
+                    577.0,
+                    1406.0,
+                    613.0,
+                    292.0,
+                    613.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    608.0,
+                    1406.0,
+                    608.0,
+                    1406.0,
+                    646.0,
+                    294.0,
+                    646.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    639.0,
+                    572.0,
+                    639.0,
+                    572.0,
+                    673.0,
+                    295.0,
+                    673.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    288.0,
+                    1405.0,
+                    288.0,
+                    1405.0,
+                    321.0,
+                    296.0,
+                    321.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    317.0,
+                    1405.0,
+                    317.0,
+                    1405.0,
+                    353.0,
+                    293.0,
+                    353.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    349.0,
+                    1407.0,
+                    349.0,
+                    1407.0,
+                    383.0,
+                    293.0,
+                    383.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    378.0,
+                    1405.0,
+                    378.0,
+                    1405.0,
+                    415.0,
+                    294.0,
+                    415.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    409.0,
+                    766.0,
+                    409.0,
+                    766.0,
+                    447.0,
+                    295.0,
+                    447.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 3,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1552,
+                    1405,
+                    1552,
+                    1405,
+                    1797,
+                    298,
+                    1797
+                ],
+                "score": 0.983
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    751,
+                    1404,
+                    751,
+                    1404,
+                    966,
+                    298,
+                    966
+                ],
+                "score": 0.98
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1332,
+                    1403,
+                    1332,
+                    1403,
+                    1518,
+                    298,
+                    1518
+                ],
+                "score": 0.979
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1083,
+                    1405,
+                    1083,
+                    1405,
+                    1297,
+                    298,
+                    1297
+                ],
+                "score": 0.979
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1834,
+                    1404,
+                    1834,
+                    1404,
+                    1926,
+                    299,
+                    1926
+                ],
+                "score": 0.972
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    300,
+                    1942,
+                    1404,
+                    1942,
+                    1404,
+                    2034,
+                    300,
+                    2034
+                ],
+                "score": 0.969
+            },
+            {
+                "category_id": 3,
+                "poly": [
+                    331,
+                    247,
+                    1367,
+                    247,
+                    1367,
+                    438,
+                    331,
+                    438
+                ],
+                "score": 0.963
+            },
+            {
+                "category_id": 4,
+                "poly": [
+                    296,
+                    461,
+                    1405,
+                    461,
+                    1405,
+                    646,
+                    296,
+                    646
+                ],
+                "score": 0.912
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    301,
+                    1012,
+                    643,
+                    1012,
+                    643,
+                    1047,
+                    301,
+                    1047
+                ],
+                "score": 0.898
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    302,
+                    694,
+                    733,
+                    694,
+                    733,
+                    724,
+                    302,
+                    724
+                ],
+                "score": 0.881
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    76,
+                    854,
+                    76,
+                    854,
+                    104,
+                    298,
+                    104
+                ],
+                "score": 0.858
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2088,
+                    858,
+                    2088,
+                    858,
+                    2112,
+                    841,
+                    2112
+                ],
+                "score": 0.711
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    299,
+                    76,
+                    852,
+                    76,
+                    852,
+                    104,
+                    299,
+                    104
+                ],
+                "score": 0.113
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    461,
+                    1405,
+                    461,
+                    1405,
+                    646,
+                    296,
+                    646
+                ],
+                "score": 0.112
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    681,
+                    1866,
+                    764,
+                    1866,
+                    764,
+                    1895,
+                    681,
+                    1895
+                ],
+                "score": 0.9,
+                "latex": "n _ { s } = 2"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    596.0,
+                    288.0,
+                    727.0,
+                    288.0,
+                    727.0,
+                    386.0,
+                    596.0,
+                    386.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    935.0,
+                    273.0,
+                    1275.0,
+                    273.0,
+                    1275.0,
+                    358.0,
+                    935.0,
+                    358.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    666.0,
+                    325.0,
+                    693.0,
+                    325.0,
+                    693.0,
+                    337.0,
+                    666.0,
+                    337.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    969.0,
+                    321.0,
+                    1140.0,
+                    321.0,
+                    1140.0,
+                    378.0,
+                    969.0,
+                    378.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1141.0,
+                    324.0,
+                    1256.0,
+                    324.0,
+                    1256.0,
+                    370.0,
+                    1141.0,
+                    370.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    519.0,
+                    409.0,
+                    640.0,
+                    409.0,
+                    640.0,
+                    435.0,
+                    519.0,
+                    435.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1006.0,
+                    407.0,
+                    1235.0,
+                    407.0,
+                    1235.0,
+                    440.0,
+                    1006.0,
+                    440.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1030.0,
+                    313.5,
+                    1066.0,
+                    313.5,
+                    1066.0,
+                    331.5,
+                    1030.0,
+                    331.5
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    462.0,
+                    1407.0,
+                    462.0,
+                    1407.0,
+                    498.0,
+                    294.0,
+                    498.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    492.0,
+                    1406.0,
+                    492.0,
+                    1406.0,
+                    528.0,
+                    295.0,
+                    528.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    526.0,
+                    1405.0,
+                    526.0,
+                    1405.0,
+                    557.0,
+                    295.0,
+                    557.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    553.0,
+                    1405.0,
+                    553.0,
+                    1405.0,
+                    589.0,
+                    296.0,
+                    589.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    584.0,
+                    1406.0,
+                    584.0,
+                    1406.0,
+                    620.0,
+                    295.0,
+                    620.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    612.0,
+                    1136.0,
+                    612.0,
+                    1136.0,
+                    650.0,
+                    293.0,
+                    650.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1011.0,
+                    646.0,
+                    1011.0,
+                    646.0,
+                    1051.0,
+                    293.0,
+                    1051.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    690.0,
+                    738.0,
+                    690.0,
+                    738.0,
+                    730.0,
+                    293.0,
+                    730.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    73.0,
+                    857.0,
+                    73.0,
+                    857.0,
+                    108.0,
+                    297.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    839.0,
+                    2085.0,
+                    861.0,
+                    2085.0,
+                    861.0,
+                    2120.0,
+                    839.0,
+                    2120.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    73.0,
+                    856.0,
+                    73.0,
+                    856.0,
+                    108.0,
+                    297.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1554.0,
+                    1405.0,
+                    1554.0,
+                    1405.0,
+                    1587.0,
+                    295.0,
+                    1587.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1585.0,
+                    1405.0,
+                    1585.0,
+                    1405.0,
+                    1618.0,
+                    292.0,
+                    1618.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1612.0,
+                    1407.0,
+                    1612.0,
+                    1407.0,
+                    1651.0,
+                    293.0,
+                    1651.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1643.0,
+                    1406.0,
+                    1643.0,
+                    1406.0,
+                    1680.0,
+                    293.0,
+                    1680.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1672.0,
+                    1405.0,
+                    1672.0,
+                    1405.0,
+                    1713.0,
+                    292.0,
+                    1713.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1704.0,
+                    1408.0,
+                    1704.0,
+                    1408.0,
+                    1742.0,
+                    293.0,
+                    1742.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1736.0,
+                    1403.0,
+                    1736.0,
+                    1403.0,
+                    1772.0,
+                    293.0,
+                    1772.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1768.0,
+                    795.0,
+                    1768.0,
+                    795.0,
+                    1799.0,
+                    294.0,
+                    1799.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    753.0,
+                    1406.0,
+                    753.0,
+                    1406.0,
+                    787.0,
+                    296.0,
+                    787.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    781.0,
+                    1406.0,
+                    781.0,
+                    1406.0,
+                    817.0,
+                    293.0,
+                    817.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    815.0,
+                    1401.0,
+                    815.0,
+                    1401.0,
+                    846.0,
+                    296.0,
+                    846.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    844.0,
+                    1405.0,
+                    844.0,
+                    1405.0,
+                    878.0,
+                    294.0,
+                    878.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    872.0,
+                    1404.0,
+                    872.0,
+                    1404.0,
+                    906.0,
+                    294.0,
+                    906.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    906.0,
+                    1404.0,
+                    906.0,
+                    1404.0,
+                    937.0,
+                    296.0,
+                    937.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    936.0,
+                    1400.0,
+                    936.0,
+                    1400.0,
+                    970.0,
+                    294.0,
+                    970.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1330.0,
+                    1405.0,
+                    1330.0,
+                    1405.0,
+                    1369.0,
+                    293.0,
+                    1369.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1360.0,
+                    1407.0,
+                    1360.0,
+                    1407.0,
+                    1403.0,
+                    292.0,
+                    1403.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1388.0,
+                    1407.0,
+                    1388.0,
+                    1407.0,
+                    1434.0,
+                    292.0,
+                    1434.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1424.0,
+                    1407.0,
+                    1424.0,
+                    1407.0,
+                    1461.0,
+                    292.0,
+                    1461.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1453.0,
+                    1407.0,
+                    1453.0,
+                    1407.0,
+                    1490.0,
+                    293.0,
+                    1490.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1488.0,
+                    1236.0,
+                    1488.0,
+                    1236.0,
+                    1521.0,
+                    293.0,
+                    1521.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1083.0,
+                    1407.0,
+                    1083.0,
+                    1407.0,
+                    1118.0,
+                    295.0,
+                    1118.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1109.0,
+                    1409.0,
+                    1109.0,
+                    1409.0,
+                    1152.0,
+                    292.0,
+                    1152.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1143.0,
+                    1405.0,
+                    1143.0,
+                    1405.0,
+                    1178.0,
+                    295.0,
+                    1178.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1173.0,
+                    1406.0,
+                    1173.0,
+                    1406.0,
+                    1210.0,
+                    293.0,
+                    1210.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1206.0,
+                    1405.0,
+                    1206.0,
+                    1405.0,
+                    1239.0,
+                    293.0,
+                    1239.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1234.0,
+                    1407.0,
+                    1234.0,
+                    1407.0,
+                    1272.0,
+                    293.0,
+                    1272.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1265.0,
+                    456.0,
+                    1265.0,
+                    456.0,
+                    1299.0,
+                    295.0,
+                    1299.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1831.0,
+                    1404.0,
+                    1831.0,
+                    1404.0,
+                    1872.0,
+                    293.0,
+                    1872.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1864.0,
+                    680.0,
+                    1864.0,
+                    680.0,
+                    1898.0,
+                    294.0,
+                    1898.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    765.0,
+                    1864.0,
+                    1404.0,
+                    1864.0,
+                    1404.0,
+                    1898.0,
+                    765.0,
+                    1898.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1893.0,
+                    1129.0,
+                    1893.0,
+                    1129.0,
+                    1929.0,
+                    294.0,
+                    1929.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1942.0,
+                    1408.0,
+                    1942.0,
+                    1408.0,
+                    1976.0,
+                    296.0,
+                    1976.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1971.0,
+                    1408.0,
+                    1971.0,
+                    1408.0,
+                    2006.0,
+                    295.0,
+                    2006.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    2000.0,
+                    1404.0,
+                    2000.0,
+                    1404.0,
+                    2038.0,
+                    294.0,
+                    2038.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    462.0,
+                    1407.0,
+                    462.0,
+                    1407.0,
+                    498.0,
+                    294.0,
+                    498.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    492.0,
+                    1406.0,
+                    492.0,
+                    1406.0,
+                    528.0,
+                    295.0,
+                    528.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    526.0,
+                    1405.0,
+                    526.0,
+                    1405.0,
+                    557.0,
+                    295.0,
+                    557.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    553.0,
+                    1405.0,
+                    553.0,
+                    1405.0,
+                    589.0,
+                    296.0,
+                    589.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    584.0,
+                    1406.0,
+                    584.0,
+                    1406.0,
+                    620.0,
+                    295.0,
+                    620.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    612.0,
+                    1136.0,
+                    612.0,
+                    1136.0,
+                    650.0,
+                    293.0,
+                    650.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 4,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1752,
+                    1405,
+                    1752,
+                    1405,
+                    1936,
+                    298,
+                    1936
+                ],
+                "score": 0.977
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1383,
+                    1404,
+                    1383,
+                    1404,
+                    1568,
+                    298,
+                    1568
+                ],
+                "score": 0.976
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1583,
+                    1403,
+                    1583,
+                    1403,
+                    1737,
+                    298,
+                    1737
+                ],
+                "score": 0.975
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1173,
+                    1405,
+                    1173,
+                    1405,
+                    1267,
+                    299,
+                    1267
+                ],
+                "score": 0.972
+            },
+            {
+                "category_id": 4,
+                "poly": [
+                    301,
+                    794,
+                    1100,
+                    794,
+                    1100,
+                    1010,
+                    301,
+                    1010
+                ],
+                "score": 0.97
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1044,
+                    1400,
+                    1044,
+                    1400,
+                    1137,
+                    297,
+                    1137
+                ],
+                "score": 0.969
+            },
+            {
+                "category_id": 4,
+                "poly": [
+                    1135,
+                    849,
+                    1385,
+                    849,
+                    1385,
+                    973,
+                    1135,
+                    973
+                ],
+                "score": 0.949
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1971,
+                    1399,
+                    1971,
+                    1399,
+                    2035,
+                    298,
+                    2035
+                ],
+                "score": 0.945
+            },
+            {
+                "category_id": 3,
+                "poly": [
+                    310,
+                    220,
+                    1088,
+                    220,
+                    1088,
+                    771,
+                    310,
+                    771
+                ],
+                "score": 0.935
+            },
+            {
+                "category_id": 3,
+                "poly": [
+                    1135,
+                    227,
+                    1383,
+                    227,
+                    1383,
+                    825,
+                    1135,
+                    825
+                ],
+                "score": 0.934
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    302,
+                    1313,
+                    705,
+                    1313,
+                    705,
+                    1348,
+                    302,
+                    1348
+                ],
+                "score": 0.904
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    75,
+                    854,
+                    75,
+                    854,
+                    104,
+                    298,
+                    104
+                ],
+                "score": 0.851
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    840,
+                    2089,
+                    858,
+                    2089,
+                    858,
+                    2112,
+                    840,
+                    2112
+                ],
+                "score": 0.78
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    299,
+                    76,
+                    852,
+                    76,
+                    852,
+                    104,
+                    299,
+                    104
+                ],
+                "score": 0.214
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    806,
+                    1205,
+                    903,
+                    1205,
+                    903,
+                    1235,
+                    806,
+                    1235
+                ],
+                "score": 0.91,
+                "latex": "n _ { c } = 3 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    645,
+                    1205,
+                    756,
+                    1205,
+                    756,
+                    1237,
+                    645,
+                    1237
+                ],
+                "score": 0.9,
+                "latex": "p _ { m } = 0 . 5"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    556,
+                    1174,
+                    646,
+                    1174,
+                    646,
+                    1202,
+                    556,
+                    1202
+                ],
+                "score": 0.9,
+                "latex": "G = 3 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1083,
+                    1175,
+                    1190,
+                    1175,
+                    1190,
+                    1205,
+                    1083,
+                    1205
+                ],
+                "score": 0.9,
+                "latex": "n _ { m } = 3 0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    703,
+                    1076,
+                    781,
+                    1076,
+                    781,
+                    1105,
+                    703,
+                    1105
+                ],
+                "score": 0.85,
+                "latex": "5 e - 5"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1021,
+                    1076,
+                    1100,
+                    1076,
+                    1100,
+                    1105,
+                    1021,
+                    1105
+                ],
+                "score": 0.84,
+                "latex": "2 e - 5"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1195,
+                    1783,
+                    1395,
+                    1783,
+                    1395,
+                    1814,
+                    1195,
+                    1814
+                ],
+                "score": 0.8,
+                "latex": "( \\log { \\mathrm { F L O P s } } > 1 0 )"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    810,
+                    827,
+                    920,
+                    827,
+                    920,
+                    858,
+                    810,
+                    858
+                ],
+                "score": 0.77,
+                "latex": "\\mathbf { B E R T _ { B a s e } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    768,
+                    256,
+                    791,
+                    256,
+                    791,
+                    278,
+                    768,
+                    278
+                ],
+                "score": 0.47,
+                "latex": "\\cdot"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    464,
+                    229,
+                    488,
+                    229,
+                    488,
+                    250,
+                    464,
+                    250
+                ],
+                "score": 0.39,
+                "latex": "0"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    769,
+                    227,
+                    792,
+                    227,
+                    792,
+                    249,
+                    769,
+                    249
+                ],
+                "score": 0.26,
+                "latex": "\\bigcirc"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    299.0,
+                    793.0,
+                    1103.0,
+                    793.0,
+                    1103.0,
+                    830.0,
+                    299.0,
+                    830.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    298.0,
+                    825.0,
+                    809.0,
+                    825.0,
+                    809.0,
+                    861.0,
+                    298.0,
+                    861.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    921.0,
+                    825.0,
+                    1102.0,
+                    825.0,
+                    1102.0,
+                    861.0,
+                    921.0,
+                    861.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    852.0,
+                    1104.0,
+                    852.0,
+                    1104.0,
+                    893.0,
+                    297.0,
+                    893.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    298.0,
+                    886.0,
+                    1103.0,
+                    886.0,
+                    1103.0,
+                    923.0,
+                    298.0,
+                    923.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    298.0,
+                    918.0,
+                    1103.0,
+                    918.0,
+                    1103.0,
+                    951.0,
+                    298.0,
+                    951.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    299.0,
+                    948.0,
+                    1102.0,
+                    948.0,
+                    1102.0,
+                    982.0,
+                    299.0,
+                    982.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    301.0,
+                    980.0,
+                    631.0,
+                    980.0,
+                    631.0,
+                    1012.0,
+                    301.0,
+                    1012.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1133.0,
+                    848.0,
+                    1386.0,
+                    848.0,
+                    1386.0,
+                    881.0,
+                    1133.0,
+                    881.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1134.0,
+                    880.0,
+                    1385.0,
+                    880.0,
+                    1385.0,
+                    912.0,
+                    1134.0,
+                    912.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1134.0,
+                    911.0,
+                    1385.0,
+                    911.0,
+                    1385.0,
+                    943.0,
+                    1134.0,
+                    943.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1134.0,
+                    941.0,
+                    1384.0,
+                    941.0,
+                    1384.0,
+                    976.0,
+                    1134.0,
+                    976.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    317.0,
+                    231.0,
+                    329.0,
+                    231.0,
+                    329.0,
+                    243.0,
+                    317.0,
+                    243.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    333.0,
+                    223.0,
+                    453.0,
+                    223.0,
+                    453.0,
+                    254.0,
+                    333.0,
+                    254.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    489.0,
+                    224.0,
+                    758.0,
+                    224.0,
+                    758.0,
+                    253.0,
+                    489.0,
+                    253.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    793.0,
+                    224.0,
+                    1092.0,
+                    224.0,
+                    1092.0,
+                    252.0,
+                    793.0,
+                    252.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    254.0,
+                    452.0,
+                    254.0,
+                    452.0,
+                    281.0,
+                    323.0,
+                    281.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    473.0,
+                    253.0,
+                    758.0,
+                    253.0,
+                    758.0,
+                    282.0,
+                    473.0,
+                    282.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    764.0,
+                    253.0,
+                    767.0,
+                    253.0,
+                    767.0,
+                    281.0,
+                    764.0,
+                    281.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    792.0,
+                    253.0,
+                    1084.0,
+                    253.0,
+                    1084.0,
+                    281.0,
+                    792.0,
+                    281.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    352.0,
+                    293.0,
+                    413.0,
+                    293.0,
+                    413.0,
+                    326.0,
+                    352.0,
+                    326.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    352.0,
+                    364.0,
+                    412.0,
+                    364.0,
+                    412.0,
+                    397.0,
+                    352.0,
+                    397.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    352.0,
+                    435.0,
+                    409.0,
+                    435.0,
+                    409.0,
+                    467.0,
+                    352.0,
+                    467.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    310.0,
+                    485.0,
+                    342.0,
+                    485.0,
+                    342.0,
+                    521.0,
+                    310.0,
+                    521.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    353.0,
+                    509.0,
+                    392.0,
+                    509.0,
+                    392.0,
+                    539.0,
+                    353.0,
+                    539.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    352.0,
+                    578.0,
+                    410.0,
+                    578.0,
+                    410.0,
+                    610.0,
+                    352.0,
+                    610.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    352.0,
+                    650.0,
+                    406.0,
+                    650.0,
+                    406.0,
+                    683.0,
+                    352.0,
+                    683.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    436.0,
+                    724.0,
+                    456.0,
+                    724.0,
+                    456.0,
+                    747.0,
+                    436.0,
+                    747.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    477.0,
+                    723.0,
+                    506.0,
+                    723.0,
+                    506.0,
+                    748.0,
+                    477.0,
+                    748.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    789.0,
+                    720.0,
+                    822.0,
+                    720.0,
+                    822.0,
+                    749.0,
+                    789.0,
+                    749.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    972.0,
+                    721.0,
+                    1005.0,
+                    721.0,
+                    1005.0,
+                    750.0,
+                    972.0,
+                    750.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    664.0,
+                    737.0,
+                    809.0,
+                    737.0,
+                    809.0,
+                    779.0,
+                    664.0,
+                    779.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    511.0,
+                    575.5,
+                    516.0,
+                    575.5,
+                    516.0,
+                    598.5,
+                    511.0,
+                    598.5
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    460.0,
+                    620.0,
+                    516.0,
+                    620.0,
+                    516.0,
+                    628.0,
+                    460.0,
+                    628.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    461.0,
+                    651.5,
+                    465.0,
+                    651.5,
+                    465.0,
+                    672.0,
+                    461.0,
+                    672.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1196.0,
+                    230.0,
+                    1256.0,
+                    230.0,
+                    1256.0,
+                    258.0,
+                    1196.0,
+                    258.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1283.0,
+                    230.0,
+                    1343.0,
+                    230.0,
+                    1343.0,
+                    257.0,
+                    1283.0,
+                    257.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1171.0,
+                    259.0,
+                    1183.0,
+                    259.0,
+                    1183.0,
+                    271.0,
+                    1171.0,
+                    271.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1189.0,
+                    254.0,
+                    1253.0,
+                    254.0,
+                    1253.0,
+                    274.0,
+                    1189.0,
+                    274.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1267.0,
+                    259.0,
+                    1281.0,
+                    259.0,
+                    1281.0,
+                    271.0,
+                    1267.0,
+                    271.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1283.0,
+                    251.0,
+                    1350.0,
+                    251.0,
+                    1350.0,
+                    276.0,
+                    1283.0,
+                    276.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1155.0,
+                    281.0,
+                    1182.0,
+                    281.0,
+                    1182.0,
+                    300.0,
+                    1155.0,
+                    300.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1182.0,
+                    287.0,
+                    1192.0,
+                    287.0,
+                    1192.0,
+                    294.0,
+                    1182.0,
+                    294.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1137.0,
+                    294.0,
+                    1159.0,
+                    294.0,
+                    1159.0,
+                    433.0,
+                    1137.0,
+                    433.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1156.0,
+                    315.0,
+                    1179.0,
+                    315.0,
+                    1179.0,
+                    335.0,
+                    1156.0,
+                    335.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1156.0,
+                    350.0,
+                    1178.0,
+                    350.0,
+                    1178.0,
+                    368.0,
+                    1156.0,
+                    368.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1163.0,
+                    385.0,
+                    1179.0,
+                    385.0,
+                    1179.0,
+                    403.0,
+                    1163.0,
+                    403.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1163.0,
+                    419.0,
+                    1179.0,
+                    419.0,
+                    1179.0,
+                    435.0,
+                    1163.0,
+                    435.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1187.0,
+                    435.0,
+                    1379.0,
+                    435.0,
+                    1379.0,
+                    463.0,
+                    1187.0,
+                    463.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1244.0,
+                    455.0,
+                    1321.0,
+                    455.0,
+                    1321.0,
+                    484.0,
+                    1244.0,
+                    484.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1212.0,
+                    484.0,
+                    1306.0,
+                    484.0,
+                    1306.0,
+                    517.0,
+                    1212.0,
+                    517.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1196.0,
+                    542.0,
+                    1255.0,
+                    542.0,
+                    1255.0,
+                    565.0,
+                    1196.0,
+                    565.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1266.0,
+                    542.0,
+                    1344.0,
+                    542.0,
+                    1344.0,
+                    566.0,
+                    1266.0,
+                    566.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1170.0,
+                    566.0,
+                    1186.0,
+                    566.0,
+                    1186.0,
+                    582.0,
+                    1170.0,
+                    582.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1188.0,
+                    562.0,
+                    1255.0,
+                    562.0,
+                    1255.0,
+                    584.0,
+                    1188.0,
+                    584.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1268.0,
+                    568.0,
+                    1282.0,
+                    568.0,
+                    1282.0,
+                    580.0,
+                    1268.0,
+                    580.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1284.0,
+                    558.0,
+                    1350.0,
+                    558.0,
+                    1350.0,
+                    586.0,
+                    1284.0,
+                    586.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1150.0,
+                    583.0,
+                    1191.0,
+                    583.0,
+                    1191.0,
+                    607.0,
+                    1150.0,
+                    607.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1189.0,
+                    592.0,
+                    1202.0,
+                    592.0,
+                    1202.0,
+                    599.0,
+                    1189.0,
+                    599.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1138.0,
+                    600.0,
+                    1163.0,
+                    600.0,
+                    1163.0,
+                    741.0,
+                    1138.0,
+                    741.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1151.0,
+                    613.0,
+                    1189.0,
+                    613.0,
+                    1189.0,
+                    634.0,
+                    1151.0,
+                    634.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1159.0,
+                    643.0,
+                    1188.0,
+                    643.0,
+                    1188.0,
+                    662.0,
+                    1159.0,
+                    662.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1157.0,
+                    669.0,
+                    1189.0,
+                    669.0,
+                    1189.0,
+                    690.0,
+                    1157.0,
+                    690.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1157.0,
+                    696.0,
+                    1189.0,
+                    696.0,
+                    1189.0,
+                    717.0,
+                    1157.0,
+                    717.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1174.0,
+                    727.0,
+                    1192.0,
+                    727.0,
+                    1192.0,
+                    742.0,
+                    1174.0,
+                    742.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1354.0,
+                    727.0,
+                    1374.0,
+                    727.0,
+                    1374.0,
+                    741.0,
+                    1354.0,
+                    741.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1199.0,
+                    743.0,
+                    1376.0,
+                    743.0,
+                    1376.0,
+                    765.0,
+                    1199.0,
+                    765.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1251.0,
+                    765.0,
+                    1325.0,
+                    765.0,
+                    1325.0,
+                    790.0,
+                    1251.0,
+                    790.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1211.0,
+                    794.0,
+                    1306.0,
+                    794.0,
+                    1306.0,
+                    824.0,
+                    1211.0,
+                    824.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1301.75,
+                    377.5,
+                    1367.75,
+                    377.5,
+                    1367.75,
+                    393.5,
+                    1301.75,
+                    393.5
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1190.0,
+                    642.0,
+                    1387.0,
+                    642.0,
+                    1387.0,
+                    669.5,
+                    1190.0,
+                    669.5
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1310.0,
+                    709.0,
+                    1310.0,
+                    709.0,
+                    1354.0,
+                    293.0,
+                    1354.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    72.0,
+                    857.0,
+                    72.0,
+                    857.0,
+                    108.0,
+                    297.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    840.0,
+                    2087.0,
+                    861.0,
+                    2087.0,
+                    861.0,
+                    2118.0,
+                    840.0,
+                    2118.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    73.0,
+                    856.0,
+                    73.0,
+                    856.0,
+                    108.0,
+                    297.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1749.0,
+                    1406.0,
+                    1749.0,
+                    1406.0,
+                    1790.0,
+                    293.0,
+                    1790.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1781.0,
+                    1194.0,
+                    1781.0,
+                    1194.0,
+                    1817.0,
+                    293.0,
+                    1817.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1396.0,
+                    1781.0,
+                    1407.0,
+                    1781.0,
+                    1407.0,
+                    1817.0,
+                    1396.0,
+                    1817.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1811.0,
+                    1406.0,
+                    1811.0,
+                    1406.0,
+                    1848.0,
+                    293.0,
+                    1848.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    291.0,
+                    1841.0,
+                    1406.0,
+                    1841.0,
+                    1406.0,
+                    1879.0,
+                    291.0,
+                    1879.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1873.0,
+                    1406.0,
+                    1873.0,
+                    1406.0,
+                    1911.0,
+                    292.0,
+                    1911.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1903.0,
+                    614.0,
+                    1903.0,
+                    614.0,
+                    1943.0,
+                    293.0,
+                    1943.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1385.0,
+                    1404.0,
+                    1385.0,
+                    1404.0,
+                    1417.0,
+                    296.0,
+                    1417.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1412.0,
+                    1409.0,
+                    1412.0,
+                    1409.0,
+                    1453.0,
+                    292.0,
+                    1453.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1446.0,
+                    1406.0,
+                    1446.0,
+                    1406.0,
+                    1481.0,
+                    292.0,
+                    1481.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1474.0,
+                    1406.0,
+                    1474.0,
+                    1406.0,
+                    1510.0,
+                    293.0,
+                    1510.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1503.0,
+                    1408.0,
+                    1503.0,
+                    1408.0,
+                    1543.0,
+                    292.0,
+                    1543.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1538.0,
+                    656.0,
+                    1538.0,
+                    656.0,
+                    1570.0,
+                    296.0,
+                    1570.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1581.0,
+                    1405.0,
+                    1581.0,
+                    1405.0,
+                    1620.0,
+                    294.0,
+                    1620.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1610.0,
+                    1407.0,
+                    1610.0,
+                    1407.0,
+                    1653.0,
+                    292.0,
+                    1653.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1644.0,
+                    1405.0,
+                    1644.0,
+                    1405.0,
+                    1681.0,
+                    293.0,
+                    1681.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1676.0,
+                    1405.0,
+                    1676.0,
+                    1405.0,
+                    1709.0,
+                    296.0,
+                    1709.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1705.0,
+                    1192.0,
+                    1705.0,
+                    1192.0,
+                    1742.0,
+                    294.0,
+                    1742.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1170.0,
+                    555.0,
+                    1170.0,
+                    555.0,
+                    1209.0,
+                    293.0,
+                    1209.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    647.0,
+                    1170.0,
+                    1082.0,
+                    1170.0,
+                    1082.0,
+                    1209.0,
+                    647.0,
+                    1209.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1191.0,
+                    1170.0,
+                    1409.0,
+                    1170.0,
+                    1409.0,
+                    1209.0,
+                    1191.0,
+                    1209.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1205.0,
+                    644.0,
+                    1205.0,
+                    644.0,
+                    1239.0,
+                    295.0,
+                    1239.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    757.0,
+                    1205.0,
+                    805.0,
+                    1205.0,
+                    805.0,
+                    1239.0,
+                    757.0,
+                    1239.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    904.0,
+                    1205.0,
+                    1403.0,
+                    1205.0,
+                    1403.0,
+                    1239.0,
+                    904.0,
+                    1239.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1232.0,
+                    689.0,
+                    1232.0,
+                    689.0,
+                    1271.0,
+                    294.0,
+                    1271.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1043.0,
+                    1405.0,
+                    1043.0,
+                    1405.0,
+                    1081.0,
+                    293.0,
+                    1081.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1076.0,
+                    702.0,
+                    1076.0,
+                    702.0,
+                    1110.0,
+                    295.0,
+                    1110.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    782.0,
+                    1076.0,
+                    1020.0,
+                    1076.0,
+                    1020.0,
+                    1110.0,
+                    782.0,
+                    1110.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1101.0,
+                    1076.0,
+                    1405.0,
+                    1076.0,
+                    1405.0,
+                    1110.0,
+                    1101.0,
+                    1110.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1106.0,
+                    1259.0,
+                    1106.0,
+                    1259.0,
+                    1139.0,
+                    295.0,
+                    1139.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1971.0,
+                    1404.0,
+                    1971.0,
+                    1404.0,
+                    2007.0,
+                    296.0,
+                    2007.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    2002.0,
+                    1404.0,
+                    2002.0,
+                    1404.0,
+                    2036.0,
+                    294.0,
+                    2036.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 5,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 5,
+                "poly": [
+                    312,
+                    223,
+                    1096,
+                    223,
+                    1096,
+                    529,
+                    312,
+                    529
+                ],
+                "score": 0.981,
+                "html": "<table><tr><td colspan=\"2\">Model</td><td colspan=\"2\">SQuAD 1.1</td><td colspan=\"2\">MNLI-m</td><td colspan=\"2\">SST-2</td></tr><tr><td>Pretrained Transformer</td><td>Method</td><td>F1</td><td>FLOPs</td><td>Acc</td><td>FLOPs</td><td>Acc</td><td>FLOPs</td></tr><tr><td rowspan=\"2\">BERTBase</td><td>Standard</td><td>88.5</td><td>1.00x</td><td>84.4</td><td>1.00x</td><td>92.8</td><td>1.00x</td></tr><tr><td>Length-Adaptive*</td><td>89.6</td><td>0.89x</td><td>85.0</td><td>0.58x</td><td>93.1</td><td>0.36x</td></tr><tr><td rowspan=\"2\"></td><td>Length-Adaptivet</td><td>88.7</td><td>0.45x</td><td>84.4</td><td>0.35x</td><td>92.8</td><td>0.35x</td></tr><tr><td>Standard</td><td>85.8</td><td>1.00x</td><td>80.9</td><td>1.00x</td><td>90.6</td><td>1.00x</td></tr><tr><td rowspan=\"2\">DistilBERT1</td><td>Length-Adaptive*</td><td>86.3</td><td>0.81x</td><td>81.5</td><td>0.56x</td><td>92.0</td><td>0.55x</td></tr><tr><td>Length-Adaptive†</td><td>85.9</td><td>0.59x</td><td>81.3</td><td>0.54x</td><td>91.7</td><td>0.54x</td></tr></table>"
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1238,
+                    1405,
+                    1238,
+                    1405,
+                    1514,
+                    298,
+                    1514
+                ],
+                "score": 0.981
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    960,
+                    1404,
+                    960,
+                    1404,
+                    1206,
+                    297,
+                    1206
+                ],
+                "score": 0.98
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    761,
+                    1406,
+                    761,
+                    1406,
+                    945,
+                    298,
+                    945
+                ],
+                "score": 0.977
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1548,
+                    1404,
+                    1548,
+                    1404,
+                    1672,
+                    299,
+                    1672
+                ],
+                "score": 0.977
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    300,
+                    1910,
+                    1403,
+                    1910,
+                    1403,
+                    2034,
+                    300,
+                    2034
+                ],
+                "score": 0.973
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1784,
+                    1403,
+                    1784,
+                    1403,
+                    1877,
+                    299,
+                    1877
+                ],
+                "score": 0.972
+            },
+            {
+                "category_id": 3,
+                "poly": [
+                    1141,
+                    240,
+                    1385,
+                    240,
+                    1385,
+                    507,
+                    1141,
+                    507
+                ],
+                "score": 0.961
+            },
+            {
+                "category_id": 4,
+                "poly": [
+                    1138,
+                    531,
+                    1389,
+                    531,
+                    1389,
+                    714,
+                    1138,
+                    714
+                ],
+                "score": 0.935
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    300,
+                    1715,
+                    587,
+                    1715,
+                    587,
+                    1751,
+                    300,
+                    1751
+                ],
+                "score": 0.904
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    76,
+                    854,
+                    76,
+                    854,
+                    104,
+                    298,
+                    104
+                ],
+                "score": 0.882
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2087,
+                    857,
+                    2087,
+                    857,
+                    2111,
+                    841,
+                    2111
+                ],
+                "score": 0.742
+            },
+            {
+                "category_id": 6,
+                "poly": [
+                    305,
+                    550,
+                    1106,
+                    550,
+                    1106,
+                    735,
+                    305,
+                    735
+                ],
+                "score": 0.684
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    305,
+                    550,
+                    1106,
+                    550,
+                    1106,
+                    735,
+                    305,
+                    735
+                ],
+                "score": 0.236
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    826,
+                    1423,
+                    887,
+                    1423,
+                    887,
+                    1453,
+                    826,
+                    1453
+                ],
+                "score": 0.87,
+                "latex": "\\geq 1 6"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    702,
+                    885,
+                    812,
+                    885,
+                    812,
+                    916,
+                    702,
+                    916
+                ],
+                "score": 0.62,
+                "latex": "\\mathbf { B E R T _ { B a s e } }"
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    772,
+                    886,
+                    812,
+                    886,
+                    812,
+                    916,
+                    772,
+                    916
+                ],
+                "score": 0.3,
+                "latex": "_ \\mathrm { B a s e } ^ { \\prime }"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1161.0,
+                    245.0,
+                    1208.0,
+                    245.0,
+                    1208.0,
+                    267.0,
+                    1161.0,
+                    267.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1160.0,
+                    284.0,
+                    1195.0,
+                    284.0,
+                    1195.0,
+                    307.0,
+                    1160.0,
+                    307.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1160.0,
+                    324.0,
+                    1196.0,
+                    324.0,
+                    1196.0,
+                    346.0,
+                    1160.0,
+                    346.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1142.0,
+                    340.0,
+                    1164.0,
+                    340.0,
+                    1164.0,
+                    381.0,
+                    1142.0,
+                    381.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1224.0,
+                    359.0,
+                    1235.0,
+                    359.0,
+                    1235.0,
+                    372.0,
+                    1224.0,
+                    372.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1161.0,
+                    362.0,
+                    1196.0,
+                    362.0,
+                    1196.0,
+                    387.0,
+                    1161.0,
+                    387.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1160.0,
+                    403.0,
+                    1197.0,
+                    403.0,
+                    1197.0,
+                    425.0,
+                    1160.0,
+                    425.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1207.0,
+                    415.0,
+                    1216.0,
+                    415.0,
+                    1216.0,
+                    426.0,
+                    1207.0,
+                    426.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1201.0,
+                    433.0,
+                    1212.0,
+                    433.0,
+                    1212.0,
+                    448.0,
+                    1201.0,
+                    448.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1160.0,
+                    441.0,
+                    1196.0,
+                    441.0,
+                    1196.0,
+                    463.0,
+                    1160.0,
+                    463.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1370.0,
+                    453.0,
+                    1381.0,
+                    453.0,
+                    1381.0,
+                    468.0,
+                    1370.0,
+                    468.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1199.0,
+                    469.0,
+                    1214.0,
+                    469.0,
+                    1214.0,
+                    486.0,
+                    1199.0,
+                    486.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1251.0,
+                    467.0,
+                    1274.0,
+                    467.0,
+                    1274.0,
+                    487.0,
+                    1251.0,
+                    487.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1306.0,
+                    467.0,
+                    1329.0,
+                    467.0,
+                    1329.0,
+                    487.0,
+                    1306.0,
+                    487.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1363.0,
+                    466.0,
+                    1384.0,
+                    466.0,
+                    1384.0,
+                    487.0,
+                    1363.0,
+                    487.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1260.0,
+                    485.0,
+                    1318.0,
+                    485.0,
+                    1318.0,
+                    509.0,
+                    1260.0,
+                    509.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1226.0,
+                    332.5,
+                    1260.0,
+                    332.5,
+                    1260.0,
+                    343.5,
+                    1226.0,
+                    343.5
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1207.0,
+                    386.5,
+                    1231.0,
+                    386.5,
+                    1231.0,
+                    394.5,
+                    1207.0,
+                    394.5
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1190.75,
+                    446.0,
+                    1214.75,
+                    446.0,
+                    1214.75,
+                    466.0,
+                    1190.75,
+                    466.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1136.0,
+                    524.0,
+                    1396.0,
+                    524.0,
+                    1396.0,
+                    565.0,
+                    1136.0,
+                    565.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1134.0,
+                    560.0,
+                    1392.0,
+                    560.0,
+                    1392.0,
+                    592.0,
+                    1134.0,
+                    592.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1137.0,
+                    592.0,
+                    1387.0,
+                    592.0,
+                    1387.0,
+                    621.0,
+                    1137.0,
+                    621.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1137.0,
+                    622.0,
+                    1390.0,
+                    622.0,
+                    1390.0,
+                    653.0,
+                    1137.0,
+                    653.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1134.0,
+                    648.0,
+                    1389.0,
+                    648.0,
+                    1389.0,
+                    685.0,
+                    1134.0,
+                    685.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1135.0,
+                    685.0,
+                    1251.0,
+                    685.0,
+                    1251.0,
+                    714.0,
+                    1135.0,
+                    714.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1713.0,
+                    593.0,
+                    1713.0,
+                    593.0,
+                    1756.0,
+                    293.0,
+                    1756.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    73.0,
+                    857.0,
+                    73.0,
+                    857.0,
+                    108.0,
+                    297.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    839.0,
+                    2086.0,
+                    860.0,
+                    2086.0,
+                    860.0,
+                    2117.0,
+                    839.0,
+                    2117.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    302.0,
+                    548.0,
+                    1108.0,
+                    548.0,
+                    1108.0,
+                    585.0,
+                    302.0,
+                    585.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    303.0,
+                    580.0,
+                    1108.0,
+                    580.0,
+                    1108.0,
+                    615.0,
+                    303.0,
+                    615.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    302.0,
+                    611.0,
+                    1109.0,
+                    611.0,
+                    1109.0,
+                    646.0,
+                    302.0,
+                    646.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    302.0,
+                    643.0,
+                    1106.0,
+                    643.0,
+                    1106.0,
+                    674.0,
+                    302.0,
+                    674.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    302.0,
+                    672.0,
+                    1108.0,
+                    672.0,
+                    1108.0,
+                    709.0,
+                    302.0,
+                    709.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    302.0,
+                    702.0,
+                    701.0,
+                    702.0,
+                    701.0,
+                    740.0,
+                    302.0,
+                    740.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1238.0,
+                    1406.0,
+                    1238.0,
+                    1406.0,
+                    1274.0,
+                    295.0,
+                    1274.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1269.0,
+                    1405.0,
+                    1269.0,
+                    1405.0,
+                    1304.0,
+                    292.0,
+                    1304.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1302.0,
+                    1402.0,
+                    1302.0,
+                    1402.0,
+                    1330.0,
+                    296.0,
+                    1330.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1330.0,
+                    1405.0,
+                    1330.0,
+                    1405.0,
+                    1367.0,
+                    295.0,
+                    1367.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1356.0,
+                    1406.0,
+                    1356.0,
+                    1406.0,
+                    1401.0,
+                    292.0,
+                    1401.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1392.0,
+                    1405.0,
+                    1392.0,
+                    1405.0,
+                    1424.0,
+                    296.0,
+                    1424.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1423.0,
+                    825.0,
+                    1423.0,
+                    825.0,
+                    1456.0,
+                    296.0,
+                    1456.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    888.0,
+                    1423.0,
+                    1407.0,
+                    1423.0,
+                    1407.0,
+                    1456.0,
+                    888.0,
+                    1456.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1450.0,
+                    1406.0,
+                    1450.0,
+                    1406.0,
+                    1490.0,
+                    292.0,
+                    1490.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1480.0,
+                    482.0,
+                    1480.0,
+                    482.0,
+                    1517.0,
+                    294.0,
+                    1517.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    962.0,
+                    1402.0,
+                    962.0,
+                    1402.0,
+                    995.0,
+                    295.0,
+                    995.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    992.0,
+                    1404.0,
+                    992.0,
+                    1404.0,
+                    1025.0,
+                    295.0,
+                    1025.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1023.0,
+                    1404.0,
+                    1023.0,
+                    1404.0,
+                    1057.0,
+                    295.0,
+                    1057.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1052.0,
+                    1405.0,
+                    1052.0,
+                    1405.0,
+                    1087.0,
+                    294.0,
+                    1087.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1083.0,
+                    1404.0,
+                    1083.0,
+                    1404.0,
+                    1117.0,
+                    295.0,
+                    1117.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1114.0,
+                    1406.0,
+                    1114.0,
+                    1406.0,
+                    1148.0,
+                    295.0,
+                    1148.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1144.0,
+                    1405.0,
+                    1144.0,
+                    1405.0,
+                    1178.0,
+                    292.0,
+                    1178.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1176.0,
+                    989.0,
+                    1176.0,
+                    989.0,
+                    1209.0,
+                    295.0,
+                    1209.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    762.0,
+                    1406.0,
+                    762.0,
+                    1406.0,
+                    796.0,
+                    293.0,
+                    796.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    792.0,
+                    1407.0,
+                    792.0,
+                    1407.0,
+                    826.0,
+                    292.0,
+                    826.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    823.0,
+                    1406.0,
+                    823.0,
+                    1406.0,
+                    858.0,
+                    295.0,
+                    858.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    852.0,
+                    1404.0,
+                    852.0,
+                    1404.0,
+                    888.0,
+                    293.0,
+                    888.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    882.0,
+                    701.0,
+                    882.0,
+                    701.0,
+                    921.0,
+                    292.0,
+                    921.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    813.0,
+                    882.0,
+                    1406.0,
+                    882.0,
+                    1406.0,
+                    921.0,
+                    813.0,
+                    921.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    914.0,
+                    588.0,
+                    914.0,
+                    588.0,
+                    947.0,
+                    295.0,
+                    947.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1546.0,
+                    1405.0,
+                    1546.0,
+                    1405.0,
+                    1584.0,
+                    294.0,
+                    1584.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1581.0,
+                    1408.0,
+                    1581.0,
+                    1408.0,
+                    1614.0,
+                    295.0,
+                    1614.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1610.0,
+                    1405.0,
+                    1610.0,
+                    1405.0,
+                    1644.0,
+                    293.0,
+                    1644.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1643.0,
+                    1036.0,
+                    1643.0,
+                    1036.0,
+                    1673.0,
+                    294.0,
+                    1673.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1909.0,
+                    1404.0,
+                    1909.0,
+                    1404.0,
+                    1948.0,
+                    295.0,
+                    1948.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1940.0,
+                    1408.0,
+                    1940.0,
+                    1408.0,
+                    1978.0,
+                    294.0,
+                    1978.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1971.0,
+                    1408.0,
+                    1971.0,
+                    1408.0,
+                    2009.0,
+                    293.0,
+                    2009.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    2004.0,
+                    1268.0,
+                    2004.0,
+                    1268.0,
+                    2036.0,
+                    295.0,
+                    2036.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1783.0,
+                    1405.0,
+                    1783.0,
+                    1405.0,
+                    1820.0,
+                    293.0,
+                    1820.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1816.0,
+                    1405.0,
+                    1816.0,
+                    1405.0,
+                    1850.0,
+                    295.0,
+                    1850.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1845.0,
+                    1407.0,
+                    1845.0,
+                    1407.0,
+                    1881.0,
+                    294.0,
+                    1881.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    302.0,
+                    548.0,
+                    1108.0,
+                    548.0,
+                    1108.0,
+                    585.0,
+                    302.0,
+                    585.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    303.0,
+                    580.0,
+                    1108.0,
+                    580.0,
+                    1108.0,
+                    615.0,
+                    303.0,
+                    615.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    302.0,
+                    611.0,
+                    1109.0,
+                    611.0,
+                    1109.0,
+                    646.0,
+                    302.0,
+                    646.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    302.0,
+                    643.0,
+                    1106.0,
+                    643.0,
+                    1106.0,
+                    674.0,
+                    302.0,
+                    674.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    302.0,
+                    672.0,
+                    1108.0,
+                    672.0,
+                    1108.0,
+                    709.0,
+                    302.0,
+                    709.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    302.0,
+                    702.0,
+                    701.0,
+                    702.0,
+                    701.0,
+                    740.0,
+                    302.0,
+                    740.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 6,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1063,
+                    1405,
+                    1063,
+                    1405,
+                    1278,
+                    298,
+                    1278
+                ],
+                "score": 0.982
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    229,
+                    1403,
+                    229,
+                    1403,
+                    474,
+                    298,
+                    474
+                ],
+                "score": 0.981
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    490,
+                    1404,
+                    490,
+                    1404,
+                    705,
+                    298,
+                    705
+                ],
+                "score": 0.98
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1392,
+                    1404,
+                    1392,
+                    1404,
+                    1669,
+                    298,
+                    1669
+                ],
+                "score": 0.98
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1684,
+                    1403,
+                    1684,
+                    1403,
+                    1867,
+                    298,
+                    1867
+                ],
+                "score": 0.979
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    877,
+                    1405,
+                    877,
+                    1405,
+                    1030,
+                    298,
+                    1030
+                ],
+                "score": 0.978
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    300,
+                    1883,
+                    1403,
+                    1883,
+                    1403,
+                    2005,
+                    300,
+                    2005
+                ],
+                "score": 0.976
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    720,
+                    1404,
+                    720,
+                    1404,
+                    842,
+                    298,
+                    842
+                ],
+                "score": 0.975
+            },
+            {
+                "category_id": 0,
+                "poly": [
+                    300,
+                    1324,
+                    842,
+                    1324,
+                    842,
+                    1359,
+                    300,
+                    1359
+                ],
+                "score": 0.912
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    300,
+                    76,
+                    852,
+                    76,
+                    852,
+                    104,
+                    300,
+                    104
+                ],
+                "score": 0.858
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    841,
+                    2089,
+                    858,
+                    2089,
+                    858,
+                    2111,
+                    841,
+                    2111
+                ],
+                "score": 0.787
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1063,
+                    1608,
+                    1095,
+                    1608,
+                    1095,
+                    1635,
+                    1063,
+                    1635
+                ],
+                "score": 0.55,
+                "latex": "3 \\mathbf { x }"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1318.0,
+                    847.0,
+                    1318.0,
+                    847.0,
+                    1365.0,
+                    292.0,
+                    1365.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    73.0,
+                    856.0,
+                    73.0,
+                    856.0,
+                    108.0,
+                    297.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    839.0,
+                    2086.0,
+                    860.0,
+                    2086.0,
+                    860.0,
+                    2116.0,
+                    839.0,
+                    2116.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1060.0,
+                    1406.0,
+                    1060.0,
+                    1406.0,
+                    1103.0,
+                    292.0,
+                    1103.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1095.0,
+                    1406.0,
+                    1095.0,
+                    1406.0,
+                    1130.0,
+                    293.0,
+                    1130.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1127.0,
+                    1406.0,
+                    1127.0,
+                    1406.0,
+                    1158.0,
+                    296.0,
+                    1158.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1152.0,
+                    1406.0,
+                    1152.0,
+                    1406.0,
+                    1195.0,
+                    292.0,
+                    1195.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1186.0,
+                    1405.0,
+                    1186.0,
+                    1405.0,
+                    1221.0,
+                    295.0,
+                    1221.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1217.0,
+                    1407.0,
+                    1217.0,
+                    1407.0,
+                    1255.0,
+                    293.0,
+                    1255.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1246.0,
+                    1041.0,
+                    1246.0,
+                    1041.0,
+                    1283.0,
+                    293.0,
+                    1283.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    228.0,
+                    1405.0,
+                    228.0,
+                    1405.0,
+                    266.0,
+                    293.0,
+                    266.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    262.0,
+                    1405.0,
+                    262.0,
+                    1405.0,
+                    295.0,
+                    292.0,
+                    295.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    292.0,
+                    1408.0,
+                    292.0,
+                    1408.0,
+                    326.0,
+                    293.0,
+                    326.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    322.0,
+                    1407.0,
+                    322.0,
+                    1407.0,
+                    356.0,
+                    292.0,
+                    356.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    353.0,
+                    1405.0,
+                    353.0,
+                    1405.0,
+                    386.0,
+                    296.0,
+                    386.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    379.0,
+                    1405.0,
+                    379.0,
+                    1405.0,
+                    419.0,
+                    292.0,
+                    419.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    413.0,
+                    1405.0,
+                    413.0,
+                    1405.0,
+                    449.0,
+                    293.0,
+                    449.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    440.0,
+                    1264.0,
+                    440.0,
+                    1264.0,
+                    481.0,
+                    292.0,
+                    481.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    487.0,
+                    1404.0,
+                    487.0,
+                    1404.0,
+                    529.0,
+                    293.0,
+                    529.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    519.0,
+                    1402.0,
+                    519.0,
+                    1402.0,
+                    557.0,
+                    293.0,
+                    557.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    552.0,
+                    1405.0,
+                    552.0,
+                    1405.0,
+                    586.0,
+                    294.0,
+                    586.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    585.0,
+                    1406.0,
+                    585.0,
+                    1406.0,
+                    616.0,
+                    296.0,
+                    616.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    612.0,
+                    1408.0,
+                    612.0,
+                    1408.0,
+                    647.0,
+                    294.0,
+                    647.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    643.0,
+                    1408.0,
+                    643.0,
+                    1408.0,
+                    677.0,
+                    294.0,
+                    677.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    673.0,
+                    1376.0,
+                    673.0,
+                    1376.0,
+                    708.0,
+                    295.0,
+                    708.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1390.0,
+                    1406.0,
+                    1390.0,
+                    1406.0,
+                    1428.0,
+                    293.0,
+                    1428.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1422.0,
+                    1408.0,
+                    1422.0,
+                    1408.0,
+                    1461.0,
+                    293.0,
+                    1461.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1453.0,
+                    1405.0,
+                    1453.0,
+                    1405.0,
+                    1490.0,
+                    294.0,
+                    1490.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1482.0,
+                    1405.0,
+                    1482.0,
+                    1405.0,
+                    1520.0,
+                    293.0,
+                    1520.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1515.0,
+                    1405.0,
+                    1515.0,
+                    1405.0,
+                    1551.0,
+                    294.0,
+                    1551.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1545.0,
+                    1406.0,
+                    1545.0,
+                    1406.0,
+                    1582.0,
+                    294.0,
+                    1582.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1574.0,
+                    1404.0,
+                    1574.0,
+                    1404.0,
+                    1612.0,
+                    293.0,
+                    1612.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1605.0,
+                    1062.0,
+                    1605.0,
+                    1062.0,
+                    1642.0,
+                    294.0,
+                    1642.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1096.0,
+                    1605.0,
+                    1406.0,
+                    1605.0,
+                    1406.0,
+                    1642.0,
+                    1096.0,
+                    1642.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1637.0,
+                    1248.0,
+                    1637.0,
+                    1248.0,
+                    1672.0,
+                    293.0,
+                    1672.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1682.0,
+                    1405.0,
+                    1682.0,
+                    1405.0,
+                    1719.0,
+                    293.0,
+                    1719.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1716.0,
+                    1405.0,
+                    1716.0,
+                    1405.0,
+                    1748.0,
+                    296.0,
+                    1748.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1746.0,
+                    1405.0,
+                    1746.0,
+                    1405.0,
+                    1779.0,
+                    293.0,
+                    1779.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1776.0,
+                    1407.0,
+                    1776.0,
+                    1407.0,
+                    1810.0,
+                    293.0,
+                    1810.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1805.0,
+                    1405.0,
+                    1805.0,
+                    1405.0,
+                    1840.0,
+                    293.0,
+                    1840.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1835.0,
+                    674.0,
+                    1835.0,
+                    674.0,
+                    1872.0,
+                    293.0,
+                    1872.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    877.0,
+                    1405.0,
+                    877.0,
+                    1405.0,
+                    910.0,
+                    296.0,
+                    910.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    906.0,
+                    1405.0,
+                    906.0,
+                    1405.0,
+                    943.0,
+                    295.0,
+                    943.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    936.0,
+                    1410.0,
+                    936.0,
+                    1410.0,
+                    975.0,
+                    293.0,
+                    975.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    963.0,
+                    1409.0,
+                    963.0,
+                    1409.0,
+                    1008.0,
+                    292.0,
+                    1008.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    998.0,
+                    644.0,
+                    998.0,
+                    644.0,
+                    1037.0,
+                    292.0,
+                    1037.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1880.0,
+                    1405.0,
+                    1880.0,
+                    1405.0,
+                    1920.0,
+                    294.0,
+                    1920.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1912.0,
+                    1405.0,
+                    1912.0,
+                    1405.0,
+                    1947.0,
+                    295.0,
+                    1947.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1943.0,
+                    1409.0,
+                    1943.0,
+                    1409.0,
+                    1980.0,
+                    293.0,
+                    1980.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1976.0,
+                    710.0,
+                    1976.0,
+                    710.0,
+                    2005.0,
+                    296.0,
+                    2005.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    719.0,
+                    1409.0,
+                    719.0,
+                    1409.0,
+                    756.0,
+                    293.0,
+                    756.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    750.0,
+                    1406.0,
+                    750.0,
+                    1406.0,
+                    784.0,
+                    293.0,
+                    784.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    783.0,
+                    1402.0,
+                    783.0,
+                    1402.0,
+                    816.0,
+                    296.0,
+                    816.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    811.0,
+                    1207.0,
+                    811.0,
+                    1207.0,
+                    846.0,
+                    293.0,
+                    846.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 7,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 0,
+                "poly": [
+                    300,
+                    227,
+                    489,
+                    227,
+                    489,
+                    261,
+                    300,
+                    261
+                ],
+                "score": 0.809
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    840,
+                    2088,
+                    859,
+                    2088,
+                    859,
+                    2111,
+                    840,
+                    2111
+                ],
+                "score": 0.776
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    75,
+                    854,
+                    75,
+                    854,
+                    105,
+                    298,
+                    105
+                ],
+                "score": 0.662
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    292,
+                    1270,
+                    1402,
+                    1270,
+                    1402,
+                    1334,
+                    292,
+                    1334
+                ],
+                "score": 0.66
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    292,
+                    1444,
+                    1402,
+                    1444,
+                    1402,
+                    1510,
+                    292,
+                    1510
+                ],
+                "score": 0.629
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    300,
+                    280,
+                    1403,
+                    280,
+                    1403,
+                    374,
+                    300,
+                    374
+                ],
+                "score": 0.629
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    293,
+                    1357,
+                    1403,
+                    1357,
+                    1403,
+                    1422,
+                    293,
+                    1422
+                ],
+                "score": 0.624
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    774,
+                    1402,
+                    774,
+                    1402,
+                    839,
+                    295,
+                    839
+                ],
+                "score": 0.608
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    1152,
+                    1401,
+                    1152,
+                    1401,
+                    1248,
+                    298,
+                    1248
+                ],
+                "score": 0.577
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    1066,
+                    1399,
+                    1066,
+                    1399,
+                    1131,
+                    295,
+                    1131
+                ],
+                "score": 0.57
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    290,
+                    861,
+                    1403,
+                    861,
+                    1403,
+                    927,
+                    290,
+                    927
+                ],
+                "score": 0.565
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    600,
+                    1402,
+                    600,
+                    1402,
+                    667,
+                    296,
+                    667
+                ],
+                "score": 0.559
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1767,
+                    1402,
+                    1767,
+                    1402,
+                    1861,
+                    297,
+                    1861
+                ],
+                "score": 0.546
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    687,
+                    1402,
+                    687,
+                    1402,
+                    754,
+                    295,
+                    754
+                ],
+                "score": 0.545
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    300,
+                    948,
+                    1402,
+                    948,
+                    1402,
+                    1043,
+                    300,
+                    1043
+                ],
+                "score": 0.543
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    292,
+                    1884,
+                    1402,
+                    1884,
+                    1402,
+                    1948,
+                    292,
+                    1948
+                ],
+                "score": 0.501
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    293,
+                    396,
+                    1402,
+                    396,
+                    1402,
+                    461,
+                    293,
+                    461
+                ],
+                "score": 0.489
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    297,
+                    1971,
+                    1399,
+                    1971,
+                    1399,
+                    2035,
+                    297,
+                    2035
+                ],
+                "score": 0.486
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    483,
+                    1402,
+                    483,
+                    1402,
+                    579,
+                    298,
+                    579
+                ],
+                "score": 0.477
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1531,
+                    1404,
+                    1531,
+                    1404,
+                    1626,
+                    296,
+                    1626
+                ],
+                "score": 0.3
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    294,
+                    1648,
+                    1408,
+                    1648,
+                    1408,
+                    1742,
+                    294,
+                    1742
+                ],
+                "score": 0.263
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    75,
+                    854,
+                    75,
+                    854,
+                    105,
+                    298,
+                    105
+                ],
+                "score": 0.222
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    229.0,
+                    490.0,
+                    229.0,
+                    490.0,
+                    263.0,
+                    297.0,
+                    263.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    839.0,
+                    2087.0,
+                    861.0,
+                    2087.0,
+                    861.0,
+                    2117.0,
+                    839.0,
+                    2117.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    73.0,
+                    857.0,
+                    73.0,
+                    857.0,
+                    108.0,
+                    297.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    73.0,
+                    857.0,
+                    73.0,
+                    857.0,
+                    108.0,
+                    297.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    1271.0,
+                    1403.0,
+                    1271.0,
+                    1403.0,
+                    1307.0,
+                    297.0,
+                    1307.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    1303.0,
+                    707.0,
+                    1303.0,
+                    707.0,
+                    1335.0,
+                    320.0,
+                    1335.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    1447.0,
+                    1403.0,
+                    1447.0,
+                    1403.0,
+                    1480.0,
+                    297.0,
+                    1480.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1474.0,
+                    1347.0,
+                    1474.0,
+                    1347.0,
+                    1512.0,
+                    321.0,
+                    1512.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    278.0,
+                    1407.0,
+                    278.0,
+                    1407.0,
+                    315.0,
+                    295.0,
+                    315.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    309.0,
+                    1405.0,
+                    309.0,
+                    1405.0,
+                    348.0,
+                    321.0,
+                    348.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    342.0,
+                    981.0,
+                    342.0,
+                    981.0,
+                    376.0,
+                    324.0,
+                    376.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1356.0,
+                    1406.0,
+                    1356.0,
+                    1406.0,
+                    1396.0,
+                    293.0,
+                    1396.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1390.0,
+                    852.0,
+                    1390.0,
+                    852.0,
+                    1423.0,
+                    322.0,
+                    1423.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    776.0,
+                    1404.0,
+                    776.0,
+                    1404.0,
+                    812.0,
+                    294.0,
+                    812.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    808.0,
+                    706.0,
+                    808.0,
+                    706.0,
+                    841.0,
+                    320.0,
+                    841.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    1151.0,
+                    1405.0,
+                    1151.0,
+                    1405.0,
+                    1189.0,
+                    293.0,
+                    1189.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1184.0,
+                    1403.0,
+                    1184.0,
+                    1403.0,
+                    1220.0,
+                    322.0,
+                    1220.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1217.0,
+                    706.0,
+                    1217.0,
+                    706.0,
+                    1248.0,
+                    321.0,
+                    1248.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1068.0,
+                    1403.0,
+                    1068.0,
+                    1403.0,
+                    1104.0,
+                    296.0,
+                    1104.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1099.0,
+                    1398.0,
+                    1099.0,
+                    1398.0,
+                    1132.0,
+                    321.0,
+                    1132.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    862.0,
+                    1404.0,
+                    862.0,
+                    1404.0,
+                    898.0,
+                    297.0,
+                    898.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    894.0,
+                    997.0,
+                    894.0,
+                    997.0,
+                    928.0,
+                    321.0,
+                    928.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    601.0,
+                    1404.0,
+                    601.0,
+                    1404.0,
+                    637.0,
+                    295.0,
+                    637.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    632.0,
+                    1289.0,
+                    632.0,
+                    1289.0,
+                    669.0,
+                    321.0,
+                    669.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1767.0,
+                    1406.0,
+                    1767.0,
+                    1406.0,
+                    1804.0,
+                    295.0,
+                    1804.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    1799.0,
+                    1406.0,
+                    1799.0,
+                    1406.0,
+                    1833.0,
+                    324.0,
+                    1833.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    1830.0,
+                    931.0,
+                    1830.0,
+                    931.0,
+                    1861.0,
+                    324.0,
+                    1861.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    685.0,
+                    1404.0,
+                    685.0,
+                    1404.0,
+                    726.0,
+                    294.0,
+                    726.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    719.0,
+                    1390.0,
+                    719.0,
+                    1390.0,
+                    756.0,
+                    323.0,
+                    756.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    950.0,
+                    1404.0,
+                    950.0,
+                    1404.0,
+                    985.0,
+                    296.0,
+                    985.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    325.0,
+                    983.0,
+                    1407.0,
+                    983.0,
+                    1407.0,
+                    1014.0,
+                    325.0,
+                    1014.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1011.0,
+                    775.0,
+                    1011.0,
+                    775.0,
+                    1045.0,
+                    321.0,
+                    1045.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1883.0,
+                    1405.0,
+                    1883.0,
+                    1405.0,
+                    1921.0,
+                    295.0,
+                    1921.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1915.0,
+                    1157.0,
+                    1915.0,
+                    1157.0,
+                    1949.0,
+                    321.0,
+                    1949.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    398.0,
+                    1404.0,
+                    398.0,
+                    1404.0,
+                    434.0,
+                    295.0,
+                    434.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    429.0,
+                    922.0,
+                    429.0,
+                    922.0,
+                    462.0,
+                    324.0,
+                    462.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1967.0,
+                    1405.0,
+                    1967.0,
+                    1405.0,
+                    2009.0,
+                    292.0,
+                    2009.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    2002.0,
+                    1082.0,
+                    2002.0,
+                    1082.0,
+                    2036.0,
+                    322.0,
+                    2036.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    483.0,
+                    1407.0,
+                    483.0,
+                    1407.0,
+                    521.0,
+                    296.0,
+                    521.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    515.0,
+                    1403.0,
+                    515.0,
+                    1403.0,
+                    549.0,
+                    323.0,
+                    549.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    546.0,
+                    857.0,
+                    546.0,
+                    857.0,
+                    581.0,
+                    322.0,
+                    581.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1532.0,
+                    1406.0,
+                    1532.0,
+                    1406.0,
+                    1566.0,
+                    296.0,
+                    1566.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1563.0,
+                    1405.0,
+                    1563.0,
+                    1405.0,
+                    1598.0,
+                    322.0,
+                    1598.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    1594.0,
+                    612.0,
+                    1594.0,
+                    612.0,
+                    1624.0,
+                    323.0,
+                    1624.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1650.0,
+                    1405.0,
+                    1650.0,
+                    1405.0,
+                    1684.0,
+                    296.0,
+                    1684.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    1682.0,
+                    1409.0,
+                    1682.0,
+                    1409.0,
+                    1716.0,
+                    324.0,
+                    1716.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1712.0,
+                    775.0,
+                    1712.0,
+                    775.0,
+                    1743.0,
+                    322.0,
+                    1743.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 8,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    75,
+                    854,
+                    75,
+                    854,
+                    105,
+                    298,
+                    105
+                ],
+                "score": 0.876
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    836,
+                    2088,
+                    864,
+                    2088,
+                    864,
+                    2113,
+                    836,
+                    2113
+                ],
+                "score": 0.831
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    972,
+                    1402,
+                    972,
+                    1402,
+                    1066,
+                    299,
+                    1066
+                ],
+                "score": 0.572
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    294,
+                    890,
+                    1402,
+                    890,
+                    1402,
+                    955,
+                    294,
+                    955
+                ],
+                "score": 0.572
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    294,
+                    809,
+                    1400,
+                    809,
+                    1400,
+                    874,
+                    294,
+                    874
+                ],
+                "score": 0.548
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    727,
+                    1402,
+                    727,
+                    1402,
+                    794,
+                    296,
+                    794
+                ],
+                "score": 0.489
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    293,
+                    1084,
+                    1402,
+                    1084,
+                    1402,
+                    1149,
+                    293,
+                    1149
+                ],
+                "score": 0.486
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    292,
+                    1634,
+                    1402,
+                    1634,
+                    1402,
+                    1699,
+                    292,
+                    1699
+                ],
+                "score": 0.485
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    295,
+                    1471,
+                    1401,
+                    1471,
+                    1401,
+                    1536,
+                    295,
+                    1536
+                ],
+                "score": 0.477
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    340,
+                    1402,
+                    340,
+                    1402,
+                    406,
+                    296,
+                    406
+                ],
+                "score": 0.474
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    296,
+                    1552,
+                    1400,
+                    1552,
+                    1400,
+                    1618,
+                    296,
+                    1618
+                ],
+                "score": 0.471
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    301,
+                    615,
+                    1403,
+                    615,
+                    1403,
+                    711,
+                    301,
+                    711
+                ],
+                "score": 0.468
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    302,
+                    1277,
+                    1401,
+                    1277,
+                    1401,
+                    1373,
+                    302,
+                    1373
+                ],
+                "score": 0.463
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    303,
+                    1165,
+                    1399,
+                    1165,
+                    1399,
+                    1261,
+                    303,
+                    1261
+                ],
+                "score": 0.462
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    303,
+                    423,
+                    1400,
+                    423,
+                    1400,
+                    517,
+                    303,
+                    517
+                ],
+                "score": 0.449
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    293,
+                    534,
+                    1404,
+                    534,
+                    1404,
+                    599,
+                    293,
+                    599
+                ],
+                "score": 0.448
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    300,
+                    229,
+                    1401,
+                    229,
+                    1401,
+                    323,
+                    300,
+                    323
+                ],
+                "score": 0.447
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    300,
+                    1717,
+                    1401,
+                    1717,
+                    1401,
+                    1811,
+                    300,
+                    1811
+                ],
+                "score": 0.438
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    290,
+                    1389,
+                    1402,
+                    1389,
+                    1402,
+                    1455,
+                    290,
+                    1455
+                ],
+                "score": 0.431
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1829,
+                    1402,
+                    1829,
+                    1402,
+                    1923,
+                    299,
+                    1923
+                ],
+                "score": 0.43
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    1942,
+                    1401,
+                    1942,
+                    1401,
+                    2033,
+                    299,
+                    2033
+                ],
+                "score": 0.289
+            },
+            {
+                "category_id": 13,
+                "poly": [
+                    1146,
+                    537,
+                    1254,
+                    537,
+                    1254,
+                    567,
+                    1146,
+                    567
+                ],
+                "score": 0.73,
+                "latex": "^ { 1 0 0 , 0 0 0 + }"
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    73.0,
+                    857.0,
+                    73.0,
+                    857.0,
+                    108.0,
+                    297.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    831.0,
+                    2085.0,
+                    869.0,
+                    2085.0,
+                    869.0,
+                    2123.0,
+                    831.0,
+                    2123.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    974.0,
+                    1404.0,
+                    974.0,
+                    1404.0,
+                    1008.0,
+                    295.0,
+                    1008.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    319.0,
+                    1001.0,
+                    1409.0,
+                    1001.0,
+                    1409.0,
+                    1040.0,
+                    319.0,
+                    1040.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    1029.0,
+                    397.0,
+                    1029.0,
+                    397.0,
+                    1070.0,
+                    320.0,
+                    1070.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    886.0,
+                    1405.0,
+                    886.0,
+                    1405.0,
+                    929.0,
+                    293.0,
+                    929.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    921.0,
+                    611.0,
+                    921.0,
+                    611.0,
+                    957.0,
+                    322.0,
+                    957.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    298.0,
+                    812.0,
+                    1405.0,
+                    812.0,
+                    1405.0,
+                    844.0,
+                    298.0,
+                    844.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    840.0,
+                    1231.0,
+                    840.0,
+                    1231.0,
+                    875.0,
+                    321.0,
+                    875.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    298.0,
+                    728.0,
+                    1404.0,
+                    728.0,
+                    1404.0,
+                    764.0,
+                    298.0,
+                    764.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    759.0,
+                    1247.0,
+                    759.0,
+                    1247.0,
+                    794.0,
+                    323.0,
+                    794.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1086.0,
+                    1404.0,
+                    1086.0,
+                    1404.0,
+                    1122.0,
+                    296.0,
+                    1122.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1115.0,
+                    1130.0,
+                    1115.0,
+                    1130.0,
+                    1150.0,
+                    321.0,
+                    1150.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1636.0,
+                    1405.0,
+                    1636.0,
+                    1405.0,
+                    1672.0,
+                    295.0,
+                    1672.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    1664.0,
+                    1143.0,
+                    1664.0,
+                    1143.0,
+                    1704.0,
+                    323.0,
+                    1704.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    298.0,
+                    1474.0,
+                    1403.0,
+                    1474.0,
+                    1403.0,
+                    1506.0,
+                    298.0,
+                    1506.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1502.0,
+                    1114.0,
+                    1502.0,
+                    1114.0,
+                    1537.0,
+                    322.0,
+                    1537.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    337.0,
+                    1406.0,
+                    337.0,
+                    1406.0,
+                    382.0,
+                    294.0,
+                    382.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    373.0,
+                    1129.0,
+                    373.0,
+                    1129.0,
+                    409.0,
+                    324.0,
+                    409.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1551.0,
+                    1402.0,
+                    1551.0,
+                    1402.0,
+                    1588.0,
+                    296.0,
+                    1588.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1585.0,
+                    932.0,
+                    1585.0,
+                    932.0,
+                    1619.0,
+                    321.0,
+                    1619.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    610.0,
+                    1405.0,
+                    610.0,
+                    1405.0,
+                    657.0,
+                    292.0,
+                    657.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    647.0,
+                    1408.0,
+                    647.0,
+                    1408.0,
+                    684.0,
+                    322.0,
+                    684.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    678.0,
+                    704.0,
+                    678.0,
+                    704.0,
+                    712.0,
+                    322.0,
+                    712.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    296.0,
+                    1277.0,
+                    1407.0,
+                    1277.0,
+                    1407.0,
+                    1315.0,
+                    296.0,
+                    1315.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    1312.0,
+                    1404.0,
+                    1312.0,
+                    1404.0,
+                    1346.0,
+                    323.0,
+                    1346.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    1341.0,
+                    810.0,
+                    1341.0,
+                    810.0,
+                    1375.0,
+                    323.0,
+                    1375.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    1165.0,
+                    1403.0,
+                    1165.0,
+                    1403.0,
+                    1202.0,
+                    295.0,
+                    1202.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    1197.0,
+                    1405.0,
+                    1197.0,
+                    1405.0,
+                    1235.0,
+                    323.0,
+                    1235.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1229.0,
+                    917.0,
+                    1229.0,
+                    917.0,
+                    1262.0,
+                    321.0,
+                    1262.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    419.0,
+                    1405.0,
+                    419.0,
+                    1405.0,
+                    462.0,
+                    294.0,
+                    462.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    453.0,
+                    1405.0,
+                    453.0,
+                    1405.0,
+                    489.0,
+                    322.0,
+                    489.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    485.0,
+                    920.0,
+                    485.0,
+                    920.0,
+                    517.0,
+                    323.0,
+                    517.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    536.0,
+                    1145.0,
+                    536.0,
+                    1145.0,
+                    572.0,
+                    295.0,
+                    572.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    1255.0,
+                    536.0,
+                    1405.0,
+                    536.0,
+                    1405.0,
+                    572.0,
+                    1255.0,
+                    572.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    567.0,
+                    1140.0,
+                    567.0,
+                    1140.0,
+                    600.0,
+                    321.0,
+                    600.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    229.0,
+                    1406.0,
+                    229.0,
+                    1406.0,
+                    266.0,
+                    294.0,
+                    266.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    261.0,
+                    1407.0,
+                    261.0,
+                    1407.0,
+                    295.0,
+                    321.0,
+                    295.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    288.0,
+                    398.0,
+                    288.0,
+                    398.0,
+                    326.0,
+                    320.0,
+                    326.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1715.0,
+                    1406.0,
+                    1715.0,
+                    1406.0,
+                    1756.0,
+                    294.0,
+                    1756.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1747.0,
+                    1406.0,
+                    1747.0,
+                    1406.0,
+                    1785.0,
+                    321.0,
+                    1785.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    321.0,
+                    1777.0,
+                    882.0,
+                    1777.0,
+                    882.0,
+                    1815.0,
+                    321.0,
+                    1815.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    292.0,
+                    1386.0,
+                    1405.0,
+                    1386.0,
+                    1405.0,
+                    1431.0,
+                    292.0,
+                    1431.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    1422.0,
+                    955.0,
+                    1422.0,
+                    955.0,
+                    1457.0,
+                    322.0,
+                    1457.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    1829.0,
+                    1404.0,
+                    1829.0,
+                    1404.0,
+                    1864.0,
+                    294.0,
+                    1864.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    1859.0,
+                    1404.0,
+                    1859.0,
+                    1404.0,
+                    1894.0,
+                    323.0,
+                    1894.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    1892.0,
+                    798.0,
+                    1892.0,
+                    798.0,
+                    1923.0,
+                    320.0,
+                    1923.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    1942.0,
+                    1406.0,
+                    1942.0,
+                    1406.0,
+                    1976.0,
+                    297.0,
+                    1976.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    320.0,
+                    1971.0,
+                    1405.0,
+                    1971.0,
+                    1405.0,
+                    2008.0,
+                    320.0,
+                    2008.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    2003.0,
+                    609.0,
+                    2003.0,
+                    609.0,
+                    2032.0,
+                    323.0,
+                    2032.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 9,
+            "width": 1700,
+            "height": 2200
+        }
+    },
+    {
+        "layout_dets": [
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    652,
+                    1402,
+                    652,
+                    1402,
+                    716,
+                    299,
+                    716
+                ],
+                "score": 0.828
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    835,
+                    2088,
+                    861,
+                    2088,
+                    861,
+                    2113,
+                    835,
+                    2113
+                ],
+                "score": 0.825
+            },
+            {
+                "category_id": 2,
+                "poly": [
+                    298,
+                    75,
+                    854,
+                    75,
+                    854,
+                    105,
+                    298,
+                    105
+                ],
+                "score": 0.824
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    229,
+                    1404,
+                    229,
+                    1404,
+                    322,
+                    299,
+                    322
+                ],
+                "score": 0.673
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    298,
+                    539,
+                    1401,
+                    539,
+                    1401,
+                    634,
+                    298,
+                    634
+                ],
+                "score": 0.64
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    293,
+                    455,
+                    1403,
+                    455,
+                    1403,
+                    519,
+                    293,
+                    519
+                ],
+                "score": 0.583
+            },
+            {
+                "category_id": 1,
+                "poly": [
+                    299,
+                    343,
+                    1402,
+                    343,
+                    1402,
+                    437,
+                    299,
+                    437
+                ],
+                "score": 0.581
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    831.0,
+                    2085.0,
+                    867.0,
+                    2085.0,
+                    867.0,
+                    2125.0,
+                    831.0,
+                    2125.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    297.0,
+                    73.0,
+                    857.0,
+                    73.0,
+                    857.0,
+                    108.0,
+                    297.0,
+                    108.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    294.0,
+                    651.0,
+                    1407.0,
+                    651.0,
+                    1407.0,
+                    689.0,
+                    294.0,
+                    689.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    683.0,
+                    1406.0,
+                    683.0,
+                    1406.0,
+                    719.0,
+                    322.0,
+                    719.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    227.0,
+                    1406.0,
+                    227.0,
+                    1406.0,
+                    267.0,
+                    293.0,
+                    267.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    260.0,
+                    1404.0,
+                    260.0,
+                    1404.0,
+                    297.0,
+                    322.0,
+                    297.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    292.0,
+                    609.0,
+                    292.0,
+                    609.0,
+                    321.0,
+                    322.0,
+                    321.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    537.0,
+                    1406.0,
+                    537.0,
+                    1406.0,
+                    577.0,
+                    293.0,
+                    577.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    569.0,
+                    1406.0,
+                    569.0,
+                    1406.0,
+                    607.0,
+                    322.0,
+                    607.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    600.0,
+                    936.0,
+                    600.0,
+                    936.0,
+                    636.0,
+                    323.0,
+                    636.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    295.0,
+                    456.0,
+                    1404.0,
+                    456.0,
+                    1404.0,
+                    492.0,
+                    295.0,
+                    492.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    322.0,
+                    487.0,
+                    1085.0,
+                    487.0,
+                    1085.0,
+                    520.0,
+                    322.0,
+                    520.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    293.0,
+                    340.0,
+                    1407.0,
+                    340.0,
+                    1407.0,
+                    380.0,
+                    293.0,
+                    380.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    324.0,
+                    377.0,
+                    1404.0,
+                    377.0,
+                    1404.0,
+                    407.0,
+                    324.0,
+                    407.0
+                ],
+                "score": 1.0,
+                "text": ""
+            },
+            {
+                "category_id": 15,
+                "poly": [
+                    323.0,
+                    403.0,
+                    1100.0,
+                    403.0,
+                    1100.0,
+                    440.0,
+                    323.0,
+                    440.0
+                ],
+                "score": 1.0,
+                "text": ""
+            }
+        ],
+        "page_info": {
+            "page_no": 10,
+            "width": 1700,
+            "height": 2200
+        }
+    }
+]
\ No newline at end of file
diff --git a/vlm/dev/3R3Pz5i0tye/0.png b/vlm/dev/3R3Pz5i0tye/0.png
new file mode 100644
index 0000000000000000000000000000000000000000..da4199ae29818795c17a555a10c4a0bf207e75b9
--- /dev/null
+++ b/vlm/dev/3R3Pz5i0tye/0.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0fedea5ebf224830e980138ab2805408ec9c2919c021ed65485ee4232476a7ac
+size 531424
diff --git a/vlm/dev/3R3Pz5i0tye/1.png b/vlm/dev/3R3Pz5i0tye/1.png
new file mode 100644
index 0000000000000000000000000000000000000000..a2e331d644299032c9f686d203656ccf49ca44d8
--- /dev/null
+++ b/vlm/dev/3R3Pz5i0tye/1.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5af5c40541bae7458bc7a6c84d7b49d747336d9c7b1c136bfe6feafc39cb6ddc
+size 736550
diff --git a/vlm/dev/3R3Pz5i0tye/10.png b/vlm/dev/3R3Pz5i0tye/10.png
new file mode 100644
index 0000000000000000000000000000000000000000..2615244ed01eae5abbb68a4d34439a1f271fba30
--- /dev/null
+++ b/vlm/dev/3R3Pz5i0tye/10.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ea44a07953166ad1d7d53e848c5f2376863ccb735a150bdbb6e2d058526c6f38
+size 555625
diff --git a/vlm/dev/3R3Pz5i0tye/11.png b/vlm/dev/3R3Pz5i0tye/11.png
new file mode 100644
index 0000000000000000000000000000000000000000..6fb52f42d3a2970a98a3263d8d74b6bddde95dc1
--- /dev/null
+++ b/vlm/dev/3R3Pz5i0tye/11.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:05ef0c283885073235f393638c38fc82cc740942318e912693dc3129c1f62b32
+size 592261
diff --git a/vlm/dev/3R3Pz5i0tye/12.png b/vlm/dev/3R3Pz5i0tye/12.png
new file mode 100644
index 0000000000000000000000000000000000000000..920591b1f9751d010a4ef64bf352ea8673cf19b4
--- /dev/null
+++ b/vlm/dev/3R3Pz5i0tye/12.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4c3e47d6bbad42b548bfcc3bb92408386a6ce44ac93b096d29699d204d2dea95
+size 563703
diff --git a/vlm/dev/3R3Pz5i0tye/13.png b/vlm/dev/3R3Pz5i0tye/13.png
new file mode 100644
index 0000000000000000000000000000000000000000..9de3cfd57a572eca9fcbccc5a46cd1d28b1cf6c4
--- /dev/null
+++ b/vlm/dev/3R3Pz5i0tye/13.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:788886d16ad08cc425fdb53b47ce7de91e25efa200805886f7f65f602b1d774d
+size 187529
diff --git a/vlm/dev/3R3Pz5i0tye/2.png b/vlm/dev/3R3Pz5i0tye/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..8173b2238e207fd6a93e97a31c2245382017b49b
--- /dev/null
+++ b/vlm/dev/3R3Pz5i0tye/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7ed759c58fd3c0f934574cac5ef5daca8838bc22628092d29e03d8643232c666
+size 790832
diff --git a/vlm/dev/3R3Pz5i0tye/3.png b/vlm/dev/3R3Pz5i0tye/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..b07c4cdaab0943bcbfc5c9c46b1977488272fce1
--- /dev/null
+++ b/vlm/dev/3R3Pz5i0tye/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:130ca474d2f54d025c5053482d929c4ffe7579eb97b3f689692b0aac14051443
+size 848761
diff --git a/vlm/dev/3R3Pz5i0tye/4.png b/vlm/dev/3R3Pz5i0tye/4.png
new file mode 100644
index 0000000000000000000000000000000000000000..2fdb1669bcd9a5cd15b4d395197d71848d7ccd80
--- /dev/null
+++ b/vlm/dev/3R3Pz5i0tye/4.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7883dff7602e331313cd4a9cf77e27960a1cbf8132438969588c73055a1e2d8a
+size 588336
diff --git a/vlm/dev/3R3Pz5i0tye/5.png b/vlm/dev/3R3Pz5i0tye/5.png
new file mode 100644
index 0000000000000000000000000000000000000000..97cef2361f441df01d7492118b8fbf34c481f5c5
--- /dev/null
+++ b/vlm/dev/3R3Pz5i0tye/5.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9700d6b7eaec132f5a94ec2e171a31751c193c45cc7cd9c91a6af5588ac270ee
+size 583404
diff --git a/vlm/dev/3R3Pz5i0tye/6.png b/vlm/dev/3R3Pz5i0tye/6.png
new file mode 100644
index 0000000000000000000000000000000000000000..93c6e0891dfadb3077270a446fc7f54dae60d575
--- /dev/null
+++ b/vlm/dev/3R3Pz5i0tye/6.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6634af8ec27c75bfbd1de2bc1547523597bd5e83a5257ff6620f30387fe57ea6
+size 573472
diff --git a/vlm/dev/3R3Pz5i0tye/7.png b/vlm/dev/3R3Pz5i0tye/7.png
new file mode 100644
index 0000000000000000000000000000000000000000..26761c8bc14271d6a6f21609b02cbe369298b50c
--- /dev/null
+++ b/vlm/dev/3R3Pz5i0tye/7.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9337bb4cb139f8b19fef175dab27a40f5fcf34a3c7e1f391390d752e7c7d6769
+size 806976
diff --git a/vlm/dev/3R3Pz5i0tye/8.png b/vlm/dev/3R3Pz5i0tye/8.png
new file mode 100644
index 0000000000000000000000000000000000000000..d5596759d8471d95e331314132f206d5c5dd1be0
--- /dev/null
+++ b/vlm/dev/3R3Pz5i0tye/8.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e0a972f625b62d1e720f52153197d6c62bcb131602975b00442cd9477ba84eb5
+size 527650
diff --git a/vlm/dev/3R3Pz5i0tye/9.png b/vlm/dev/3R3Pz5i0tye/9.png
new file mode 100644
index 0000000000000000000000000000000000000000..32d70295e23521cbde5d9eaf1ad30de72961dea3
--- /dev/null
+++ b/vlm/dev/3R3Pz5i0tye/9.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b940293ca7dd6ae051a82ce0d59e918ed19a67ab5a9deb7293ada6ad7b2776db
+size 575275
diff --git a/vlm/dev/401LFvBGIb/0.png b/vlm/dev/401LFvBGIb/0.png
new file mode 100644
index 0000000000000000000000000000000000000000..bbebabde0f46238abb1d2a66a0c5161d57f32d6f
--- /dev/null
+++ b/vlm/dev/401LFvBGIb/0.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:92e8ef8ccdf626f7de2962a7f2d353c7f5d174b7bfadfcb871572103bb579996
+size 436579
diff --git a/vlm/dev/401LFvBGIb/1.png b/vlm/dev/401LFvBGIb/1.png
new file mode 100644
index 0000000000000000000000000000000000000000..0bd0d8842ebbc5eefb4e7e4098d5497131d09430
--- /dev/null
+++ b/vlm/dev/401LFvBGIb/1.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6c05f53f9b3230745adef239e7909271b8659bd10a9f02d2c335c9752c36a529
+size 490493
diff --git a/vlm/dev/401LFvBGIb/2.png b/vlm/dev/401LFvBGIb/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..6b1d25d36a8f8d3f201390385ceb4e31f49b8cd7
--- /dev/null
+++ b/vlm/dev/401LFvBGIb/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:060f02880e069b1148ca3f72286189f965f38497ce6b5fd5910c9f1fc890ef26
+size 422767
diff --git a/vlm/dev/401LFvBGIb/3.png b/vlm/dev/401LFvBGIb/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..8ad103a6f9a7a0c51fb60cd4dd2bbfc77ff53384
--- /dev/null
+++ b/vlm/dev/401LFvBGIb/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:00f9671aa6cfede300d117ef74e91ac4ac81cb9624a892918c623cccc22c36e9
+size 405437
diff --git a/vlm/dev/401LFvBGIb/4.png b/vlm/dev/401LFvBGIb/4.png
new file mode 100644
index 0000000000000000000000000000000000000000..ee50b388360faf3c6f2f2747ebbcd23386e7ba51
--- /dev/null
+++ b/vlm/dev/401LFvBGIb/4.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ccec683eb69f8af84206e2b487b1c9657eaed9fd0fe46b547ec6abd9c9ab7ecd
+size 526713
diff --git a/vlm/dev/401LFvBGIb/5.png b/vlm/dev/401LFvBGIb/5.png
new file mode 100644
index 0000000000000000000000000000000000000000..ee54403c290d28b2af2fb95047fd31fee03e912e
--- /dev/null
+++ b/vlm/dev/401LFvBGIb/5.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4d0fcaf14dcb61f1ae029973bbe8129553195a12a73dd4a41cf9fbd25ad18caa
+size 60370
diff --git a/vlm/dev/401LFvBGIb/6.png b/vlm/dev/401LFvBGIb/6.png
new file mode 100644
index 0000000000000000000000000000000000000000..b162ffb63bfe39dd8b62d782f5ee1bd2d64765bd
--- /dev/null
+++ b/vlm/dev/401LFvBGIb/6.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:02da432c19b7c3827ea22ac5b70441d19436eccc0b83259953adbca395baab55
+size 516135
diff --git a/vlm/dev/401LFvBGIb/7.png b/vlm/dev/401LFvBGIb/7.png
new file mode 100644
index 0000000000000000000000000000000000000000..06c31dfee9d1d08502bdc858d9b0908fd137d1b1
--- /dev/null
+++ b/vlm/dev/401LFvBGIb/7.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2d618261683ad6d755572cf8440b16bfa8798914bd62ceab113add6f7d35e982
+size 499375
diff --git a/vlm/dev/401LFvBGIb/8.png b/vlm/dev/401LFvBGIb/8.png
new file mode 100644
index 0000000000000000000000000000000000000000..9ea5d2db6b37cf034277ba523328c066e5543626
--- /dev/null
+++ b/vlm/dev/401LFvBGIb/8.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:baa92d69ad1c5eb41909f8581e47c20f1e7898a7d0bd45254c01e3bb9100cf23
+size 479219
diff --git a/vlm/dev/6u6N8WWwYSM/0.png b/vlm/dev/6u6N8WWwYSM/0.png
new file mode 100644
index 0000000000000000000000000000000000000000..001bc8ae588e64e4db51df0d0a2f2705ce692ccc
--- /dev/null
+++ b/vlm/dev/6u6N8WWwYSM/0.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:43b167799284084da274ca211c50ec0f0d4b3c66fae6c613b6f7082b36d95a12
+size 603380
diff --git a/vlm/dev/6u6N8WWwYSM/1.png b/vlm/dev/6u6N8WWwYSM/1.png
new file mode 100644
index 0000000000000000000000000000000000000000..06655d169301db7fcc1765b82d6a9a4e0f7bb748
--- /dev/null
+++ b/vlm/dev/6u6N8WWwYSM/1.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6063abddd0db2e2d53aff682ccc02d810d98a728a56bb39451d511e072f0acb9
+size 614714
diff --git a/vlm/dev/6u6N8WWwYSM/10.png b/vlm/dev/6u6N8WWwYSM/10.png
new file mode 100644
index 0000000000000000000000000000000000000000..470bc0c6b69fcf9944ba055218ba3e8bb92c4051
--- /dev/null
+++ b/vlm/dev/6u6N8WWwYSM/10.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:536e8c2341aded40def944cba8491aa3b94e166926638ce65a8193e3c8321cec
+size 567768
diff --git a/vlm/dev/6u6N8WWwYSM/11.png b/vlm/dev/6u6N8WWwYSM/11.png
new file mode 100644
index 0000000000000000000000000000000000000000..3b52acf4e4415b483eb969edb3d80f35dc3250f2
--- /dev/null
+++ b/vlm/dev/6u6N8WWwYSM/11.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8b30724b7ba3dbd929d71d18a131ce610abf6da3e463a25456c4c7256770d7b6
+size 383052
diff --git a/vlm/dev/6u6N8WWwYSM/12.png b/vlm/dev/6u6N8WWwYSM/12.png
new file mode 100644
index 0000000000000000000000000000000000000000..29d8a35b0cd46c71b5feec3abe25f676ad37f6c4
--- /dev/null
+++ b/vlm/dev/6u6N8WWwYSM/12.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4bced22b9be5e198a4920a6f8373e0a56ca153efb211fdc5e18a40d574dd77a8
+size 527264
diff --git a/vlm/dev/6u6N8WWwYSM/13.png b/vlm/dev/6u6N8WWwYSM/13.png
new file mode 100644
index 0000000000000000000000000000000000000000..d97f6d03f2b1b89d650dedd04e65f03034f0f6f9
--- /dev/null
+++ b/vlm/dev/6u6N8WWwYSM/13.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3d5832f058e645823efd5a6143f004c25b3374934a5de74ee308c59eb4883071
+size 410630
diff --git a/vlm/dev/6u6N8WWwYSM/14.png b/vlm/dev/6u6N8WWwYSM/14.png
new file mode 100644
index 0000000000000000000000000000000000000000..c8b27cca8ab09ac2cb459434bb5c49150f7c7036
--- /dev/null
+++ b/vlm/dev/6u6N8WWwYSM/14.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:42ad05681c507232a4b03584d5347747fb8b0181dd19f609e974108104a44b92
+size 1444192
diff --git a/vlm/dev/6u6N8WWwYSM/15.png b/vlm/dev/6u6N8WWwYSM/15.png
new file mode 100644
index 0000000000000000000000000000000000000000..78f4c0fca552966007b1540a31d19610496998c6
--- /dev/null
+++ b/vlm/dev/6u6N8WWwYSM/15.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7467d4e321dc78ba49d4223588c1310b069a228ff8606cc01e0a341b4e5f42d6
+size 846964
diff --git a/vlm/dev/6u6N8WWwYSM/16.png b/vlm/dev/6u6N8WWwYSM/16.png
new file mode 100644
index 0000000000000000000000000000000000000000..4ef114dc8573b6f5c7c8ad6ea9cea5604bc87463
--- /dev/null
+++ b/vlm/dev/6u6N8WWwYSM/16.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6f31dd06d1e13f2628d0b4b4b41257266aa004dfa6ca3cf0a62da61e9c5e3a5e
+size 370776
diff --git a/vlm/dev/6u6N8WWwYSM/2.png b/vlm/dev/6u6N8WWwYSM/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..f645914287a90b5b04ad639356570d03b73c627e
--- /dev/null
+++ b/vlm/dev/6u6N8WWwYSM/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7dc66075ca03a04e4efa36faddc8d9b12ee85411d3b99ba33ee759eab1e09872
+size 536052
diff --git a/vlm/dev/6u6N8WWwYSM/3.png b/vlm/dev/6u6N8WWwYSM/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..0630d990b8b7c50047442caa2f5ec3bf8cfa8b71
--- /dev/null
+++ b/vlm/dev/6u6N8WWwYSM/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7a42eace5dbcecfcc05baac9c84c390a6101368abdf1b63a8197cb41a6c0de58
+size 710785
diff --git a/vlm/dev/6u6N8WWwYSM/4.png b/vlm/dev/6u6N8WWwYSM/4.png
new file mode 100644
index 0000000000000000000000000000000000000000..f1d820d161fb8accc61092dd13ca34f266afe9a5
--- /dev/null
+++ b/vlm/dev/6u6N8WWwYSM/4.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0f3cd0b1964b06417f4b119e7a2e711a20269793cfd79dc4e6800e588da26f22
+size 574177
diff --git a/vlm/dev/6u6N8WWwYSM/5.png b/vlm/dev/6u6N8WWwYSM/5.png
new file mode 100644
index 0000000000000000000000000000000000000000..12269f22debb9f48ad9f23910c039abc48b616d4
--- /dev/null
+++ b/vlm/dev/6u6N8WWwYSM/5.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b373cedc0d4e1860059196441ef464ced36c3467e43ddd9e820c704ccc229527
+size 610126
diff --git a/vlm/dev/6u6N8WWwYSM/6.png b/vlm/dev/6u6N8WWwYSM/6.png
new file mode 100644
index 0000000000000000000000000000000000000000..86812de949a1a353f0329e7ab713b2e9c2cac862
--- /dev/null
+++ b/vlm/dev/6u6N8WWwYSM/6.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:707a2b25a054d185f496de43699743133e4d2f66322d60696058f2cca855ca31
+size 1069859
diff --git a/vlm/dev/6u6N8WWwYSM/7.png b/vlm/dev/6u6N8WWwYSM/7.png
new file mode 100644
index 0000000000000000000000000000000000000000..c3460d78fdc32397d6b6f5d4cd7fc5705fd9cd4d
--- /dev/null
+++ b/vlm/dev/6u6N8WWwYSM/7.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1f1b4b4d9a76f45fb3582a7700e7c2643245835e42799e767cb443c8c6bcdd90
+size 1042816
diff --git a/vlm/dev/6u6N8WWwYSM/8.png b/vlm/dev/6u6N8WWwYSM/8.png
new file mode 100644
index 0000000000000000000000000000000000000000..0268ce57b4726e64ddcd9bb0ac59ff4caebac1e6
--- /dev/null
+++ b/vlm/dev/6u6N8WWwYSM/8.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8968d049dbfa4ad7956c7f7eac8a37daff0eafab2cf7dc901754742a7efb7b6f
+size 517975
diff --git a/vlm/dev/6u6N8WWwYSM/9.png b/vlm/dev/6u6N8WWwYSM/9.png
new file mode 100644
index 0000000000000000000000000000000000000000..6d75a25b457ad1968ca4e2fd6bf710f16986e842
--- /dev/null
+++ b/vlm/dev/6u6N8WWwYSM/9.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:59702a20824f4cbf4410f1bb882c5a92a05d2b22cc3aca8d802d58089ab01240
+size 496540
diff --git a/vlm/dev/8aHzds2uUyB/13.png b/vlm/dev/8aHzds2uUyB/13.png
new file mode 100644
index 0000000000000000000000000000000000000000..987ac794d381b369c22024c1f828bc4fa8daf750
--- /dev/null
+++ b/vlm/dev/8aHzds2uUyB/13.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9005e95fa68a9a8d621a239f9878dd998ada3178fabb3a9502b63f9402285ad2
+size 548515
diff --git a/vlm/dev/8aHzds2uUyB/16.png b/vlm/dev/8aHzds2uUyB/16.png
new file mode 100644
index 0000000000000000000000000000000000000000..b90843300b03cc5f3936d1d7733fb72dadb43bc5
--- /dev/null
+++ b/vlm/dev/8aHzds2uUyB/16.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2bed3a2672986738f8d79606a7946f72c5549ba286a174ba2cd134ba0f52fd38
+size 150985
diff --git a/vlm/dev/8aHzds2uUyB/18.png b/vlm/dev/8aHzds2uUyB/18.png
new file mode 100644
index 0000000000000000000000000000000000000000..c688d1a95d144c3c05d3af6d333a885ad055ea45
--- /dev/null
+++ b/vlm/dev/8aHzds2uUyB/18.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ffa011ab078f8f43433d6500fba3ff8c465e844250f1e59545553eeca32d221b
+size 507984
diff --git a/vlm/dev/8aHzds2uUyB/19.png b/vlm/dev/8aHzds2uUyB/19.png
new file mode 100644
index 0000000000000000000000000000000000000000..07db9320a789243f0b00094f76340e7828103828
--- /dev/null
+++ b/vlm/dev/8aHzds2uUyB/19.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2c913e64018da73ffe7d61abc77114d7479b4f9f14f78bdb8b614e17ae547cfc
+size 369083
diff --git a/vlm/dev/8aHzds2uUyB/26.png b/vlm/dev/8aHzds2uUyB/26.png
new file mode 100644
index 0000000000000000000000000000000000000000..3d1eed8131e7590067b42b65e81d504ab3081b3f
--- /dev/null
+++ b/vlm/dev/8aHzds2uUyB/26.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:48abbf261dc8dfb8c4007b1780589f35ee3607054bd80f23c79329afaaf7b342
+size 116550
diff --git a/vlm/dev/8aHzds2uUyB/32.png b/vlm/dev/8aHzds2uUyB/32.png
new file mode 100644
index 0000000000000000000000000000000000000000..d66592b440a9b5b48a906adfa3acc1b3ec540cd6
--- /dev/null
+++ b/vlm/dev/8aHzds2uUyB/32.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:28a9f1617f9eef9fc8fc60dbe86412a431d81d3a0d67f9d710ed8426f9b60dcc
+size 556368
diff --git a/vlm/dev/8aHzds2uUyB/34.png b/vlm/dev/8aHzds2uUyB/34.png
new file mode 100644
index 0000000000000000000000000000000000000000..f07cd66fb5568230f7983e7e212b60281dbb0f52
--- /dev/null
+++ b/vlm/dev/8aHzds2uUyB/34.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5bd5df9cea7950736ba3cf278aba603b4df9f6c3cefff8b223853ca2adb41ae1
+size 340162
diff --git a/vlm/dev/8aHzds2uUyB/35.png b/vlm/dev/8aHzds2uUyB/35.png
new file mode 100644
index 0000000000000000000000000000000000000000..0eb4be599c37916be261a85367cdab2a0e0cca17
--- /dev/null
+++ b/vlm/dev/8aHzds2uUyB/35.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:81bf3b32e917892b4c6dd64be60789fc5afed688d6e4f7814f62735618dc6720
+size 247633
diff --git a/vlm/dev/8aHzds2uUyB/39.png b/vlm/dev/8aHzds2uUyB/39.png
new file mode 100644
index 0000000000000000000000000000000000000000..0c0281c98a2f0c14d3401fdef7559cd3cb5500bd
--- /dev/null
+++ b/vlm/dev/8aHzds2uUyB/39.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3ef271fa201ce247bb8ada49e7449c8e9f254d2f35503db298480cad2535ea0f
+size 687586
diff --git a/vlm/dev/8aHzds2uUyB/4.png b/vlm/dev/8aHzds2uUyB/4.png
new file mode 100644
index 0000000000000000000000000000000000000000..447d63b9d56b904e259eb821cb699ef1ed5511cf
--- /dev/null
+++ b/vlm/dev/8aHzds2uUyB/4.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:adf4bd2229862eb9d31090cfe5f0380e6f1d7fc2b86dbc7fcdc5f5514a53f8aa
+size 472127
diff --git a/vlm/dev/8aHzds2uUyB/44.png b/vlm/dev/8aHzds2uUyB/44.png
new file mode 100644
index 0000000000000000000000000000000000000000..aa9b8fb6eb8e8c1c9d50161b5c093a150bf45bc7
--- /dev/null
+++ b/vlm/dev/8aHzds2uUyB/44.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:70eac9a9e96e841f50f3e9ca511023f1862ab454f1f6913a801f10aa1d62483b
+size 283400
diff --git a/vlm/dev/8aHzds2uUyB/47.png b/vlm/dev/8aHzds2uUyB/47.png
new file mode 100644
index 0000000000000000000000000000000000000000..9e73c2d7843f0b7c9d197817df3ff5911b4e8c34
--- /dev/null
+++ b/vlm/dev/8aHzds2uUyB/47.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:24e796f900315ad21e9e4e2fd80d06bba7a9e7fde41909a6fa67eeaac62c8cbe
+size 596296
diff --git a/vlm/dev/8aHzds2uUyB/48.png b/vlm/dev/8aHzds2uUyB/48.png
new file mode 100644
index 0000000000000000000000000000000000000000..13caeb2af41c3281dda93b298ef70b98c2f92c09
--- /dev/null
+++ b/vlm/dev/8aHzds2uUyB/48.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ccbe1276129521cecd270e388f30b144edb7321d4a895f18a0489b7ad28208aa
+size 258648
diff --git a/vlm/dev/8aHzds2uUyB/50.png b/vlm/dev/8aHzds2uUyB/50.png
new file mode 100644
index 0000000000000000000000000000000000000000..6c79115445ab0a5b1ec3c188ed9ce49a56cf9d5c
--- /dev/null
+++ b/vlm/dev/8aHzds2uUyB/50.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3c7da367de9ac96a56e7bc8175764d59e07dd59687d85b0b9b6c04151018eefa
+size 619377
diff --git a/vlm/dev/8aHzds2uUyB/51.png b/vlm/dev/8aHzds2uUyB/51.png
new file mode 100644
index 0000000000000000000000000000000000000000..a90fc426b2e5f5061a1bd0ce5ea9cb53fa189efb
--- /dev/null
+++ b/vlm/dev/8aHzds2uUyB/51.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:abfc7aaa835255a9cbcb7c3796286e9b67660d721a8d9f09608d56168181a97b
+size 465250
diff --git a/vlm/dev/9h3KsOVXhLZ/0.png b/vlm/dev/9h3KsOVXhLZ/0.png
new file mode 100644
index 0000000000000000000000000000000000000000..3225ed07297c37d155873d74071ed789cc7a6fc4
--- /dev/null
+++ b/vlm/dev/9h3KsOVXhLZ/0.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:90859135256a87eb68d8a3593c5c74deeb3d9afeed984e4966f62a754a3f65fb
+size 449702
diff --git a/vlm/dev/9h3KsOVXhLZ/1.png b/vlm/dev/9h3KsOVXhLZ/1.png
new file mode 100644
index 0000000000000000000000000000000000000000..f7d4bca08325c610a9ee96099e54d2ac17d7cf7c
--- /dev/null
+++ b/vlm/dev/9h3KsOVXhLZ/1.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8c2cd82b597b070216dc3b22b9d7308b356ddcf5f70dbb9df1d6e4b4a4b23d7d
+size 496069
diff --git a/vlm/dev/9h3KsOVXhLZ/10.png b/vlm/dev/9h3KsOVXhLZ/10.png
new file mode 100644
index 0000000000000000000000000000000000000000..da2f9b9bd3a49fa0e28117f1acf41fe7e9b0c567
--- /dev/null
+++ b/vlm/dev/9h3KsOVXhLZ/10.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:dcd8d4697a82f072d335a821d954ebaadf2b4d4f30a8d73dfe505675f16789fe
+size 436567
diff --git a/vlm/dev/9h3KsOVXhLZ/11.png b/vlm/dev/9h3KsOVXhLZ/11.png
new file mode 100644
index 0000000000000000000000000000000000000000..3e84448ee4c076c5e44b30bbdc02f2d6f119ddd7
--- /dev/null
+++ b/vlm/dev/9h3KsOVXhLZ/11.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1d4dde70efe5ad669568dee3e45b14f1a8c8f2367e4a05360c6f1f8a599634a9
+size 336185
diff --git a/vlm/dev/9h3KsOVXhLZ/2.png b/vlm/dev/9h3KsOVXhLZ/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..67c9bdfef3818e3e7f8cd35eb53e0fc4dfa6cc47
--- /dev/null
+++ b/vlm/dev/9h3KsOVXhLZ/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cf9e5dac57dcadb854514944fd9c8bd5a864064127f0ec3dad697303d4f53192
+size 618328
diff --git a/vlm/dev/9h3KsOVXhLZ/3.png b/vlm/dev/9h3KsOVXhLZ/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..450b474dae35e15b214679b323dfd4057834b8b0
--- /dev/null
+++ b/vlm/dev/9h3KsOVXhLZ/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2724a0bb12c839271393066d164e08c68eb2a16302ce84c3e480189ea97e95e5
+size 501991
diff --git a/vlm/dev/9h3KsOVXhLZ/4.png b/vlm/dev/9h3KsOVXhLZ/4.png
new file mode 100644
index 0000000000000000000000000000000000000000..eeacc5c08132d6ec91362ba82f4fc231207408e9
--- /dev/null
+++ b/vlm/dev/9h3KsOVXhLZ/4.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e2d2e207d70b971938425e742cb49a4705d4c15d024733b0ec45d735fbcfc5c1
+size 487446
diff --git a/vlm/dev/9h3KsOVXhLZ/5.png b/vlm/dev/9h3KsOVXhLZ/5.png
new file mode 100644
index 0000000000000000000000000000000000000000..7cbba15eb2b972b2093207ba3042738015b1c5de
--- /dev/null
+++ b/vlm/dev/9h3KsOVXhLZ/5.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:295e5ed8729a69fac8dc87b3a33b65d1f7c8603333d040f4041194e746745e89
+size 561667
diff --git a/vlm/dev/9h3KsOVXhLZ/6.png b/vlm/dev/9h3KsOVXhLZ/6.png
new file mode 100644
index 0000000000000000000000000000000000000000..bab0f12f0222feb207612c84a997e782602a82b7
--- /dev/null
+++ b/vlm/dev/9h3KsOVXhLZ/6.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:71f5966411bd0daad2dc62220f61df14d19ac3174daf506f55565898ee644077
+size 531859
diff --git a/vlm/dev/9h3KsOVXhLZ/7.png b/vlm/dev/9h3KsOVXhLZ/7.png
new file mode 100644
index 0000000000000000000000000000000000000000..e213a48748c23ffa3cdcc30cd178cda62fcbc83a
--- /dev/null
+++ b/vlm/dev/9h3KsOVXhLZ/7.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b07297f49d98e47fc15e3e8d67e600d93875f315e3de006f29b6446e90998a5f
+size 550814
diff --git a/vlm/dev/9h3KsOVXhLZ/8.png b/vlm/dev/9h3KsOVXhLZ/8.png
new file mode 100644
index 0000000000000000000000000000000000000000..5e93ed517c2c395f2c78b17ac322b76db2891afc
--- /dev/null
+++ b/vlm/dev/9h3KsOVXhLZ/8.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:64895223491af1f87c1f6e97f877f0a4bb76776965b30b8452dca790a5a2cdf0
+size 513206
diff --git a/vlm/dev/9h3KsOVXhLZ/9.png b/vlm/dev/9h3KsOVXhLZ/9.png
new file mode 100644
index 0000000000000000000000000000000000000000..072f82f9030c7c54dc3fcf438bc350a520c8f2c8
--- /dev/null
+++ b/vlm/dev/9h3KsOVXhLZ/9.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:25adb67dda9ba5ea5f620492d0633a86187b2ba68f5f16fde602733dbfad6c8d
+size 493096
diff --git a/vlm/dev/CQsmMYmlP5T/10.png b/vlm/dev/CQsmMYmlP5T/10.png
new file mode 100644
index 0000000000000000000000000000000000000000..21578523b22e21a94f6b7417d3f5d8e406ab07d0
--- /dev/null
+++ b/vlm/dev/CQsmMYmlP5T/10.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:35819ffa9ae703ffa71402e59071ec605ac526d019ff52d3f03e1e6dc13f8faf
+size 610548
diff --git a/vlm/dev/CQsmMYmlP5T/11.png b/vlm/dev/CQsmMYmlP5T/11.png
new file mode 100644
index 0000000000000000000000000000000000000000..5abbdea0a393708b76ff387957650f5fdb2f4d1a
--- /dev/null
+++ b/vlm/dev/CQsmMYmlP5T/11.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:56c82145bf213d03c21d410b585299604cc13354bb1cf781834b5084db32bdb2
+size 655937
diff --git a/vlm/dev/CQsmMYmlP5T/14.png b/vlm/dev/CQsmMYmlP5T/14.png
new file mode 100644
index 0000000000000000000000000000000000000000..25ed7180b0a72974605ee584d79ee8f77096f99a
--- /dev/null
+++ b/vlm/dev/CQsmMYmlP5T/14.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bba4d3ec785e9e74b88934440555329fde76dc70bbd88781688fb836b85c8336
+size 638539
diff --git a/vlm/dev/CQsmMYmlP5T/15.png b/vlm/dev/CQsmMYmlP5T/15.png
new file mode 100644
index 0000000000000000000000000000000000000000..0b66fcd594d698896bc614a8e8a2ff6347e5182c
--- /dev/null
+++ b/vlm/dev/CQsmMYmlP5T/15.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:73ca758339e512f39c0062d68e2ef0a00c3348db6bf28fbbaca11a6b62eb33c9
+size 620567
diff --git a/vlm/dev/CQsmMYmlP5T/17.png b/vlm/dev/CQsmMYmlP5T/17.png
new file mode 100644
index 0000000000000000000000000000000000000000..98dc03b4d49c22aa0e40943f0e35be27a947395b
--- /dev/null
+++ b/vlm/dev/CQsmMYmlP5T/17.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c4cbe71a13695158cb11d27a039e9401900345fd608dee7f75be2363c33ba2a3
+size 302311
diff --git a/vlm/dev/CQsmMYmlP5T/2.png b/vlm/dev/CQsmMYmlP5T/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..1844180b15de0898c02d61da0d7432022685f877
--- /dev/null
+++ b/vlm/dev/CQsmMYmlP5T/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6cde9b5c060ec876fd55f9292e1d0329f8d0c5d272661d63bf7bb880204dd00a
+size 606787
diff --git a/vlm/dev/CQsmMYmlP5T/21.png b/vlm/dev/CQsmMYmlP5T/21.png
new file mode 100644
index 0000000000000000000000000000000000000000..31124c4d9a2bda54e2018e422020e70ffc0c1136
--- /dev/null
+++ b/vlm/dev/CQsmMYmlP5T/21.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7c511ab04b0b0d26521a50218ea420641b604f8a7caa42e4cb12747aca145606
+size 580702
diff --git a/vlm/dev/CQsmMYmlP5T/23.png b/vlm/dev/CQsmMYmlP5T/23.png
new file mode 100644
index 0000000000000000000000000000000000000000..0bc3f997e2e95d1c6b2289375c3962a59a550a03
--- /dev/null
+++ b/vlm/dev/CQsmMYmlP5T/23.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b83f47dee508ee927b7b2a12e9e313aabf3c100c53dd9e752dbc0106454bd381
+size 417234
diff --git a/vlm/dev/CQsmMYmlP5T/24.png b/vlm/dev/CQsmMYmlP5T/24.png
new file mode 100644
index 0000000000000000000000000000000000000000..cbb2e59473ae5a27d497993ca32b64ecb76b08b2
--- /dev/null
+++ b/vlm/dev/CQsmMYmlP5T/24.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c4805c8fac72db46829c6118cbfee16a2c25a7c2be72907f2cc734caf097f5c5
+size 371732
diff --git a/vlm/dev/CQsmMYmlP5T/3.png b/vlm/dev/CQsmMYmlP5T/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..0891a2739b2bf8bcf5499304c307dc52c4aaa1f4
--- /dev/null
+++ b/vlm/dev/CQsmMYmlP5T/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:af048b5c8062b25f9f5bc056d26926723f02f2886e3679a14351da65621de23d
+size 531296
diff --git a/vlm/dev/CQsmMYmlP5T/6.png b/vlm/dev/CQsmMYmlP5T/6.png
new file mode 100644
index 0000000000000000000000000000000000000000..1fe72ae14a415b8b5adacebb618b96ee6160214a
--- /dev/null
+++ b/vlm/dev/CQsmMYmlP5T/6.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0d6f54099aeb38e728bbd2083258bb07948001c739d6e2616313ed268491f279
+size 529393
diff --git a/vlm/dev/CQsmMYmlP5T/9.png b/vlm/dev/CQsmMYmlP5T/9.png
new file mode 100644
index 0000000000000000000000000000000000000000..1f7dba41e351d9940c65f61c34ee2fc53e47c21b
--- /dev/null
+++ b/vlm/dev/CQsmMYmlP5T/9.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0d6ad1e18956861ce4278b624f9734389c16393cc089a73252ac2f151604d825
+size 245193
diff --git a/vlm/dev/ECvgmYVyeUz/0.png b/vlm/dev/ECvgmYVyeUz/0.png
new file mode 100644
index 0000000000000000000000000000000000000000..aeab4c10938db00afef99d699df09a4c4731450b
--- /dev/null
+++ b/vlm/dev/ECvgmYVyeUz/0.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0b662c2ee43cdba9be38b0e61565817b4311494446f10507e31b1027db7d7b95
+size 541485
diff --git a/vlm/dev/ECvgmYVyeUz/1.png b/vlm/dev/ECvgmYVyeUz/1.png
new file mode 100644
index 0000000000000000000000000000000000000000..2925aca7f888a50da379a9638098f1fc37a1637a
--- /dev/null
+++ b/vlm/dev/ECvgmYVyeUz/1.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d86a50b8d0be55a3435c765cf9c063a3e3d1d2aeaf218d9c9b48407b566be67a
+size 786275
diff --git a/vlm/dev/ECvgmYVyeUz/10.png b/vlm/dev/ECvgmYVyeUz/10.png
new file mode 100644
index 0000000000000000000000000000000000000000..0ae95e7a416f73edc1052f93d5badc25efad61fa
--- /dev/null
+++ b/vlm/dev/ECvgmYVyeUz/10.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:afcc54def8c01c6d6771572c0dbda472cadf88ea11c874c6fd5d0928326546f4
+size 312068
diff --git a/vlm/dev/ECvgmYVyeUz/11.png b/vlm/dev/ECvgmYVyeUz/11.png
new file mode 100644
index 0000000000000000000000000000000000000000..10bd02b502be429ee92582474be1202f0aae3139
--- /dev/null
+++ b/vlm/dev/ECvgmYVyeUz/11.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5ce2ab37056d7e9e3fa4d55765c06b9446ae275022045711b790e1c97f62ebf6
+size 379459
diff --git a/vlm/dev/ECvgmYVyeUz/12.png b/vlm/dev/ECvgmYVyeUz/12.png
new file mode 100644
index 0000000000000000000000000000000000000000..98faed2878e22038a984d6a5eb1397000b6eaa34
--- /dev/null
+++ b/vlm/dev/ECvgmYVyeUz/12.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6195107bc31420bd1219f8acb67afbe6e235e2da81caa823cda0554fac9a376f
+size 391063
diff --git a/vlm/dev/ECvgmYVyeUz/13.png b/vlm/dev/ECvgmYVyeUz/13.png
new file mode 100644
index 0000000000000000000000000000000000000000..0f151c024ec1ed1f9c069593d48863c032af44ee
--- /dev/null
+++ b/vlm/dev/ECvgmYVyeUz/13.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4555484cc1bd5cf506c1c953237d0f08e3e0b06b7a68f492475569e93b5e700a
+size 362238
diff --git a/vlm/dev/ECvgmYVyeUz/14.png b/vlm/dev/ECvgmYVyeUz/14.png
new file mode 100644
index 0000000000000000000000000000000000000000..c32f9ea689bdeffe4c42d389424b2b50b172b4ab
--- /dev/null
+++ b/vlm/dev/ECvgmYVyeUz/14.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:419995c241b121d417dc35fed94bf1d7e6e172a8430ba2971fd51381768b8cd8
+size 416745
diff --git a/vlm/dev/ECvgmYVyeUz/15.png b/vlm/dev/ECvgmYVyeUz/15.png
new file mode 100644
index 0000000000000000000000000000000000000000..cabf0776997f85f563bdc0d2ea166414beff9d58
--- /dev/null
+++ b/vlm/dev/ECvgmYVyeUz/15.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:63369deb14ebe62fd003542a36cb9cac5a9b26755c3344f497aa5cad1cb362c2
+size 486448
diff --git a/vlm/dev/ECvgmYVyeUz/16.png b/vlm/dev/ECvgmYVyeUz/16.png
new file mode 100644
index 0000000000000000000000000000000000000000..fa070f5f2b57ccf1e9593ef681bc35daaac153aa
--- /dev/null
+++ b/vlm/dev/ECvgmYVyeUz/16.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:568fa64aeb2314da8b43dca87e45506ecaa731ca9519b51ee7842e2a291dad95
+size 416673
diff --git a/vlm/dev/ECvgmYVyeUz/17.png b/vlm/dev/ECvgmYVyeUz/17.png
new file mode 100644
index 0000000000000000000000000000000000000000..579a05603e8abbb8c62d44c44b8de55cf0eb3d72
--- /dev/null
+++ b/vlm/dev/ECvgmYVyeUz/17.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a2cbeb8f45674351019628024b436bf25747479e35056a33d474672f915eda16
+size 376249
diff --git a/vlm/dev/ECvgmYVyeUz/18.png b/vlm/dev/ECvgmYVyeUz/18.png
new file mode 100644
index 0000000000000000000000000000000000000000..96d1a2521fed0058cb8a01a892dbb09ca05a5662
--- /dev/null
+++ b/vlm/dev/ECvgmYVyeUz/18.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6546f0decee590e029c5d75efd3327f0faa9dc77a0e37a377b5090d288dd9657
+size 671849
diff --git a/vlm/dev/ECvgmYVyeUz/19.png b/vlm/dev/ECvgmYVyeUz/19.png
new file mode 100644
index 0000000000000000000000000000000000000000..2fd214b057235a3952996facf518ef514aebb491
--- /dev/null
+++ b/vlm/dev/ECvgmYVyeUz/19.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fcd3216392c1e85e04f8b2625b1c3714f5f3537511dd3ff114f209fee90f7395
+size 541819
diff --git a/vlm/dev/ECvgmYVyeUz/2.png b/vlm/dev/ECvgmYVyeUz/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..4ba1eb92fcbfeaf45fa1fc5a9a0f222f827d19e4
--- /dev/null
+++ b/vlm/dev/ECvgmYVyeUz/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3813508d72ff943ce1a5b529885290475d2235fad9295085f30ea41299cb2539
+size 601821
diff --git a/vlm/dev/ECvgmYVyeUz/20.png b/vlm/dev/ECvgmYVyeUz/20.png
new file mode 100644
index 0000000000000000000000000000000000000000..ff2ac862d4666f444567f374de00d659b0c77ce1
--- /dev/null
+++ b/vlm/dev/ECvgmYVyeUz/20.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fed1c1032df484ec795756ba4be7f2fab1aa310fe07bba4c618cfad9415889f4
+size 453403
diff --git a/vlm/dev/ECvgmYVyeUz/3.png b/vlm/dev/ECvgmYVyeUz/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..f5f4dae66e0aae7428edc4c289ae6958f6391e3d
--- /dev/null
+++ b/vlm/dev/ECvgmYVyeUz/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:62416afdb478464e8d8b1d41748f63f7b98cff15e7ded046641325c28321aff4
+size 585343
diff --git a/vlm/dev/ECvgmYVyeUz/4.png b/vlm/dev/ECvgmYVyeUz/4.png
new file mode 100644
index 0000000000000000000000000000000000000000..112e881be50b9bfde1a4c19b03990232f8301cd5
--- /dev/null
+++ b/vlm/dev/ECvgmYVyeUz/4.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8052adb273fc9bb53b3a508dc283c89d21da3f231384f8663fa734932c094441
+size 557715
diff --git a/vlm/dev/ECvgmYVyeUz/5.png b/vlm/dev/ECvgmYVyeUz/5.png
new file mode 100644
index 0000000000000000000000000000000000000000..e1ee5e086b0dc2829b543c4e9f24b290b040010a
--- /dev/null
+++ b/vlm/dev/ECvgmYVyeUz/5.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:daed9a4408b04bfbe2d664ef85572fec2fa0555bd1bad08130f470f310b446dc
+size 624785
diff --git a/vlm/dev/ECvgmYVyeUz/6.png b/vlm/dev/ECvgmYVyeUz/6.png
new file mode 100644
index 0000000000000000000000000000000000000000..01cb55bc247d1b94fdd9838138ecdce2244706ca
--- /dev/null
+++ b/vlm/dev/ECvgmYVyeUz/6.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8d06c20a415dc9b871f8f26a6308b78932d70eac7106d7bdb2827012573a74cb
+size 645501
diff --git a/vlm/dev/ECvgmYVyeUz/7.png b/vlm/dev/ECvgmYVyeUz/7.png
new file mode 100644
index 0000000000000000000000000000000000000000..8cd543f1249c04640ab9899df5a5b67ecf9ba076
--- /dev/null
+++ b/vlm/dev/ECvgmYVyeUz/7.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bc0740d7c4d2b0c354d05dd06606795b8b024717a73508f8a26a1f0040142fb1
+size 587168
diff --git a/vlm/dev/ECvgmYVyeUz/8.png b/vlm/dev/ECvgmYVyeUz/8.png
new file mode 100644
index 0000000000000000000000000000000000000000..24c4fba446fc5768834d3975731bab0726f04745
--- /dev/null
+++ b/vlm/dev/ECvgmYVyeUz/8.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d2d30c3a248bd27b5f49510d6b63fd025502f54726efef9a267df8a186730049
+size 534900
diff --git a/vlm/dev/ECvgmYVyeUz/9.png b/vlm/dev/ECvgmYVyeUz/9.png
new file mode 100644
index 0000000000000000000000000000000000000000..61565121789f48cc0b49edcfd07b9e82bf10bd96
--- /dev/null
+++ b/vlm/dev/ECvgmYVyeUz/9.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5ff541557f5e299868e2df0b7d3a6c4f3982720d4c7e51ae9210b4461bb02935
+size 539942
diff --git a/vlm/dev/FWMQYjFso-a/0.png b/vlm/dev/FWMQYjFso-a/0.png
new file mode 100644
index 0000000000000000000000000000000000000000..abefb67170c83ec627d19739a5b9e379e2e49296
--- /dev/null
+++ b/vlm/dev/FWMQYjFso-a/0.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c4d9a6764f65c394e855d58c0402a99f45e523f9b3fba9ef653caae4d65ff0a6
+size 440329
diff --git a/vlm/dev/FWMQYjFso-a/1.png b/vlm/dev/FWMQYjFso-a/1.png
new file mode 100644
index 0000000000000000000000000000000000000000..c4c06967f8433e28abd40a87a0fcfe47d0ce8c6b
--- /dev/null
+++ b/vlm/dev/FWMQYjFso-a/1.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:dfc32508c4e2b5697cce9759dd0c0b816f69a0779203493a0f7f774c2ca277f2
+size 646764
diff --git a/vlm/dev/FWMQYjFso-a/10.png b/vlm/dev/FWMQYjFso-a/10.png
new file mode 100644
index 0000000000000000000000000000000000000000..2c921bc2b6d264147298b3dda99756c88b893c63
--- /dev/null
+++ b/vlm/dev/FWMQYjFso-a/10.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8d94add13ce58458c107ddd8b37c13d9a12580416fa4d4138f32a0b98e388a71
+size 507290
diff --git a/vlm/dev/FWMQYjFso-a/11.png b/vlm/dev/FWMQYjFso-a/11.png
new file mode 100644
index 0000000000000000000000000000000000000000..e02dedfe4cbe966fd61b0d004dc79a373e2b379a
--- /dev/null
+++ b/vlm/dev/FWMQYjFso-a/11.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:165c998f78dfe925513b8bba3d7a53b9752c2f5b32c1c059e19ddefdaf0f1ca2
+size 541789
diff --git a/vlm/dev/FWMQYjFso-a/12.png b/vlm/dev/FWMQYjFso-a/12.png
new file mode 100644
index 0000000000000000000000000000000000000000..3c4130fe775a19bfe6687637a4697c45d6e382ce
--- /dev/null
+++ b/vlm/dev/FWMQYjFso-a/12.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:28834385d1f278d3248cf539feb85b6e44b1c6de141499b8282f72bb03ed3a20
+size 405088
diff --git a/vlm/dev/FWMQYjFso-a/13.png b/vlm/dev/FWMQYjFso-a/13.png
new file mode 100644
index 0000000000000000000000000000000000000000..b3dbeb11554096d955bb4baf7d86595dbcf19a24
--- /dev/null
+++ b/vlm/dev/FWMQYjFso-a/13.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:35c93f0edf0535c00cd7c668d90734a6c6972fcdbc719db9de71b88aff04dc58
+size 336551
diff --git a/vlm/dev/FWMQYjFso-a/2.png b/vlm/dev/FWMQYjFso-a/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..bb8a55ecf081b6c409694efe7b7214a24a959db4
--- /dev/null
+++ b/vlm/dev/FWMQYjFso-a/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:230af9f088abd6688174924f2ee2b20a834fbf3e374bcd96fbf84ee95613c790
+size 549574
diff --git a/vlm/dev/FWMQYjFso-a/3.png b/vlm/dev/FWMQYjFso-a/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..7f791045131513a3e414547ef20e1e3069027235
--- /dev/null
+++ b/vlm/dev/FWMQYjFso-a/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a970052857b544d27f0404758aa4a97095fc2fefe12bdc7553188c3397ac7ccc
+size 541998
diff --git a/vlm/dev/FWMQYjFso-a/4.png b/vlm/dev/FWMQYjFso-a/4.png
new file mode 100644
index 0000000000000000000000000000000000000000..4d7577d2f4b8c5e0de834bd1fe7f40284ce034b8
--- /dev/null
+++ b/vlm/dev/FWMQYjFso-a/4.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:891d3b466912d93633f12d81d0acf4f7aa470ff6b7c45b6a6451d2e332c15b3c
+size 683304
diff --git a/vlm/dev/FWMQYjFso-a/5.png b/vlm/dev/FWMQYjFso-a/5.png
new file mode 100644
index 0000000000000000000000000000000000000000..526ac5b50e4901093dbc2c4bc8a34508796177eb
--- /dev/null
+++ b/vlm/dev/FWMQYjFso-a/5.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:edad8ae87dd0f68c9b95249c00e9efe15ccc40666c65ca5eb7d6f9758ebcd33f
+size 486648
diff --git a/vlm/dev/FWMQYjFso-a/6.png b/vlm/dev/FWMQYjFso-a/6.png
new file mode 100644
index 0000000000000000000000000000000000000000..06b84b610f05e69bdc3792fcba4d84141b173ed9
--- /dev/null
+++ b/vlm/dev/FWMQYjFso-a/6.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cd95663ab08dc724f83abcbe423091a8783f443c2aa12da091176e2c15cd61da
+size 587757
diff --git a/vlm/dev/FWMQYjFso-a/7.png b/vlm/dev/FWMQYjFso-a/7.png
new file mode 100644
index 0000000000000000000000000000000000000000..cbfdd6f7313b23d41bb7a17b9316a76497f9f0ab
--- /dev/null
+++ b/vlm/dev/FWMQYjFso-a/7.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f5b6090d1107cfc54d54e505a199c49c6c003dd29be811eb2c7e6e3cc89c8310
+size 625130
diff --git a/vlm/dev/FWMQYjFso-a/8.png b/vlm/dev/FWMQYjFso-a/8.png
new file mode 100644
index 0000000000000000000000000000000000000000..de1d488e1e7db42aab7c9fa342ab0c31c81c0bff
--- /dev/null
+++ b/vlm/dev/FWMQYjFso-a/8.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bf8ff7952bcc124cea291578fdaaefba63704b3f3770bcf4bdd68dc5ea7765fb
+size 580563
diff --git a/vlm/dev/FWMQYjFso-a/9.png b/vlm/dev/FWMQYjFso-a/9.png
new file mode 100644
index 0000000000000000000000000000000000000000..e5c6f09ef23432aae54f5060fcb23c07806bbfea
--- /dev/null
+++ b/vlm/dev/FWMQYjFso-a/9.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0ef49741f7f5fc50eb6c83074fa5bc95deea7f4c9551358b9368d82569fd1089
+size 1161303
diff --git a/vlm/dev/IajGRJuM7D3/0.png b/vlm/dev/IajGRJuM7D3/0.png
new file mode 100644
index 0000000000000000000000000000000000000000..2ba21a929fd1d157414df7eae39a55ec1bbea5bb
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/0.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:83611cb6fc7169290003b79b97ec23225e17409f52a36864395d28b1402971c3
+size 600052
diff --git a/vlm/dev/IajGRJuM7D3/1.png b/vlm/dev/IajGRJuM7D3/1.png
new file mode 100644
index 0000000000000000000000000000000000000000..a12086d5b7276903806dd3f65079f881fe94e410
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/1.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9fed235bf4490a13d98a42599dc3a20b79dd9e24f49bb831f4e283067776d687
+size 693711
diff --git a/vlm/dev/IajGRJuM7D3/10.png b/vlm/dev/IajGRJuM7D3/10.png
new file mode 100644
index 0000000000000000000000000000000000000000..d7475763b007f87758d03a3dc2c3ea1ad4f3b4e1
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/10.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:92b19f525b6bc0151b7c8ad2609a3001f8d21c2a202d8408bcb56ab96d2d3292
+size 581991
diff --git a/vlm/dev/IajGRJuM7D3/11.png b/vlm/dev/IajGRJuM7D3/11.png
new file mode 100644
index 0000000000000000000000000000000000000000..b8d4c5a34dd21a86db95dbdc57bb2221026ef52e
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/11.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8a381a991e898f0e3c4a667f05aed97c700cad61b950c7594813a90acc83be23
+size 553847
diff --git a/vlm/dev/IajGRJuM7D3/12.png b/vlm/dev/IajGRJuM7D3/12.png
new file mode 100644
index 0000000000000000000000000000000000000000..aa6eb136cd315061a61ed5c134c12d15de134e03
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/12.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:30cef0515869531b449d33669b3ac433d0b278edb8b767e4a42ef734bc1405ae
+size 567473
diff --git a/vlm/dev/IajGRJuM7D3/13.png b/vlm/dev/IajGRJuM7D3/13.png
new file mode 100644
index 0000000000000000000000000000000000000000..2955a006322275cb0a1d0d1dc8682f187e5eec0e
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/13.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4e0833c6027b2f8a02fddad2c4f25c9e63df6b134bc5ac9182ef32e9c48f5408
+size 554449
diff --git a/vlm/dev/IajGRJuM7D3/14.png b/vlm/dev/IajGRJuM7D3/14.png
new file mode 100644
index 0000000000000000000000000000000000000000..71069ab1dc56f3c6eee6bc123a2c2c9f667ecfa0
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/14.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e40613561ea3c653a6b5d679567f89012a8909b97fe95d14d4231004d137c6af
+size 488855
diff --git a/vlm/dev/IajGRJuM7D3/15.png b/vlm/dev/IajGRJuM7D3/15.png
new file mode 100644
index 0000000000000000000000000000000000000000..f8350db72d65f035463c5615523b1a808f30fb11
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/15.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:385c754ec45a9720282c74ef2e92d3e5aebd696f3617b182e8587209284156be
+size 294626
diff --git a/vlm/dev/IajGRJuM7D3/16.png b/vlm/dev/IajGRJuM7D3/16.png
new file mode 100644
index 0000000000000000000000000000000000000000..f3d941a8c1df478a7498994a53eab4affee3ad99
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/16.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b93bfef7f61ad90257363564d9e4ba002b6af1e0732f748e12ceb0dbec86a279
+size 381209
diff --git a/vlm/dev/IajGRJuM7D3/17.png b/vlm/dev/IajGRJuM7D3/17.png
new file mode 100644
index 0000000000000000000000000000000000000000..fa55c9cf136e938ca9eca376fda5587d49e9b6e4
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/17.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:37105d61f7584c2fcdbb5ba9504168843ef6d1d336650f339d55330404b13948
+size 354503
diff --git a/vlm/dev/IajGRJuM7D3/18.png b/vlm/dev/IajGRJuM7D3/18.png
new file mode 100644
index 0000000000000000000000000000000000000000..825848ce4fded95fb2203df965c55f541f9e504f
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/18.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9381d95537b9a383a17d8ab14aecaec4855bfff8b070ae1dbe0d4a98c0e4daf1
+size 426787
diff --git a/vlm/dev/IajGRJuM7D3/19.png b/vlm/dev/IajGRJuM7D3/19.png
new file mode 100644
index 0000000000000000000000000000000000000000..34fd27707b2fbae496b4449330dfcc8a20f9409c
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/19.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:470895fb0796ebc1fad6747c7f44b2ce5504753d7c3b163625c7aa097c8afebc
+size 426926
diff --git a/vlm/dev/IajGRJuM7D3/2.png b/vlm/dev/IajGRJuM7D3/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..d06a1885183136c287d92ddd5b006aa845f0770f
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3d3720b4b9cb9b16fa88d581a18f649ff98b06fd509f3886eeab9b189268c11f
+size 617321
diff --git a/vlm/dev/IajGRJuM7D3/20.png b/vlm/dev/IajGRJuM7D3/20.png
new file mode 100644
index 0000000000000000000000000000000000000000..1e38a5ce66c7de9fa659c940faebeab868741aa9
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/20.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d8e997fb8ffada540d51ca63a9d21dafc57433949aacfeef3c86b8ebdbc8bed7
+size 406493
diff --git a/vlm/dev/IajGRJuM7D3/21.png b/vlm/dev/IajGRJuM7D3/21.png
new file mode 100644
index 0000000000000000000000000000000000000000..cc0be26f44b7392441db86c5f80064c0b2182b5a
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/21.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f68da1e169ae6f1a0e1d04095dba1bc0b2ae4c4dd9216011acaf69d94cd4cdd8
+size 320898
diff --git a/vlm/dev/IajGRJuM7D3/22.png b/vlm/dev/IajGRJuM7D3/22.png
new file mode 100644
index 0000000000000000000000000000000000000000..bf94713d448ae084f15ebc3a8bf9e92efba2251c
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/22.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:50c5e9561a1d9613eba1bf8e93743556779c49a340d65e536d72bc6dd3a2b2ce
+size 383011
diff --git a/vlm/dev/IajGRJuM7D3/23.png b/vlm/dev/IajGRJuM7D3/23.png
new file mode 100644
index 0000000000000000000000000000000000000000..8b05f504e467a15b42d5beebc42d90b9ced34cdb
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/23.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9854c7e0c89fb83fbd277b02a1307cd5a8189df37770a727079646cb7e266922
+size 358972
diff --git a/vlm/dev/IajGRJuM7D3/24.png b/vlm/dev/IajGRJuM7D3/24.png
new file mode 100644
index 0000000000000000000000000000000000000000..9f7f656a00246afee7f3ab6ea8ce8f5e79cb8414
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/24.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3dd7a396be3e4af30f3e4699f8e09e90310a1823b01ba19e9b02dc7313c19fbe
+size 285974
diff --git a/vlm/dev/IajGRJuM7D3/25.png b/vlm/dev/IajGRJuM7D3/25.png
new file mode 100644
index 0000000000000000000000000000000000000000..93e745c6a27b5421bd189545e48769d26082a9b7
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/25.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b6c59d1f49dfd406d32bee9f6d4a77fe4fdb4913214bb7fd94dd5e7edaf59bcd
+size 344642
diff --git a/vlm/dev/IajGRJuM7D3/26.png b/vlm/dev/IajGRJuM7D3/26.png
new file mode 100644
index 0000000000000000000000000000000000000000..f6ed43e59d1a905e44dbac367243f326c384813e
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/26.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:06fa3220b10e988900ad0515bbea6fb167d342561a694a09d4c8712d44e0ff81
+size 486161
diff --git a/vlm/dev/IajGRJuM7D3/27.png b/vlm/dev/IajGRJuM7D3/27.png
new file mode 100644
index 0000000000000000000000000000000000000000..53ed886ad803ead09628048b14019eba5197fa1c
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/27.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4c39dc5e7b8d849292acdf4973fd2e73bca328cae602c2e6e6d0a9e1fd3aa6fb
+size 427426
diff --git a/vlm/dev/IajGRJuM7D3/28.png b/vlm/dev/IajGRJuM7D3/28.png
new file mode 100644
index 0000000000000000000000000000000000000000..3249edb4327f8740497cb87ffa2e35514d556d16
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/28.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d9e1345a373ecc7ba74546e944804f9cdda274a8964e09cc06b216e641945130
+size 476608
diff --git a/vlm/dev/IajGRJuM7D3/29.png b/vlm/dev/IajGRJuM7D3/29.png
new file mode 100644
index 0000000000000000000000000000000000000000..4faf15df900aecb9e34ee449348a894391a56ec2
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/29.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:daface36d016db49995d1808bb4c798f8c57b17e37510b211058ce1be39ea903
+size 508026
diff --git a/vlm/dev/IajGRJuM7D3/3.png b/vlm/dev/IajGRJuM7D3/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..b441726fdd152e805e050f4ddd6154d89ecb5a7e
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b87482823781167ce03dd6824bf50dae5d1c987462d63b80a8d5e2094556084c
+size 570996
diff --git a/vlm/dev/IajGRJuM7D3/30.png b/vlm/dev/IajGRJuM7D3/30.png
new file mode 100644
index 0000000000000000000000000000000000000000..26cf196d5d2bba5b9b8881ba138097fc13a07bd6
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/30.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:01bee97dc8932cef0391ba27842a3e40e332289ae042ba2b87a831f542b9c9ae
+size 419187
diff --git a/vlm/dev/IajGRJuM7D3/4.png b/vlm/dev/IajGRJuM7D3/4.png
new file mode 100644
index 0000000000000000000000000000000000000000..2b42d209fe230767d9ef0742f1911290d3a8320c
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/4.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:117783ad6aaba86b158766e5128d149a047bd2c46b1992951fcd85575fed357c
+size 574904
diff --git a/vlm/dev/IajGRJuM7D3/5.png b/vlm/dev/IajGRJuM7D3/5.png
new file mode 100644
index 0000000000000000000000000000000000000000..8c589e3cd61e876dbb158c74f72d9431cb09f30d
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/5.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1e143eb1c588d3ea2835acbc7dcc1ce9c01c2daa51f6e40acaaf5382bab0441c
+size 597306
diff --git a/vlm/dev/IajGRJuM7D3/6.png b/vlm/dev/IajGRJuM7D3/6.png
new file mode 100644
index 0000000000000000000000000000000000000000..1db4b5d720e16b623a88ce8e699a32bef7675a0a
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/6.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ddfe18ff965ed79a00e4ba2bae977c860898333169c85c75f42cae0ae46db77b
+size 649525
diff --git a/vlm/dev/IajGRJuM7D3/7.png b/vlm/dev/IajGRJuM7D3/7.png
new file mode 100644
index 0000000000000000000000000000000000000000..7c258ac8519dbc1b12b8184668f92f7a9f7d96ac
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/7.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:044af5ae57e6f21be6d35371d8788c6af096972dc6b7d313ea0e8d80acb3cabf
+size 642479
diff --git a/vlm/dev/IajGRJuM7D3/8.png b/vlm/dev/IajGRJuM7D3/8.png
new file mode 100644
index 0000000000000000000000000000000000000000..9b0f2669ed3e169264126a2b5111ee7a43a82b18
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/8.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:916cc27c564642d4a7f9d5ac1b72b24f9ccba9006a618ec3d9f0e73468430673
+size 659528
diff --git a/vlm/dev/IajGRJuM7D3/9.png b/vlm/dev/IajGRJuM7D3/9.png
new file mode 100644
index 0000000000000000000000000000000000000000..b1aeadb3fd63c4a47d4ba4d0bea5c5c760518fc1
--- /dev/null
+++ b/vlm/dev/IajGRJuM7D3/9.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4c1fd753692ceb78466df32b8a81835aeebe4321cc530639387d53dc66ea4721
+size 530266
diff --git a/vlm/dev/Ih2bG6h1r4S/0.png b/vlm/dev/Ih2bG6h1r4S/0.png
new file mode 100644
index 0000000000000000000000000000000000000000..d80be410cabc2963e438ef05d8c253b27b0e7eec
--- /dev/null
+++ b/vlm/dev/Ih2bG6h1r4S/0.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0857829102f18b483e2508b9f77521e9aa1fe86aabe0b5d8ed125cf7cdc8794d
+size 336465
diff --git a/vlm/dev/Ih2bG6h1r4S/1.png b/vlm/dev/Ih2bG6h1r4S/1.png
new file mode 100644
index 0000000000000000000000000000000000000000..7971993fb62050d67ab559035fb356b03ac95bce
--- /dev/null
+++ b/vlm/dev/Ih2bG6h1r4S/1.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f6e28fa95a2645a44fc15de9b8ff9f50b976dfbf478abb824267af1ddfc43650
+size 606293
diff --git a/vlm/dev/Ih2bG6h1r4S/10.png b/vlm/dev/Ih2bG6h1r4S/10.png
new file mode 100644
index 0000000000000000000000000000000000000000..c6f5e5938cd207ad0561e6d76b59b9678a35f329
--- /dev/null
+++ b/vlm/dev/Ih2bG6h1r4S/10.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a286a8d8e7a50da9e67c1292546a358d514bbe78bf3d90e51919c923b8096810
+size 519502
diff --git a/vlm/dev/Ih2bG6h1r4S/11.png b/vlm/dev/Ih2bG6h1r4S/11.png
new file mode 100644
index 0000000000000000000000000000000000000000..cd662acaeb7a6542daa8d8c586148edb4dce833b
--- /dev/null
+++ b/vlm/dev/Ih2bG6h1r4S/11.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d04cc246c9469e1c3b66cf20802de84a10fc061e9bd69c05b5a6d79e51a15a98
+size 207911
diff --git a/vlm/dev/Ih2bG6h1r4S/2.png b/vlm/dev/Ih2bG6h1r4S/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..803e84e89c54563e22faecfa6e4e862d15fcd469
--- /dev/null
+++ b/vlm/dev/Ih2bG6h1r4S/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d0dd2a424fd020c2a6fee036d3001a1a0511a4a4a3dac587b5467bbb52276956
+size 408104
diff --git a/vlm/dev/Ih2bG6h1r4S/3.png b/vlm/dev/Ih2bG6h1r4S/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..ad22a5ccdc9bf54096ea4a699a7e5a334d2063e3
--- /dev/null
+++ b/vlm/dev/Ih2bG6h1r4S/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5d76efbe5872dd4306c11abfdb6f93e8dab6caa7b03c2e5aac2074d2ee638c43
+size 506349
diff --git a/vlm/dev/Ih2bG6h1r4S/4.png b/vlm/dev/Ih2bG6h1r4S/4.png
new file mode 100644
index 0000000000000000000000000000000000000000..fd6d7d856c4a779c7cc6c0dce4d000670240cc41
--- /dev/null
+++ b/vlm/dev/Ih2bG6h1r4S/4.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:16780f8fa1ecd041be8454115885642b8c00c5b64ce0d388406f2ae9bfb9412e
+size 408747
diff --git a/vlm/dev/Ih2bG6h1r4S/5.png b/vlm/dev/Ih2bG6h1r4S/5.png
new file mode 100644
index 0000000000000000000000000000000000000000..ab205fe04c51bd8df68aa9dfbc87292667ae6836
--- /dev/null
+++ b/vlm/dev/Ih2bG6h1r4S/5.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:00f45d14ae4cdfb3c0ece6bc8f63aeebcd47a86ec8bfb545b7f6a42beb7f7ff6
+size 479704
diff --git a/vlm/dev/Ih2bG6h1r4S/6.png b/vlm/dev/Ih2bG6h1r4S/6.png
new file mode 100644
index 0000000000000000000000000000000000000000..c150b4638013943929e46b933da6161928db0367
--- /dev/null
+++ b/vlm/dev/Ih2bG6h1r4S/6.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ac211e7cea8f8d4cfeea62939002d89ddf49584a961bf4912126cf2fc15289d7
+size 578781
diff --git a/vlm/dev/Ih2bG6h1r4S/7.png b/vlm/dev/Ih2bG6h1r4S/7.png
new file mode 100644
index 0000000000000000000000000000000000000000..c262e1902d48b597a055a4bff251f12df361d355
--- /dev/null
+++ b/vlm/dev/Ih2bG6h1r4S/7.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6453d498bc87e50d734ae96ab8fece6750407e4fe5230425f2907e7cf4b01c94
+size 614723
diff --git a/vlm/dev/Ih2bG6h1r4S/8.png b/vlm/dev/Ih2bG6h1r4S/8.png
new file mode 100644
index 0000000000000000000000000000000000000000..fdf3021e82ef08e53961ae8cf2c5175e4f4a34d7
--- /dev/null
+++ b/vlm/dev/Ih2bG6h1r4S/8.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:efbff181b538d91d7a8c648192e3ea7f9950aea98fc519308a1b71dab90d27e2
+size 391883
diff --git a/vlm/dev/Ih2bG6h1r4S/9.png b/vlm/dev/Ih2bG6h1r4S/9.png
new file mode 100644
index 0000000000000000000000000000000000000000..de11ad71aec05c3ed6631516323acd7e1a43205e
--- /dev/null
+++ b/vlm/dev/Ih2bG6h1r4S/9.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e3a4ab840657ea0a3caccb0ab8a520a047711a7e0e77e9273139ed1ab8fd2905
+size 574441
diff --git a/vlm/dev/JavFPcsscd5/0.png b/vlm/dev/JavFPcsscd5/0.png
new file mode 100644
index 0000000000000000000000000000000000000000..5f517aeb9e8fc06945017b1c80673fcf9a822f94
--- /dev/null
+++ b/vlm/dev/JavFPcsscd5/0.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ed352a4681750645ca403e531336a6d575c8d5f6aaeba906c4addfdf8d0e5cf2
+size 456215
diff --git a/vlm/dev/JavFPcsscd5/1.png b/vlm/dev/JavFPcsscd5/1.png
new file mode 100644
index 0000000000000000000000000000000000000000..416a492d20f915a15da91a69e527881aeed1e3dc
--- /dev/null
+++ b/vlm/dev/JavFPcsscd5/1.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6f99d0f24ca02b4c08d0a9cff418a95786c270d3efaa42036389205f4650ce01
+size 596842
diff --git a/vlm/dev/JavFPcsscd5/10.png b/vlm/dev/JavFPcsscd5/10.png
new file mode 100644
index 0000000000000000000000000000000000000000..cdecc1a8a2f027198c119b15c4a75d41383050d4
--- /dev/null
+++ b/vlm/dev/JavFPcsscd5/10.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:05b5ac02854de9a26e8ac8b4ef822660bc8f9707eb139c8629116493d3dc2a2d
+size 547361
diff --git a/vlm/dev/JavFPcsscd5/11.png b/vlm/dev/JavFPcsscd5/11.png
new file mode 100644
index 0000000000000000000000000000000000000000..364cf5bc815b56b5bd4a119bbe07e62340bd9e97
--- /dev/null
+++ b/vlm/dev/JavFPcsscd5/11.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e44720711589e5da95b0387e9d7acc0a216e13f4dc5b4045ad208ce95c7e105e
+size 538893
diff --git a/vlm/dev/JavFPcsscd5/12.png b/vlm/dev/JavFPcsscd5/12.png
new file mode 100644
index 0000000000000000000000000000000000000000..6093b26d33f32f89dccb83eaf9f3b6cb0f3b3e14
--- /dev/null
+++ b/vlm/dev/JavFPcsscd5/12.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:be2a26d7f8fdea2e2b55f8683e409b29cab0a3c8ec8dcf3d23498e5cdcc427c2
+size 495415
diff --git a/vlm/dev/JavFPcsscd5/13.png b/vlm/dev/JavFPcsscd5/13.png
new file mode 100644
index 0000000000000000000000000000000000000000..a1edf1543710ba90df116e72d878ae66612e24bd
--- /dev/null
+++ b/vlm/dev/JavFPcsscd5/13.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:586ccba71b239f20cf165fc14a728d157e8f037d461b1340510e809256140425
+size 105309
diff --git a/vlm/dev/JavFPcsscd5/2.png b/vlm/dev/JavFPcsscd5/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..5ef3e1d8d043a6fe7e4df1ffcd930f1f64178706
--- /dev/null
+++ b/vlm/dev/JavFPcsscd5/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8f7472268e5e74b51c4b00e6eff412493f71813bddafb512c6bcd0caa45a17c4
+size 598286
diff --git a/vlm/dev/JavFPcsscd5/3.png b/vlm/dev/JavFPcsscd5/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..b682052d16fca0f3bea450bc388cfc57a4f2caf8
--- /dev/null
+++ b/vlm/dev/JavFPcsscd5/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:872f560492d5a2201a0380b011e84adae2f34587017a28b1c4db4bdc736677fb
+size 642361
diff --git a/vlm/dev/JavFPcsscd5/4.png b/vlm/dev/JavFPcsscd5/4.png
new file mode 100644
index 0000000000000000000000000000000000000000..bcffde0f3ebc5385a21bedf25dfb1ad93e6139de
--- /dev/null
+++ b/vlm/dev/JavFPcsscd5/4.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:41e07627423c9cf6529892ed202ab42931b22ad851b2b60c7a2d46bf6c6028b3
+size 573324
diff --git a/vlm/dev/JavFPcsscd5/5.png b/vlm/dev/JavFPcsscd5/5.png
new file mode 100644
index 0000000000000000000000000000000000000000..00ff73118436bba3909b56821dbdf929cc0edea7
--- /dev/null
+++ b/vlm/dev/JavFPcsscd5/5.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a3923b5fbb87dfcfeb018a37a0bbe45cc6cc57139cd52ce1202b5122d91ef687
+size 583762
diff --git a/vlm/dev/JavFPcsscd5/6.png b/vlm/dev/JavFPcsscd5/6.png
new file mode 100644
index 0000000000000000000000000000000000000000..036a7cda2001af4709a5e7e70ba0f138b241d0ae
--- /dev/null
+++ b/vlm/dev/JavFPcsscd5/6.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8cc2d429aa3fdd8aa4bc708fc045a841095c07d4595a4c64816ccd2b7a7aad0b
+size 1015066
diff --git a/vlm/dev/JavFPcsscd5/7.png b/vlm/dev/JavFPcsscd5/7.png
new file mode 100644
index 0000000000000000000000000000000000000000..8c41c3c9fc3e99339a70edb359836a60a1fe59af
--- /dev/null
+++ b/vlm/dev/JavFPcsscd5/7.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0ff858c95ec6c0b813ff0f299a53a55a8f8bc4d317527c1c1734aac756188596
+size 715602
diff --git a/vlm/dev/JavFPcsscd5/8.png b/vlm/dev/JavFPcsscd5/8.png
new file mode 100644
index 0000000000000000000000000000000000000000..6f7bc52c63d9c6ec17e8b01035a5062b72945bba
--- /dev/null
+++ b/vlm/dev/JavFPcsscd5/8.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a66cc5724e744dc5dab1af97477309d23bfb65a098b3522528821246b29335b2
+size 549906
diff --git a/vlm/dev/JavFPcsscd5/9.png b/vlm/dev/JavFPcsscd5/9.png
new file mode 100644
index 0000000000000000000000000000000000000000..19e7328f257e7c0149d68623c9b8406eca2a5674
--- /dev/null
+++ b/vlm/dev/JavFPcsscd5/9.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c06c13d500e700624f199ba04e3d830a5e85166e778b04ff6bdefeb6d40ea3d5
+size 490309
diff --git a/vlm/dev/RKiWwhocuiU/0.png b/vlm/dev/RKiWwhocuiU/0.png
new file mode 100644
index 0000000000000000000000000000000000000000..015a6305af83f14bceb15e44d6a0ca4897a5bd70
--- /dev/null
+++ b/vlm/dev/RKiWwhocuiU/0.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a0e5a7ab5f437296c6ccf80e5a336f83f0a858037d646991e6be68c4fdb6392e
+size 509098
diff --git a/vlm/dev/RKiWwhocuiU/1.png b/vlm/dev/RKiWwhocuiU/1.png
new file mode 100644
index 0000000000000000000000000000000000000000..7c958da0ecaf86a2e7c2d2fe39ab44eaa00a3015
--- /dev/null
+++ b/vlm/dev/RKiWwhocuiU/1.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ea7dd9fbb7215567030015a51ad4f1c9cb976cc6224b209a073afef0c836a93c
+size 762171
diff --git a/vlm/dev/RKiWwhocuiU/10.png b/vlm/dev/RKiWwhocuiU/10.png
new file mode 100644
index 0000000000000000000000000000000000000000..24f53ab49e0d7332d6c8733e84ac8dc668a046b7
--- /dev/null
+++ b/vlm/dev/RKiWwhocuiU/10.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:46e97b3477f52e4ee8ed722b54517a7402ab29efa5ffe15b07c410633da72186
+size 555942
diff --git a/vlm/dev/RKiWwhocuiU/11.png b/vlm/dev/RKiWwhocuiU/11.png
new file mode 100644
index 0000000000000000000000000000000000000000..e2c0862dc9478993840718f9763cd8be5d8644cc
--- /dev/null
+++ b/vlm/dev/RKiWwhocuiU/11.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0fe4f7268c74643fe5a6be394462e17f0aff245a20a5f6ac9ca9de7be927dcaf
+size 544634
diff --git a/vlm/dev/RKiWwhocuiU/12.png b/vlm/dev/RKiWwhocuiU/12.png
new file mode 100644
index 0000000000000000000000000000000000000000..a5c985e81615621a756f5bc9f8fb7ae31569b7fa
--- /dev/null
+++ b/vlm/dev/RKiWwhocuiU/12.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a67e6c82268fef8d80b552ef0a2e6ddfc58b613b1191db7824a5d756601ebf04
+size 595503
diff --git a/vlm/dev/RKiWwhocuiU/13.png b/vlm/dev/RKiWwhocuiU/13.png
new file mode 100644
index 0000000000000000000000000000000000000000..22c994181046ae4fe8ecab48b1864dca45604307
--- /dev/null
+++ b/vlm/dev/RKiWwhocuiU/13.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:485756b9936dc0956ea93f129a7f2fe0a5f1e2d208944f27bbc4df95abd3c820
+size 549305
diff --git a/vlm/dev/RKiWwhocuiU/14.png b/vlm/dev/RKiWwhocuiU/14.png
new file mode 100644
index 0000000000000000000000000000000000000000..4abdaba2fd1316ee15fdedc20b66814479fcb6ee
--- /dev/null
+++ b/vlm/dev/RKiWwhocuiU/14.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:95ef69b574cf1de9860fc2149356e9bbb2911673671a879a96e96255c57278da
+size 496889
diff --git a/vlm/dev/RKiWwhocuiU/15.png b/vlm/dev/RKiWwhocuiU/15.png
new file mode 100644
index 0000000000000000000000000000000000000000..562a6100d4f28b7b7b3d00a516ec70f912939af7
--- /dev/null
+++ b/vlm/dev/RKiWwhocuiU/15.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7e478e548c28915c84bd8cf2aca859b92502fa168f8d01846324d1f12650beb7
+size 503642
diff --git a/vlm/dev/RKiWwhocuiU/16.png b/vlm/dev/RKiWwhocuiU/16.png
new file mode 100644
index 0000000000000000000000000000000000000000..8f992b4a8e73fc932482badc2db346f733623529
--- /dev/null
+++ b/vlm/dev/RKiWwhocuiU/16.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:560b626ae0844459aee18893a869985c791b2bb65b10d2f9137f5826dd8fbf60
+size 551371
diff --git a/vlm/dev/RKiWwhocuiU/17.png b/vlm/dev/RKiWwhocuiU/17.png
new file mode 100644
index 0000000000000000000000000000000000000000..ec25cdb27fdaa49c93310c81d5c0d3585f627e07
--- /dev/null
+++ b/vlm/dev/RKiWwhocuiU/17.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:191322a463410e6ffb870342d740048a651ab58fa181253ba5ebd38a4f2aa984
+size 341387
diff --git a/vlm/dev/RKiWwhocuiU/18.png b/vlm/dev/RKiWwhocuiU/18.png
new file mode 100644
index 0000000000000000000000000000000000000000..a193791e44b9fd6888a64525faa426724cb1e875
--- /dev/null
+++ b/vlm/dev/RKiWwhocuiU/18.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e24aad0f42aa2db2ac33ea72288c716f2cab0ce85cf200d5960866bfa8d2ceb9
+size 511103
diff --git a/vlm/dev/RKiWwhocuiU/19.png b/vlm/dev/RKiWwhocuiU/19.png
new file mode 100644
index 0000000000000000000000000000000000000000..52c502c98f8e47eec7f90cf4cf008ed3c5932a19
--- /dev/null
+++ b/vlm/dev/RKiWwhocuiU/19.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3fa1dc7d913c104a32fdd89fced86af0c0252341ca8a104e3dc52aa6309fad58
+size 427152
diff --git a/vlm/dev/RKiWwhocuiU/2.png b/vlm/dev/RKiWwhocuiU/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..8854fa589bf63ae8bc921240220024d33e6fe5e3
--- /dev/null
+++ b/vlm/dev/RKiWwhocuiU/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:45899dca1c24d3c28ff0368f448b6c3bc54246ccf8aa30aee6e404d002538191
+size 569587
diff --git a/vlm/dev/RKiWwhocuiU/20.png b/vlm/dev/RKiWwhocuiU/20.png
new file mode 100644
index 0000000000000000000000000000000000000000..b4fccc5079b5e032b596c5b75f24af5844c729b2
--- /dev/null
+++ b/vlm/dev/RKiWwhocuiU/20.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:330803247822d2265268d2402d65523044689aa8dcf7f0abc54fe309b0be621a
+size 36863
diff --git a/vlm/dev/RKiWwhocuiU/3.png b/vlm/dev/RKiWwhocuiU/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..e93e7b4c15252bc6791cf9c8bef09ffe33b8629c
--- /dev/null
+++ b/vlm/dev/RKiWwhocuiU/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fb8fd6af6377b50e49bc9fb1f982c1c38ab525042c4933dadc1b9db3777712b3
+size 584301
diff --git a/vlm/dev/RKiWwhocuiU/4.png b/vlm/dev/RKiWwhocuiU/4.png
new file mode 100644
index 0000000000000000000000000000000000000000..87c3dbeef772d4ad86c85dc1d8b8f28dd792906d
--- /dev/null
+++ b/vlm/dev/RKiWwhocuiU/4.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e5eb62177875ffb7895e8941113fc08921d7ad7f88ec45bd1ba78df387249b5c
+size 419174
diff --git a/vlm/dev/RKiWwhocuiU/5.png b/vlm/dev/RKiWwhocuiU/5.png
new file mode 100644
index 0000000000000000000000000000000000000000..66c2f70ee3996d8830288de9ac07ec54406e8cc3
--- /dev/null
+++ b/vlm/dev/RKiWwhocuiU/5.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9a01541b6d88ce302a334d38100cd45f224e9c1094647d2f9938bb2cba4ad02b
+size 573163
diff --git a/vlm/dev/RKiWwhocuiU/6.png b/vlm/dev/RKiWwhocuiU/6.png
new file mode 100644
index 0000000000000000000000000000000000000000..eba7c75092949e89c900a80bcf909131b8ec16b2
--- /dev/null
+++ b/vlm/dev/RKiWwhocuiU/6.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8cd04b6b266cb1dec1df87e203b4d85b68c740bc5a0d923361e38b5d36816b07
+size 619181
diff --git a/vlm/dev/RKiWwhocuiU/7.png b/vlm/dev/RKiWwhocuiU/7.png
new file mode 100644
index 0000000000000000000000000000000000000000..da29a3ea35cb9ce57e59c4ff84da13a287234adb
--- /dev/null
+++ b/vlm/dev/RKiWwhocuiU/7.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5945331539f97b33f46c382911328bbdb0a3ea111112954b2580409db5f96cf6
+size 601064
diff --git a/vlm/dev/RKiWwhocuiU/8.png b/vlm/dev/RKiWwhocuiU/8.png
new file mode 100644
index 0000000000000000000000000000000000000000..2919d52e96ecc1d2fa30dc5cd2bb749eba7509be
--- /dev/null
+++ b/vlm/dev/RKiWwhocuiU/8.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3d010e7fe757f35ae48432c24a4e94df5ba37e9fa2ac331c0025c765a6ebcca8
+size 612861
diff --git a/vlm/dev/RKiWwhocuiU/9.png b/vlm/dev/RKiWwhocuiU/9.png
new file mode 100644
index 0000000000000000000000000000000000000000..499c5fd83c909ec3cc499b72d551cdf3ffafb67c
--- /dev/null
+++ b/vlm/dev/RKiWwhocuiU/9.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9d6150bbc6f81f1b035e4f3b58dcb33f7a9f3422b48aa94ed5309e7b4cdb05bf
+size 515503
diff --git a/vlm/dev/RecZ9nB9Q4/16.png b/vlm/dev/RecZ9nB9Q4/16.png
new file mode 100644
index 0000000000000000000000000000000000000000..5a044adb97395da21c8192876c5e9286685a44cb
--- /dev/null
+++ b/vlm/dev/RecZ9nB9Q4/16.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e75a6ea8fd0e0b0a946805dfdab6f2a563b02484f063904c0f2cb4997d55a55a
+size 208671
diff --git a/vlm/dev/RecZ9nB9Q4/19.png b/vlm/dev/RecZ9nB9Q4/19.png
new file mode 100644
index 0000000000000000000000000000000000000000..505ecbe636691c6a638f584a8b4734a76b50c2df
--- /dev/null
+++ b/vlm/dev/RecZ9nB9Q4/19.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d8c9b9c257f93c5125289146d6de76959dbc735b6175aba972ab9821b044b265
+size 497853
diff --git a/vlm/dev/RecZ9nB9Q4/32.png b/vlm/dev/RecZ9nB9Q4/32.png
new file mode 100644
index 0000000000000000000000000000000000000000..43a32f5df8dbb5446278acd057853d4325459ee2
--- /dev/null
+++ b/vlm/dev/RecZ9nB9Q4/32.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e6f54fb44d794a26135f55f07f5fe77200f03665e696dce45090ad4510264b86
+size 319167
diff --git a/vlm/dev/S5wmbQc1We/0.png b/vlm/dev/S5wmbQc1We/0.png
new file mode 100644
index 0000000000000000000000000000000000000000..4ea14404c87a96b9b7efd0badb90ad196b090e4c
--- /dev/null
+++ b/vlm/dev/S5wmbQc1We/0.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:84d0c0dfec799f03bd5b87dae1b97324604697ebaefe93111c3b42b7acb36bb2
+size 442401
diff --git a/vlm/dev/S5wmbQc1We/1.png b/vlm/dev/S5wmbQc1We/1.png
new file mode 100644
index 0000000000000000000000000000000000000000..420425a00a043cc4e1d9bc80acad813121d72521
--- /dev/null
+++ b/vlm/dev/S5wmbQc1We/1.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b670568ff1342dcb037243ba11d66d4835503fd5932eab7410cca3cd91ea345b
+size 486479
diff --git a/vlm/dev/S5wmbQc1We/10.png b/vlm/dev/S5wmbQc1We/10.png
new file mode 100644
index 0000000000000000000000000000000000000000..c54efb2fecd3a6c77301bd498ad584e5d45658c2
--- /dev/null
+++ b/vlm/dev/S5wmbQc1We/10.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:55dbea1d6cbb204c0eb53622fb1730db3cd3f2cc044326a178fdcda7b7e6d751
+size 633782
diff --git a/vlm/dev/S5wmbQc1We/11.png b/vlm/dev/S5wmbQc1We/11.png
new file mode 100644
index 0000000000000000000000000000000000000000..43a892b5e1d75af7df6634bbb2146cd94cf55159
--- /dev/null
+++ b/vlm/dev/S5wmbQc1We/11.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:90334a6437edd2ba804d63e31ffb9520ade4f31bef3f4e4ec2f1b2e2075911d2
+size 340544
diff --git a/vlm/dev/S5wmbQc1We/12.png b/vlm/dev/S5wmbQc1We/12.png
new file mode 100644
index 0000000000000000000000000000000000000000..7dff7445294a98e758727002426e9b75e3694e86
--- /dev/null
+++ b/vlm/dev/S5wmbQc1We/12.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:312af12105454ca5ebcc1c683487c12f37ae8a2a38ec6228bb1d7687e57cf709
+size 355799
diff --git a/vlm/dev/S5wmbQc1We/13.png b/vlm/dev/S5wmbQc1We/13.png
new file mode 100644
index 0000000000000000000000000000000000000000..1d67f2d40bc7ba1b17b219846f469b02a606902c
--- /dev/null
+++ b/vlm/dev/S5wmbQc1We/13.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a5f45c32088825573f67d9dfbd3da1e5c38914f1386bff72b19c74359adfdb20
+size 450712
diff --git a/vlm/dev/S5wmbQc1We/14.png b/vlm/dev/S5wmbQc1We/14.png
new file mode 100644
index 0000000000000000000000000000000000000000..49b90d23f8dbad75b7926152b7889bbc68cff8d8
--- /dev/null
+++ b/vlm/dev/S5wmbQc1We/14.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1544d06eaa2391af81ee9424e84892ee842d142decab807dfebd8705f52d7853
+size 722289
diff --git a/vlm/dev/S5wmbQc1We/15.png b/vlm/dev/S5wmbQc1We/15.png
new file mode 100644
index 0000000000000000000000000000000000000000..4774b102f560778a99139f9e781ab90db88e5317
--- /dev/null
+++ b/vlm/dev/S5wmbQc1We/15.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c46b467d816128d65328314e760b7ac87808b3acab17c563e35afa6098ee05b2
+size 656929
diff --git a/vlm/dev/S5wmbQc1We/16.png b/vlm/dev/S5wmbQc1We/16.png
new file mode 100644
index 0000000000000000000000000000000000000000..8c8cefa287a2a412fd8139ea8872bbe1c5086297
--- /dev/null
+++ b/vlm/dev/S5wmbQc1We/16.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:05ec8c996f10cd8563306020fcf65fd2bb327f022e0d499336b0d1919535641e
+size 609569
diff --git a/vlm/dev/S5wmbQc1We/17.png b/vlm/dev/S5wmbQc1We/17.png
new file mode 100644
index 0000000000000000000000000000000000000000..9cc5503ebc0081cd4e139716eaf6ce1f8f0cb9c1
--- /dev/null
+++ b/vlm/dev/S5wmbQc1We/17.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3da8250a0d344302d523873cdc95b424f728710ea0a745d98a0fbb272ba67008
+size 444115
diff --git a/vlm/dev/S5wmbQc1We/18.png b/vlm/dev/S5wmbQc1We/18.png
new file mode 100644
index 0000000000000000000000000000000000000000..119920ff7e5de805d773b8a163b92b9b355f86bf
--- /dev/null
+++ b/vlm/dev/S5wmbQc1We/18.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c49276898a30a1903d316de4c3b1ce9cfa7de2201776f925250a535dd21e79d3
+size 761710
diff --git a/vlm/dev/S5wmbQc1We/19.png b/vlm/dev/S5wmbQc1We/19.png
new file mode 100644
index 0000000000000000000000000000000000000000..8f2caf7995506c07adfe44ca2b669c69fdd28be7
--- /dev/null
+++ b/vlm/dev/S5wmbQc1We/19.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e1e3c78aadb5132fba4e77a71d4878dcb16867b6ca2c9634d7150664a990e936
+size 411952
diff --git a/vlm/dev/S5wmbQc1We/2.png b/vlm/dev/S5wmbQc1We/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..dca605bf04adca87a0183fd6f8fd974940394e89
--- /dev/null
+++ b/vlm/dev/S5wmbQc1We/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ffdea256f4e1228d944568d64027d0624a48a6413d738d41376cc83696d7717a
+size 498871
diff --git a/vlm/dev/S5wmbQc1We/20.png b/vlm/dev/S5wmbQc1We/20.png
new file mode 100644
index 0000000000000000000000000000000000000000..76bf889b0a104d7ccce8cbd0a98ad7772ef84737
--- /dev/null
+++ b/vlm/dev/S5wmbQc1We/20.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5d664e30b48cda6be743b56427a5ea46a1ff51aac389e6453869069cbdce0b66
+size 606897
diff --git a/vlm/dev/S5wmbQc1We/21.png b/vlm/dev/S5wmbQc1We/21.png
new file mode 100644
index 0000000000000000000000000000000000000000..b3c516c9c00d472519568151f5de61c24bc8032e
--- /dev/null
+++ b/vlm/dev/S5wmbQc1We/21.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ba28eee704cd990cc29251ff2dca4f9514751ab8617ead9a816244b80d41bde2
+size 469185
diff --git a/vlm/dev/S5wmbQc1We/22.png b/vlm/dev/S5wmbQc1We/22.png
new file mode 100644
index 0000000000000000000000000000000000000000..0ca24348265a20737bf011eb3d0128640176a767
--- /dev/null
+++ b/vlm/dev/S5wmbQc1We/22.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:58f39fc97b529ff83bb87b8aff4b36c4d3d72746942cf917798b47d82006653d
+size 678154
diff --git a/vlm/dev/S5wmbQc1We/23.png b/vlm/dev/S5wmbQc1We/23.png
new file mode 100644
index 0000000000000000000000000000000000000000..86f93befbee8d449dd87337548fc154e0085737b
--- /dev/null
+++ b/vlm/dev/S5wmbQc1We/23.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2197cc2abf6e3f9ec4eca98dcca782bffeb542924cda89615977d187c0ad95c0
+size 1379131
diff --git a/vlm/dev/S5wmbQc1We/24.png b/vlm/dev/S5wmbQc1We/24.png
new file mode 100644
index 0000000000000000000000000000000000000000..43e2270eccf6ebb322328fc0497dd607f067f0a3
--- /dev/null
+++ b/vlm/dev/S5wmbQc1We/24.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bf1bc56f6a425c361800b11f09a837837435cf918a1eebccd200dfaf3172c1d2
+size 484040
diff --git a/vlm/dev/S5wmbQc1We/25.png b/vlm/dev/S5wmbQc1We/25.png
new file mode 100644
index 0000000000000000000000000000000000000000..7df11aa55110175c30a3f8849eb91046aa327773
--- /dev/null
+++ b/vlm/dev/S5wmbQc1We/25.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ab2ee7e379a7f5f48fa0611cd3a6e3b4125f52d1c60c65f7a3fb0fa9878617d5
+size 524990
diff --git a/vlm/dev/S5wmbQc1We/26.png b/vlm/dev/S5wmbQc1We/26.png
new file mode 100644
index 0000000000000000000000000000000000000000..3457809c1d4227f7a988f03afea2aac64d685e48
--- /dev/null
+++ b/vlm/dev/S5wmbQc1We/26.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:dea0a3b36eb27fe8626f80cad9ed6f3b0ebd35db80b7764d962be2c50e1709e4
+size 507334
diff --git a/vlm/dev/S5wmbQc1We/27.png b/vlm/dev/S5wmbQc1We/27.png
new file mode 100644
index 0000000000000000000000000000000000000000..a0ad6b5ff9cbc62ab3f8469b53b4218b4a14124e
--- /dev/null
+++ b/vlm/dev/S5wmbQc1We/27.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8c13ea515626853a263db0341a90a74732a05445c5e822496d03a8f4946c57c0
+size 67814
diff --git a/vlm/dev/S5wmbQc1We/3.png b/vlm/dev/S5wmbQc1We/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..d8ffba3d6652a4be3ab864b89a4a9307e8d14fd1
--- /dev/null
+++ b/vlm/dev/S5wmbQc1We/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:803ac46b45bfb68a30babbc623c4d3d721664a6cc01cb24fd0530a390c186cd6
+size 632446
diff --git a/vlm/dev/S5wmbQc1We/4.png b/vlm/dev/S5wmbQc1We/4.png
new file mode 100644
index 0000000000000000000000000000000000000000..a59a14753968ee2c34728a5bb3de2cde26246d9e
--- /dev/null
+++ b/vlm/dev/S5wmbQc1We/4.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3429e3d45bd6d1ef1a6655997b52854a041faa5f748301136c73de3aa188ba7e
+size 777776
diff --git a/vlm/dev/S5wmbQc1We/5.png b/vlm/dev/S5wmbQc1We/5.png
new file mode 100644
index 0000000000000000000000000000000000000000..ac861d0f7676e2445b842917e55025e094e83e70
--- /dev/null
+++ b/vlm/dev/S5wmbQc1We/5.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1f01e048421aed0a7b3826af318a3b6e7b000ff856b3cf63e7f1836f55adf177
+size 762453
diff --git a/vlm/dev/S5wmbQc1We/6.png b/vlm/dev/S5wmbQc1We/6.png
new file mode 100644
index 0000000000000000000000000000000000000000..b908879f169c508a7835f89a1b468d0b17fe5e65
--- /dev/null
+++ b/vlm/dev/S5wmbQc1We/6.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4bf81c1f05cdeb82171911e8b4eaf4344f6bb25dadf1412993631ce0beec4d80
+size 494789
diff --git a/vlm/dev/S5wmbQc1We/7.png b/vlm/dev/S5wmbQc1We/7.png
new file mode 100644
index 0000000000000000000000000000000000000000..837be7ae0ca307819830903873275262bfbd38f7
--- /dev/null
+++ b/vlm/dev/S5wmbQc1We/7.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3bb28b8ef2ab0ceebc8ab2c0fa664331c01e3d51920cd1d4c8fcb3e4402dc8ff
+size 518497
diff --git a/vlm/dev/S5wmbQc1We/8.png b/vlm/dev/S5wmbQc1We/8.png
new file mode 100644
index 0000000000000000000000000000000000000000..3e4725ad1494cb38ea31a0c87983aecfc94866fe
--- /dev/null
+++ b/vlm/dev/S5wmbQc1We/8.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3ea243293d03d421382f310cd3f6b89e5fef4e6a901384d8b3ac5a798e9cfed9
+size 787008
diff --git a/vlm/dev/S5wmbQc1We/9.png b/vlm/dev/S5wmbQc1We/9.png
new file mode 100644
index 0000000000000000000000000000000000000000..1b7bd9bab03f64c9135af2e24ab2ab0814a2a56f
--- /dev/null
+++ b/vlm/dev/S5wmbQc1We/9.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d1e931c86e8c92043f033f50d126515d2a084efefb35bf39c4408ed09252ac3d
+size 529101
diff --git a/vlm/dev/S9GpoS2TmN/0.png b/vlm/dev/S9GpoS2TmN/0.png
new file mode 100644
index 0000000000000000000000000000000000000000..e31a8e5b62f755e8aad2a1a3be3c8e6862e8df93
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/0.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:94d547225f3e2ca1e4933f754aa63fa8de53500055ffcd8724ff491196f922e9
+size 505600
diff --git a/vlm/dev/S9GpoS2TmN/1.png b/vlm/dev/S9GpoS2TmN/1.png
new file mode 100644
index 0000000000000000000000000000000000000000..07365c3e0bf477ec2b650aec10453bd6f580abc1
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/1.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b8ad8873ccdf3483e14598a6e19ae13d02091304f0f98b30d8a8ab73c3efe968
+size 583566
diff --git a/vlm/dev/S9GpoS2TmN/10.png b/vlm/dev/S9GpoS2TmN/10.png
new file mode 100644
index 0000000000000000000000000000000000000000..c27aac7826dfcc8716a1c9ca512199e1428872fe
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/10.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:99c585b09113f8bc0a455482769d492bdcb1665a4a50f82a06486278c50579e2
+size 552981
diff --git a/vlm/dev/S9GpoS2TmN/11.png b/vlm/dev/S9GpoS2TmN/11.png
new file mode 100644
index 0000000000000000000000000000000000000000..ff2ccf9bcc309f9002b7acc659dfee8e589c67ab
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/11.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a4c92310f5bdf372160260b25d414efe6667939e922398f7a1b2dc61d81cc4ad
+size 571623
diff --git a/vlm/dev/S9GpoS2TmN/12.png b/vlm/dev/S9GpoS2TmN/12.png
new file mode 100644
index 0000000000000000000000000000000000000000..ca7527e5e46f9854b1b3bbd12ed2c13c9f8dfe11
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/12.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a0d1afaf1db4b7adc1b8c6b25ffa25910e5a06b37e9651cfec6da8026dd0c6cc
+size 547658
diff --git a/vlm/dev/S9GpoS2TmN/13.png b/vlm/dev/S9GpoS2TmN/13.png
new file mode 100644
index 0000000000000000000000000000000000000000..d8c6219eaa44e89c538f8d3ec20767d2e4cd1bef
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/13.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:499658f9714c8a20f13684a6449b93f5e3c0110be18a9fd708523a6cc82fdf74
+size 494225
diff --git a/vlm/dev/S9GpoS2TmN/14.png b/vlm/dev/S9GpoS2TmN/14.png
new file mode 100644
index 0000000000000000000000000000000000000000..334e5da889b09e6cc488bc12682a9523ae05667f
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/14.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:662f3aab4b605b44b50a2af26031233d1211292c36c66cc51766a983c00e7608
+size 175981
diff --git a/vlm/dev/S9GpoS2TmN/15.png b/vlm/dev/S9GpoS2TmN/15.png
new file mode 100644
index 0000000000000000000000000000000000000000..bb6d5fdea6aed2abe6fcafc00d67957a32c56d40
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/15.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:965d2367498ed1d43787fcb80dc0e9e62584ff6e0c247e3bc12eece947ada421
+size 456225
diff --git a/vlm/dev/S9GpoS2TmN/16.png b/vlm/dev/S9GpoS2TmN/16.png
new file mode 100644
index 0000000000000000000000000000000000000000..96603dd98ebd5e3f0a93cde4f9cf63ee2e44fea2
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/16.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a18e7829b52074e4f99ad066bfb372c33db43a12b50da0e62a16a1b72636e692
+size 1251660
diff --git a/vlm/dev/S9GpoS2TmN/17.png b/vlm/dev/S9GpoS2TmN/17.png
new file mode 100644
index 0000000000000000000000000000000000000000..2c62525812a8568bbab68ee78aa340729cb38328
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/17.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:73481a0ad2764dd08be5423e639af8aaa0ce28310c26f14b839518857d4e2e91
+size 524658
diff --git a/vlm/dev/S9GpoS2TmN/18.png b/vlm/dev/S9GpoS2TmN/18.png
new file mode 100644
index 0000000000000000000000000000000000000000..b83043c1db7197f678d087fbafca6d182d7a6eb8
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/18.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4063e88cb9d287944ca8d3c78d048f5ede388a2cad7e06a8aa27f9d437082298
+size 321961
diff --git a/vlm/dev/S9GpoS2TmN/19.png b/vlm/dev/S9GpoS2TmN/19.png
new file mode 100644
index 0000000000000000000000000000000000000000..b0c52fa34a7fb3fdd2aa0d208c8305e8439cafa1
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/19.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4039103cb7a320720d4dae2352ad39a1e49eb5b122bec23b3af7c4279a0a236c
+size 504993
diff --git a/vlm/dev/S9GpoS2TmN/2.png b/vlm/dev/S9GpoS2TmN/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..72ce6bc6a78bd16da3be879694963c3a57f625c9
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8e70da6af50b1d35fd0163229fa9ddffcf7507cf7c273a1c8176639bb3230fc5
+size 610975
diff --git a/vlm/dev/S9GpoS2TmN/20.png b/vlm/dev/S9GpoS2TmN/20.png
new file mode 100644
index 0000000000000000000000000000000000000000..454b1e9db6201bbef68eade034ca6928fa48ecb8
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/20.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:dbf5090d544812e4ea8900974f29c02f0f37b72969df2edb87c48e9ed4b2eb83
+size 265866
diff --git a/vlm/dev/S9GpoS2TmN/21.png b/vlm/dev/S9GpoS2TmN/21.png
new file mode 100644
index 0000000000000000000000000000000000000000..ae89d52cb07d1844afc325e3ba497e643772d3e4
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/21.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:91e7150fbf8385bd9ea49aec58ae46567f209d608203397281bbad7190d8c631
+size 478473
diff --git a/vlm/dev/S9GpoS2TmN/22.png b/vlm/dev/S9GpoS2TmN/22.png
new file mode 100644
index 0000000000000000000000000000000000000000..eeddab47abe156f694b45c2e64ab50446e24dd1f
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/22.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4cb3daeb7252f1b4467e71ebb724fc50522d7645ec1d30c925cf38ded049ec21
+size 290586
diff --git a/vlm/dev/S9GpoS2TmN/23.png b/vlm/dev/S9GpoS2TmN/23.png
new file mode 100644
index 0000000000000000000000000000000000000000..052ed8c69eb70002b776468077f1bc455b4df080
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/23.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cdbaaa9ac00c40c5bcc4755bd7dbe49c60b7f56f2a886dd4751fb9ca22bc3722
+size 334145
diff --git a/vlm/dev/S9GpoS2TmN/24.png b/vlm/dev/S9GpoS2TmN/24.png
new file mode 100644
index 0000000000000000000000000000000000000000..7712a7088d82756bbcd84a7a630ce5f144c62981
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/24.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7eca09f48cfcbb9794b69c4052bf18f4dc93c90801a718b1b22bfed5175e19d2
+size 402600
diff --git a/vlm/dev/S9GpoS2TmN/25.png b/vlm/dev/S9GpoS2TmN/25.png
new file mode 100644
index 0000000000000000000000000000000000000000..0474686a0ffaa56a6d6c19c64100234c4b978816
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/25.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7a13559e628dc710cf68d8dc0ca0635c2931c41c2b743bce8af01f3afc4c86db
+size 427143
diff --git a/vlm/dev/S9GpoS2TmN/26.png b/vlm/dev/S9GpoS2TmN/26.png
new file mode 100644
index 0000000000000000000000000000000000000000..1b83a06b9074a70653539bbb80a96cddb17fd4dd
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/26.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:efe1912aa0add3c772639f1a4eee5e40c9abeebb6729181505006f3eae7d44e9
+size 412362
diff --git a/vlm/dev/S9GpoS2TmN/27.png b/vlm/dev/S9GpoS2TmN/27.png
new file mode 100644
index 0000000000000000000000000000000000000000..bdda84ac7ef67ed58748fd43fadb327ad1e0aae8
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/27.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c7c6bfcf963d257ae5221a4b8873a3a3e728b6d165212cfa77c1b151349d2f7b
+size 627175
diff --git a/vlm/dev/S9GpoS2TmN/28.png b/vlm/dev/S9GpoS2TmN/28.png
new file mode 100644
index 0000000000000000000000000000000000000000..0b12a75ebbddb8dfbe0cf4219a318ea49e50befc
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/28.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d8f726c28a7af219dfe64bb2f1965d61874f76a2559e5e65a6c9947298eb3b4f
+size 488497
diff --git a/vlm/dev/S9GpoS2TmN/29.png b/vlm/dev/S9GpoS2TmN/29.png
new file mode 100644
index 0000000000000000000000000000000000000000..9caa0d80c5d91b036de7fd592b5f3331ea83ae3c
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/29.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:afa619588f5ab97b07e897848ba30447e744fd54fcf262788a7663cc68b2a4a9
+size 428489
diff --git a/vlm/dev/S9GpoS2TmN/3.png b/vlm/dev/S9GpoS2TmN/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..615d90f7b845f1b45ad4cb63a12b0747db70073d
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:559a13845cfd4543cce5e38ab13b2d365a68ac7b9b7838d32991a29de99ba286
+size 633408
diff --git a/vlm/dev/S9GpoS2TmN/30.png b/vlm/dev/S9GpoS2TmN/30.png
new file mode 100644
index 0000000000000000000000000000000000000000..a2de0d666772b9e08f6de2aeea53c439d055305d
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/30.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:447038a1b64c98f36ca821406f3d0a47013b18bbed4dc9ea74cbe1dea6b34c5b
+size 254230
diff --git a/vlm/dev/S9GpoS2TmN/31.png b/vlm/dev/S9GpoS2TmN/31.png
new file mode 100644
index 0000000000000000000000000000000000000000..4e6632c49843b00a0fb12615708851624e2bd2aa
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/31.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e80d30e074f78b79f676699332d2998f71d6d9dcdcb73e90513be551fde33d05
+size 352221
diff --git a/vlm/dev/S9GpoS2TmN/32.png b/vlm/dev/S9GpoS2TmN/32.png
new file mode 100644
index 0000000000000000000000000000000000000000..23027d4cc307010f8d0e5bf54a739f5ba2b86e14
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/32.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1753c8aa8562df9a4fa90884746a6b7a6919e39b2186c1e7a0e9c8ad29b66500
+size 224910
diff --git a/vlm/dev/S9GpoS2TmN/33.png b/vlm/dev/S9GpoS2TmN/33.png
new file mode 100644
index 0000000000000000000000000000000000000000..fc81845787416f95ef58ae140da4039ffce8095e
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/33.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2c40847d528d0ba7687c4020bd51f6f72de761f71f1a6dc366fd74bb82515506
+size 445363
diff --git a/vlm/dev/S9GpoS2TmN/34.png b/vlm/dev/S9GpoS2TmN/34.png
new file mode 100644
index 0000000000000000000000000000000000000000..9e583628eb1226b73a6f8148cc70cec71cdc8297
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/34.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:936bafd9ba01363cf79ae7dd0de56451cd4a5f264a84d3011625f856b44d678b
+size 276633
diff --git a/vlm/dev/S9GpoS2TmN/4.png b/vlm/dev/S9GpoS2TmN/4.png
new file mode 100644
index 0000000000000000000000000000000000000000..0bb41e330de39a89275484dba47600e2c0f481c4
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/4.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:47e0641906c753a23ee5439f671ffcf65731ad1f8ce226adf7890e619f820b27
+size 566456
diff --git a/vlm/dev/S9GpoS2TmN/5.png b/vlm/dev/S9GpoS2TmN/5.png
new file mode 100644
index 0000000000000000000000000000000000000000..b1626fd68a47cdd9596af5d940ffc9d56cd2e230
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/5.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2d00ba50bc89b70795f9c51876706bbcc79fdffc50a36a8ca4d775bd81e408e1
+size 562659
diff --git a/vlm/dev/S9GpoS2TmN/6.png b/vlm/dev/S9GpoS2TmN/6.png
new file mode 100644
index 0000000000000000000000000000000000000000..9a1771742e84309f8ee09bc45dc06db2599f5d34
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/6.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:979035efdf6ac8da62eb875ac641b36f176c38b0a3a02e0642a163b3923ddf60
+size 553726
diff --git a/vlm/dev/S9GpoS2TmN/7.png b/vlm/dev/S9GpoS2TmN/7.png
new file mode 100644
index 0000000000000000000000000000000000000000..da27c7d7b543640d6105c3c766fdfee99c29371f
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/7.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:adbb0baf06d7d6ebb88af70488e797d48d8a48a3bacd81a4f49816bda012b1e8
+size 563557
diff --git a/vlm/dev/S9GpoS2TmN/8.png b/vlm/dev/S9GpoS2TmN/8.png
new file mode 100644
index 0000000000000000000000000000000000000000..c8ad03070b6ca555a539ff63115e7e8898dda91a
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/8.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1f728b666e573490149b064a89d983d6634cee0927dbf1390dd4d8423b8cb530
+size 449659
diff --git a/vlm/dev/S9GpoS2TmN/9.png b/vlm/dev/S9GpoS2TmN/9.png
new file mode 100644
index 0000000000000000000000000000000000000000..2a29cbf5aa920bd66c4331256a61cf6329c7908b
--- /dev/null
+++ b/vlm/dev/S9GpoS2TmN/9.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cb437eafc6c8e4821597d421f8f1d2e2a0dab94421fad31233902191f89f1d19
+size 117602
diff --git a/vlm/dev/SMa9EAovKMC/0.png b/vlm/dev/SMa9EAovKMC/0.png
new file mode 100644
index 0000000000000000000000000000000000000000..4dc65eff40469efcb449ccd819b3d359c3f3eb0f
--- /dev/null
+++ b/vlm/dev/SMa9EAovKMC/0.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c2c0fee7381e2139d30db7798798f09fad019f3e345384d7defad0413e7f80d2
+size 527958
diff --git a/vlm/dev/SMa9EAovKMC/1.png b/vlm/dev/SMa9EAovKMC/1.png
new file mode 100644
index 0000000000000000000000000000000000000000..165cb7ce3ce65129a448762d67643ba5792b813e
--- /dev/null
+++ b/vlm/dev/SMa9EAovKMC/1.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:529e5743a7430da7e099a42a902a08c1b4158b2542fa75d77337f424101ba824
+size 592786
diff --git a/vlm/dev/SMa9EAovKMC/10.png b/vlm/dev/SMa9EAovKMC/10.png
new file mode 100644
index 0000000000000000000000000000000000000000..dc703ef929bc08febc90e08b8a1a3645e6812101
--- /dev/null
+++ b/vlm/dev/SMa9EAovKMC/10.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f84701fd94894e0f693da5ebddc4e54c22dc3c1f61e713939d0a080749453ad4
+size 606931
diff --git a/vlm/dev/SMa9EAovKMC/11.png b/vlm/dev/SMa9EAovKMC/11.png
new file mode 100644
index 0000000000000000000000000000000000000000..7e20b079fda8ae8e9586455f77e78449af37fbd1
--- /dev/null
+++ b/vlm/dev/SMa9EAovKMC/11.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:103bb5896cd482d8097a1bbe34d48c070865668b16be8eb2bd949167aa000a3d
+size 622996
diff --git a/vlm/dev/SMa9EAovKMC/12.png b/vlm/dev/SMa9EAovKMC/12.png
new file mode 100644
index 0000000000000000000000000000000000000000..1a37d87f7a5f95e75fce05ec124937e8e132bd67
--- /dev/null
+++ b/vlm/dev/SMa9EAovKMC/12.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1fea0af6734346f2a3fe60ad62ac1c97adf3b2cbff86ba82be4569b43c4d2ae1
+size 298111
diff --git a/vlm/dev/SMa9EAovKMC/13.png b/vlm/dev/SMa9EAovKMC/13.png
new file mode 100644
index 0000000000000000000000000000000000000000..64f5d62f1ddbeb7897997726cab37a5b40572973
--- /dev/null
+++ b/vlm/dev/SMa9EAovKMC/13.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:577132acdc0dcf0f20410eb5500f149632a87fa517886c334fe4c013f6f8c52f
+size 488660
diff --git a/vlm/dev/SMa9EAovKMC/14.png b/vlm/dev/SMa9EAovKMC/14.png
new file mode 100644
index 0000000000000000000000000000000000000000..6e8cf525b3f5c7a4a305703e347b7940fee70c04
--- /dev/null
+++ b/vlm/dev/SMa9EAovKMC/14.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:889df542dfb4be9b79b0843665b029734c2b68b0b5ac50b7df8ec36d5afc587a
+size 148976
diff --git a/vlm/dev/SMa9EAovKMC/15.png b/vlm/dev/SMa9EAovKMC/15.png
new file mode 100644
index 0000000000000000000000000000000000000000..3d8c894ffcbf87b42dcedc3b6d55e02642047f36
--- /dev/null
+++ b/vlm/dev/SMa9EAovKMC/15.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:edbf4175568c2810239436e5f0d851a008081b8de0e2679a532f9dda579a4ee6
+size 203276
diff --git a/vlm/dev/SMa9EAovKMC/16.png b/vlm/dev/SMa9EAovKMC/16.png
new file mode 100644
index 0000000000000000000000000000000000000000..a8d6040e69d7f284870729cdbef631139d212b6f
--- /dev/null
+++ b/vlm/dev/SMa9EAovKMC/16.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:526c7c6de7214f982d19aa5f1103c6b382fdb27e604893e73957ea35ce53db47
+size 303865
diff --git a/vlm/dev/SMa9EAovKMC/17.png b/vlm/dev/SMa9EAovKMC/17.png
new file mode 100644
index 0000000000000000000000000000000000000000..eb8bb7ce98a461b719e5f0bdbc54d38ed9a779d0
--- /dev/null
+++ b/vlm/dev/SMa9EAovKMC/17.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:34be60830986089508725709f7542f2072a298a73121e99c99bbdc56aefbef80
+size 496984
diff --git a/vlm/dev/SMa9EAovKMC/18.png b/vlm/dev/SMa9EAovKMC/18.png
new file mode 100644
index 0000000000000000000000000000000000000000..61a6e6a3ed1c2fb2bd27d6d33a00e9e9af47a3f9
--- /dev/null
+++ b/vlm/dev/SMa9EAovKMC/18.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bd98e7f823eb5182cd23030bf61462fbce1f3174d2d2ad58217e83995fe91cb4
+size 524938
diff --git a/vlm/dev/SMa9EAovKMC/2.png b/vlm/dev/SMa9EAovKMC/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..662deebfaca6baa594ac69df1b7368589c7bb8b0
--- /dev/null
+++ b/vlm/dev/SMa9EAovKMC/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b55200984487b178080b7839190fd312807734fecdb2bed365d9eb7d2a41a93a
+size 617050
diff --git a/vlm/dev/SMa9EAovKMC/3.png b/vlm/dev/SMa9EAovKMC/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..80c6f8fc5be4bed6200ca3ea2ab695219dd72be4
--- /dev/null
+++ b/vlm/dev/SMa9EAovKMC/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:14e31594eadeb12a0a6d62f61a3e0d2a29d4bd3d7c88af16a74a8ebc0aee9aa7
+size 517828
diff --git a/vlm/dev/SMa9EAovKMC/4.png b/vlm/dev/SMa9EAovKMC/4.png
new file mode 100644
index 0000000000000000000000000000000000000000..21461c5a6ef789383ab5aa35064ea449511ff7ff
--- /dev/null
+++ b/vlm/dev/SMa9EAovKMC/4.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bdc59b620be69c872f6a9e2884eb400490cbc8e104c52a192e8789beb350e6c3
+size 646783
diff --git a/vlm/dev/SMa9EAovKMC/5.png b/vlm/dev/SMa9EAovKMC/5.png
new file mode 100644
index 0000000000000000000000000000000000000000..c49bab4ab21c2b10a130828186b84331942aaf09
--- /dev/null
+++ b/vlm/dev/SMa9EAovKMC/5.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c3cf63f71e51f2f31d0c0be04c4af18d39511ab9a2581661ed3b3e2f948cf3b1
+size 552498
diff --git a/vlm/dev/SMa9EAovKMC/6.png b/vlm/dev/SMa9EAovKMC/6.png
new file mode 100644
index 0000000000000000000000000000000000000000..814589b55ec929923fb4c515cdfbb5cb473fcfc1
--- /dev/null
+++ b/vlm/dev/SMa9EAovKMC/6.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5345c3b144ae5c20377413893095932a36fecbcec931df24be20c0ff7fb69ab8
+size 604114
diff --git a/vlm/dev/SMa9EAovKMC/7.png b/vlm/dev/SMa9EAovKMC/7.png
new file mode 100644
index 0000000000000000000000000000000000000000..c844dd91ef28f813783015c383fbbc344b6ec95e
--- /dev/null
+++ b/vlm/dev/SMa9EAovKMC/7.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9d243c010d950068f5e36df9b88412b8212275a382f6fe043d25f2a85a2a3805
+size 465620
diff --git a/vlm/dev/SMa9EAovKMC/8.png b/vlm/dev/SMa9EAovKMC/8.png
new file mode 100644
index 0000000000000000000000000000000000000000..ca3d08222a88aefa6163830de89d550c8a38ca08
--- /dev/null
+++ b/vlm/dev/SMa9EAovKMC/8.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b7c56324687d2febc07343634e0463e12cdf6b48278fd16069cd53cf76bdb065
+size 565572
diff --git a/vlm/dev/SMa9EAovKMC/9.png b/vlm/dev/SMa9EAovKMC/9.png
new file mode 100644
index 0000000000000000000000000000000000000000..90e4453f579a48836be9b9411eec7c80823387be
--- /dev/null
+++ b/vlm/dev/SMa9EAovKMC/9.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d453dd3a7da2942ecec668832d5c999c621bef9917035af1fcf5f0d3905afad1
+size 599350
diff --git a/vlm/dev/SVBR6xBaMl/0.png b/vlm/dev/SVBR6xBaMl/0.png
new file mode 100644
index 0000000000000000000000000000000000000000..e2f5ff974397db3fa5056aa452311a9b8706561e
--- /dev/null
+++ b/vlm/dev/SVBR6xBaMl/0.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a4bbd85ac91902a16d2087392bc9f0c5c00b50ebe9b4404e8d6c6894ac7fba1b
+size 456886
diff --git a/vlm/dev/SVBR6xBaMl/1.png b/vlm/dev/SVBR6xBaMl/1.png
new file mode 100644
index 0000000000000000000000000000000000000000..9a974419464a37097ac5460b8ebb5e2b7bc6f61d
--- /dev/null
+++ b/vlm/dev/SVBR6xBaMl/1.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:aa8bf14fc9700411bedbe10cf184d2d2a80e6a899d36ded6317199a2fa2f8ab6
+size 661697
diff --git a/vlm/dev/SVBR6xBaMl/10.png b/vlm/dev/SVBR6xBaMl/10.png
new file mode 100644
index 0000000000000000000000000000000000000000..9a297597ca78dd8f007d487779b7856d339481c6
--- /dev/null
+++ b/vlm/dev/SVBR6xBaMl/10.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:44d5a7332e75ecaa73801dc65fee8760b5d2517015ff85e2a205cd23b5d710c6
+size 571047
diff --git a/vlm/dev/SVBR6xBaMl/11.png b/vlm/dev/SVBR6xBaMl/11.png
new file mode 100644
index 0000000000000000000000000000000000000000..e64fe7bdb105f07d966b4baaee65708fc1349a7c
--- /dev/null
+++ b/vlm/dev/SVBR6xBaMl/11.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0c7e241583d237344dbda43487633a58cd1b8984074887a3f962d394bdccfc71
+size 582470
diff --git a/vlm/dev/SVBR6xBaMl/12.png b/vlm/dev/SVBR6xBaMl/12.png
new file mode 100644
index 0000000000000000000000000000000000000000..1ec902ee02bc7142423fd0ace02eb5a8075c1c09
--- /dev/null
+++ b/vlm/dev/SVBR6xBaMl/12.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:786bb4518a236ed724e9faf563858638cc7733972794a9ee1d48badc28e48fe1
+size 590039
diff --git a/vlm/dev/SVBR6xBaMl/13.png b/vlm/dev/SVBR6xBaMl/13.png
new file mode 100644
index 0000000000000000000000000000000000000000..26f5911aefc5866c744af26d1802e411984e412c
--- /dev/null
+++ b/vlm/dev/SVBR6xBaMl/13.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:777d031427700735dcb52e0f06f7a8c5ca07a8fe31ed1eda497ad86ebaf54c3d
+size 493227
diff --git a/vlm/dev/SVBR6xBaMl/14.png b/vlm/dev/SVBR6xBaMl/14.png
new file mode 100644
index 0000000000000000000000000000000000000000..7ec0ac48439fe60e09e583612bfc6c083ecc311a
--- /dev/null
+++ b/vlm/dev/SVBR6xBaMl/14.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:089ef7f77852543ed9ad98bd84ac714436be4f4798250ebdd6896c5fb34dfba3
+size 389354
diff --git a/vlm/dev/SVBR6xBaMl/15.png b/vlm/dev/SVBR6xBaMl/15.png
new file mode 100644
index 0000000000000000000000000000000000000000..6df851be2d0da046c6d7ff2a7515b5604b31f220
--- /dev/null
+++ b/vlm/dev/SVBR6xBaMl/15.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:aa091fea8e105bf054824304c60eef278b581d53cc7ef6d4c1c918a1de94830e
+size 226317
diff --git a/vlm/dev/SVBR6xBaMl/16.png b/vlm/dev/SVBR6xBaMl/16.png
new file mode 100644
index 0000000000000000000000000000000000000000..5b9dee69425bd1e13601f1ab243875bc90b9c19c
--- /dev/null
+++ b/vlm/dev/SVBR6xBaMl/16.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d481dce2339ae0f6fba10889305a9093635e46129eab894ff86d900e9668a1ae
+size 203791
diff --git a/vlm/dev/SVBR6xBaMl/17.png b/vlm/dev/SVBR6xBaMl/17.png
new file mode 100644
index 0000000000000000000000000000000000000000..79f8466e50bafcc8fb078362ef79e29b713ffeab
--- /dev/null
+++ b/vlm/dev/SVBR6xBaMl/17.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8a825d0f6a75ddfeb5445100239825dd0e143bd6fefe9b3f492d6fba7285bb0e
+size 232003
diff --git a/vlm/dev/SVBR6xBaMl/18.png b/vlm/dev/SVBR6xBaMl/18.png
new file mode 100644
index 0000000000000000000000000000000000000000..26ea1459022b6e09d3b62209dffb002843d5b5cf
--- /dev/null
+++ b/vlm/dev/SVBR6xBaMl/18.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d6182b32340fce428cf8b84b8cf8b9463d66edeefcca00e4348e338e959f9193
+size 483288
diff --git a/vlm/dev/SVBR6xBaMl/19.png b/vlm/dev/SVBR6xBaMl/19.png
new file mode 100644
index 0000000000000000000000000000000000000000..fb00e00b2fd7f3df78ee43796dec7d0c09adbb92
--- /dev/null
+++ b/vlm/dev/SVBR6xBaMl/19.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:364535f43765c2b4f65166d34707a2585ac67f0c6cc8f621f9cb8d9b84a3867d
+size 401356
diff --git a/vlm/dev/SVBR6xBaMl/2.png b/vlm/dev/SVBR6xBaMl/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..71032d184deabe3ddeadd5df0df0e8285bd1ca0c
--- /dev/null
+++ b/vlm/dev/SVBR6xBaMl/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:067d77b5edf7e0851fa21914887ac869fa9319e19fb4da44e8867ce3e17e92f7
+size 627719
diff --git a/vlm/dev/SVBR6xBaMl/20.png b/vlm/dev/SVBR6xBaMl/20.png
new file mode 100644
index 0000000000000000000000000000000000000000..21f33a3e8c8ca3f100beba28c9143f019d0f83f0
--- /dev/null
+++ b/vlm/dev/SVBR6xBaMl/20.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:62b831368b8e604e711a15c9be2fde2d34b441b1746dcaaa1a4a415ca22c5c08
+size 87149
diff --git a/vlm/dev/SVBR6xBaMl/3.png b/vlm/dev/SVBR6xBaMl/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..89b3022ca6d922bb70b91bb47d5bd70e34d6baac
--- /dev/null
+++ b/vlm/dev/SVBR6xBaMl/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:18c70b482f62a853335c69d6917f5aa65b2cbde2ea1d5a4e830e9c431af70e94
+size 680230
diff --git a/vlm/dev/SVBR6xBaMl/4.png b/vlm/dev/SVBR6xBaMl/4.png
new file mode 100644
index 0000000000000000000000000000000000000000..eb807a566c3574fe38bca8377224d22e350b3b35
--- /dev/null
+++ b/vlm/dev/SVBR6xBaMl/4.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f8ad38f8ad5901d5888d2ce9d77981a49f22326cbefa1422cc248a992ed47a21
+size 556489
diff --git a/vlm/dev/SVBR6xBaMl/5.png b/vlm/dev/SVBR6xBaMl/5.png
new file mode 100644
index 0000000000000000000000000000000000000000..d72b75b7ee782408d3b7b6aef35e493672e4d2b7
--- /dev/null
+++ b/vlm/dev/SVBR6xBaMl/5.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e7ba40d152f345689e49d942d1120e1c0c53db902bba40c9e8c2ba4b71630c1f
+size 600102
diff --git a/vlm/dev/SVBR6xBaMl/6.png b/vlm/dev/SVBR6xBaMl/6.png
new file mode 100644
index 0000000000000000000000000000000000000000..e2469ba1edd430a995b0e921c0d3a3fe5087db18
--- /dev/null
+++ b/vlm/dev/SVBR6xBaMl/6.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2f44d422f57c3dc5052c1f4bcbd3c6c67e956b2f09a52e1066af833360dd7f7a
+size 621859
diff --git a/vlm/dev/SVBR6xBaMl/7.png b/vlm/dev/SVBR6xBaMl/7.png
new file mode 100644
index 0000000000000000000000000000000000000000..1136b1428252b03d51086e168475914169e539cd
--- /dev/null
+++ b/vlm/dev/SVBR6xBaMl/7.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a5f705a0b9bcb823f2de4d3640c0096cf7b77e87bc53577617f9bfc85be2b4ba
+size 249169
diff --git a/vlm/dev/SVBR6xBaMl/8.png b/vlm/dev/SVBR6xBaMl/8.png
new file mode 100644
index 0000000000000000000000000000000000000000..2dd4e5dafe5ba7c5970f37a34eb06aab8bc55d5a
--- /dev/null
+++ b/vlm/dev/SVBR6xBaMl/8.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7fb127a286ed6d349ea6816894df720508c5db2e997db27fb4ae6ca7536e108d
+size 521680
diff --git a/vlm/dev/SVBR6xBaMl/9.png b/vlm/dev/SVBR6xBaMl/9.png
new file mode 100644
index 0000000000000000000000000000000000000000..d778913abf769ef322b45d24ef0a0b5b4c33118a
--- /dev/null
+++ b/vlm/dev/SVBR6xBaMl/9.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:658e925987371e6c0557dadb051c29a034c0c64d0b94b14580a86465d6e8efec
+size 479621
diff --git a/vlm/dev/T0GpzBQ1Fg6/0.png b/vlm/dev/T0GpzBQ1Fg6/0.png
new file mode 100644
index 0000000000000000000000000000000000000000..fe18740911792b0c1e72e496413fdc4e20a6a620
--- /dev/null
+++ b/vlm/dev/T0GpzBQ1Fg6/0.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:caa4ab4bddbe63982e6c5e73e771d290ed5cd4bf450fa6037b69bf7943a4a2ef
+size 546622
diff --git a/vlm/dev/T0GpzBQ1Fg6/1.png b/vlm/dev/T0GpzBQ1Fg6/1.png
new file mode 100644
index 0000000000000000000000000000000000000000..bafdb6a39651e256b3320172af6bc676253820b7
--- /dev/null
+++ b/vlm/dev/T0GpzBQ1Fg6/1.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:aa27e88790e4c69552fe0acc531721b684b2d23a00234564b06aa76b6421e282
+size 457731
diff --git a/vlm/dev/T0GpzBQ1Fg6/10.png b/vlm/dev/T0GpzBQ1Fg6/10.png
new file mode 100644
index 0000000000000000000000000000000000000000..c016343415312882aee24b999f36d0c700ee8402
--- /dev/null
+++ b/vlm/dev/T0GpzBQ1Fg6/10.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:779676c2780e99ad1c0a52101f6e412e06a32a55daf7ec2a7d182b69a523bd8f
+size 547267
diff --git a/vlm/dev/T0GpzBQ1Fg6/11.png b/vlm/dev/T0GpzBQ1Fg6/11.png
new file mode 100644
index 0000000000000000000000000000000000000000..a770babf2c2dd4ac9e32f2abde0c1a8ea1a3d4b3
--- /dev/null
+++ b/vlm/dev/T0GpzBQ1Fg6/11.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:02080f2b85f0790905337829fed1d4eba60d87d751fd7b2cc60a8e419af462e7
+size 521147
diff --git a/vlm/dev/T0GpzBQ1Fg6/12.png b/vlm/dev/T0GpzBQ1Fg6/12.png
new file mode 100644
index 0000000000000000000000000000000000000000..a04a1901641b25a05e32ee940f752de422982331
--- /dev/null
+++ b/vlm/dev/T0GpzBQ1Fg6/12.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3473f7c2a862b258eb2e360ab142fbd5cbc0db1011eb2d97c201f358b8d1e49c
+size 502253
diff --git a/vlm/dev/T0GpzBQ1Fg6/13.png b/vlm/dev/T0GpzBQ1Fg6/13.png
new file mode 100644
index 0000000000000000000000000000000000000000..84710bbf04c46570d3e8d065f663a3138afe4d03
--- /dev/null
+++ b/vlm/dev/T0GpzBQ1Fg6/13.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a266e16a166973fd0f3770bed8a38b15e620d3f47e66be3d80dedcb3bb28f3db
+size 333475
diff --git a/vlm/dev/T0GpzBQ1Fg6/14.png b/vlm/dev/T0GpzBQ1Fg6/14.png
new file mode 100644
index 0000000000000000000000000000000000000000..73eeaa5a5da0b3824599bcf5192b2174f42d209c
--- /dev/null
+++ b/vlm/dev/T0GpzBQ1Fg6/14.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9ed2d02a2cba28b8158251573c4c9b569ea1f346efd4bb30bf3f83b5515e1ae7
+size 472611
diff --git a/vlm/dev/T0GpzBQ1Fg6/15.png b/vlm/dev/T0GpzBQ1Fg6/15.png
new file mode 100644
index 0000000000000000000000000000000000000000..5fc9722b0dbb09c43ae5c1dfed11d6889264b3c7
--- /dev/null
+++ b/vlm/dev/T0GpzBQ1Fg6/15.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:de495c5a0115bc48ac7430885dd8f316197978c46f958fe545855e1bf6335e78
+size 403560
diff --git a/vlm/dev/T0GpzBQ1Fg6/16.png b/vlm/dev/T0GpzBQ1Fg6/16.png
new file mode 100644
index 0000000000000000000000000000000000000000..0ba2b3816e915a9ec9057cf0d22da6c60729f033
--- /dev/null
+++ b/vlm/dev/T0GpzBQ1Fg6/16.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e5369388e293faeaa91d08bbd19ff88f845d79bed0e2f8e32da37324317ae736
+size 471649
diff --git a/vlm/dev/T0GpzBQ1Fg6/17.png b/vlm/dev/T0GpzBQ1Fg6/17.png
new file mode 100644
index 0000000000000000000000000000000000000000..12edc3ac33bdab5ce4ae3baca667d1e75bf40664
--- /dev/null
+++ b/vlm/dev/T0GpzBQ1Fg6/17.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5f01fcaf6cac4a7add9bf64edc1894a9a92f9e08eb2505955926fa5d276f7abc
+size 358152
diff --git a/vlm/dev/T0GpzBQ1Fg6/18.png b/vlm/dev/T0GpzBQ1Fg6/18.png
new file mode 100644
index 0000000000000000000000000000000000000000..59cbe83ac54b9c190759c67454d10dead9ec3ede
--- /dev/null
+++ b/vlm/dev/T0GpzBQ1Fg6/18.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:01199ed0cc23b1388e21627a1a3d685a3baa9123ff25152374fa378b814f6f4d
+size 460683
diff --git a/vlm/dev/T0GpzBQ1Fg6/19.png b/vlm/dev/T0GpzBQ1Fg6/19.png
new file mode 100644
index 0000000000000000000000000000000000000000..f17074030ee85139cef0b03f10599b438b1c3442
--- /dev/null
+++ b/vlm/dev/T0GpzBQ1Fg6/19.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a875abc193a2e0cb1455c7237bc684d83b985b1444c9212aba1ac29aa53d8d56
+size 224241
diff --git a/vlm/dev/T0GpzBQ1Fg6/2.png b/vlm/dev/T0GpzBQ1Fg6/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..9385c9fb5787a5fcd64f81686b960cf816ff0fd9
--- /dev/null
+++ b/vlm/dev/T0GpzBQ1Fg6/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cd4bff22047403c90d33633bfdec39b0d53b343072246aadf8ad889a946034fd
+size 539819
diff --git a/vlm/dev/T0GpzBQ1Fg6/3.png b/vlm/dev/T0GpzBQ1Fg6/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..7a9c351302883a99ac5d4b4f5c3fcb0ef86a9477
--- /dev/null
+++ b/vlm/dev/T0GpzBQ1Fg6/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3c3623350b060a72db881fd912143f4d096bd899facfa72d4bd7f6a31739f9f1
+size 585618
diff --git a/vlm/dev/T0GpzBQ1Fg6/4.png b/vlm/dev/T0GpzBQ1Fg6/4.png
new file mode 100644
index 0000000000000000000000000000000000000000..4cf29a5c0b4153d9965986897926174a762a9125
--- /dev/null
+++ b/vlm/dev/T0GpzBQ1Fg6/4.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:96af9b3649b2f8bdd6a68dc21be3064662791403aa0a7539a19533ba36baea11
+size 707574
diff --git a/vlm/dev/T0GpzBQ1Fg6/5.png b/vlm/dev/T0GpzBQ1Fg6/5.png
new file mode 100644
index 0000000000000000000000000000000000000000..d41d611f2b9b4c7b30791170f4523dcfe612bdfc
--- /dev/null
+++ b/vlm/dev/T0GpzBQ1Fg6/5.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f8f98a88d46cdd7d83023f8d7edd9dfcb16a107bcc9c027d951d7880955c32fb
+size 637787
diff --git a/vlm/dev/T0GpzBQ1Fg6/6.png b/vlm/dev/T0GpzBQ1Fg6/6.png
new file mode 100644
index 0000000000000000000000000000000000000000..07849a56ad2653435495d0855099fd2f4c19c5a0
--- /dev/null
+++ b/vlm/dev/T0GpzBQ1Fg6/6.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:423a2de88aa534cac1b78097cc4dd57e8dd402ee16a8a6911a79f824298c9a58
+size 636973
diff --git a/vlm/dev/T0GpzBQ1Fg6/7.png b/vlm/dev/T0GpzBQ1Fg6/7.png
new file mode 100644
index 0000000000000000000000000000000000000000..f4f762cf7a44a9ebcdc04411e81b174b934b7e6e
--- /dev/null
+++ b/vlm/dev/T0GpzBQ1Fg6/7.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:598a03de3ed9390ac6dbba34d1ff25697a139d7fb1aee1c997042fb2c0fe0e26
+size 549607
diff --git a/vlm/dev/T0GpzBQ1Fg6/8.png b/vlm/dev/T0GpzBQ1Fg6/8.png
new file mode 100644
index 0000000000000000000000000000000000000000..d1fde3f5cda5db76521a2b0bb8f54914f9d99be9
--- /dev/null
+++ b/vlm/dev/T0GpzBQ1Fg6/8.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0ff5c5db2415eee47b508f469e27337943017bf3a7c55e4ca09e641816760df2
+size 687401
diff --git a/vlm/dev/T0GpzBQ1Fg6/9.png b/vlm/dev/T0GpzBQ1Fg6/9.png
new file mode 100644
index 0000000000000000000000000000000000000000..6d7e5f409dff22f4beaede81cccacf6fdf945176
--- /dev/null
+++ b/vlm/dev/T0GpzBQ1Fg6/9.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3191d0fe587547a14ff8a4b1593ba99588e89eb3310fb3fb0cf5ec85b78dbc76
+size 534952
diff --git a/vlm/dev/TVHS5Y4dNvM/0.png b/vlm/dev/TVHS5Y4dNvM/0.png
new file mode 100644
index 0000000000000000000000000000000000000000..78ee523abe3e127f2a2231b6540267dba4845753
--- /dev/null
+++ b/vlm/dev/TVHS5Y4dNvM/0.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d16069e32fdcb9e599cc40100a4bac9df34c87021306da8efe629c33d202c48b
+size 521303
diff --git a/vlm/dev/TVHS5Y4dNvM/1.png b/vlm/dev/TVHS5Y4dNvM/1.png
new file mode 100644
index 0000000000000000000000000000000000000000..4a321ebe9ed009c228cacf3ad683a8d9eee4f10f
--- /dev/null
+++ b/vlm/dev/TVHS5Y4dNvM/1.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:66756fc7f61d345a3a3c504a5bc975b64892ec2adf5acba469010daeda1d1591
+size 554276
diff --git a/vlm/dev/TVHS5Y4dNvM/10.png b/vlm/dev/TVHS5Y4dNvM/10.png
new file mode 100644
index 0000000000000000000000000000000000000000..76189b1afb948242a2e456556c16b6702a41e095
--- /dev/null
+++ b/vlm/dev/TVHS5Y4dNvM/10.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e06aa84ec977a9ce2048b246a798672f2c6e2c95dfb43869eb3c5d01b1b621a7
+size 617692
diff --git a/vlm/dev/TVHS5Y4dNvM/11.png b/vlm/dev/TVHS5Y4dNvM/11.png
new file mode 100644
index 0000000000000000000000000000000000000000..40ac69d025bad8344fcfdb25f7dd7c59114ff7b0
--- /dev/null
+++ b/vlm/dev/TVHS5Y4dNvM/11.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cff62268a43e112b4f8e3fe41733f5c65bca13baede94827b3a9848caa10656b
+size 336863
diff --git a/vlm/dev/TVHS5Y4dNvM/12.png b/vlm/dev/TVHS5Y4dNvM/12.png
new file mode 100644
index 0000000000000000000000000000000000000000..b14002ac6a13d3bec726c8979e1571e5acc98725
--- /dev/null
+++ b/vlm/dev/TVHS5Y4dNvM/12.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c61ad9fc103eb9ea0cd8dbd3a5c729bb2babd4debb2a13ecad34c577d09fc0fb
+size 2091281
diff --git a/vlm/dev/TVHS5Y4dNvM/13.png b/vlm/dev/TVHS5Y4dNvM/13.png
new file mode 100644
index 0000000000000000000000000000000000000000..209eb65dd35552a9a7c9267b305e8dc5f0dcbbd2
--- /dev/null
+++ b/vlm/dev/TVHS5Y4dNvM/13.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b40cb5fd22dbcff2f489cda21110106e27d840883f05257d0e531d88ec5ce183
+size 823576
diff --git a/vlm/dev/TVHS5Y4dNvM/14.png b/vlm/dev/TVHS5Y4dNvM/14.png
new file mode 100644
index 0000000000000000000000000000000000000000..c83434c8031de2befbbbe7c7b2daf04fb92c2342
--- /dev/null
+++ b/vlm/dev/TVHS5Y4dNvM/14.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9d982c6990db1a1ea6ec41e732322083f30d929cdd6904866e30f59f3ed77066
+size 307727
diff --git a/vlm/dev/TVHS5Y4dNvM/2.png b/vlm/dev/TVHS5Y4dNvM/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..d1996d988fece7590fba5dc02f292b05083faffa
--- /dev/null
+++ b/vlm/dev/TVHS5Y4dNvM/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:36ab3b4cc029d5661a4979e012ea3b5786cd13921606271273e209b380ffa741
+size 598300
diff --git a/vlm/dev/TVHS5Y4dNvM/3.png b/vlm/dev/TVHS5Y4dNvM/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..1696734af0193bbf56180bf232dd89a3c7366d45
--- /dev/null
+++ b/vlm/dev/TVHS5Y4dNvM/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:dc00acac0750b24a1f559b102a996ef233977df6185ec188103746d1d997cd0e
+size 644661
diff --git a/vlm/dev/TVHS5Y4dNvM/4.png b/vlm/dev/TVHS5Y4dNvM/4.png
new file mode 100644
index 0000000000000000000000000000000000000000..0be3e548118cf5014ec8a0140df6fc39130b4a11
--- /dev/null
+++ b/vlm/dev/TVHS5Y4dNvM/4.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:50c8c70856bdf76838e83b64c1d9b36a631a586ad7dce0eaeedd710aa1fe1065
+size 582545
diff --git a/vlm/dev/TVHS5Y4dNvM/5.png b/vlm/dev/TVHS5Y4dNvM/5.png
new file mode 100644
index 0000000000000000000000000000000000000000..c8ebb22c1fedfb2edc95a9a77aca833e7dcab27c
--- /dev/null
+++ b/vlm/dev/TVHS5Y4dNvM/5.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6ca4a6f589412f3969a55be4323682a1573cb89019a5b7a37479b92a78796fc7
+size 556654
diff --git a/vlm/dev/TVHS5Y4dNvM/6.png b/vlm/dev/TVHS5Y4dNvM/6.png
new file mode 100644
index 0000000000000000000000000000000000000000..edb8f0bc001f77bd69638be47dfaa839df306e5b
--- /dev/null
+++ b/vlm/dev/TVHS5Y4dNvM/6.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:13201960b0722b447cb6c238f0ea48c4e670d4c4eb2d6c176f08e9354db88afd
+size 239972
diff --git a/vlm/dev/TVHS5Y4dNvM/7.png b/vlm/dev/TVHS5Y4dNvM/7.png
new file mode 100644
index 0000000000000000000000000000000000000000..a8f1ffefe0ba301b39346e4d996b1141997f5771
--- /dev/null
+++ b/vlm/dev/TVHS5Y4dNvM/7.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ff0a962ae94e521afae7c1d0e6a72e86e4849738c0d8faa16bd5b6ebd771ffce
+size 495838
diff --git a/vlm/dev/TVHS5Y4dNvM/8.png b/vlm/dev/TVHS5Y4dNvM/8.png
new file mode 100644
index 0000000000000000000000000000000000000000..02dc34523521fa25e5e3ba42a61ae4d80b14c8ec
--- /dev/null
+++ b/vlm/dev/TVHS5Y4dNvM/8.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d5e43c3d7ee67e22cd013f0e7122840f76c9409acce6905805425ec2218486e1
+size 679519
diff --git a/vlm/dev/TVHS5Y4dNvM/9.png b/vlm/dev/TVHS5Y4dNvM/9.png
new file mode 100644
index 0000000000000000000000000000000000000000..2a3f08cdd793001e9c0344a65c5f613f07429996
--- /dev/null
+++ b/vlm/dev/TVHS5Y4dNvM/9.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9509e4a11ad96cdae945ebd7430bc56b32087051463c24030da625a428aa7632
+size 495197
diff --git a/vlm/dev/UaXD4Al3mdb/0.png b/vlm/dev/UaXD4Al3mdb/0.png
new file mode 100644
index 0000000000000000000000000000000000000000..78b435ec314b8b511fff91f00b8ff0cd80f7e891
--- /dev/null
+++ b/vlm/dev/UaXD4Al3mdb/0.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:61712f8ee4bf904c796f64f781bc3471485426036dc9f725eb7b2525516b31f2
+size 504518
diff --git a/vlm/dev/UaXD4Al3mdb/1.png b/vlm/dev/UaXD4Al3mdb/1.png
new file mode 100644
index 0000000000000000000000000000000000000000..68bb9423c84e4eec229618f6e9dfb5b87f315a1c
--- /dev/null
+++ b/vlm/dev/UaXD4Al3mdb/1.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0e3058caee58b1a5253c829e2104da2a868479f09fe9abc4019391d7efaa4947
+size 708495
diff --git a/vlm/dev/UaXD4Al3mdb/10.png b/vlm/dev/UaXD4Al3mdb/10.png
new file mode 100644
index 0000000000000000000000000000000000000000..c24617567a9538130f887bb59e3c8317830b3bfd
--- /dev/null
+++ b/vlm/dev/UaXD4Al3mdb/10.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2925e959a46a6678b9c330783e2cb7d646ae79d029486e03cb78099668b5de5b
+size 624329
diff --git a/vlm/dev/UaXD4Al3mdb/11.png b/vlm/dev/UaXD4Al3mdb/11.png
new file mode 100644
index 0000000000000000000000000000000000000000..ec16f071bc4f892c107d91eb79f5178ae9bdf2f5
--- /dev/null
+++ b/vlm/dev/UaXD4Al3mdb/11.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d899ea3c7b3a57f7206d325b27fe0414b0ef217141db129e88429be912ef06f5
+size 632609
diff --git a/vlm/dev/UaXD4Al3mdb/12.png b/vlm/dev/UaXD4Al3mdb/12.png
new file mode 100644
index 0000000000000000000000000000000000000000..65ce84a783104f788c389a75873afbb85a932fc6
--- /dev/null
+++ b/vlm/dev/UaXD4Al3mdb/12.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c847453fcfe1c9777fe0a512e4a928af9c6b8e6abe43dd02f1d5172e405e573c
+size 341463
diff --git a/vlm/dev/UaXD4Al3mdb/2.png b/vlm/dev/UaXD4Al3mdb/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..e5e59f7b012cb685d9ffc319b8c390f00d14e2a1
--- /dev/null
+++ b/vlm/dev/UaXD4Al3mdb/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d23f15328eecc505956d06f62eeaefb813950fd795aea9156ca19bf279b9cf93
+size 1630063
diff --git a/vlm/dev/UaXD4Al3mdb/3.png b/vlm/dev/UaXD4Al3mdb/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..0ef4420638c38aa5082b375b8823f8ba7e91ac59
--- /dev/null
+++ b/vlm/dev/UaXD4Al3mdb/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b251b2cd360affb5c50535c767b6ee0e2b7a48104a83a27bdd327f73a9281a8f
+size 724774
diff --git a/vlm/dev/UaXD4Al3mdb/4.png b/vlm/dev/UaXD4Al3mdb/4.png
new file mode 100644
index 0000000000000000000000000000000000000000..d9912c8cd42574ef7141cc158380a1446371cbe6
--- /dev/null
+++ b/vlm/dev/UaXD4Al3mdb/4.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2b908e4a12bc3b80907204a1167a722803e2c170838034383f8f7127ca541730
+size 535791
diff --git a/vlm/dev/UaXD4Al3mdb/5.png b/vlm/dev/UaXD4Al3mdb/5.png
new file mode 100644
index 0000000000000000000000000000000000000000..dff66788a068e3795290ee8524899a979d321953
--- /dev/null
+++ b/vlm/dev/UaXD4Al3mdb/5.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:23c2b771422d00eaecdb38e7c93331142a4ac37234fc77b9a19df617ed72a7b7
+size 553355
diff --git a/vlm/dev/UaXD4Al3mdb/6.png b/vlm/dev/UaXD4Al3mdb/6.png
new file mode 100644
index 0000000000000000000000000000000000000000..e0b26a4c75dc66e93a80b694e6e6d2ac2216fcdf
--- /dev/null
+++ b/vlm/dev/UaXD4Al3mdb/6.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1f62858e7e56caea1ef688a4f008124e2fe9aea2941b52c81c6d606e7ae7c14e
+size 583900
diff --git a/vlm/dev/UaXD4Al3mdb/7.png b/vlm/dev/UaXD4Al3mdb/7.png
new file mode 100644
index 0000000000000000000000000000000000000000..69b1454c3dd1128454a38af542ba56dc5d25d349
--- /dev/null
+++ b/vlm/dev/UaXD4Al3mdb/7.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:27d08e7dab9e8a6e98f8a76a5b5b38374fd69394d3edf3031248c39a13f9c8b9
+size 601144
diff --git a/vlm/dev/UaXD4Al3mdb/8.png b/vlm/dev/UaXD4Al3mdb/8.png
new file mode 100644
index 0000000000000000000000000000000000000000..a06cce917f548debf1a101feb126ebfaee8f342b
--- /dev/null
+++ b/vlm/dev/UaXD4Al3mdb/8.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b782296eeccab062973c1bfd39435d4265192b79e1b4ccfad13075d05f150112
+size 530793
diff --git a/vlm/dev/UaXD4Al3mdb/9.png b/vlm/dev/UaXD4Al3mdb/9.png
new file mode 100644
index 0000000000000000000000000000000000000000..481530e44237dad577de1db9d30383f650131755
--- /dev/null
+++ b/vlm/dev/UaXD4Al3mdb/9.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e4105fa067a8fc37a001c887a789b630b1eea484683a62ccf957f2398d270c6f
+size 631866
diff --git a/vlm/dev/UmvSlP-PyV/0.png b/vlm/dev/UmvSlP-PyV/0.png
new file mode 100644
index 0000000000000000000000000000000000000000..d20a4da4629c37d15264043450aa931e035ad270
--- /dev/null
+++ b/vlm/dev/UmvSlP-PyV/0.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d7402ca687d764d704c242755dadb284701e83ac8c26ea34da6621e3ad3f8445
+size 352657
diff --git a/vlm/dev/UmvSlP-PyV/1.png b/vlm/dev/UmvSlP-PyV/1.png
new file mode 100644
index 0000000000000000000000000000000000000000..4375916afec36ab9bb23b0f7675ede800681983d
--- /dev/null
+++ b/vlm/dev/UmvSlP-PyV/1.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:02575d0a4b7d2bcbfeaf0113bba3f23b5d14d8c76b4b77ff5a20b77ea2c4a26f
+size 688882
diff --git a/vlm/dev/UmvSlP-PyV/10.png b/vlm/dev/UmvSlP-PyV/10.png
new file mode 100644
index 0000000000000000000000000000000000000000..e272fe478094cbb3ef40416ba0e943b914dfbbea
--- /dev/null
+++ b/vlm/dev/UmvSlP-PyV/10.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:18d287ed93e8fc677e6f4127d9fbd8a7ea47fa133d70c5be7c01c9fe468c40fd
+size 612066
diff --git a/vlm/dev/UmvSlP-PyV/11.png b/vlm/dev/UmvSlP-PyV/11.png
new file mode 100644
index 0000000000000000000000000000000000000000..2221afbaa7a5e94adda19d499e14186ed2ffade4
--- /dev/null
+++ b/vlm/dev/UmvSlP-PyV/11.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2dfa0b36ba90759c95febc40df6f4c1bfb4854e964aa4d98ea17de19d60e9767
+size 596064
diff --git a/vlm/dev/UmvSlP-PyV/12.png b/vlm/dev/UmvSlP-PyV/12.png
new file mode 100644
index 0000000000000000000000000000000000000000..8192e24cf519e4da9772b938d76d7aaec9a1f122
--- /dev/null
+++ b/vlm/dev/UmvSlP-PyV/12.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1dd0d59bc0f01881c0925180a15ad6a0741180c38894f64de4f95e851f06b92b
+size 331411
diff --git a/vlm/dev/UmvSlP-PyV/13.png b/vlm/dev/UmvSlP-PyV/13.png
new file mode 100644
index 0000000000000000000000000000000000000000..c41b9e943b26f0efbcde72475a63a36e5e6d945f
--- /dev/null
+++ b/vlm/dev/UmvSlP-PyV/13.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:555a264f11beb7d71b958eacff4dc384fdf1f07f8205f7ef316c80e62b0cea38
+size 384753
diff --git a/vlm/dev/UmvSlP-PyV/2.png b/vlm/dev/UmvSlP-PyV/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..b8c37deeb990f6169390b924f2c6e507436ef962
--- /dev/null
+++ b/vlm/dev/UmvSlP-PyV/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5d80a81b504b9a7cef85499f04debdcad425d3ff255ada391a7a8a07ee9c0cc4
+size 559681
diff --git a/vlm/dev/UmvSlP-PyV/3.png b/vlm/dev/UmvSlP-PyV/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..f53f9c02e2fd6f9def2909667730f60339c67bd4
--- /dev/null
+++ b/vlm/dev/UmvSlP-PyV/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5a444ba227ce09f43c8388d717e6bdbf6bbe2d3cbe4f6d6ed1ee0fda89aa86e4
+size 600265
diff --git a/vlm/dev/UmvSlP-PyV/4.png b/vlm/dev/UmvSlP-PyV/4.png
new file mode 100644
index 0000000000000000000000000000000000000000..d45372ead782670666c785b604cbb6d3c51173d0
--- /dev/null
+++ b/vlm/dev/UmvSlP-PyV/4.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:da5ec66dd20bdc0272c74caddd0561aed4f7e51d674ecf69b2133bf06ab62e5a
+size 629361
diff --git a/vlm/dev/UmvSlP-PyV/5.png b/vlm/dev/UmvSlP-PyV/5.png
new file mode 100644
index 0000000000000000000000000000000000000000..8f63032dd6c82a49193383d3c14e0f8ff2e433f2
--- /dev/null
+++ b/vlm/dev/UmvSlP-PyV/5.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b648ef4d51701527c34e0ee43e66680d28c15ab7970c5573ec0d0737d8924fb5
+size 682351
diff --git a/vlm/dev/UmvSlP-PyV/6.png b/vlm/dev/UmvSlP-PyV/6.png
new file mode 100644
index 0000000000000000000000000000000000000000..73be2393b48cd911a8552adf44586e7cd2a16992
--- /dev/null
+++ b/vlm/dev/UmvSlP-PyV/6.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9cb477f7457279f62cf67b2b350fdb88c16da43d4d8f64d8bca93a6bb593c376
+size 745611
diff --git a/vlm/dev/UmvSlP-PyV/7.png b/vlm/dev/UmvSlP-PyV/7.png
new file mode 100644
index 0000000000000000000000000000000000000000..123f5ce7171c625f660841c319bb48428b60a3d7
--- /dev/null
+++ b/vlm/dev/UmvSlP-PyV/7.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2cc735b19a41b94eed691a2502c64629fd8ef3ee8a9451f044f3edf9c8db9976
+size 623923
diff --git a/vlm/dev/UmvSlP-PyV/8.png b/vlm/dev/UmvSlP-PyV/8.png
new file mode 100644
index 0000000000000000000000000000000000000000..88b6220d21354d25b30d9cd5e3aabe1eb7e2263f
--- /dev/null
+++ b/vlm/dev/UmvSlP-PyV/8.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bfd0be84bb0d74b0a5971cacf5218e4bc03a6d5fb539c5799cc6f1350c081616
+size 860256
diff --git a/vlm/dev/UmvSlP-PyV/9.png b/vlm/dev/UmvSlP-PyV/9.png
new file mode 100644
index 0000000000000000000000000000000000000000..2110a6371f58c2e8526dcb5e98c7d2e61359352c
--- /dev/null
+++ b/vlm/dev/UmvSlP-PyV/9.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:be63bc7037614edee125aa100e8df1251687f2e223710749876f27c5673f0793
+size 581648
diff --git a/vlm/dev/Uynr3iPhksa/0.png b/vlm/dev/Uynr3iPhksa/0.png
new file mode 100644
index 0000000000000000000000000000000000000000..71e76808b0e8936671558f7e8da1f9746080bb1b
--- /dev/null
+++ b/vlm/dev/Uynr3iPhksa/0.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:31ae81c89202467f341f17356e492d752ce31090e31b6b4ab1aed6961e009ab5
+size 442328
diff --git a/vlm/dev/Uynr3iPhksa/1.png b/vlm/dev/Uynr3iPhksa/1.png
new file mode 100644
index 0000000000000000000000000000000000000000..0ab4a53ebb1b39bc5a2788bb7dca02861d291fe9
--- /dev/null
+++ b/vlm/dev/Uynr3iPhksa/1.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:89a8a49aba049d4f98365813fa5c454648f8663514efb1b8fef71df0ddf3defd
+size 584959
diff --git a/vlm/dev/Uynr3iPhksa/10.png b/vlm/dev/Uynr3iPhksa/10.png
new file mode 100644
index 0000000000000000000000000000000000000000..54c6eb772e2c0a7cd5a6065f88e76732e70a20f2
--- /dev/null
+++ b/vlm/dev/Uynr3iPhksa/10.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:eee727312c6937d28474ebfd818bcfb310cada514b24ad0d9c40a016316ee5ee
+size 539339
diff --git a/vlm/dev/Uynr3iPhksa/11.png b/vlm/dev/Uynr3iPhksa/11.png
new file mode 100644
index 0000000000000000000000000000000000000000..b84b755e2fed09b9968efa223caedfd4de43134a
--- /dev/null
+++ b/vlm/dev/Uynr3iPhksa/11.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6de57b1cc01286c00dc5bddd380205c8dc030c33a56e5c8f6bb63abb0efcb711
+size 372940
diff --git a/vlm/dev/Uynr3iPhksa/12.png b/vlm/dev/Uynr3iPhksa/12.png
new file mode 100644
index 0000000000000000000000000000000000000000..a239677224b14ccb791e7765f2b2b9ef1e54bccd
--- /dev/null
+++ b/vlm/dev/Uynr3iPhksa/12.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:22661994a386eb8bb6ae2255f323ff0260b7d83da70546e7b277d9b983a97c9a
+size 473290
diff --git a/vlm/dev/Uynr3iPhksa/2.png b/vlm/dev/Uynr3iPhksa/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..733d64f4ca8f291e68fc74d9faca8958e18d3725
--- /dev/null
+++ b/vlm/dev/Uynr3iPhksa/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5ef1212059c24356d137f5b6d329238f9ab1cfd979a1d7748ea6fb2d293bd4e5
+size 584129
diff --git a/vlm/dev/Uynr3iPhksa/3.png b/vlm/dev/Uynr3iPhksa/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..180b161aa61cc883e9d7040849754207ad40a4a2
--- /dev/null
+++ b/vlm/dev/Uynr3iPhksa/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:355848bf1ecdd7ac851fb7d4efd435100456f4b6fe4659245fb7b7cdcecb90ac
+size 564206
diff --git a/vlm/dev/Uynr3iPhksa/4.png b/vlm/dev/Uynr3iPhksa/4.png
new file mode 100644
index 0000000000000000000000000000000000000000..6a92facc6e0a31ed12ee0ac9765e0f5a4a3104e4
--- /dev/null
+++ b/vlm/dev/Uynr3iPhksa/4.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:87d1f05423d19af570bdfb2544b3687736f088793ee75c3fa6b1ffc1a11d1eca
+size 583373
diff --git a/vlm/dev/Uynr3iPhksa/5.png b/vlm/dev/Uynr3iPhksa/5.png
new file mode 100644
index 0000000000000000000000000000000000000000..f11fb79ba739db6c42ce3ec0406e5ea290f3687b
--- /dev/null
+++ b/vlm/dev/Uynr3iPhksa/5.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8bc8187ac9831a10f4fe8dd7106b5ff6b5394d8e761ab1c908ed38c31602c474
+size 577897
diff --git a/vlm/dev/Uynr3iPhksa/6.png b/vlm/dev/Uynr3iPhksa/6.png
new file mode 100644
index 0000000000000000000000000000000000000000..2c75bcde14cf59b050cf62256b7734d244e1a429
--- /dev/null
+++ b/vlm/dev/Uynr3iPhksa/6.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e996d39cebe77e0dea90701c91290ca1fcc0240d539f0b07ad9832190bf31c45
+size 602946
diff --git a/vlm/dev/Uynr3iPhksa/7.png b/vlm/dev/Uynr3iPhksa/7.png
new file mode 100644
index 0000000000000000000000000000000000000000..52ceb74316d511f104f4b5726f34670ff4ab46e1
--- /dev/null
+++ b/vlm/dev/Uynr3iPhksa/7.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:55784aa96c877cc20991bf0478a561b6afe35ebeedfc86dfe2a7280e3c890820
+size 588796
diff --git a/vlm/dev/Uynr3iPhksa/8.png b/vlm/dev/Uynr3iPhksa/8.png
new file mode 100644
index 0000000000000000000000000000000000000000..97e99f575f501f2d92cf26e1ee1e6237b37d57e1
--- /dev/null
+++ b/vlm/dev/Uynr3iPhksa/8.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0e79c99aaa8e9cb77b3b64712dac53ced0fa2bca04799522280d9a89d7d4b1b0
+size 617107
diff --git a/vlm/dev/Uynr3iPhksa/9.png b/vlm/dev/Uynr3iPhksa/9.png
new file mode 100644
index 0000000000000000000000000000000000000000..0ecf8b41fdca614be5c880e6529aaac61ccd6fa9
--- /dev/null
+++ b/vlm/dev/Uynr3iPhksa/9.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b5588f0540d96f0269ada9a0556dac1c80f2942c1c01a8e2f6f8c94d8baf0098
+size 559664
diff --git a/vlm/dev/ZBESeIUB5k/0.png b/vlm/dev/ZBESeIUB5k/0.png
new file mode 100644
index 0000000000000000000000000000000000000000..6cbbf489ed9eadc648bfe4844ddb015a7853825b
--- /dev/null
+++ b/vlm/dev/ZBESeIUB5k/0.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c6e9aca6140468bda3b6f6980946836127234c308d907dc6c7245aea8c8874df
+size 483200
diff --git a/vlm/dev/ZBESeIUB5k/1.png b/vlm/dev/ZBESeIUB5k/1.png
new file mode 100644
index 0000000000000000000000000000000000000000..669410ee905b0c2e12dbdfbaf8cc36cb9039b9c3
--- /dev/null
+++ b/vlm/dev/ZBESeIUB5k/1.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:de8f44a22a2091907140fe8c6cde420b33125b054f9fcdaad900e50b992b9c7e
+size 567586
diff --git a/vlm/dev/ZBESeIUB5k/10.png b/vlm/dev/ZBESeIUB5k/10.png
new file mode 100644
index 0000000000000000000000000000000000000000..2021ee29c05e837473b0d8f276eaef07015c7c49
--- /dev/null
+++ b/vlm/dev/ZBESeIUB5k/10.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e96627126646b9fadb401d9c4fb7734a1238ae6029a85c7ac7b00917dfd58a1a
+size 629815
diff --git a/vlm/dev/ZBESeIUB5k/11.png b/vlm/dev/ZBESeIUB5k/11.png
new file mode 100644
index 0000000000000000000000000000000000000000..c46d5ec84aa9639a47db21f631f6d3bea6cdda70
--- /dev/null
+++ b/vlm/dev/ZBESeIUB5k/11.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:362b2631c6aaf942d3c8353a98037d7571b79f3f839415369d39626826ecda45
+size 625618
diff --git a/vlm/dev/ZBESeIUB5k/12.png b/vlm/dev/ZBESeIUB5k/12.png
new file mode 100644
index 0000000000000000000000000000000000000000..ce061fe3d2bc8ee90fd65b7c893731cbdf16c3f3
--- /dev/null
+++ b/vlm/dev/ZBESeIUB5k/12.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bf4441dac197ac02304b418a10e2b1188134611925b820a414da1aab5de95d57
+size 571622
diff --git a/vlm/dev/ZBESeIUB5k/13.png b/vlm/dev/ZBESeIUB5k/13.png
new file mode 100644
index 0000000000000000000000000000000000000000..f47413bd9876d7b3d9261b53957cf07f3e857712
--- /dev/null
+++ b/vlm/dev/ZBESeIUB5k/13.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:858f067c429b1d4da14d0ceaa7c01416b05eb668d3fdfd66b5c083b537e8cf12
+size 582759
diff --git a/vlm/dev/ZBESeIUB5k/14.png b/vlm/dev/ZBESeIUB5k/14.png
new file mode 100644
index 0000000000000000000000000000000000000000..2d76c8356d2d58aeaf70783daaa9d3f1a43f4f1b
--- /dev/null
+++ b/vlm/dev/ZBESeIUB5k/14.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7181f995d433beb51c9e1c27429e2633a28f627c6e884e8c29f44a27fab5ed22
+size 607714
diff --git a/vlm/dev/ZBESeIUB5k/15.png b/vlm/dev/ZBESeIUB5k/15.png
new file mode 100644
index 0000000000000000000000000000000000000000..267be600c51545220fa0a186e661ca2ca0d1a916
--- /dev/null
+++ b/vlm/dev/ZBESeIUB5k/15.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d1b0605a49c5550e5d14883f094992eca861450528fa0542f7971285bcb40dc8
+size 581172
diff --git a/vlm/dev/ZBESeIUB5k/16.png b/vlm/dev/ZBESeIUB5k/16.png
new file mode 100644
index 0000000000000000000000000000000000000000..4009957bf418b7b84baabe0281722a95a7dc026f
--- /dev/null
+++ b/vlm/dev/ZBESeIUB5k/16.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6acba8307ed80cb3a011ad0e39af9c44dd4629b7337a2edeae622c6f3b31b5e1
+size 490063
diff --git a/vlm/dev/ZBESeIUB5k/17.png b/vlm/dev/ZBESeIUB5k/17.png
new file mode 100644
index 0000000000000000000000000000000000000000..a15b3e982c211e7c1fed1b7dfa6e37c9acf3b450
--- /dev/null
+++ b/vlm/dev/ZBESeIUB5k/17.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8cd3c668a22e0d75237cbadb2b49095b56ada7230aa6c722d07155b9909579e6
+size 465117
diff --git a/vlm/dev/ZBESeIUB5k/18.png b/vlm/dev/ZBESeIUB5k/18.png
new file mode 100644
index 0000000000000000000000000000000000000000..f1204d54bcd89892021c49852d1344f118bd51a1
--- /dev/null
+++ b/vlm/dev/ZBESeIUB5k/18.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:65ebbda7995991d49c9120ae95815ad76fa51826af4054d842e1a81da518249c
+size 487415
diff --git a/vlm/dev/ZBESeIUB5k/19.png b/vlm/dev/ZBESeIUB5k/19.png
new file mode 100644
index 0000000000000000000000000000000000000000..13beffc04cb2adf3025ac725b6545730d9811f59
--- /dev/null
+++ b/vlm/dev/ZBESeIUB5k/19.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:555160e7da6709b5e6cd9c90318e6023d8a96855ae7659e167048c93bb31529a
+size 586355
diff --git a/vlm/dev/ZBESeIUB5k/2.png b/vlm/dev/ZBESeIUB5k/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..529268ec4d146971679a3b4b5cceaa5ebee22faa
--- /dev/null
+++ b/vlm/dev/ZBESeIUB5k/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:405e8ba963255d305b1e87d49f8879dd59e25e4eed6d4727abb36c18bd685ab3
+size 634825
diff --git a/vlm/dev/ZBESeIUB5k/20.png b/vlm/dev/ZBESeIUB5k/20.png
new file mode 100644
index 0000000000000000000000000000000000000000..b566a0ff65e64ad337c2a824e0d67b76b52d9357
--- /dev/null
+++ b/vlm/dev/ZBESeIUB5k/20.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e6c9f8970a2b00a15fda2d324d008e9482a314efb361022c395adcc00ee8a639
+size 552533
diff --git a/vlm/dev/ZBESeIUB5k/21.png b/vlm/dev/ZBESeIUB5k/21.png
new file mode 100644
index 0000000000000000000000000000000000000000..7ffb05b0ce71cf8522ed70d5b680d53627b21843
--- /dev/null
+++ b/vlm/dev/ZBESeIUB5k/21.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:57d8d20e06f7450a3131cca65d3e0f455cf833763e85f6b95a8eb1ee7de89e7a
+size 579019
diff --git a/vlm/dev/ZBESeIUB5k/22.png b/vlm/dev/ZBESeIUB5k/22.png
new file mode 100644
index 0000000000000000000000000000000000000000..9d2aea3fd8c64b9830d659d35d810f206bc2c5d9
--- /dev/null
+++ b/vlm/dev/ZBESeIUB5k/22.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2bfefabf453c9951480da51d4735ecd259bdefcda196990848ca5a826128b413
+size 447495
diff --git a/vlm/dev/ZBESeIUB5k/23.png b/vlm/dev/ZBESeIUB5k/23.png
new file mode 100644
index 0000000000000000000000000000000000000000..1d71170d4436a5cf919b832a6fe97865ad640a18
--- /dev/null
+++ b/vlm/dev/ZBESeIUB5k/23.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0a5f5e00443a80a99a67832ac52b03dede9daaf1cff6eba9b3a111305d14307a
+size 276482
diff --git a/vlm/dev/ZBESeIUB5k/3.png b/vlm/dev/ZBESeIUB5k/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..0f09b9ce5440ff355f1b97bc238754702b95b12f
--- /dev/null
+++ b/vlm/dev/ZBESeIUB5k/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1481bd244923e4fe6914570ba96b8c5b0b684d180289db97fc8a42ee9bc27f3e
+size 601813
diff --git a/vlm/dev/ZBESeIUB5k/4.png b/vlm/dev/ZBESeIUB5k/4.png
new file mode 100644
index 0000000000000000000000000000000000000000..cf95e345196085de81687a9096245d3f0dc26549
--- /dev/null
+++ b/vlm/dev/ZBESeIUB5k/4.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:062a0069d4e5a434d0fe32edc72cdbaf648866fa857f142d111cbe5739bd78cc
+size 590082
diff --git a/vlm/dev/ZBESeIUB5k/5.png b/vlm/dev/ZBESeIUB5k/5.png
new file mode 100644
index 0000000000000000000000000000000000000000..92df9ad228782680d6f5527ecbcf9949a47a7953
--- /dev/null
+++ b/vlm/dev/ZBESeIUB5k/5.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:38fa47da237f2507dddcfba28078b845284b09e2a51e2de55d4788757b0eb3bc
+size 587668
diff --git a/vlm/dev/ZBESeIUB5k/6.png b/vlm/dev/ZBESeIUB5k/6.png
new file mode 100644
index 0000000000000000000000000000000000000000..06fee40cfdb64f668a0f11bb0b46cf9875be8fdd
--- /dev/null
+++ b/vlm/dev/ZBESeIUB5k/6.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ac376fe446c335d2ad964a9bdaa9cb74a9b3331dc4454ccb55240cdda45fad40
+size 544341
diff --git a/vlm/dev/ZBESeIUB5k/7.png b/vlm/dev/ZBESeIUB5k/7.png
new file mode 100644
index 0000000000000000000000000000000000000000..d1db18bacc718d3851aec841d3e76e570ae5884d
--- /dev/null
+++ b/vlm/dev/ZBESeIUB5k/7.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:95b77d0be2dc2028233a5d9a97ddcf70bf222d7f797b611c4cd4cebc8334dec8
+size 613380
diff --git a/vlm/dev/ZBESeIUB5k/8.png b/vlm/dev/ZBESeIUB5k/8.png
new file mode 100644
index 0000000000000000000000000000000000000000..14f07e5925704a5242afb6a61f046bb5e0a33ba5
--- /dev/null
+++ b/vlm/dev/ZBESeIUB5k/8.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:104a0714a3e07aae6326c477529d9a6697051c292ff95115228cbcb00522da93
+size 561304
diff --git a/vlm/dev/ZBESeIUB5k/9.png b/vlm/dev/ZBESeIUB5k/9.png
new file mode 100644
index 0000000000000000000000000000000000000000..e007010875043d05050befec24f9183d4b4969f5
--- /dev/null
+++ b/vlm/dev/ZBESeIUB5k/9.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a77c590638346b8d16dad0c144b803a5efa86151a933d9868644dd6aff21eb15
+size 536206
diff --git a/vlm/dev/a6NvoZ5DLoe/0.png b/vlm/dev/a6NvoZ5DLoe/0.png
new file mode 100644
index 0000000000000000000000000000000000000000..c85169bea1d6bebbb893b303b2356b7a1bd19b28
--- /dev/null
+++ b/vlm/dev/a6NvoZ5DLoe/0.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7c56b212c551f5adcae5fdfc596e779a7f762b777d3761622a1bba2ba3539929
+size 500876
diff --git a/vlm/dev/a6NvoZ5DLoe/1.png b/vlm/dev/a6NvoZ5DLoe/1.png
new file mode 100644
index 0000000000000000000000000000000000000000..363e13bbc8a969e8685bf255cb1420655b700e38
--- /dev/null
+++ b/vlm/dev/a6NvoZ5DLoe/1.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4e475c79a090962fd6ec5f485421728f133ff9952fa264e637f2d06f65421828
+size 557200
diff --git a/vlm/dev/a6NvoZ5DLoe/10.png b/vlm/dev/a6NvoZ5DLoe/10.png
new file mode 100644
index 0000000000000000000000000000000000000000..04b455994107261fc57a56b2aa18672b0f1c9e5f
--- /dev/null
+++ b/vlm/dev/a6NvoZ5DLoe/10.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:38321077c3bfa94204a3c59213ac6e07147f57c7d8eb1d1a95e926bfe7b789d1
+size 553137
diff --git a/vlm/dev/a6NvoZ5DLoe/11.png b/vlm/dev/a6NvoZ5DLoe/11.png
new file mode 100644
index 0000000000000000000000000000000000000000..1d58372fa239c047c98bddc76c9d1a9ab88da208
--- /dev/null
+++ b/vlm/dev/a6NvoZ5DLoe/11.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:14404df222fb467174c47aa438d91a0f8d053b27353d8be9c0feb1e8dda2f0b4
+size 491518
diff --git a/vlm/dev/a6NvoZ5DLoe/12.png b/vlm/dev/a6NvoZ5DLoe/12.png
new file mode 100644
index 0000000000000000000000000000000000000000..5730571e423d1d281cef37bc65c92dcab6b60aee
--- /dev/null
+++ b/vlm/dev/a6NvoZ5DLoe/12.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bc4696c090d41c9fe23051683428ee524d4ea371ca2371d259d4da0146c56604
+size 358275
diff --git a/vlm/dev/a6NvoZ5DLoe/13.png b/vlm/dev/a6NvoZ5DLoe/13.png
new file mode 100644
index 0000000000000000000000000000000000000000..2873d0d56ef5322819204c5c8018e9ca44a85c17
--- /dev/null
+++ b/vlm/dev/a6NvoZ5DLoe/13.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b63990b4391de9be57382a1a27df36ce54ebea60ac18084adf2bd72e8213d0bc
+size 175290
diff --git a/vlm/dev/a6NvoZ5DLoe/2.png b/vlm/dev/a6NvoZ5DLoe/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..8f92cb8c24704fa5b7edae46a9edea6d52e87c9c
--- /dev/null
+++ b/vlm/dev/a6NvoZ5DLoe/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:84ca66fbf4a70881754ba1dfe8ade7df71f8e71e47152caa577092f28690e57b
+size 596126
diff --git a/vlm/dev/a6NvoZ5DLoe/3.png b/vlm/dev/a6NvoZ5DLoe/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..4cf976d8afc2cf2a26519dee09f42a8ca187eafe
--- /dev/null
+++ b/vlm/dev/a6NvoZ5DLoe/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4f491f4ae6ffb9d1057ea4e4abb41ca67c306065863bccfac257c27c2e80b0fa
+size 489716
diff --git a/vlm/dev/a6NvoZ5DLoe/4.png b/vlm/dev/a6NvoZ5DLoe/4.png
new file mode 100644
index 0000000000000000000000000000000000000000..1c2e0ae02686e5d59bc3266873b01a784766c195
--- /dev/null
+++ b/vlm/dev/a6NvoZ5DLoe/4.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fbd1f8dbeb685df10b8c5936e2e7b8acbd71c86baa7aed1168ebfdb3c6e71725
+size 548583
diff --git a/vlm/dev/a6NvoZ5DLoe/5.png b/vlm/dev/a6NvoZ5DLoe/5.png
new file mode 100644
index 0000000000000000000000000000000000000000..1aea81881b8948658f9c8d38c4c2bf9a781eca83
--- /dev/null
+++ b/vlm/dev/a6NvoZ5DLoe/5.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:187529f31859b8b21beeddf927c046b967ecd7ba64e01dc0c453b5a3c8c1b715
+size 521582
diff --git a/vlm/dev/a6NvoZ5DLoe/6.png b/vlm/dev/a6NvoZ5DLoe/6.png
new file mode 100644
index 0000000000000000000000000000000000000000..4bda26338568fc8af38d663b4b4d5018c89c21be
--- /dev/null
+++ b/vlm/dev/a6NvoZ5DLoe/6.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a01fff6a822764230af0cc36f71a1cd6794fbc9390c736b4c21c433de3cfe101
+size 518974
diff --git a/vlm/dev/a6NvoZ5DLoe/7.png b/vlm/dev/a6NvoZ5DLoe/7.png
new file mode 100644
index 0000000000000000000000000000000000000000..7148d6400698068a087752c28a8388cd0aff3f2e
--- /dev/null
+++ b/vlm/dev/a6NvoZ5DLoe/7.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a47739c3b544252f1b501151eaab71f2cd42c7a312b13c418b778d9815341544
+size 566885
diff --git a/vlm/dev/a6NvoZ5DLoe/8.png b/vlm/dev/a6NvoZ5DLoe/8.png
new file mode 100644
index 0000000000000000000000000000000000000000..2e2903d571d55cabc649d0dcd08e231abb690cad
--- /dev/null
+++ b/vlm/dev/a6NvoZ5DLoe/8.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:06fad3cf641931cf2c2a6f0c09a4ff3fc82f7d855184e50447505f238cfaedcf
+size 571488
diff --git a/vlm/dev/a6NvoZ5DLoe/9.png b/vlm/dev/a6NvoZ5DLoe/9.png
new file mode 100644
index 0000000000000000000000000000000000000000..320a10b36fcfcf5e8e0e65f98184fdbeacc3dc9a
--- /dev/null
+++ b/vlm/dev/a6NvoZ5DLoe/9.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d93634d6084d2a55457b740daaf8b90fd3f1b8245fd4868f1c9f385c45e07d99
+size 536436
diff --git a/vlm/dev/aa8KsqfTPa/0.png b/vlm/dev/aa8KsqfTPa/0.png
new file mode 100644
index 0000000000000000000000000000000000000000..166deeccb9a5638294ab3cf0f4617b397cae9d70
--- /dev/null
+++ b/vlm/dev/aa8KsqfTPa/0.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5be6f8c1f3ef6947fbcd4c3ce4bfb31e5470b4325425bd7fd2d1616b3ae0b7d1
+size 480633
diff --git a/vlm/dev/aa8KsqfTPa/1.png b/vlm/dev/aa8KsqfTPa/1.png
new file mode 100644
index 0000000000000000000000000000000000000000..6ae45ea3be4f12b3ac27b2910a4e9be195bd3ef6
--- /dev/null
+++ b/vlm/dev/aa8KsqfTPa/1.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fd5616005bef713d9ae1b13a3423456b0a21adcccb2315c3a1f7e0674e0e3e65
+size 591900
diff --git a/vlm/dev/aa8KsqfTPa/10.png b/vlm/dev/aa8KsqfTPa/10.png
new file mode 100644
index 0000000000000000000000000000000000000000..3d03e69ed585e7a1927670822bbee44e5fa9f715
--- /dev/null
+++ b/vlm/dev/aa8KsqfTPa/10.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1774d1a59b224cca7aead1b63675503ee9c96c48e96ad23d726a601ec295abf0
+size 513064
diff --git a/vlm/dev/aa8KsqfTPa/11.png b/vlm/dev/aa8KsqfTPa/11.png
new file mode 100644
index 0000000000000000000000000000000000000000..40e83569b63e3dfa814c693690f8e904c622add2
--- /dev/null
+++ b/vlm/dev/aa8KsqfTPa/11.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2c42fe8bc7ae224a8030273dbd303296848f1ebafae341d2c8e1dc98b42af022
+size 535394
diff --git a/vlm/dev/aa8KsqfTPa/12.png b/vlm/dev/aa8KsqfTPa/12.png
new file mode 100644
index 0000000000000000000000000000000000000000..0d55851b10438e35ee77a16d13b3f4ceca65485c
--- /dev/null
+++ b/vlm/dev/aa8KsqfTPa/12.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a678896f15ee266965da22ffacacdb78ebc40636a695ebc5466f6bb79a36d554
+size 233437
diff --git a/vlm/dev/aa8KsqfTPa/13.png b/vlm/dev/aa8KsqfTPa/13.png
new file mode 100644
index 0000000000000000000000000000000000000000..1aa8b6f5b59592f2a7f33bd7db8a62d86c967a21
--- /dev/null
+++ b/vlm/dev/aa8KsqfTPa/13.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5ceda1f14273b7f1430181231e6feb9acbbc60610505a7e0598cd5d231799407
+size 205361
diff --git a/vlm/dev/aa8KsqfTPa/14.png b/vlm/dev/aa8KsqfTPa/14.png
new file mode 100644
index 0000000000000000000000000000000000000000..c6ffbf85f96b3f96ab11706c037f86252e5ca4f9
--- /dev/null
+++ b/vlm/dev/aa8KsqfTPa/14.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9223434cccbbbfa243abb0a670ad05294e56ccb59d6f490d0441eb33eaaf8d35
+size 91814
diff --git a/vlm/dev/aa8KsqfTPa/2.png b/vlm/dev/aa8KsqfTPa/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..17535259e93da17164f0d4b2c58da160b4506ea9
--- /dev/null
+++ b/vlm/dev/aa8KsqfTPa/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b7546a3de5b65f05464f91d57920af753149da2d2641dc129c454b9dd577f85a
+size 609910
diff --git a/vlm/dev/aa8KsqfTPa/3.png b/vlm/dev/aa8KsqfTPa/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..b1f7034f5bbae7ebcefebba0a1e6147154fddb93
--- /dev/null
+++ b/vlm/dev/aa8KsqfTPa/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2a08b399c49d7ac72ab054b7b1966835efb0736220fc4410f8fb12308a53af8d
+size 512006
diff --git a/vlm/dev/aa8KsqfTPa/4.png b/vlm/dev/aa8KsqfTPa/4.png
new file mode 100644
index 0000000000000000000000000000000000000000..c4e02058c3a9b8bfe302427cee955155bd7a12b2
--- /dev/null
+++ b/vlm/dev/aa8KsqfTPa/4.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2f30c3038e83eb987fb4d8fec5111be9566b8c841e956c3ba0cfa8394b2e1ad2
+size 533117
diff --git a/vlm/dev/aa8KsqfTPa/5.png b/vlm/dev/aa8KsqfTPa/5.png
new file mode 100644
index 0000000000000000000000000000000000000000..b01c3ef256e72d22c61fba977b5e1e071bb41421
--- /dev/null
+++ b/vlm/dev/aa8KsqfTPa/5.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4f893ab665f3f2da9d23a88e1856676936734fdc1fd906846b76b468b2805cbc
+size 479759
diff --git a/vlm/dev/aa8KsqfTPa/6.png b/vlm/dev/aa8KsqfTPa/6.png
new file mode 100644
index 0000000000000000000000000000000000000000..e0ff267d9ebd5dc49ba613775d6c8076c558c65e
--- /dev/null
+++ b/vlm/dev/aa8KsqfTPa/6.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ed9188a0144ed0a6020e982d50c28bca7df2261be229419e52082f1247fee29b
+size 511408
diff --git a/vlm/dev/aa8KsqfTPa/7.png b/vlm/dev/aa8KsqfTPa/7.png
new file mode 100644
index 0000000000000000000000000000000000000000..34a1f2266a2dd0106981f3b517f1e0e346e04e66
--- /dev/null
+++ b/vlm/dev/aa8KsqfTPa/7.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7e158b4d1ea9ae914fbf38a737ddb41626d2ccbe974ef2df5b0459b09c03adf1
+size 517577
diff --git a/vlm/dev/aa8KsqfTPa/8.png b/vlm/dev/aa8KsqfTPa/8.png
new file mode 100644
index 0000000000000000000000000000000000000000..2a4ef521d1dc9713e3a03ad94922343869476756
--- /dev/null
+++ b/vlm/dev/aa8KsqfTPa/8.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bf63c85061e2907de78f371c820b6732708581623171c149345d4c205c64534f
+size 639912
diff --git a/vlm/dev/aa8KsqfTPa/9.png b/vlm/dev/aa8KsqfTPa/9.png
new file mode 100644
index 0000000000000000000000000000000000000000..91e0cd37773666aa9e45f72504b56e528ecc1c20
--- /dev/null
+++ b/vlm/dev/aa8KsqfTPa/9.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d22f5de6a58435cdd8ec6043258f1666a0abd68cd7487c946d5ebbc187b70a79
+size 545272
diff --git a/vlm/dev/bdHkMjBJG_w/0.png b/vlm/dev/bdHkMjBJG_w/0.png
new file mode 100644
index 0000000000000000000000000000000000000000..bf564c02fb421573140b310b3ac59e52a0f43814
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/0.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:665b166190c6bbc23a0516a1193097de2820c09523d545f4fa5c989e073361ae
+size 654296
diff --git a/vlm/dev/bdHkMjBJG_w/1.png b/vlm/dev/bdHkMjBJG_w/1.png
new file mode 100644
index 0000000000000000000000000000000000000000..1c5309028b6de8e0298667af29c59f189c19567a
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/1.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:274a80b31bf945d0562e07166821d6f5d6cedffc08f1bb2497d1adfdc2ae255f
+size 625502
diff --git a/vlm/dev/bdHkMjBJG_w/10.png b/vlm/dev/bdHkMjBJG_w/10.png
new file mode 100644
index 0000000000000000000000000000000000000000..958b8f6accf7a06a4b44f6f8ff410c9416ee4512
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/10.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:86fa3e6571d2fe5dd39d35ff8c47ced48d3ab73481cb68899cd341cf2640d060
+size 506952
diff --git a/vlm/dev/bdHkMjBJG_w/11.png b/vlm/dev/bdHkMjBJG_w/11.png
new file mode 100644
index 0000000000000000000000000000000000000000..cd5a88b22613e5b9e03ea6c107481ddc335453e5
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/11.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:50cf3c8b8ed1727caba013c6de58e14750338d69458754c5ec5e4d213c616ac2
+size 521534
diff --git a/vlm/dev/bdHkMjBJG_w/12.png b/vlm/dev/bdHkMjBJG_w/12.png
new file mode 100644
index 0000000000000000000000000000000000000000..3b471fd6f7a0fd477847ccedf937ffd88bf208b0
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/12.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:262792b9b99c3f6b0b72be04ed03f6107547e05255e4823f7c5b451e9645dd75
+size 544219
diff --git a/vlm/dev/bdHkMjBJG_w/13.png b/vlm/dev/bdHkMjBJG_w/13.png
new file mode 100644
index 0000000000000000000000000000000000000000..073f7610eeb6fd7e249b516e1b762abb049ef239
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/13.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4d271dee3d937aa3befbcebacc2cd388ef29536390605f488e982d00ed7e7d2f
+size 523015
diff --git a/vlm/dev/bdHkMjBJG_w/14.png b/vlm/dev/bdHkMjBJG_w/14.png
new file mode 100644
index 0000000000000000000000000000000000000000..4e8bd1e3a524bd889b1b8d469562d836f70ea077
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/14.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:eac9252f85aa32db1c49ca49f64203ed664834cfd2499c938d1b5bacbe7a3fc7
+size 549562
diff --git a/vlm/dev/bdHkMjBJG_w/15.png b/vlm/dev/bdHkMjBJG_w/15.png
new file mode 100644
index 0000000000000000000000000000000000000000..c54255779401d6d0ab5cc3fdb546c9eb4031e730
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/15.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:217cafe99c966ba76a044f2eebf2666c50dead5b0d3f65a09b20b7062463fc3f
+size 582159
diff --git a/vlm/dev/bdHkMjBJG_w/16.png b/vlm/dev/bdHkMjBJG_w/16.png
new file mode 100644
index 0000000000000000000000000000000000000000..aa673f38f607b8b638bb7c0ba178fba449b2d9a7
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/16.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6be93581521095b9891c6222df8bc24c1d19c497302ca9b87608344328ba733f
+size 537924
diff --git a/vlm/dev/bdHkMjBJG_w/17.png b/vlm/dev/bdHkMjBJG_w/17.png
new file mode 100644
index 0000000000000000000000000000000000000000..f00a483cf012d35fd4598dd0ab6f427e8dc3e600
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/17.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:433fd90704ce8cda286e671b168ba923bf4e921f4647f1177d3d9452dc558a0f
+size 497396
diff --git a/vlm/dev/bdHkMjBJG_w/18.png b/vlm/dev/bdHkMjBJG_w/18.png
new file mode 100644
index 0000000000000000000000000000000000000000..4546a50cc636b30507e0e560b5113ca5c8e98012
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/18.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4648afa552d3caa338c094317de791b408f682a019799ee50949a50a952df141
+size 786103
diff --git a/vlm/dev/bdHkMjBJG_w/19.png b/vlm/dev/bdHkMjBJG_w/19.png
new file mode 100644
index 0000000000000000000000000000000000000000..e1744d6e8568ae85adbd000c9b3b5a81aad6f620
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/19.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:930177ac13992a75f90dd7a4a1533bda0ca4d56a1a7beea61287f8545d4a7b38
+size 554015
diff --git a/vlm/dev/bdHkMjBJG_w/2.png b/vlm/dev/bdHkMjBJG_w/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..fd502f33083045695c4ac30f958d40a922335f1d
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1f453c340752470f979f53f397f32b16d3d68f522f94dfd1f33ec07693b0f3b1
+size 625263
diff --git a/vlm/dev/bdHkMjBJG_w/20.png b/vlm/dev/bdHkMjBJG_w/20.png
new file mode 100644
index 0000000000000000000000000000000000000000..3e40038470a3b6d6e8f5c91fe0107f36dcc10677
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/20.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3714b3c770ad0f7a3f4023f6e8aa3d25227ca38b6a5c8274d26a616385f88b1f
+size 526881
diff --git a/vlm/dev/bdHkMjBJG_w/21.png b/vlm/dev/bdHkMjBJG_w/21.png
new file mode 100644
index 0000000000000000000000000000000000000000..7449709b6f223cc5303b4a3fd0a2d25c35fe148d
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/21.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e08ed6ed475012663605289956010be0555c2aab20f2d8f3954223b3e4ad782f
+size 448202
diff --git a/vlm/dev/bdHkMjBJG_w/22.png b/vlm/dev/bdHkMjBJG_w/22.png
new file mode 100644
index 0000000000000000000000000000000000000000..86daa1a1bfb111b8fff258119d9dcdd5cb2bdaa9
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/22.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c46e01e309b94bebed22f61590a762014e23e84251c7413c666acbad0e2845e7
+size 499842
diff --git a/vlm/dev/bdHkMjBJG_w/23.png b/vlm/dev/bdHkMjBJG_w/23.png
new file mode 100644
index 0000000000000000000000000000000000000000..a98ad995a618329e62a07f51f149d01b8397eea1
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/23.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:537b310ad398c0d0129d8163830410f3f0f54cda355dbca0da5facdf759cf757
+size 427543
diff --git a/vlm/dev/bdHkMjBJG_w/24.png b/vlm/dev/bdHkMjBJG_w/24.png
new file mode 100644
index 0000000000000000000000000000000000000000..d1ed52294a0f4d7ce9a02bf25352780dd5929497
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/24.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cf5d5a8daf95cac1a816c6d54abd18eac4794a3126c332b09ab8de38ca6a303b
+size 351471
diff --git a/vlm/dev/bdHkMjBJG_w/25.png b/vlm/dev/bdHkMjBJG_w/25.png
new file mode 100644
index 0000000000000000000000000000000000000000..b76a7d115c28e3f8e8cc927bd8e66eaba175ec9b
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/25.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:00a7bbe551cf3cdc6b5064fdbd76abcd351dd2c4fb70ca44cc73bdb43e569476
+size 385643
diff --git a/vlm/dev/bdHkMjBJG_w/26.png b/vlm/dev/bdHkMjBJG_w/26.png
new file mode 100644
index 0000000000000000000000000000000000000000..bb0823da870b52b00867cc0dec6430410a0684ed
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/26.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ad2d74c2510c5fbb0da60c67e48c6a7fcaa6908218785b929dae657c2080a598
+size 435023
diff --git a/vlm/dev/bdHkMjBJG_w/27.png b/vlm/dev/bdHkMjBJG_w/27.png
new file mode 100644
index 0000000000000000000000000000000000000000..5bbd82412c7d2c5dc3e285f2c66cf24bde138b13
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/27.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3a9976ea8b824bb6f83c91bd4c44e485ba4d630f9268fb5718a3e6b9a962fc6f
+size 402083
diff --git a/vlm/dev/bdHkMjBJG_w/28.png b/vlm/dev/bdHkMjBJG_w/28.png
new file mode 100644
index 0000000000000000000000000000000000000000..a4de93feb9ef9b53593e3c028c50c8a374231b92
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/28.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0fcb6de872fe0d806ccab2cfe0ddf0a56f462d28e98b871f17e90d919e237fc3
+size 871697
diff --git a/vlm/dev/bdHkMjBJG_w/29.png b/vlm/dev/bdHkMjBJG_w/29.png
new file mode 100644
index 0000000000000000000000000000000000000000..bfc3454d4322bd1d503156cfa22d5259dc162b58
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/29.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bf1772a536b3a95196593d80040544f5de376a672c4afac46142ce2a94cd57e9
+size 941778
diff --git a/vlm/dev/bdHkMjBJG_w/3.png b/vlm/dev/bdHkMjBJG_w/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..4b7cb8c4348293ae615848cd85fc1439ca1f38a8
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:763ba1b8d23217c1e38ec14934e48dfd18b50ff47cd76c9339d21093c4ba4951
+size 690088
diff --git a/vlm/dev/bdHkMjBJG_w/30.png b/vlm/dev/bdHkMjBJG_w/30.png
new file mode 100644
index 0000000000000000000000000000000000000000..7dcf2a75e1e49a613d5ec61f882dd8b78fe0c4fb
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/30.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c5f38b1c3e69762f215a0528fc0b9ddc27f86e48cd90aff1c5ad3ca4cc68aa73
+size 895710
diff --git a/vlm/dev/bdHkMjBJG_w/31.png b/vlm/dev/bdHkMjBJG_w/31.png
new file mode 100644
index 0000000000000000000000000000000000000000..8078e2c1c58d2dff2e7e621e689f4d1126d74d26
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/31.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cf60c4c6284f7bd27b83cff32d09f8c6065ac16bc4fbb97c39dd0cc317080820
+size 602046
diff --git a/vlm/dev/bdHkMjBJG_w/4.png b/vlm/dev/bdHkMjBJG_w/4.png
new file mode 100644
index 0000000000000000000000000000000000000000..eda96c8106459786025bded53bf25b8eb51e25c8
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/4.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9e05ace25c3e17d53d27ff793f9c96b802454ec336af2f9b4506d97629bf2fd6
+size 820778
diff --git a/vlm/dev/bdHkMjBJG_w/5.png b/vlm/dev/bdHkMjBJG_w/5.png
new file mode 100644
index 0000000000000000000000000000000000000000..9b8df702ebab828f0aa149c3af20a7617fbda71e
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/5.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1ca20c3c49c30ad2dc624595c369cb0ec6b6a710685df1fc5d1e979e898bc595
+size 1155287
diff --git a/vlm/dev/bdHkMjBJG_w/6.png b/vlm/dev/bdHkMjBJG_w/6.png
new file mode 100644
index 0000000000000000000000000000000000000000..3e89a87d5125e74033b34f4c0024b9e7e7c9eb15
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/6.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a286cd9fb2d6cb63338770946261fdad933685e97eadc9f88b2d49b25d698e85
+size 629421
diff --git a/vlm/dev/bdHkMjBJG_w/7.png b/vlm/dev/bdHkMjBJG_w/7.png
new file mode 100644
index 0000000000000000000000000000000000000000..c5c18e0da4825c238859d2ebef24a06c8977cb8d
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/7.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:de10b38aa413fcf144743e59f9c1c77171f10b8575d8fe1db4887098b31a126e
+size 637477
diff --git a/vlm/dev/bdHkMjBJG_w/8.png b/vlm/dev/bdHkMjBJG_w/8.png
new file mode 100644
index 0000000000000000000000000000000000000000..2c44ac7d8ce4bc5c612fc9f90efebdf5791cf8d0
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/8.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:baf0fbb69a5abba19ce2fc4fd3689e3efc5fdde8902affe3facec870dd5e38e2
+size 534772
diff --git a/vlm/dev/bdHkMjBJG_w/9.png b/vlm/dev/bdHkMjBJG_w/9.png
new file mode 100644
index 0000000000000000000000000000000000000000..65c621e0fc4b8b0033355e68bb3317d77121713b
--- /dev/null
+++ b/vlm/dev/bdHkMjBJG_w/9.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ee8118436a3fa8ed8b982975303b9d229d2dc4781ae6040c83e9f58319ab7530
+size 537119
diff --git a/vlm/dev/c5Inzw6giM/0.png b/vlm/dev/c5Inzw6giM/0.png
new file mode 100644
index 0000000000000000000000000000000000000000..5980bdd046a061f7acf0e9377ca60df90f83e57c
--- /dev/null
+++ b/vlm/dev/c5Inzw6giM/0.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3fcc3ac70fd15f36b69d6326bbf5ea5b9eb82e806e03f411cb7e2d0c608776be
+size 424895
diff --git a/vlm/dev/c5Inzw6giM/1.png b/vlm/dev/c5Inzw6giM/1.png
new file mode 100644
index 0000000000000000000000000000000000000000..05b6871fb4308bee361be59e81fcfc9f88c25973
--- /dev/null
+++ b/vlm/dev/c5Inzw6giM/1.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c49814ee63abc199367255037e277195655c3b29d46f825798be274981b8f842
+size 510764
diff --git a/vlm/dev/c5Inzw6giM/2.png b/vlm/dev/c5Inzw6giM/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..eb7163a1c2652da7525c36a901ef7a2721863c72
--- /dev/null
+++ b/vlm/dev/c5Inzw6giM/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d7cb56fdbb6ea2b6899f6c3bbfe2b242cfc97feaa5b99f949353402795d3b6ad
+size 443000
diff --git a/vlm/dev/c5Inzw6giM/3.png b/vlm/dev/c5Inzw6giM/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..f7747cd5c6b6fa13638736044d71667b43a9c811
--- /dev/null
+++ b/vlm/dev/c5Inzw6giM/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4c459d1592cad3ff877ce2a49984c612698d847aa0b15348cf3de89528110e72
+size 319896
diff --git a/vlm/dev/c5Inzw6giM/4.png b/vlm/dev/c5Inzw6giM/4.png
new file mode 100644
index 0000000000000000000000000000000000000000..8a72dbbd32add99c6315236252761aaf16118273
--- /dev/null
+++ b/vlm/dev/c5Inzw6giM/4.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:68b5782623bb38290bcd0d90b69fc699165c7febe8192a09406dd9ca8d13b702
+size 480297
diff --git a/vlm/dev/c5Inzw6giM/5.png b/vlm/dev/c5Inzw6giM/5.png
new file mode 100644
index 0000000000000000000000000000000000000000..384b1fe699a15853d7c3591bb22ddedfcf202bea
--- /dev/null
+++ b/vlm/dev/c5Inzw6giM/5.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e91ae52c83e4481572f8790c6e9c87b0d9d04beb6ba1a465cfb5990edd944579
+size 373558
diff --git a/vlm/dev/c5Inzw6giM/6.png b/vlm/dev/c5Inzw6giM/6.png
new file mode 100644
index 0000000000000000000000000000000000000000..6468d6e3a01ff6d30a734ed081d8ea3056d9d395
--- /dev/null
+++ b/vlm/dev/c5Inzw6giM/6.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f05f3d4a7c92fe7de11fd316251363013f6968c4097fe1783829deaab2407ada
+size 341484
diff --git a/vlm/dev/c5Inzw6giM/7.png b/vlm/dev/c5Inzw6giM/7.png
new file mode 100644
index 0000000000000000000000000000000000000000..46144d7f0be4733324b578dbc6fb3a4a7325c8c4
--- /dev/null
+++ b/vlm/dev/c5Inzw6giM/7.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:441b2871d9ca679de63d17b2bd820577b42b5948db92e76834bbc7661d68dc17
+size 344836
diff --git a/vlm/dev/c5Inzw6giM/8.png b/vlm/dev/c5Inzw6giM/8.png
new file mode 100644
index 0000000000000000000000000000000000000000..731dee8e71be72ef21d94003404541bcfee5edad
--- /dev/null
+++ b/vlm/dev/c5Inzw6giM/8.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:dcdb88b4ab6754eb83bda7f8d65970138fbaa7e34d78d31812d3858b2d643d8a
+size 513051
diff --git a/vlm/dev/c5Inzw6giM/9.png b/vlm/dev/c5Inzw6giM/9.png
new file mode 100644
index 0000000000000000000000000000000000000000..114ffc3c2f76603ccabae83b431a38d318c853e6
--- /dev/null
+++ b/vlm/dev/c5Inzw6giM/9.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:283ce2cc52921a2efde80eb835235b4c4146e724a0f601d073633a2535efaae3
+size 512762
diff --git a/vlm/dev/gUL6zYN4Uaf/0.png b/vlm/dev/gUL6zYN4Uaf/0.png
new file mode 100644
index 0000000000000000000000000000000000000000..6f88809d2538eb45366ab231507f48a8fbc26f5b
--- /dev/null
+++ b/vlm/dev/gUL6zYN4Uaf/0.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8bcf0b296be9810ef0728261ba7566220bccc4a7fecd087fca0847f4c60ba74c
+size 526846
diff --git a/vlm/dev/gUL6zYN4Uaf/1.png b/vlm/dev/gUL6zYN4Uaf/1.png
new file mode 100644
index 0000000000000000000000000000000000000000..5e85d16e3864f385248409804a4018a889410318
--- /dev/null
+++ b/vlm/dev/gUL6zYN4Uaf/1.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e4dcb054ffd60be39d81822833d913acf4f588d3cf254b77072c5e4db22d70cc
+size 590066
diff --git a/vlm/dev/gUL6zYN4Uaf/11.png b/vlm/dev/gUL6zYN4Uaf/11.png
new file mode 100644
index 0000000000000000000000000000000000000000..0c30566fb2ce2a5f89134aa98e4185a593df11da
--- /dev/null
+++ b/vlm/dev/gUL6zYN4Uaf/11.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f53912b2f827782073c9e728c67ead641ec7287ace3b826406470e1c1e67fea8
+size 606528
diff --git a/vlm/dev/gUL6zYN4Uaf/12.png b/vlm/dev/gUL6zYN4Uaf/12.png
new file mode 100644
index 0000000000000000000000000000000000000000..e3c808093ec8754368e5d94e806ed3b188a10ad7
--- /dev/null
+++ b/vlm/dev/gUL6zYN4Uaf/12.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:81c6707d694f2a8383c4679b8f743557e053029a88a275872af761a99f6f3ac6
+size 631964
diff --git a/vlm/dev/gUL6zYN4Uaf/13.png b/vlm/dev/gUL6zYN4Uaf/13.png
new file mode 100644
index 0000000000000000000000000000000000000000..e3f7399009f0c9e40990ce44090d054bcf196823
--- /dev/null
+++ b/vlm/dev/gUL6zYN4Uaf/13.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c90264f50e176e47f2c125d8129456e8023556110021320411d91bbafaaa07bf
+size 611033
diff --git a/vlm/dev/gUL6zYN4Uaf/14.png b/vlm/dev/gUL6zYN4Uaf/14.png
new file mode 100644
index 0000000000000000000000000000000000000000..9c14add5fc95eb8b4458401ee4f1f5fc4c8df8b6
--- /dev/null
+++ b/vlm/dev/gUL6zYN4Uaf/14.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b477c1b2c0aa7d89cd35d7af27f3a8154188e1419557a35232f7305fee813a61
+size 602033
diff --git a/vlm/dev/gUL6zYN4Uaf/15.png b/vlm/dev/gUL6zYN4Uaf/15.png
new file mode 100644
index 0000000000000000000000000000000000000000..bb908b7393244b30cee7c04d985310e78add6dbb
--- /dev/null
+++ b/vlm/dev/gUL6zYN4Uaf/15.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9f3dd9f1e9113947f8e02a73625f7da6f65f23d490ff953dc4fef8625f77efd8
+size 662269
diff --git a/vlm/dev/gUL6zYN4Uaf/16.png b/vlm/dev/gUL6zYN4Uaf/16.png
new file mode 100644
index 0000000000000000000000000000000000000000..b0f2866f80142dc2ef29900ffcb6718b05634044
--- /dev/null
+++ b/vlm/dev/gUL6zYN4Uaf/16.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d3557b6810b330402fab5777591de23d17bdc581ca265b325c44e0bd6a3541d1
+size 602667
diff --git a/vlm/dev/gUL6zYN4Uaf/17.png b/vlm/dev/gUL6zYN4Uaf/17.png
new file mode 100644
index 0000000000000000000000000000000000000000..c6c7d26f3e04b41a1e87671812d85205cacd7ff4
--- /dev/null
+++ b/vlm/dev/gUL6zYN4Uaf/17.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:91a39a613ca59359836676097a44a45907034844a02ff7cc9e4a7d4ccb7efe95
+size 624825
diff --git a/vlm/dev/gUL6zYN4Uaf/18.png b/vlm/dev/gUL6zYN4Uaf/18.png
new file mode 100644
index 0000000000000000000000000000000000000000..dc3168d52fcf2c33869c2e7532f91514a67265e8
--- /dev/null
+++ b/vlm/dev/gUL6zYN4Uaf/18.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7e3320f1763c407e3500cc32b84da02508f590b172db2f0ed8e2b248f26c0b97
+size 616951
diff --git a/vlm/dev/gUL6zYN4Uaf/19.png b/vlm/dev/gUL6zYN4Uaf/19.png
new file mode 100644
index 0000000000000000000000000000000000000000..e4204a4be441520bef6a748afbc3ade0dfa4294d
--- /dev/null
+++ b/vlm/dev/gUL6zYN4Uaf/19.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:29194fbebf041d610c2e5864408b19905e3692fbb54de8893d262c0e77079828
+size 460128
diff --git a/vlm/dev/gUL6zYN4Uaf/2.png b/vlm/dev/gUL6zYN4Uaf/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..58c78be7dcec817389e54dac0cdb1a8957b5b780
--- /dev/null
+++ b/vlm/dev/gUL6zYN4Uaf/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:427ef3bdd6a950cf86d77c6ee9f6d71f8fc685ac01faba4815e6da16cdb4ea20
+size 671439
diff --git a/vlm/dev/gUL6zYN4Uaf/20.png b/vlm/dev/gUL6zYN4Uaf/20.png
new file mode 100644
index 0000000000000000000000000000000000000000..557a8496b7cb491d9774d62606dc0e5ebbd46359
--- /dev/null
+++ b/vlm/dev/gUL6zYN4Uaf/20.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:57f9ff169a34b73de143f24cb3878b9cd698c92fc2a8a0f095d3fd3e275d4360
+size 341160
diff --git a/vlm/dev/gUL6zYN4Uaf/3.png b/vlm/dev/gUL6zYN4Uaf/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..5266249c25ae414a8cffb3a7bfdd6fa018f7d95a
--- /dev/null
+++ b/vlm/dev/gUL6zYN4Uaf/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e9ffa801412a5c1e7b209b570a296cf6837cfd3d7f60b513db93f951d446893f
+size 647955
diff --git a/vlm/dev/gUL6zYN4Uaf/4.png b/vlm/dev/gUL6zYN4Uaf/4.png
new file mode 100644
index 0000000000000000000000000000000000000000..98978740fcc4e88e499472884b58b4d792bc1f11
--- /dev/null
+++ b/vlm/dev/gUL6zYN4Uaf/4.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a3ac5733e31f2b159b19ffb8b5a693babfd0350f4d840c8fe1c472823e6a9c3a
+size 644245
diff --git a/vlm/dev/gUL6zYN4Uaf/5.png b/vlm/dev/gUL6zYN4Uaf/5.png
new file mode 100644
index 0000000000000000000000000000000000000000..39220ba00428bcfccfad24f1f65dd97ed2ad0af0
--- /dev/null
+++ b/vlm/dev/gUL6zYN4Uaf/5.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f322ffc368b69fc3619adc2af3a367f7918cc97d80def013769e74cfd1a544d4
+size 635266
diff --git a/vlm/dev/gUL6zYN4Uaf/7.png b/vlm/dev/gUL6zYN4Uaf/7.png
new file mode 100644
index 0000000000000000000000000000000000000000..45710b2fea3fdf2ccc79e7e38b2a2bf5b6b9a5f5
--- /dev/null
+++ b/vlm/dev/gUL6zYN4Uaf/7.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:137e478eee42caa24086ad3c26abfe52d900ef82dd57b6e2332b483173523a72
+size 554742
diff --git a/vlm/dev/gUL6zYN4Uaf/8.png b/vlm/dev/gUL6zYN4Uaf/8.png
new file mode 100644
index 0000000000000000000000000000000000000000..8d713f820a3fa53b4d03e860e15e394a501c0590
--- /dev/null
+++ b/vlm/dev/gUL6zYN4Uaf/8.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:706ae0fd1a9f33a8386b28b70636491bce4b21fed890d4bebfc8b88e5104853e
+size 621170
diff --git a/vlm/dev/gUL6zYN4Uaf/9.png b/vlm/dev/gUL6zYN4Uaf/9.png
new file mode 100644
index 0000000000000000000000000000000000000000..197bf16cd9203234339c043ac23555eaf765c745
--- /dev/null
+++ b/vlm/dev/gUL6zYN4Uaf/9.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6b530fb1ac83e1edd60e5c765576ee49b13ea18c73d6a5a9cd8633e935523a1d
+size 599166
diff --git a/vlm/dev/hfjbX1UKNx/0.png b/vlm/dev/hfjbX1UKNx/0.png
new file mode 100644
index 0000000000000000000000000000000000000000..493082396e599b7e990d8c51ebeb6fe6acc4fdf5
--- /dev/null
+++ b/vlm/dev/hfjbX1UKNx/0.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:07d3efd03731f4b390562c1e8f620d3d2f698cbe2daf1ec7a0c8f025c5a0e81b
+size 511655
diff --git a/vlm/dev/hfjbX1UKNx/1.png b/vlm/dev/hfjbX1UKNx/1.png
new file mode 100644
index 0000000000000000000000000000000000000000..4e2cdfd32823940f30e248abbb96321e76cf3148
--- /dev/null
+++ b/vlm/dev/hfjbX1UKNx/1.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:02e9d42ab7155b73ef7266b1ffe1ba0125250de6b56cadb098f78ebd6f9af4dd
+size 588257
diff --git a/vlm/dev/hfjbX1UKNx/10.png b/vlm/dev/hfjbX1UKNx/10.png
new file mode 100644
index 0000000000000000000000000000000000000000..e6c909dfc2337721ef6c6f0f9ddfce2b1559e107
--- /dev/null
+++ b/vlm/dev/hfjbX1UKNx/10.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5c568f3ec1fe0f8c2911bd27428907b46d39e90db47bdb0ef0978793476c7186
+size 503262
diff --git a/vlm/dev/hfjbX1UKNx/11.png b/vlm/dev/hfjbX1UKNx/11.png
new file mode 100644
index 0000000000000000000000000000000000000000..05677c404093fcb879dc9a112ca0e895ee3b251b
--- /dev/null
+++ b/vlm/dev/hfjbX1UKNx/11.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:822ad89fc66069dc230fe23cc3ac79838aa16684b4f1803aaf777f09fb8d35b7
+size 374274
diff --git a/vlm/dev/hfjbX1UKNx/12.png b/vlm/dev/hfjbX1UKNx/12.png
new file mode 100644
index 0000000000000000000000000000000000000000..783011655f2c9d61caa451ec44f7dbb655239d23
--- /dev/null
+++ b/vlm/dev/hfjbX1UKNx/12.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:18986a78bf1140707d9a2c0c78e5b2c47c6fa51f2ac6d20d40e59931caf1c54c
+size 387426
diff --git a/vlm/dev/hfjbX1UKNx/13.png b/vlm/dev/hfjbX1UKNx/13.png
new file mode 100644
index 0000000000000000000000000000000000000000..e1b59f80b898c4dbe497820e867afbc42006107b
--- /dev/null
+++ b/vlm/dev/hfjbX1UKNx/13.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:53281f15d949609047d975bdacc1ac1f488093d61697570d14445e16ba215630
+size 1699558
diff --git a/vlm/dev/hfjbX1UKNx/14.png b/vlm/dev/hfjbX1UKNx/14.png
new file mode 100644
index 0000000000000000000000000000000000000000..a3c990e0d1a56b0e04b49cd4adb32a2850a95a65
--- /dev/null
+++ b/vlm/dev/hfjbX1UKNx/14.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e1d760f1c4cfe4d50fc40ce5c5caaf9da938944dd63ad6ed4fd51369e7b10af2
+size 1601420
diff --git a/vlm/dev/hfjbX1UKNx/15.png b/vlm/dev/hfjbX1UKNx/15.png
new file mode 100644
index 0000000000000000000000000000000000000000..7c67ac6af720f47a7f06e3cb11812a09d94fa443
--- /dev/null
+++ b/vlm/dev/hfjbX1UKNx/15.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d75dc95b1481bc4fa200c25b93ba18c719f89a87514a45c562391df20a43351b
+size 792453
diff --git a/vlm/dev/hfjbX1UKNx/16.png b/vlm/dev/hfjbX1UKNx/16.png
new file mode 100644
index 0000000000000000000000000000000000000000..d3f5d0f9ddb7417f971bf07d523d6c6ca2b9cf0b
--- /dev/null
+++ b/vlm/dev/hfjbX1UKNx/16.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1fcc106bcbdf2d0028f631780ddfe6dc27f834ac0c4aef364ee1541d4fa4175f
+size 312262
diff --git a/vlm/dev/hfjbX1UKNx/17.png b/vlm/dev/hfjbX1UKNx/17.png
new file mode 100644
index 0000000000000000000000000000000000000000..a00545e24d863cd0917f7f2b3ab544c7cdb01947
--- /dev/null
+++ b/vlm/dev/hfjbX1UKNx/17.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bcca20ebed1f30ce2512e776748d315525e917072c6475ade82db6872822f0d0
+size 848571
diff --git a/vlm/dev/hfjbX1UKNx/18.png b/vlm/dev/hfjbX1UKNx/18.png
new file mode 100644
index 0000000000000000000000000000000000000000..61d6dd7ad1a026cde628fa1bcec48ccf78d9158c
--- /dev/null
+++ b/vlm/dev/hfjbX1UKNx/18.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f96a4fa30a957bf9789053a897da52553cb9b60729d7c521786eaf832fb5f045
+size 447578
diff --git a/vlm/dev/hfjbX1UKNx/19.png b/vlm/dev/hfjbX1UKNx/19.png
new file mode 100644
index 0000000000000000000000000000000000000000..5d120df043924768a7a3774d7659ee08ab81ec4b
--- /dev/null
+++ b/vlm/dev/hfjbX1UKNx/19.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:de4b799a5b91afc08c3321c1a29a627e70224ada41c57dca5a0eac71b931e64b
+size 347208
diff --git a/vlm/dev/hfjbX1UKNx/2.png b/vlm/dev/hfjbX1UKNx/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..8c17c13e537b1f1cf4e161ae02352398184bc9b7
--- /dev/null
+++ b/vlm/dev/hfjbX1UKNx/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0087ad4cdf243c6512dc320103153541516f9fc851bdbe6d877a35beaaf69726
+size 532648
diff --git a/vlm/dev/hfjbX1UKNx/20.png b/vlm/dev/hfjbX1UKNx/20.png
new file mode 100644
index 0000000000000000000000000000000000000000..1937167431fd13cf8a8da06bd68a1c2c74b9f792
--- /dev/null
+++ b/vlm/dev/hfjbX1UKNx/20.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e1e1284acf0c5050f829ba5e98ceb353bb16528177f5fcd508bbcb70eb0f7992
+size 2222210
diff --git a/vlm/dev/hfjbX1UKNx/21.png b/vlm/dev/hfjbX1UKNx/21.png
new file mode 100644
index 0000000000000000000000000000000000000000..508bc7a67bc128fd167d40be826ccb338644df30
--- /dev/null
+++ b/vlm/dev/hfjbX1UKNx/21.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:623006ef0e9f2e7afd4827bc7c1cb6266e0d97d33471ba193fa9a5d9e0587b1a
+size 977999
diff --git a/vlm/dev/hfjbX1UKNx/22.png b/vlm/dev/hfjbX1UKNx/22.png
new file mode 100644
index 0000000000000000000000000000000000000000..be997ad621c3ea0bf5ab7581ccd5cecaed7aa817
--- /dev/null
+++ b/vlm/dev/hfjbX1UKNx/22.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:819a3f85598e6497c67d366c020e24e9ded6f8f176303d7985b305e6323e8a65
+size 1335169
diff --git a/vlm/dev/hfjbX1UKNx/3.png b/vlm/dev/hfjbX1UKNx/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..884e44440aefc909d644877e7a904d35d469c1a5
--- /dev/null
+++ b/vlm/dev/hfjbX1UKNx/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fb909d11c08771527aff0197d99ab18c0ff5f8d2db475207f35684ff8d87e41a
+size 410238
diff --git a/vlm/dev/hfjbX1UKNx/4.png b/vlm/dev/hfjbX1UKNx/4.png
new file mode 100644
index 0000000000000000000000000000000000000000..edb4980b0fbec8d9cd52a45043b6d2719f39fa17
--- /dev/null
+++ b/vlm/dev/hfjbX1UKNx/4.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3bd14d4a5c96a7c22bebc20b6d1c0012003b11ebabb79afeb987f59e695b5d0c
+size 514010
diff --git a/vlm/dev/hfjbX1UKNx/5.png b/vlm/dev/hfjbX1UKNx/5.png
new file mode 100644
index 0000000000000000000000000000000000000000..6b7de49844f5e50959c841f9abb7774ef453d658
--- /dev/null
+++ b/vlm/dev/hfjbX1UKNx/5.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:13e24fb8a73115f8083f0921039cdb483ebe0b80fa2c97586a1df0cd8f00c1c1
+size 532493
diff --git a/vlm/dev/hfjbX1UKNx/6.png b/vlm/dev/hfjbX1UKNx/6.png
new file mode 100644
index 0000000000000000000000000000000000000000..d733d038336d3ef36f3d81f14177942587d64ddd
--- /dev/null
+++ b/vlm/dev/hfjbX1UKNx/6.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:da5b0388e83b83462479a9ebc7222940d64bf01ead9b3bac15eca4a5aa5790eb
+size 566837
diff --git a/vlm/dev/hfjbX1UKNx/7.png b/vlm/dev/hfjbX1UKNx/7.png
new file mode 100644
index 0000000000000000000000000000000000000000..e15a09e1a2a18fc6317063695bac96cbe117b645
--- /dev/null
+++ b/vlm/dev/hfjbX1UKNx/7.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f219056cfbac5485a2a38cdd0e9ffc16607bce22dc6df4103ee0cb118b598ffa
+size 795439
diff --git a/vlm/dev/hfjbX1UKNx/8.png b/vlm/dev/hfjbX1UKNx/8.png
new file mode 100644
index 0000000000000000000000000000000000000000..44e962f60489e639b932a21768d093478de04aac
--- /dev/null
+++ b/vlm/dev/hfjbX1UKNx/8.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d26f87ca047e47d5d311bfec44cbe862cd16b2217a2e8edd5bb12e22210f2258
+size 528251
diff --git a/vlm/dev/hfjbX1UKNx/9.png b/vlm/dev/hfjbX1UKNx/9.png
new file mode 100644
index 0000000000000000000000000000000000000000..1d8771a120e31e071c172bec2c55a22487384111
--- /dev/null
+++ b/vlm/dev/hfjbX1UKNx/9.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:849a12da823e6e35b1f53cad4aa2ad356ccb87a64f32922b28df3c3e3efa8b25
+size 495119
diff --git a/vlm/dev/mTiHLHu3sP/0.png b/vlm/dev/mTiHLHu3sP/0.png
new file mode 100644
index 0000000000000000000000000000000000000000..7134948b2502b37141a6413f442e9c77457bc7b8
--- /dev/null
+++ b/vlm/dev/mTiHLHu3sP/0.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5924780e80a96f990abf96b94bdac86f55f9a9b8d394007eff1a8ddc776ff8fb
+size 675381
diff --git a/vlm/dev/mTiHLHu3sP/1.png b/vlm/dev/mTiHLHu3sP/1.png
new file mode 100644
index 0000000000000000000000000000000000000000..0e66288f6830b453f25080f058ae878d54a70b73
--- /dev/null
+++ b/vlm/dev/mTiHLHu3sP/1.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c86c4f0b4052f35f62d429137ee2edd6aac05e0bfc894c200c78c878ccf76cd0
+size 743017
diff --git a/vlm/dev/mTiHLHu3sP/10.png b/vlm/dev/mTiHLHu3sP/10.png
new file mode 100644
index 0000000000000000000000000000000000000000..a4e50e655a109a7fbd7ea711975e57ad88e3fa00
--- /dev/null
+++ b/vlm/dev/mTiHLHu3sP/10.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d7d220604973c3f710025ab5333c29b6ed5dfd237c3e7d9312e00384acaa7be5
+size 964997
diff --git a/vlm/dev/mTiHLHu3sP/11.png b/vlm/dev/mTiHLHu3sP/11.png
new file mode 100644
index 0000000000000000000000000000000000000000..ae8a3bf9a800a279a07b38df45dde31b79454adf
--- /dev/null
+++ b/vlm/dev/mTiHLHu3sP/11.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bade80f2ad5ef5040259af2b5137f28c280d8b4e66235b7f71dcffcabdc6bc09
+size 81450
diff --git a/vlm/dev/mTiHLHu3sP/12.png b/vlm/dev/mTiHLHu3sP/12.png
new file mode 100644
index 0000000000000000000000000000000000000000..fe8d22d8e6237dfc8e51620d1c827d31964cfd3e
--- /dev/null
+++ b/vlm/dev/mTiHLHu3sP/12.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7d6afd1e88c795b9ab658d7d6582a2d43847df3989866f213663ed772267bea1
+size 635799
diff --git a/vlm/dev/mTiHLHu3sP/2.png b/vlm/dev/mTiHLHu3sP/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..4f667d506c85dfa8cac7ebf6c3816b62a1383d69
--- /dev/null
+++ b/vlm/dev/mTiHLHu3sP/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:28807de0ea3f9748ac6b3d8659a0c9a97525ff479da559d30cb8e2a49c7ab778
+size 696033
diff --git a/vlm/dev/mTiHLHu3sP/3.png b/vlm/dev/mTiHLHu3sP/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..61ff74159085a2fa5e6356aa0f47e475709db148
--- /dev/null
+++ b/vlm/dev/mTiHLHu3sP/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9cbaa52405d03744364852b2717b5f811a162977630d806671309475424f096b
+size 761975
diff --git a/vlm/dev/mTiHLHu3sP/5.png b/vlm/dev/mTiHLHu3sP/5.png
new file mode 100644
index 0000000000000000000000000000000000000000..2ffd0acc116cb4da6fe14f11c927fac02f76ca98
--- /dev/null
+++ b/vlm/dev/mTiHLHu3sP/5.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f482cc9fee2d3581144f2fbf62a41b1f36bda8337b96213915a62630e08ad41e
+size 742699
diff --git a/vlm/dev/mTiHLHu3sP/6.png b/vlm/dev/mTiHLHu3sP/6.png
new file mode 100644
index 0000000000000000000000000000000000000000..31e55df6639a52c2aaeeeb3c44386ca57d888f2c
--- /dev/null
+++ b/vlm/dev/mTiHLHu3sP/6.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:48601503ed76613d5dcc5002d91ee380a0737fd199290175ac5621fdd6c13b43
+size 625888
diff --git a/vlm/dev/mTiHLHu3sP/7.png b/vlm/dev/mTiHLHu3sP/7.png
new file mode 100644
index 0000000000000000000000000000000000000000..659bd8b635a53ee77d3ac50c9933529efde6b506
--- /dev/null
+++ b/vlm/dev/mTiHLHu3sP/7.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:556645e44bea1495530ad7527faca392d0b7fdcafb97e8408972501945cfedef
+size 763802
diff --git a/vlm/dev/mTiHLHu3sP/9.png b/vlm/dev/mTiHLHu3sP/9.png
new file mode 100644
index 0000000000000000000000000000000000000000..1cad0ac23aeb57195c19328382283e8b068baa71
--- /dev/null
+++ b/vlm/dev/mTiHLHu3sP/9.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:04964f83a395df8e646b7463b57494a1f297d9257f7e74f85b276aab8263856d
+size 955692
diff --git a/vlm/dev/pAq8iDy00Oa/0.png b/vlm/dev/pAq8iDy00Oa/0.png
new file mode 100644
index 0000000000000000000000000000000000000000..c62a37bda319b78c8e58db528fdbaa1ed40ee0db
--- /dev/null
+++ b/vlm/dev/pAq8iDy00Oa/0.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e0cac8c65d6cd503d7c15dbdf37f057b7706ed367b014a2a1af35a7ba270b482
+size 457040
diff --git a/vlm/dev/pAq8iDy00Oa/1.png b/vlm/dev/pAq8iDy00Oa/1.png
new file mode 100644
index 0000000000000000000000000000000000000000..b31c0bdff0579c4ba43d2eaafb78880337c6b86d
--- /dev/null
+++ b/vlm/dev/pAq8iDy00Oa/1.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b679e16ba79b61e7e8fea84b93ec2c1f3b6384a58727643fc1013da66edc5274
+size 631026
diff --git a/vlm/dev/pAq8iDy00Oa/10.png b/vlm/dev/pAq8iDy00Oa/10.png
new file mode 100644
index 0000000000000000000000000000000000000000..8550b131aba09e21a8b4bac5279bc97f37463f85
--- /dev/null
+++ b/vlm/dev/pAq8iDy00Oa/10.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:aaf9863a423520267ccafde861e5b542dcc3542670ec95bd2e5283e374829c45
+size 589878
diff --git a/vlm/dev/pAq8iDy00Oa/11.png b/vlm/dev/pAq8iDy00Oa/11.png
new file mode 100644
index 0000000000000000000000000000000000000000..d88acb4ea599c86a120627dd4f81b1c98eefd233
--- /dev/null
+++ b/vlm/dev/pAq8iDy00Oa/11.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2993e3047621b7e6036e4553f8202b3b4e2a6a11fc1662d5750c2ef47a1ae04b
+size 588219
diff --git a/vlm/dev/pAq8iDy00Oa/12.png b/vlm/dev/pAq8iDy00Oa/12.png
new file mode 100644
index 0000000000000000000000000000000000000000..2f04eebd922fc5d27ae86ac18baf31e88f48327f
--- /dev/null
+++ b/vlm/dev/pAq8iDy00Oa/12.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:782917c864070b7e4c04cf3fad6de3d8d7c696cfdeaeee774ba382c9bdcc9fc2
+size 410666
diff --git a/vlm/dev/pAq8iDy00Oa/13.png b/vlm/dev/pAq8iDy00Oa/13.png
new file mode 100644
index 0000000000000000000000000000000000000000..97ee4ca3e2a6ff1c653ddfb7ac02b2410f4d6d0d
--- /dev/null
+++ b/vlm/dev/pAq8iDy00Oa/13.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9254c9760d07be8d647884a6f60993dddbb3af75b5360a28d15e837e6a49a850
+size 485416
diff --git a/vlm/dev/pAq8iDy00Oa/14.png b/vlm/dev/pAq8iDy00Oa/14.png
new file mode 100644
index 0000000000000000000000000000000000000000..caf38fde77bc1687fcb62286e58254bce4cd72ea
--- /dev/null
+++ b/vlm/dev/pAq8iDy00Oa/14.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6f3b712c4cd33f21ac36e038d5a3d44b9dc87fd09b138569af3f1de09ad476ed
+size 440324
diff --git a/vlm/dev/pAq8iDy00Oa/15.png b/vlm/dev/pAq8iDy00Oa/15.png
new file mode 100644
index 0000000000000000000000000000000000000000..486181ab98723245cfabdc5261aa4403376453e3
--- /dev/null
+++ b/vlm/dev/pAq8iDy00Oa/15.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cfbfc3d59180b10df1acec5029f0aca92d70a5fe8c1b3da6f9cf4300eccf35aa
+size 551775
diff --git a/vlm/dev/pAq8iDy00Oa/16.png b/vlm/dev/pAq8iDy00Oa/16.png
new file mode 100644
index 0000000000000000000000000000000000000000..f8633d26d6d09475bd7880e0322b02b39e3c9109
--- /dev/null
+++ b/vlm/dev/pAq8iDy00Oa/16.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e66d66d10de5323bca7bba85fc9685de67b8038bc7dc670e5677401731d123e4
+size 311061
diff --git a/vlm/dev/pAq8iDy00Oa/17.png b/vlm/dev/pAq8iDy00Oa/17.png
new file mode 100644
index 0000000000000000000000000000000000000000..2b3851c75babdd268771c128658da839e3a16c8a
--- /dev/null
+++ b/vlm/dev/pAq8iDy00Oa/17.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1a08cb28d35cd43620485655d4d0821b7fd2cd73da30f733fcddfc6518d069ba
+size 1011582
diff --git a/vlm/dev/pAq8iDy00Oa/18.png b/vlm/dev/pAq8iDy00Oa/18.png
new file mode 100644
index 0000000000000000000000000000000000000000..06b66d0df7e5c7e333b8d22fc52a41cbfeb7dd83
--- /dev/null
+++ b/vlm/dev/pAq8iDy00Oa/18.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6138243cf05e043db47f9235447d6e785d15f17a38f858a2a00a81a4d35ad621
+size 655289
diff --git a/vlm/dev/pAq8iDy00Oa/19.png b/vlm/dev/pAq8iDy00Oa/19.png
new file mode 100644
index 0000000000000000000000000000000000000000..d8b5b47e01086274aad4248589d368fa10d39899
--- /dev/null
+++ b/vlm/dev/pAq8iDy00Oa/19.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:83f53f4b5f73c3c0078fa6e16e635ba74102cc657dd54a7031c057e2f5812633
+size 473580
diff --git a/vlm/dev/pAq8iDy00Oa/2.png b/vlm/dev/pAq8iDy00Oa/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..0aefc3a2b4de2a747f9dc0fe06c83b744bdd2e97
--- /dev/null
+++ b/vlm/dev/pAq8iDy00Oa/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e015da04aed2ed7a6a9110f4a5328bb700090db3d27924827d44c7f6db4a89fd
+size 537247
diff --git a/vlm/dev/pAq8iDy00Oa/20.png b/vlm/dev/pAq8iDy00Oa/20.png
new file mode 100644
index 0000000000000000000000000000000000000000..36828d3d7156c4259a245153ceae12e9d814a505
--- /dev/null
+++ b/vlm/dev/pAq8iDy00Oa/20.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9917351bb054bcdd3115560b0743b60c06276572b6af21d10265c3591b85005c
+size 284659
diff --git a/vlm/dev/pAq8iDy00Oa/3.png b/vlm/dev/pAq8iDy00Oa/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..cfb5cd702ba4855d94dfce4e5ce333cce09c64e6
--- /dev/null
+++ b/vlm/dev/pAq8iDy00Oa/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:28ee412361894e222da27f3c90835b25a05d14d450363ca69b397db2ff2f703b
+size 619601
diff --git a/vlm/dev/pAq8iDy00Oa/4.png b/vlm/dev/pAq8iDy00Oa/4.png
new file mode 100644
index 0000000000000000000000000000000000000000..3a1533bb6ae6f948b59b8762d26e820bd5bb2b8f
--- /dev/null
+++ b/vlm/dev/pAq8iDy00Oa/4.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:64a72af5c8bcbf282d5e1a1d63a6c50a87cda0c1c3a8d25080348630d918a7b9
+size 498849
diff --git a/vlm/dev/pAq8iDy00Oa/5.png b/vlm/dev/pAq8iDy00Oa/5.png
new file mode 100644
index 0000000000000000000000000000000000000000..74c8dd9abd6ab1a5505d22d1a8973df4bca32849
--- /dev/null
+++ b/vlm/dev/pAq8iDy00Oa/5.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cd0ab8a2d78257efe2717ec04f0dc60841071dc0e870aa24d97ea2730af8d4d9
+size 631388
diff --git a/vlm/dev/pAq8iDy00Oa/6.png b/vlm/dev/pAq8iDy00Oa/6.png
new file mode 100644
index 0000000000000000000000000000000000000000..5d86dd2c9bc2dc06e425b8eb920deefbdb39975e
--- /dev/null
+++ b/vlm/dev/pAq8iDy00Oa/6.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6e54208d5c0caccbc0b2d24e7514de976f274fd359aed678faf367ebae9c1869
+size 847513
diff --git a/vlm/dev/pAq8iDy00Oa/7.png b/vlm/dev/pAq8iDy00Oa/7.png
new file mode 100644
index 0000000000000000000000000000000000000000..f62afb8095bb9855c8fafbb75fde9c0f5d662c52
--- /dev/null
+++ b/vlm/dev/pAq8iDy00Oa/7.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1126dc335d6efaad9462867b7d343f5d0041bf9bb043fde0da97b820a8a6bd77
+size 568680
diff --git a/vlm/dev/pAq8iDy00Oa/8.png b/vlm/dev/pAq8iDy00Oa/8.png
new file mode 100644
index 0000000000000000000000000000000000000000..6815591c0f21bb44b688f953254d4aa30f10c325
--- /dev/null
+++ b/vlm/dev/pAq8iDy00Oa/8.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c1736e20c315d3be3605f05253aa0669a5b7a57c9642d71f0b42f6efc97b81fd
+size 563767
diff --git a/vlm/dev/pAq8iDy00Oa/9.png b/vlm/dev/pAq8iDy00Oa/9.png
new file mode 100644
index 0000000000000000000000000000000000000000..f29e052231174240d4717bbf35e2f6159de05d9d
--- /dev/null
+++ b/vlm/dev/pAq8iDy00Oa/9.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8adf7a7bb4bb9a4db9d859ab4d745a1ab2cfc066bd4676d45dab79e2541531cd
+size 631762
diff --git a/vlm/dev/uKiE0VIluA-/0.png b/vlm/dev/uKiE0VIluA-/0.png
new file mode 100644
index 0000000000000000000000000000000000000000..229680cfac9ac55ed2ca006b4ac729a521941828
--- /dev/null
+++ b/vlm/dev/uKiE0VIluA-/0.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f4d74531bac8f34cdb50f13e18b17c08a96b1551ed0156f5f625959f921c3459
+size 542405
diff --git a/vlm/dev/uKiE0VIluA-/1.png b/vlm/dev/uKiE0VIluA-/1.png
new file mode 100644
index 0000000000000000000000000000000000000000..fe23f38b1e878f6da4b4c7ef3768c272f718b758
--- /dev/null
+++ b/vlm/dev/uKiE0VIluA-/1.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7a3ff439c57acb233f81a235ee688290929f0c9d1904c88e3654479e873e16cc
+size 594649
diff --git a/vlm/dev/uKiE0VIluA-/10.png b/vlm/dev/uKiE0VIluA-/10.png
new file mode 100644
index 0000000000000000000000000000000000000000..6698ca7742b562972efa88eff354e93235fc9f97
--- /dev/null
+++ b/vlm/dev/uKiE0VIluA-/10.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:35806b4d471aa8730e38d901a3d186b9390a3af79b821335facf7bcf5bb78213
+size 584031
diff --git a/vlm/dev/uKiE0VIluA-/11.png b/vlm/dev/uKiE0VIluA-/11.png
new file mode 100644
index 0000000000000000000000000000000000000000..b61f3e1246575d2a60964057b4216fd47cd8a627
--- /dev/null
+++ b/vlm/dev/uKiE0VIluA-/11.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1ab8f154d0f463ec46321840c267126c545a62a30a37ecf847b01f8223317bed
+size 553595
diff --git a/vlm/dev/uKiE0VIluA-/12.png b/vlm/dev/uKiE0VIluA-/12.png
new file mode 100644
index 0000000000000000000000000000000000000000..a087d57293187b47123fe20927774e88ab39ba99
--- /dev/null
+++ b/vlm/dev/uKiE0VIluA-/12.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ced70629a06e2a3be91ea415710c6278868fe43f708b83f5e97a416b4c650208
+size 339171
diff --git a/vlm/dev/uKiE0VIluA-/13.png b/vlm/dev/uKiE0VIluA-/13.png
new file mode 100644
index 0000000000000000000000000000000000000000..74afdb2fa0461da6bea1f7f98c65eea03482f5c5
--- /dev/null
+++ b/vlm/dev/uKiE0VIluA-/13.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6fe4bcc5e587b970213aa72cb4ae896f9c0fdd0e4de356f6ed8366c7a0d0780a
+size 376727
diff --git a/vlm/dev/uKiE0VIluA-/14.png b/vlm/dev/uKiE0VIluA-/14.png
new file mode 100644
index 0000000000000000000000000000000000000000..2407a9fbf89610b7eeb270a5a5a83c2894d117d3
--- /dev/null
+++ b/vlm/dev/uKiE0VIluA-/14.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fff9b54468d5c373057390326955cbd4d7668343c6a12d0f0e6dbd0612148df5
+size 437359
diff --git a/vlm/dev/uKiE0VIluA-/15.png b/vlm/dev/uKiE0VIluA-/15.png
new file mode 100644
index 0000000000000000000000000000000000000000..3896ed49057fbcc142bb6499faade3741c8d555e
--- /dev/null
+++ b/vlm/dev/uKiE0VIluA-/15.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8fcfdf33e6757cde2f1ccc616c54f20a3cebdc5a909804bac7b77878a092387d
+size 479910
diff --git a/vlm/dev/uKiE0VIluA-/16.png b/vlm/dev/uKiE0VIluA-/16.png
new file mode 100644
index 0000000000000000000000000000000000000000..3516d5463d99a8f23a4491af54a73c2889c418c6
--- /dev/null
+++ b/vlm/dev/uKiE0VIluA-/16.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f3e805c04b942b9233e350e1b244793af6de09338a29f2a4dd92d9021a9b455d
+size 286117
diff --git a/vlm/dev/uKiE0VIluA-/17.png b/vlm/dev/uKiE0VIluA-/17.png
new file mode 100644
index 0000000000000000000000000000000000000000..be87f49f24113f545e81780763c0fcf891dda663
--- /dev/null
+++ b/vlm/dev/uKiE0VIluA-/17.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fbefde5e5c3ad69ec9c67869b6ec1f7255bd9003509b528b442dec0d5348b363
+size 382839
diff --git a/vlm/dev/uKiE0VIluA-/18.png b/vlm/dev/uKiE0VIluA-/18.png
new file mode 100644
index 0000000000000000000000000000000000000000..0ac092985018c8841beea58c52c522b967765c21
--- /dev/null
+++ b/vlm/dev/uKiE0VIluA-/18.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f300bd6bcc5de766b553284417da508aff6ae4dc55a630a4623971019f34561b
+size 558143
diff --git a/vlm/dev/uKiE0VIluA-/19.png b/vlm/dev/uKiE0VIluA-/19.png
new file mode 100644
index 0000000000000000000000000000000000000000..22c2bbc9a122c16eb7f11a41680aa0470be58ffd
--- /dev/null
+++ b/vlm/dev/uKiE0VIluA-/19.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a55631802f7552139c5a6dbee7786b97db0686f5bc7a0425ab6bcce7e59d0801
+size 594377
diff --git a/vlm/dev/uKiE0VIluA-/2.png b/vlm/dev/uKiE0VIluA-/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..43c42744f8b670b93676269d48918ebfef3dfbf4
--- /dev/null
+++ b/vlm/dev/uKiE0VIluA-/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:29eed802d8bc1639c333515888c28aeedb70237edefe0c5c0862b02b090a1697
+size 618786
diff --git a/vlm/dev/uKiE0VIluA-/20.png b/vlm/dev/uKiE0VIluA-/20.png
new file mode 100644
index 0000000000000000000000000000000000000000..dbfa54885ecaaa963d53c4c62911e70e346d4518
--- /dev/null
+++ b/vlm/dev/uKiE0VIluA-/20.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:89a5d7e5216a744dd6cf0e5a5608a1b3fad35b4f896031fc4cf859d8cabde380
+size 504926
diff --git a/vlm/dev/uKiE0VIluA-/21.png b/vlm/dev/uKiE0VIluA-/21.png
new file mode 100644
index 0000000000000000000000000000000000000000..151b71551146414d8a52f173691e0291e2f6e384
--- /dev/null
+++ b/vlm/dev/uKiE0VIluA-/21.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:63d792d039c5edd8174fbdefe4b968950f362f71df1dbf77c221b545cbb68a6b
+size 399896
diff --git a/vlm/dev/uKiE0VIluA-/22.png b/vlm/dev/uKiE0VIluA-/22.png
new file mode 100644
index 0000000000000000000000000000000000000000..2a450ab2c333b32c75483d5f82a8aa5be1feebac
--- /dev/null
+++ b/vlm/dev/uKiE0VIluA-/22.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f3db5a98ff35a08efc29ab77e4401a99833d4cf15fb19b35c918ab29350959f3
+size 512869
diff --git a/vlm/dev/uKiE0VIluA-/23.png b/vlm/dev/uKiE0VIluA-/23.png
new file mode 100644
index 0000000000000000000000000000000000000000..878013fd564227410dffb8cdbd86f3598c0f1139
--- /dev/null
+++ b/vlm/dev/uKiE0VIluA-/23.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5e2c479c9ffdfc9b4634a1e32f1a57e2d9132f3ce04069d4531a5ef511fe2f12
+size 485454
diff --git a/vlm/dev/uKiE0VIluA-/3.png b/vlm/dev/uKiE0VIluA-/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..7efc637813d62a446e2a995ba16a5ec4c623eb5b
--- /dev/null
+++ b/vlm/dev/uKiE0VIluA-/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f277dfef5dc4290e4192e249c0bfb2f5eeaf4ca594972803261b5f5406bea9ff
+size 652942
diff --git a/vlm/dev/uKiE0VIluA-/4.png b/vlm/dev/uKiE0VIluA-/4.png
new file mode 100644
index 0000000000000000000000000000000000000000..e93637d9d62da70523dd92eb76b4ce55189ee612
--- /dev/null
+++ b/vlm/dev/uKiE0VIluA-/4.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9526e5f026023037317804d6918f3b64d68d4eaa7b09db4db1a4aaab505d59b5
+size 616595
diff --git a/vlm/dev/uKiE0VIluA-/5.png b/vlm/dev/uKiE0VIluA-/5.png
new file mode 100644
index 0000000000000000000000000000000000000000..8eba72e3b59757cd801a6c60070b2bf61f92c563
--- /dev/null
+++ b/vlm/dev/uKiE0VIluA-/5.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:27e272532eed8fedba6803bb920d32104da18e1cf9dfb96dc9420bfd1980d100
+size 637318
diff --git a/vlm/dev/uKiE0VIluA-/6.png b/vlm/dev/uKiE0VIluA-/6.png
new file mode 100644
index 0000000000000000000000000000000000000000..047cb7e98a021dfb2b70303eb46c383c56d13c7f
--- /dev/null
+++ b/vlm/dev/uKiE0VIluA-/6.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b69484417b789f4e6f4757270f6193d95e975c0d811a01faeab7a0fd084309b7
+size 609452
diff --git a/vlm/dev/uKiE0VIluA-/7.png b/vlm/dev/uKiE0VIluA-/7.png
new file mode 100644
index 0000000000000000000000000000000000000000..0445b58eab883c42986515efd31f1c7b767cc409
--- /dev/null
+++ b/vlm/dev/uKiE0VIluA-/7.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b9369f579751d520e52b2665e0dbabdc077c3ed5fc05ec2ba59c3affb2fbf1bf
+size 580814
diff --git a/vlm/dev/uKiE0VIluA-/8.png b/vlm/dev/uKiE0VIluA-/8.png
new file mode 100644
index 0000000000000000000000000000000000000000..cfefdec9095b7670013a09f21a816a5b25b405e5
--- /dev/null
+++ b/vlm/dev/uKiE0VIluA-/8.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7af0322518c453d68e8733daef8fbfda164a5f0bdfaa5f4e06512bcb1a5c257c
+size 663469
diff --git a/vlm/dev/uKiE0VIluA-/9.png b/vlm/dev/uKiE0VIluA-/9.png
new file mode 100644
index 0000000000000000000000000000000000000000..b7886f7052d2f7c43ffd560bace912e98606b70f
--- /dev/null
+++ b/vlm/dev/uKiE0VIluA-/9.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:13f122591bdeadd420ff6a62cb8c4988f1a6b2e0012f6959f42e87772af255d8
+size 545018
diff --git a/vlm/dev/vKBdabh_WV/10.png b/vlm/dev/vKBdabh_WV/10.png
new file mode 100644
index 0000000000000000000000000000000000000000..76cbd32cec33d988fbca79f6763efcc36a51774d
--- /dev/null
+++ b/vlm/dev/vKBdabh_WV/10.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8f1d29bd7a0aa37ef00788f50e8d1b4cc8ca707235ba6bc23f99e36480106789
+size 626191
diff --git a/vlm/dev/vKBdabh_WV/11.png b/vlm/dev/vKBdabh_WV/11.png
new file mode 100644
index 0000000000000000000000000000000000000000..8b2469f0d5a81c1bdd1dc2bee493a9ca9f844970
--- /dev/null
+++ b/vlm/dev/vKBdabh_WV/11.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:86f5f1102056385f794cb8b0b7ff5c204d716554d75a0c5a875142f68548e069
+size 568420
diff --git a/vlm/dev/vKBdabh_WV/14.png b/vlm/dev/vKBdabh_WV/14.png
new file mode 100644
index 0000000000000000000000000000000000000000..27be4b7181dd75ef87f1cdc86e02cf1f6f223862
--- /dev/null
+++ b/vlm/dev/vKBdabh_WV/14.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:628041b37591b89ca1600c34da522a1bb56ed7d725b79346742ed0a5269c4af8
+size 489932
diff --git a/vlm/dev/vKBdabh_WV/17.png b/vlm/dev/vKBdabh_WV/17.png
new file mode 100644
index 0000000000000000000000000000000000000000..e8597e543feb500af87852a731e412ddf0fc6420
--- /dev/null
+++ b/vlm/dev/vKBdabh_WV/17.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2a431440068dda7e7893ffe5507961f40330d69421882ced78485240ff7a5d40
+size 275564
diff --git a/vlm/dev/vKBdabh_WV/2.png b/vlm/dev/vKBdabh_WV/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..94374f22a2c71b6126e815234e0cab8629170f24
--- /dev/null
+++ b/vlm/dev/vKBdabh_WV/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:84da1a4069f0a67357f60a8e5273de056ba1e0aab9d4dbfcb8925c2ada2dcba0
+size 604604
diff --git a/vlm/dev/vKBdabh_WV/21.png b/vlm/dev/vKBdabh_WV/21.png
new file mode 100644
index 0000000000000000000000000000000000000000..7d4e969f2535f5c76b96007296b3583b79ed0daa
--- /dev/null
+++ b/vlm/dev/vKBdabh_WV/21.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:179c3603ca2996deeb4d6f9ee138854a8ff4cf27565c1584b170a195bf027d88
+size 4012312
diff --git a/vlm/dev/vKBdabh_WV/3.png b/vlm/dev/vKBdabh_WV/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..4924683dcd8b90626a3a29a18880ef6e3fc917bb
--- /dev/null
+++ b/vlm/dev/vKBdabh_WV/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f87f8287a8124d62195a8f576081987a46edd07c686df7615a58e38a38304402
+size 507435
diff --git a/vlm/dev/vKBdabh_WV/6.png b/vlm/dev/vKBdabh_WV/6.png
new file mode 100644
index 0000000000000000000000000000000000000000..67f7557e1dc5c3b808148344611ef4965cab5266
--- /dev/null
+++ b/vlm/dev/vKBdabh_WV/6.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4620d4fe2dc4da773bab13acbd8643d6eefd5ef5c16a7ef27c8072da747a7c00
+size 579954
diff --git a/vlm/dev/vKBdabh_WV/9.png b/vlm/dev/vKBdabh_WV/9.png
new file mode 100644
index 0000000000000000000000000000000000000000..1f34db2d1a20a167f9228026a6f0aff250b77df4
--- /dev/null
+++ b/vlm/dev/vKBdabh_WV/9.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ac5b54d760a3fc47bef8f84232ef91590553db8c46cfd00f73fa215f97f9904e
+size 547503
diff --git a/vlm/dev/xT5rDp5VqKO/0.png b/vlm/dev/xT5rDp5VqKO/0.png
new file mode 100644
index 0000000000000000000000000000000000000000..f87d205d4ed8f10c75b79d8346d6c5e6a468f692
--- /dev/null
+++ b/vlm/dev/xT5rDp5VqKO/0.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9ff5e6b30f06b3638448488432b45870ea7be8b37a464344334ed24052462dfa
+size 385272
diff --git a/vlm/dev/xT5rDp5VqKO/1.png b/vlm/dev/xT5rDp5VqKO/1.png
new file mode 100644
index 0000000000000000000000000000000000000000..ba9c703d106b2376333e36e44c627d8d59f306a4
--- /dev/null
+++ b/vlm/dev/xT5rDp5VqKO/1.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c98ce1e8bd6aae18911eb453fd3f6540f3200ea8a1b25ef2a63896bc22ede06d
+size 459829
diff --git a/vlm/dev/xT5rDp5VqKO/2.png b/vlm/dev/xT5rDp5VqKO/2.png
new file mode 100644
index 0000000000000000000000000000000000000000..458a10849a2d4318421e250287099c727474c93c
--- /dev/null
+++ b/vlm/dev/xT5rDp5VqKO/2.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3318830ddf9b1811ff1287d751716338aeb583ca51fc1e3e8a5b1d11517b5b83
+size 465499
diff --git a/vlm/dev/xT5rDp5VqKO/3.png b/vlm/dev/xT5rDp5VqKO/3.png
new file mode 100644
index 0000000000000000000000000000000000000000..fee2f2f25e7da6f1100010d1c99d3d78711e2385
--- /dev/null
+++ b/vlm/dev/xT5rDp5VqKO/3.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e792a30620e5595c7663711669fc986da9db8790cb21489bb344354d3d32742f
+size 169626
diff --git a/vlm/dev/xT5rDp5VqKO/4.png b/vlm/dev/xT5rDp5VqKO/4.png
new file mode 100644
index 0000000000000000000000000000000000000000..f89e4ee628a07c03b1e47a7b2ff4acba852e90ed
--- /dev/null
+++ b/vlm/dev/xT5rDp5VqKO/4.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:803109dd3f51a186b4fd64443c2d77ac20d1d7247c48a6637513b3c76d066167
+size 106451